https://wiki.swarma.org/api.php?action=feedcontributions&user=Imp&feedformat=atom集智百科 - 复杂系统|人工智能|复杂科学|复杂网络|自组织 - 用户贡献 [zh-cn]2024-03-29T15:44:53Z用户贡献MediaWiki 1.35.0https://wiki.swarma.org/index.php?title=%E7%BD%91%E7%BB%9C%E6%A8%A1%E4%BD%93_Network_motifs&diff=7172网络模体 Network motifs2020-05-07T08:29:18Z<p>Imp:/* ESU (FANMOD)算法及对应的软件 */</p>
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<div>大家好,我们的公众号计划要推送一篇关于网络模体的综述文章,我们希望可以配套建议该重要概念:网络模体。现在希望可以大家一起协作完成这个词条。<br />
翻译任务主要分为以下5个内容:<br />
* 网络定义和历史 ---许菁 <br />
* 网络模体的发现算法 mfinder和FPF算法---李鹏<br />
* 网络模体的发现算法 ESU和对应的软件FANMOD---Imp<br />
* 网络模体的发现算法 G-Trie、算法对比和算法分类——Ricky(中英对照[[用户讨论:Qige96|初稿在这里]])<br />
* 已有网络模体及其函数表示 --周佳欣<br />
* 活动模体+批判 --- 孙宇<br />
* 代码实现<br />
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大家可以在对应感兴趣的部分下面,写上姓名。我们的协作方式是石墨文档上翻译,最后再编辑成文。<br />
对应的词条链接:https://en.wikipedia.org/wiki/Network_motif#Well-established_motifs_and_their_functions<br />
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截止时间:今晚12:00<br />
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All networks, including [[biological network]]s, social networks, technological networks (e.g., computer networks and electrical circuits) and more, can be represented as [[complex network|graphs]], which include a wide variety of subgraphs. One important local property of networks are so-called '''network motifs''', which are defined as recurrent and [[statistically significant]] sub-graphs or patterns.<br />
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所有网络,包括生物网络(biological networks)、社会网络(social networks)、技术网络(例如计算机网络和电路)等,都可以用图的形式来表示,这些图中会包括各种各样的子图(subgraphs)。网络的一个重要的局部性质是所谓的网络基序,即重复且具有统计意义的子图或模式(patterns)。<br />
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Network motifs are sub-graphs that repeat themselves in a specific network or even among various networks. Each of these sub-graphs, defined by a particular pattern of interactions between vertices, may reflect a framework in which particular functions are achieved efficiently. Indeed, motifs are of notable importance largely because they may reflect functional properties. They have recently gathered much attention as a useful concept to uncover structural design principles of complex networks.<ref name="mas1">{{cite journal |vauthors=Masoudi-Nejad A, Schreiber F, Razaghi MK Z |title=Building Blocks of Biological Networks: A Review on Major Network Motif Discovery Algorithms |journal=IET Systems Biology |volume=6 |issue=5 |pages=164–74 |year=2012|doi=10.1049/iet-syb.2011.0011 |pmid=23101871 }}</ref> Although network motifs may provide a deep insight into the network's functional abilities, their detection is computationally challenging.<br />
网络模体(Network motifs)是指在特定网络或各种网络中重复出现的相同的子图。这些子图由顶点之间特定的交互模式定义,一个子图便可以反映一个框架,这个框架可以有效地实现某个特定的功能。事实上,之所以说模体是一个重要的特性,正是因为它们可能反映出对应网络功能的这一性质。近年来这一概念作为揭示复杂网络结构设计原理的一个有用概念而受到了广泛的关注。<ref name="mas1">{{cite journal |vauthors=Masoudi-Nejad A, Schreiber F, Razaghi MK Z |title=Building Blocks of Biological Networks: A Review on Major Network Motif Discovery Algorithms |journal=IET Systems Biology |volume=6 |issue=5 |pages=164–74 |year=2012|doi=10.1049/iet-syb.2011.0011 |pmid=23101871 }}</ref> 但是,虽然通过研究网络模体可以深入了解网络的功能,但是对于模体的检测在计算上是具有挑战性的。<br />
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==Definition==<br />
Let {{math|G {{=}} (V, E)}} and {{math|G&prime; {{=}} (V&prime;, E&prime;)}} be two graphs. Graph {{math|G&prime;}} is a ''sub-graph'' of graph {{math|G}} (written as {{math|G&prime; ⊆ G}}) if {{math|V&prime; ⊆ V}} and {{math|E&prime; ⊆ E ∩ (V&prime; &times; V&prime;)}}. If {{math|G&prime; ⊆ G}} and {{math|G&prime;}} contains all of the edges {{math|&lang;u, v&rang; ∈ E}} with {{math|u, v ∈ V&prime;}}, then {{math|G&prime;}} is an ''induced sub-graph'' of {{math|G}}. We call {{math|G&prime;}} and {{math|G}} isomorphic (written as {{math|G&prime; ↔ G}}), if there exists a bijection (one-to-one) {{math|f:V&prime; → V}} with {{math|&lang;u, v&rang; ∈ E&prime; ⇔ &lang;f(u), f(v)&rang; ∈ E}} for all {{math|u, v ∈ V&prime;}}. The mapping {{math|f}} is called an isomorphism between {{math|G}} and {{math|G&prime;}}.<ref name="die1">{{cite journal |author=Diestel R |title=Graph Theory (Graduate Texts in Mathematics) |volume=173 |year=2005|publisher=New York: Springer-Verlag Heidelberg}}</ref><br />
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设{{math|G {{=}} (V, E)}} 和 {{math|G&prime; {{=}} (V&prime;, E&prime;)}} 是两个图。若{{math|V&prime; ⊆ V}}且满足{{math|E&prime; ⊆ E ∩ (V&prime; &times; V&prime;)}})(即图{{math|G&prime; ⊆ G}的所有边和点都属于图{{math|G}})则称图{{math|G&prime; ⊆ G}是图{{math|G}}的一个子图<ref name="die1">{{cite journal |author=Diestel R |title=Graph Theory (Graduate Texts in Mathematics) |volume=173 |year=2005|publisher=New York: Springer-Verlag Heidelberg}}</ref><br />
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若{{math|G&prime; ⊆ G}},且对于顶点{{math|u}}、{{math|v}}及其连边,只要{{math|u}}和{{math|v}}存在于{{math|G&prime;}}(即若{{math|U}}, {{math|V&prime; ⊆ V}}),那么{{math|G&prime; ⊆ G}}中就应该包含原图{{math|G}}中的所有{{math|u}}和{{math|V}}的对应连边(即{{math|&lang;u, v&rang; ∈ E}}),则称此时图{{math|G&prime;}}就是图{{math|G}}的导出子图。<br />
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如果存在一个双射(一对一){{math|f:V&prime; → V}},且对所有{{math|u, v ∈ V&prime;}}都有{{math|&lang;u, v&rang; ∈ E&prime; ⇔ &lang;f(u), f(v)&rang; ∈ E}} ,则称{{math|G&prime }}是{{math|G}}的同构图(记作:{{math|G&prime; → G}}),映射f则称为{{math|G}}与{{math|G&prime;}}之间的同构(isomorphism)。[2]<br />
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When {{math|G&Prime; ⊂ G}} and there exists an isomorphism between the sub-graph {{math|G&Prime;}} and a graph {{math|G&prime;}}, this mapping represents an ''appearance'' of {{math|G&prime;}} in {{math|G}}. The number of appearances of graph {{math|G&prime;}} in {{math|G}} is called the frequency {{math|F<sub>G</sub>}} of {{math|G&prime;}} in {{math|G}}. A graph is called ''recurrent'' (or ''frequent'') in {{math|G}}, when its ''frequency'' {{math|F<sub>G</sub>(G&prime;)}} is above a predefined threshold or cut-off value. We use terms ''pattern'' and ''frequent sub-graph'' in this review interchangeably. There is an [[Statistical ensemble (mathematical physics)|ensemble]] {{math|Ω(G)}} of random graphs corresponding to the [[Null model|null-model]] associated to {{math|G}}. We should choose {{math|N}} random graphs uniformly from {{math|Ω(G)}} and calculate the frequency for a particular frequent sub-graph {{math|G&prime;}} in {{math|G}}. If the frequency of {{math|G&prime;}} in {{math|G}} is higher than its arithmetic mean frequency in {{math|N}} random graphs {{math|R<sub>i</sub>}}, where {{math|1 ≤ i ≤ N}}, we call this recurrent pattern ''significant'' and hence treat {{math|G&prime;}} as a ''network motif'' for {{math|G}}. For a small graph {{math|G&prime;}}, the network {{math|G}} and a set of randomized networks {{math|R(G) ⊆ Ω(R)}}, where {{math|1=R(G) {{=}} N}}, the ''Z-Score'' that has been defined by the following formula:<br />
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<math>Z(G^\prime) = \frac{F_G(G^\prime) - \mu_R(G^\prime)}{\sigma_R(G^\prime)}</math><br />
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当{{math|G&Prime; ⊂ G}},且{{math|G&Prime;}}与图{{math|G&prime;}}之间存在同构时,该映射表示{{math|G&prime;}}对于{{math|G}}存在。图{{math|G&prime;}}在{{math|G}}的出现次数称为{{math|G&prime;}}出现在{{math|G}}的频率{{math|F<sub>G</sub>}}。当一个子图的频率{{math|F<sub>G</sub>}}高于预定的阈值或截止值时,则称{{math|G&prime;}}是{{math|G}}中的递归(或频繁)子图。<br />
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在接下来的内容中,我们交替使用术语“模式(motifs)”和“频繁子图(frequent sub-graph)”。<br />
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设从与{{math|G}}相关联的零模型(the null-model)获得的随机图集合为{{math|Ω(G)}},我们从{{math|Ω(G)}}中均匀地选择N个随机图,并计算其特定频繁子图的频率。如果{{math|G&prime;}}出现在{{math|G}}的频率高于N个随机图Ri的算术平均频率,其中{{math|1 ≤ i ≤ N}},我们称此递归模式是有意义的,因此可以将{{math|G&prime;}}视为{{math|G}}的网络模体。<br />
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对于一个小图{{math|G&prime;}},网络{{math|G}}和一组随机网络{{math|R(G) ⊆ Ω(R)}},当{{math|1=R(G) {{=}} N}}时,由其Z分数(Z-score)的定义如下式:<br />
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<math>Z(G^\prime) = \frac{F_G(G^\prime) - \mu_R(G^\prime)}{\sigma_R(G^\prime)}</math><br />
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where {{math|μ<sub>R</sub>(G&prime;)}} and {{math|σ<sub>R</sub>(G&prime;)}} stand for mean and standard deviation frequency in set {{math|R(G)}}, respectively.<ref name="mil1">{{cite journal |vauthors=Milo R, Shen-Orr SS, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |volume=298 |year=2002|journal=Science|issue=5594|pages=824–827 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="alb1">{{cite journal |vauthors=Albert R, Barabási AL |title=Statistical mechanics of complex networks |journal=Reviews of Modern Physics |volume=74 |issue=1 |year=2002 |pages=47–49 |doi=10.1103/RevModPhys.74.47 |bibcode=2002RvMP...74...47A|arxiv=cond-mat/0106096 |citeseerx=10.1.1.242.4753 }}</ref><ref name="mil2">{{cite journal |vauthors=Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheffer M, Alon U |title=Superfamilies of designed and evolved networks |journal=Science |volume=303 |issue=5663 |year=2004 |pages=1538–1542 |pmid=15001784 |doi=10.1126/science.1089167 |bibcode=2004Sci...303.1538M |url=https://semanticscholar.org/paper/87ad24efd5329046d37cd704f970323e878710ca }}</ref><ref name="sch1">{{cite encyclopedia|last=Schwöbbermeyer |first=H |title=Network Motifs |encyclopedia=Analysis of Biological Networks |editor=Junker BH, Schreiber F |publisher=Hoboken, New Jersey: John Wiley & Sons |year=2008 |pages=85–108}}</ref><ref name="bor1">{{cite encyclopedia |last1=Bornholdt |first1=S |last2=Schuster |first2=HG |title=Handbook of graphs and networks : from the genome to the Internet |journal=Handbook of Graphs and Networks: From the Genome to the Internet |pages=417 |year=2003|bibcode=2003hgnf.book.....B }}</ref><ref name="cir1">{{cite journal |vauthors=Ciriello G, Guerra C |title=A review on models and algorithms for motif discovery in protein-protein interaction networks |journal=Briefings in Functional Genomics and Proteomics |year=2008 |volume=7 |issue=2 |pages=147–156 |doi=10.1093/bfgp/eln015|pmid=18443014 |doi-access=free }}</ref> The larger the {{math|Z(G&prime;)}}, the more significant is the sub-graph {{math|G&prime;}} as a motif. Alternatively, another measurement in statistical hypothesis testing that can be considered in motif detection is the P-Value, given as the probability of {{math|F<sub>R</sub>(G&prime;) ≥ F<sub>G</sub>(G&prime;)}} (as its null-hypothesis), where {{math|F<sub>R</sub>(G&prime;)}} indicates the frequency of G' in a randomized network.<ref name="sch1" /> A sub-graph with P-value less than a threshold (commonly 0.01 or 0.05) will be treated as a significant pattern. The P-value is defined as<br />
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<math>P(G^\prime) = \frac{1}{N}\sum_{i=1}^N \delta(c(i)) ; c(i): F_R^i(G^\prime) \ge F_G(G^\prime)</math><br />
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式中,{{math|μ<sub>R</sub>(G&prime;)}} 和 {{math|σ<sub>R</sub>(G&prime;)}}分别代表集合{{math|R(G)}}中的平均和标准偏差频率。.<ref name="mil1">{{cite journal |vauthors=Milo R, Shen-Orr SS, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |volume=298 |year=2002|journal=Science|issue=5594|pages=824–827 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="alb1">{{cite journal |vauthors=Albert R, Barabási AL |title=Statistical mechanics of complex networks |journal=Reviews of Modern Physics |volume=74 |issue=1 |year=2002 |pages=47–49 |doi=10.1103/RevModPhys.74.47 |bibcode=2002RvMP...74...47A|arxiv=cond-mat/0106096 |citeseerx=10.1.1.242.4753 }}</ref><ref name="mil2">{{cite journal |vauthors=Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheffer M, Alon U |title=Superfamilies of designed and evolved networks |journal=Science |volume=303 |issue=5663 |year=2004 |pages=1538–1542 |pmid=15001784 |doi=10.1126/science.1089167 |bibcode=2004Sci...303.1538M |url=https://semanticscholar.org/paper/87ad24efd5329046d37cd704f970323e878710ca }}</ref><ref name="sch1">{{cite encyclopedia|last=Schwöbbermeyer |first=H |title=Network Motifs |encyclopedia=Analysis of Biological Networks |editor=Junker BH, Schreiber F |publisher=Hoboken, New Jersey: John Wiley & Sons |year=2008 |pages=85–108}}</ref><ref name="bor1">{{cite encyclopedia |last1=Bornholdt |first1=S |last2=Schuster |first2=HG |title=Handbook of graphs and networks : from the genome to the Internet |journal=Handbook of Graphs and Networks: From the Genome to the Internet |pages=417 |year=2003|bibcode=2003hgnf.book.....B }}</ref><ref name="cir1">{{cite journal |vauthors=Ciriello G, Guerra C |title=A review on models and algorithms for motif discovery in protein-protein interaction networks |journal=Briefings in Functional Genomics and Proteomics |year=2008 |volume=7 |issue=2 |pages=147–156 |doi=10.1093/bfgp/eln015|pmid=18443014 |doi-access=free }}</ref> {{math|Z(G&prime;)}}越大,子图{{math|G&prime;}}作为模体的意义也就越大。<br />
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此外还可以使用统计假设检验中的另一个测量方法,可以作为模体检测中的一种方法,即P值(P-value),以 {{math|F<sub>R</sub>(G&prime;) ≥ F<sub>G</sub>(G&prime;)}}的概率给出(作为其零假设null-hypothesis),其中{{math|F<sub>R</sub>(G&prime;)}}表示随机网络中{{math|G&prime;}}的频率。<ref name="sch1" /> 当P值小于阈值(通常为0.01或0.05)时,该子图可以被称为显著模式。该P值定义为:<br />
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<math>P(G^\prime) = \frac{1}{N}\sum_{i=1}^N \delta(c(i)) ; c(i): F_R^i(G^\prime) \ge F_G(G^\prime)</math><br />
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[[File:Different occurrences of a sub-graph in a graph.jpg|thumb|''Different occurrences of a sub-graph in a graph''. (M1 – M4) are different occurrences of sub-graph (b) in graph (a). For frequency concept {{math|F<sub>1</sub>}}, the set M1, M2, M3, M4 represent all matches, so {{math|F<sub>1</sub> {{=}} 4}}. For {{math|F<sub>2</sub>}}, one of the two set M1, M4 or M2, M3 are possible matches, {{math|F<sub>2</sub> {{=}} 2}}. Finally, for frequency concept {{math|F<sub>3</sub>}}, merely one of the matches (M1 to M4) is allowed, therefore {{math|F<sub>3</sub> {{=}} 1}}. The frequency of these three frequency concepts decrease as the usage of network elements are restricted.]]<br />
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Where {{math|N}} indicates number of randomized networks, {{math|i}} is defined over an ensemble of randomized networks and the Kronecker delta function {{math|δ(c(i))}} is one if the condition {{math|c(i)}} holds. The concentration <ref name="kas1">{{cite journal |vauthors=Kashtan N, Itzkovitz S, Milo R, Alon U |title=Efficient sampling algorithm for estimating sub-graph concentrations and detecting network motifs |journal=Bioinformatics |year=2004 |volume=20 |issue=11 |pages=1746–1758 |doi=10.1093/bioinformatics/bth163|pmid=15001476 |doi-access=free }}</ref><ref name="wer1">{{cite journal |author=Wernicke S |title=Efficient detection of network motifs |journal=IEEE/ACM Transactions on Computational Biology and Bioinformatics |year=2006 |volume=3 |issue=4 |pages=347–359 |doi=10.1109/tcbb.2006.51|pmid=17085844 |citeseerx=10.1.1.304.2576 }}</ref> of a particular n-size sub-graph {{math|G&prime;}} in network {{math|G}} refers to the ratio of the sub-graph appearance in the network to the total ''n''-size non-isomorphic sub-graphs’ frequencies, which is formulated by<br />
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<math>C_G(G^\prime) = \frac{F_G(G^\prime)}{\sum_i F_G(G_i)}</math><br />
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where index {{math|i}} is defined over the set of all non-isomorphic n-size graphs. Another statistical measurement is defined for evaluating network motifs, but it is rarely used in known algorithms. This measurement is introduced by Picard ''et al.'' in 2008 and used the Poisson distribution, rather than the Gaussian normal distribution that is implicitly being used above.<ref name="pic1">{{cite journal |vauthors=Picard F, Daudin JJ, Schbath S, Robin S |title=Assessing the Exceptionality of Network Motifs |journal=J. Comp. Bio. |year=2005 |volume=15 |issue=1 |pages=1–20|doi=10.1089/cmb.2007.0137 |pmid=18257674 |citeseerx=10.1.1.475.4300 }}</ref><br />
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其中索引 i 定义在所有非同构 n 大小图的集合上。 另一种统计测量是用来评估网络主题的,但在已知的算法中很少使用。 这种测量方法是由 Picard 等人在2008年提出的,使用的是泊松分佈分布,而不是上面隐含使用的高斯正态分布。<ref name="pic1">{{cite journal |vauthors=Picard F, Daudin JJ, Schbath S, Robin S |title=Assessing the Exceptionality of Network Motifs |journal=J. Comp. Bio. |year=2005 |volume=15 |issue=1 |pages=1–20|doi=10.1089/cmb.2007.0137 |pmid=18257674 |citeseerx=10.1.1.475.4300 }}</ref>其中{{math|N}}表示随机网络的数目,{{math|i}}定义在随机网络的集合上,若条件{{math|c(i)}}成立,则Kroneckerδ函数{{math|δ(c(i))}}是1。在网络{{math|G}}中,一个特定的n维子图{{math|N&prime;}}的集中度是指子图在网络中出现频率与n维非同构子图的总频率之比,其计算公式如下:<br />
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<math>C_G(G^\prime) = \frac{F_G(G^\prime)}{\sum_i F_G(G_i)}</math><br />
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In addition, three specific concepts of sub-graph frequency have been proposed.<ref name="schr1">{{cite book |vauthors=Schreiber F, Schwöbbermeyer H |title=Frequency concepts and pattern detection for the analysis of motifs in networks |journal=Transactions on Computational Systems Biology III |volume=3737 |year=2005 |pages=89–104|doi=10.1007/11599128_7 |citeseerx=10.1.1.73.1130 |series=Lecture Notes in Computer Science |isbn=978-3-540-30883-6 }}</ref> As the figure illustrates, the first frequency concept {{math|F<sub>1</sub>}} considers all matches of a graph in original network. This definition is similar to what we have introduced above. The second concept {{math|F<sub>2</sub>}} is defined as the maximum number of edge-disjoint instances of a given graph in original network. And finally, the frequency concept {{math|F<sub>3</sub>}} entails matches with disjoint edges and nodes. Therefore, the two concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}} restrict the usage of elements of the graph, and as can be inferred, the frequency of a sub-graph declines by imposing restrictions on network element usage. As a result, a network motif detection algorithm would pass over more candidate sub-graphs if we insist on frequency concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}}.<br />
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此外,他们还提出了子图频率的三个具体概念。<ref name="schr1">{{cite book |vauthors=Schreiber F, Schwöbbermeyer H |title=Frequency concepts and pattern detection for the analysis of motifs in networks |journal=Transactions on Computational Systems Biology III |volume=3737 |year=2005 |pages=89–104|doi=10.1007/11599128_7 |citeseerx=10.1.1.73.1130 |series=Lecture Notes in Computer Science |isbn=978-3-540-30883-6 }}</ref> 如图所示,第一频率概念 {{math|F<sub>1</sub>}}考虑原始网络中图的所有匹配,这与我们前面介绍过的类似。第二个概念{{math|F<sub>2</sub>}}定义为原始网络中给定图的最大不相交边的数量。最后,频率概念{{math|F<sub>3</sub>}}包含与不相交边(disjoint edges)和节点的匹配。因此,两个概念F2和F3限制了图元素的使用,并且可以看出,通过对网络元素的使用施加限制,子图的频率下降。因此,如果我们坚持使用频率概念{{math|F<sub>2</sub>}}和{{math|F<sub>3</sub>}},网络模体检测算法将可以筛选出更多的候选子图。<br />
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==History==<br />
The study of network motifs was pioneered by Holland and Leinhardt<ref>Holland, P. W., & Leinhardt, S. (1974). The statistical analysis of local structure in social networks. Working Paper No. 44, National Bureau of Economic Research.</ref><ref>Hollandi, P., & Leinhardt, S. (1975). The Statistical Analysis of Local. Structure in Social Networks. Sociological Methodology, David Heise, ed. San Francisco: Josey-Bass.</ref><ref> Holland, P. W., & Leinhardt, S. (1976). Local structure in social networks. Sociological methodology, 7, 1-45.</ref><ref>Holland, P. W., & Leinhardt, S. (1977). A method for detecting structure in sociometric data. In Social Networks (pp. 411-432). Academic Press.</ref> who introduced the concept of a triad census of networks. They introduced methods to enumerate various types of subgraph configurations, and test whether the subgraph counts are statistically different from those expected in random networks. <br />
霍兰(Holland)和莱因哈特(Leinhardt)率先提出了'''网络三合会普查'''(a triad census of networks)的概念,开创了网络模体研究的先河。<ref>Holland, P. W., & Leinhardt, S. (1974). The statistical analysis of local structure in social networks. Working Paper No. 44, National Bureau of Economic Research.</ref><ref>Hollandi, P., & Leinhardt, S. (1975). The Statistical Analysis of Local. Structure in Social Networks. Sociological Methodology, David Heise, ed. San Francisco: Josey-Bass.</ref><ref> Holland, P. W., & Leinhardt, S. (1976). Local structure in social networks. Sociological methodology, 7, 1-45.</ref><ref>Holland, P. W., & Leinhardt, S. (1977). A method for detecting structure in sociometric data. In Social Networks (pp. 411-432). Academic Press.</ref> 他们介绍了枚举各种子图配置的方法,并测试子图计数是否与随机网络中的期望值存在统计学上的差异。<br />
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这里对于'''网络三合会普查'''(a triad census of networks)这一概念的翻译存疑<br />
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This idea was further generalized in 2002 by [[Uri Alon]] and his group <ref name="she1">{{cite journal |vauthors=Shen-Orr SS, Milo R, Mangan S, Alon U |title=Network motifs in the transcriptional regulation network of ''Escherichia coli'' |journal=Nat. Genet. |volume=31 |issue=1 |pages=64–8 |date=May 2002 |pmid=11967538 |doi=10.1038/ng881}}</ref> when network motifs were discovered in the gene regulation (transcription) network of the bacteria ''[[Escherichia coli|E. coli]]'' and then in a large set of natural networks. Since then, a considerable number of studies have been conducted on the subject. Some of these studies focus on the biological applications, while others focus on the computational theory of network motifs.<br />
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2002年,Uri Alon和他的团队[17]在大肠杆菌的基因调控(gene regulation network)(转录 transcription)网络中发现了网络模体,随后在大量的自然网络中也发现了网络模体,从而进一步推广了这一观点。自那时起,许多科学家都对这一问题进行了大量的研究。其中一些研究集中在生物学应用上,而另一些则集中在网络模体的计算理论上。<ref name="she1">{{cite journal |vauthors=Shen-Orr SS, Milo R, Mangan S, Alon U |title=Network motifs in the transcriptional regulation network of ''Escherichia coli'' |journal=Nat. Genet. |volume=31 |issue=1 |pages=64–8 |date=May 2002 |pmid=11967538 |doi=10.1038/ng881}}</ref> <br />
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The biological studies endeavor to interpret the motifs detected for biological networks. For example, in work following,<ref name="she1" /> the network motifs found in ''[[Escherichia coli|E. coli]]'' were discovered in the transcription networks of other bacteria<ref name="eic1">{{cite journal |vauthors=Eichenberger P, Fujita M, Jensen ST, etal |title=The program of gene transcription for a single differentiating cell type during sporulation in ''Bacillus subtilis'' |journal=PLOS Biology |volume=2 |issue=10 |pages=e328 |date=October 2004 |pmid=15383836 |pmc=517825 |doi=10.1371/journal.pbio.0020328 }} </ref> as well as yeast<ref name="mil3">{{cite journal |vauthors=Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |journal=Science |volume=298 |issue=5594 |pages=824–7 |date=October 2002 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="lee1">{{cite journal |vauthors=Lee TI, Rinaldi NJ, Robert F, etal |title=Transcriptional regulatory networks in Saccharomyces cerevisiae |journal=Science |volume=298 |issue=5594 |pages=799–804 |date=October 2002 |pmid=12399584 |doi=10.1126/science.1075090 |bibcode=2002Sci...298..799L }}</ref> and higher organisms.<ref name="odo1">{{cite journal |vauthors=Odom DT, Zizlsperger N, Gordon DB, etal |title=Control of pancreas and liver gene expression by HNF transcription factors |journal=Science |volume=303 |issue=5662 |pages=1378–81 |date=February 2004 |pmid=14988562 |pmc=3012624 |doi=10.1126/science.1089769 |bibcode=2004Sci...303.1378O }}</ref><ref name="boy1">{{cite journal |vauthors=Boyer LA, Lee TI, Cole MF, etal |title=Core transcriptional regulatory circuitry in human embryonic stem cells |journal=Cell |volume=122 |issue=6 |pages=947–56 |date=September 2005 |pmid=16153702 |pmc=3006442 |doi=10.1016/j.cell.2005.08.020 }}</ref><ref name="ira1">{{cite journal |vauthors=Iranfar N, Fuller D, Loomis WF |title=Transcriptional regulation of post-aggregation genes in Dictyostelium by a feed-forward loop involving GBF and LagC |journal=Dev. Biol. |volume=290 |issue=2 |pages=460–9 |date=February 2006 |pmid=16386729 |doi=10.1016/j.ydbio.2005.11.035 |doi-access=free }}</ref> A distinct set of network motifs were identified in other types of biological networks such as neuronal networks and protein interaction networks.<ref name="mil2" /><ref name="maa1">{{cite journal |vauthors=Ma'ayan A, Jenkins SL, Neves S, etal |title=Formation of regulatory patterns during signal propagation in a Mammalian cellular network |journal=Science |volume=309 |issue=5737 |pages=1078–83 |date=August 2005 |pmid=16099987 |pmc=3032439 |doi=10.1126/science.1108876 |bibcode=2005Sci...309.1078M }}</ref><ref name="pta1">{{cite journal |vauthors=Ptacek J, Devgan G, Michaud G, etal |title=Global analysis of protein phosphorylation in yeast |journal=Nature |volume=438 |issue=7068 |pages=679–84 |date=December 2005 |pmid=16319894 |doi=10.1038/nature04187|bibcode=2005Natur.438..679P |url=https://authors.library.caltech.edu/56271/2/Tables.pdf |type=Submitted manuscript }}</ref><br />
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生物学研究试图解释为生物网络检测到的模体。例如,在接下来的工作中,文献[17]在大肠杆菌中发现的网络模体存在于其他细菌<ref name="eic1">{{cite journal |vauthors=Eichenberger P, Fujita M, Jensen ST, etal |title=The program of gene transcription for a single differentiating cell type during sporulation in ''Bacillus subtilis'' |journal=PLOS Biology |volume=2 |issue=10 |pages=e328 |date=October 2004 |pmid=15383836 |pmc=517825 |doi=10.1371/journal.pbio.0020328 }} </ref>以及酵母<ref name="mil3">{{cite journal |vauthors=Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |journal=Science |volume=298 |issue=5594 |pages=824–7 |date=October 2002 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="lee1">{{cite journal |vauthors=Lee TI, Rinaldi NJ, Robert F, etal |title=Transcriptional regulatory networks in Saccharomyces cerevisiae |journal=Science |volume=298 |issue=5594 |pages=799–804 |date=October 2002 |pmid=12399584 |doi=10.1126/science.1075090 |bibcode=2002Sci...298..799L }}</ref>和高等生物的转录网络中。文献<ref name="odo1">{{cite journal |vauthors=Odom DT, Zizlsperger N, Gordon DB, etal |title=Control of pancreas and liver gene expression by HNF transcription factors |journal=Science |volume=303 |issue=5662 |pages=1378–81 |date=February 2004 |pmid=14988562 |pmc=3012624 |doi=10.1126/science.1089769 |bibcode=2004Sci...303.1378O }}</ref><ref name="boy1">{{cite journal |vauthors=Boyer LA, Lee TI, Cole MF, etal |title=Core transcriptional regulatory circuitry in human embryonic stem cells |journal=Cell |volume=122 |issue=6 |pages=947–56 |date=September 2005 |pmid=16153702 |pmc=3006442 |doi=10.1016/j.cell.2005.08.020 }}</ref><ref name="ira1">{{cite journal |vauthors=Iranfar N, Fuller D, Loomis WF |title=Transcriptional regulation of post-aggregation genes in Dictyostelium by a feed-forward loop involving GBF and LagC |journal=Dev. Biol. |volume=290 |issue=2 |pages=460–9 |date=February 2006 |pmid=16386729 |doi=10.1016/j.ydbio.2005.11.035 |doi-access=free }}</ref>在其他类型的生物网络中发现了一组不同的网络模体,如神经元网络和蛋白质相互作用网络。<ref name="mil2" /><ref name="maa1">{{cite journal |vauthors=Ma'ayan A, Jenkins SL, Neves S, etal |title=Formation of regulatory patterns during signal propagation in a Mammalian cellular network |journal=Science |volume=309 |issue=5737 |pages=1078–83 |date=August 2005 |pmid=16099987 |pmc=3032439 |doi=10.1126/science.1108876 |bibcode=2005Sci...309.1078M }}</ref><ref name="pta1">{{cite journal |vauthors=Ptacek J, Devgan G, Michaud G, etal |title=Global analysis of protein phosphorylation in yeast |journal=Nature |volume=438 |issue=7068 |pages=679–84 |date=December 2005 |pmid=16319894 |doi=10.1038/nature04187|bibcode=2005Natur.438..679P |url=https://authors.library.caltech.edu/56271/2/Tables.pdf |type=Submitted manuscript }}</ref><br />
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The computational research has focused on improving existing motif detection tools to assist the biological investigations and allow larger networks to be analyzed. Several different algorithms have been provided so far, which are elaborated in the next section in chronological order.<br />
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另一方面,对于计算研究的重点则是改进现有的模体检测工具,以协助生物学研究,并允许对更大的网络进行分析。到目前为止,已经提供了几种不同的算法,这些算法将在下一节按时间顺序进行阐述。<br />
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Most recently, the acc-MOTIF tool to detect network motifs was released.<ref>{{Cite web | url=http://www.ft.unicamp.br/docentes/meira/accmotifs/ |title = Acc-Motif: Accelerated Motif Detection}}</ref><br />
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最近,还发布了用于检测网络基序的acc基序工具。<ref>{{Cite web | url=http://www.ft.unicamp.br/docentes/meira/accmotifs/ |title = Acc-Motif: Accelerated Motif Detection}}</ref><br />
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==模体发现算法 Motif discovery algorithms==<br />
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Various solutions have been proposed for the challenging problem of motif discovery. These algorithms can be classified under various paradigms such as exact counting methods, sampling methods, pattern growth methods and so on. However, motif discovery problem comprises two main steps: first, calculating the number of occurrences of a sub-graph and then, evaluating the sub-graph significance. The recurrence is significant if it is detectably far more than expected. Roughly speaking, the expected number of appearances of a sub-graph can be determined by a Null-model, which is defined by an ensemble of random networks with some of the same properties as the original network.<br />
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针对模体发现这一问题存在多种解决方案。这些算法可以归纳为不同的范式:例如精确计数方法,采样方法,模式增长方法等。但模体发现问题包括两个主要步骤:首先,计算子图的出现次数,然后评估子图的重要性。如果检测到的重现性远超过预期,那么这种重现性是很显著的。粗略地讲,子图的预期出现次数可以由'''零模型 Null-model''' 确定,该模型定义为具有与原始网络某些属性相同的随机网络的集合。<br />
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Here, a review on computational aspects of major algorithms is given and their related benefits and drawbacks from an algorithmic perspective are discussed.<br />
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接下来,对下列算法的计算原理进行简要回顾,并从算法的角度讨论了它们的优缺点。<br />
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===mfinder 算法===<br />
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''mfinder'', the first motif-mining tool, implements two kinds of motif finding algorithms: a full enumeration and a sampling method. Until 2004, the only exact counting method for NM (network motif) detection was the brute-force one proposed by Milo ''et al.''.<ref name="mil1" /> This algorithm was successful for discovering small motifs, but using this method for finding even size 5 or 6 motifs was not computationally feasible. Hence, a new approach to this problem was needed.<br />
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'''mfinder'''是第一个模体挖掘工具,它主要有两种模体查找算法:完全枚举 full enumeration 和采样方法 sampling method。直到2004年,用于NM('''网络模体 networkmotif''')检测的唯一精确计数方法是'''Milo'''等人提出的暴力穷举方法。<ref name="mil1" />该算法成功地发现了小规模的模体,但是这种方法甚至对于发现规模为5个或6个的模体在计算上都不可行的。因此,需要一种解决该问题的新方法。<br />
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Kashtan ''et al.'' <ref name="kas1" /> presented the first sampling NM discovery algorithm, which was based on ''edge sampling'' throughout the network. This algorithm estimates concentrations of induced sub-graphs and can be utilized for motif discovery in directed or undirected networks. The sampling procedure of the algorithm starts from an arbitrary edge of the network that leads to a sub-graph of size two, and then expands the sub-graph by choosing a random edge that is incident to the current sub-graph. After that, it continues choosing random neighboring edges until a sub-graph of size n is obtained. Finally, the sampled sub-graph is expanded to include all of the edges that exist in the network between these n nodes. When an algorithm uses a sampling approach, taking unbiased samples is the most important issue that the algorithm might address. The sampling procedure, however, does not take samples uniformly and therefore Kashtan ''et al.'' proposed a weighting scheme that assigns different weights to the different sub-graphs within network.<ref name="kas1" /> The underlying principle of weight allocation is exploiting the information of the [[sampling probability]] for each sub-graph, i.e. the probable sub-graphs will obtain comparatively less weights in comparison to the improbable sub-graphs; hence, the algorithm must calculate the sampling probability of each sub-graph that has been sampled. This weighting technique assists ''mfinder'' to determine sub-graph concentrations impartially.<br />
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'''Kashtan''' 等人<ref name="kas1" />首次提出了一种基于边缘采样的网络模体(NM)采样发现算法。该算法估计了<font color="red">所含子图 induced sub-graphs 的集中度 concentrations </font>,可用于有向或无向网络中的模体发现。该算法的采样过程从网络的任意一条边开始,该边连向大小为2的子图,然后选择一条与当前子图相关的随机边对子图进行扩展。之后,它将继续选择随机的相邻边,直到获得大小为n的子图为止。最后,采样得到的子图扩展为包括这n个节点在内的网络中存在的所有边。当使用采样方法时,获取无偏样本是这类算法可能面临的最重要问题。而且,采样过程并不能保证采到所有的样本(也就是不能保证得到所有的子图,译者注),因此,Kashtan 等人又提出了一种加权方案,为网络中的不同子图分配不同的权重。<ref name="kas1" /> 权重分配的基本原理是利用每个子图的抽样概率信息,即,与不可能的子图相比,可能的子图将获得相对较少的权重;因此,该算法必须计算已采样的每个子图的采样概率。这种加权技术有助于mfinder公正地确定子图的<font color="red">集中度 concentrations </font>。<br />
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In expanded to include sharp contrast to exhaustive search, the computational time of the algorithm surprisingly is asymptotically independent of the network size. An analysis of the computational time of the algorithm has shown that it takes {{math|O(n<sup>n</sup>)}} for each sample of a sub-graph of size {{math|n}} from the network. On the other hand, there is no analysis in <ref name="kas1" /> on the classification time of sampled sub-graphs that requires solving the ''graph isomorphism'' problem for each sub-graph sample. Additionally, an extra computational effort is imposed on the algorithm by the sub-graph weight calculation. But it is unavoidable to say that the algorithm may sample the same sub-graph multiple times – spending time without gathering any information.<ref name="wer1" /> In conclusion, by taking the advantages of sampling, the algorithm performs more efficiently than an exhaustive search algorithm; however, it only determines sub-graphs concentrations approximately. This algorithm can find motifs up to size 6 because of its main implementation, and as result it gives the most significant motif, not all the others too. Also, it is necessary to mention that this tool has no option of visual presentation. The sampling algorithm is shown briefly:<br />
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与穷举搜索形成鲜明对比的是,该算法的计算时间竟然与网络大小渐近无关。对算法时间复杂度的分析表明,对于网络中大小为n的子图的每个样本,它的时间复杂度为<math>O(n^n)</math>。另一方面,<font color="red">并没有对已采样子图的每一个子图样本判断图同构问题的分类时间进行分析</font><ref name="kas1" />。另外,子图权重计算将额外增加该算法的计算负担。但是不得不指出的是,该算法可能会多次采样相同的子图——花费时间而不收集任何有用信息。<ref name="wer1" />总之,通过利用采样的优势,该算法的性能比穷举搜索算法更有效;但是,它只能大致确定子图的<font color="red">集中度 concentrations </font>。由于该算法的实现方式,使得它可以找到最大为6的模体,并且它会给出的最重要的模体,而不是其他所有模体。另外,有必要提到此工具没有可视化的呈现。采样算法简要显示如下:<br />
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{| class="wikitable"<br />
|-<br />
! mfinder<br />
|-<br />
| '''Definitions:''' {{math|E<sub>s</sub>}}is the set of picked edges. {{math|V<sub>s</sub>}} is the set of all nodes that are touched by the edges in {{math|E}}.<br />
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| Init {{math|V<sub>s</sub>}} and {{math|E<sub>s</sub>}} to be empty sets.<br />
1. Pick a random edge {{math|e<sub>1</sub> {{=}} (v<sub>i</sub>, v<sub>j</sub>)}}. Update {{math|E<sub>s</sub> {{=}} {e<sub>1</sub>}}}, {{math|V<sub>s</sub> {{=}} {v<sub>i</sub>, v<sub>j</sub>}}}<br />
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2. Make a list {{math|L}} of all neighbor edges of {{math|E<sub>s</sub>}}. Omit from {{math|L}} all edges between members of {{math|V<sub>s</sub>}}.<br />
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3. Pick a random edge {{math|e {{=}} {v<sub>k</sub>,v<sub>l</sub>}}} from {{math|L}}. Update {{math|E<sub>s</sub> {{=}} E<sub>s</sub> ⋃ {e}}}, {{math|V<sub>s</sub> {{=}} V<sub>s</sub> ⋃ {v<sub>k</sub>, v<sub>l</sub>}}}.<br />
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4. Repeat steps 2-3 until completing an ''n''-node subgraph (until {{math|{{!}}V<sub>s</sub>{{!}} {{=}} n}}).<br />
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5. Calculate the probability to sample the picked ''n''-node subgraph.<br />
|}<br />
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{|class="wikitable"<br />
|+ mfinder<br />
|-<br />
!rowspan="1"|定义:<math>E_{s}</math>是采集的边集合。<math>V_{s}</math>是<math>E</math>中所有边的顶点的集合。<br />
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|rowspan="5"|初始化<math>V_{s}</math>和<math>E_{s}</math>为空集。<br><br />
1. 随机选择一条边<math> e_{1} = (v_{i}, v_{j}) </math>,更新 <math>E_{s} = \{e_{1}\}, V{s} = \{v_{i}, v_{j}\}</math><br />
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2. 列出<math>E{s}</math>的所有邻边列表<math> L </math>,从<math> L </math>中删除<math>V{s}</math>中所有元素组成的边。<br />
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3. 从<math> L </math>中随机选择一条边<math> e = \{v_{k},v_{l}\} </math>, 更新<math>E_{s} = E_{s} \cup \{e\} , V_{s} = V_{s} \cup \{v_{k}, v_{l}\}</math>。<br />
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4. 重复步骤2-3,直到完成包含n个节点的子图 (<math>\left | V_{s} \right | = n</math>)。<br />
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5. 计算对选取的n节点子图进行采样的概率。<br />
|}<br />
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===FPF (Mavisto)算法===<br />
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Schreiber and Schwöbbermeyer <ref name="schr1" /> proposed an algorithm named ''flexible pattern finder (FPF)'' for extracting frequent sub-graphs of an input network and implemented it in a system named ''Mavisto''.<ref name="schr2">{{cite journal |vauthors=Schreiber F, Schwobbermeyer H |title=MAVisto: a tool for the exploration of network motifs |journal=Bioinformatics |volume=21 |issue=17|pages=3572–3574 |year=2005 |doi=10.1093/bioinformatics/bti556|pmid=16020473 |doi-access=free }}</ref> Their algorithm exploits the ''downward closure'' property which is applicable for frequency concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}}. The downward closure property asserts that the frequency for sub-graphs decrease monotonically by increasing the size of sub-graphs; however, this property does not hold necessarily for frequency concept {{math|F<sub>1</sub>}}. FPF is based on a ''pattern tree'' (see figure) consisting of nodes that represents different graphs (or patterns), where the parent of each node is a sub-graph of its children nodes; in other words, the corresponding graph of each pattern tree's node is expanded by adding a new edge to the graph of its parent node.<br />
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Schreiber和Schwöbbermeyer <ref name="schr1" />提出了一种称为灵活模式查找器(FPF)的算法,用于提取输入网络的频繁子图,并将其在名为Mavisto的系统中加以实现。<ref name="schr2">{{cite journal |vauthors=Schreiber F, Schwobbermeyer H |title=MAVisto: a tool for the exploration of network motifs |journal=Bioinformatics |volume=21 |issue=17|pages=3572–3574 |year=2005 |doi=10.1093/bioinformatics/bti556|pmid=16020473 |doi-access=free }}</ref> 他们的算法利用了向下闭包特性,该特性适用于频率概念<math>F_{2}</math>和<math>F_{3}</math>。向下闭包性质表明,子图的频率随着子图的大小而单调下降;但这一性质并不一定适用于频率概念<math>F_{1}</math>。FPF算法基于模式树(见右图),由代表不同图形(或模式)的节点组成,其中每个节点的父节点是其子节点的子图;换句话说,每个模式树节点的对应图通过向其父节点图添加新边来扩展。<br />
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[[Image:The pattern tree in FPF algorithm.jpg|right|thumb|''FPF算法中的模式树展示''.<ref name="schr1" />]]<br />
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At first, the FPF algorithm enumerates and maintains the information of all matches of a sub-graph located at the root of the pattern tree. Then, one-by-one it builds child nodes of the previous node in the pattern tree by adding one edge supported by a matching edge in the target graph, and tries to expand all of the previous information about matches to the new sub-graph (child node). In next step, it decides whether the frequency of the current pattern is lower than a predefined threshold or not. If it is lower and if downward closure holds, FPF can abandon that path and not traverse further in this part of the tree; as a result, unnecessary computation is avoided. This procedure is continued until there is no remaining path to traverse.<br />
<br />
首先,FPF算法枚举并维护位于模式树根部的子图的所有匹配信息。然后,它通过在目标图中添加匹配边缘支持的一条边缘,在模式树中一一建立前一节点的子节点,然后通过在目标图中添加匹配边支持的一条边,逐个构建模式树中前一个节点的子节点,并尝试将以前关于匹配的所有信息拓展到新的子图(子节点)中。下一步,它判断当前模式的频率是否低于预定义的阈值。如果它低于阈值且保持向下闭包,则FPF算法会放弃该路径,而不会在树的此部分进一步遍历;这样就避免了不必要的计算。重复此过程,直到没有剩余可遍历的路径为止。<br />
<br />
<br />
The advantage of the algorithm is that it does not consider infrequent sub-graphs and tries to finish the enumeration process as soon as possible; therefore, it only spends time for promising nodes in the pattern tree and discards all other nodes. As an added bonus, the pattern tree notion permits FPF to be implemented and executed in a parallel manner since it is possible to traverse each path of the pattern tree independently. However, FPF is most useful for frequency concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}}, because downward closure is not applicable to {{math|F<sub>1</sub>}}. Nevertheless, the pattern tree is still practical for {{math|F<sub>1</sub>}} if the algorithm runs in parallel. Another advantage of the algorithm is that the implementation of this algorithm has no limitation on motif size, which makes it more amenable to improvements. The pseudocode of FPF (Mavisto) is shown below:<br />
<br />
该算法的优点是它不会考虑不频繁的子图,并尝试尽快完成枚举过程;因此,它只花时间在模式树中用于有希望的节点上,而放弃所有其他节点。还有一点额外的好处,模式树概念允许 FPF 以并行方式实现和执行,因为它可以独立地遍历模式树的每个路径。但是,FPF对于频率概念<math>F_{2}</math>和<math>F_{3}</math>最为有用,因为向下闭包不适用于<math>F_{1}</math>。尽管如此,如果算法并行运行,那么模式树对于<math>F_{1}</math>仍然是可行的。该算法的另一个优点是它的实现对模体大小没有限制,这使其更易于改进。FPF(Mavisto)的伪代码如下所示:<br />
<br />
<br />
{| class="wikitable"<br />
|-<br />
! Mavisto<br />
|-<br />
| '''Data:''' Graph {{math|G}}, target pattern size {{math|t}}, frequency concept {{math|F}}<br />
<br />
'''Result:''' Set {{math|R}} of patterns of size {{math|t}} with maximum frequency.<br />
|-<br />
| {{math|R ← φ}}, {{math|f<sub>max</sub> ← 0}}<br />
<br />
{{math|P ←}}start pattern {{math|p1}} of size 1<br />
<br />
{{math|M<sub>p<sub>1</sub></sub> ←}}all matches of {{math|p<sub>1</sub>}} in {{math|G}}<br />
<br />
'''While''' {{math|P &ne; φ}} '''do'''<br />
<br />
{{pad|1em}}{{math|P<sub>max</sub> ←}}select all patterns from {{math|P}} with maximum size.<br />
<br />
{{pad|1em}}{{math|P ←}} select pattern with maximum frequency from {{math|P<sub>max</sub>}}<br />
<br />
{{pad|1em}}{{math|Ε {{=}} ''ExtensionLoop''(G, p, M<sub>p</sub>)}}<br />
<br />
{{pad|1em}}'''Foreach''' pattern {{math|p &isin; E}}<br />
<br />
{{pad|2em}}'''If''' {{math|F {{=}} F<sub>1</sub>}} '''then''' {{math|f ← ''size''(M<sub>p</sub>)}}<br />
<br />
{{pad|2em}}'''Else''' {{math|f ←}} ''Maximum Independent set''{{math|(F, M<sub>p</sub>)}}<br />
<br />
{{pad|2em}}'''End'''<br />
<br />
{{pad|2em}}'''If''' {{math|''size''(p) {{=}} t}} '''then'''<br />
<br />
{{pad|3em}}'''If''' {{math|f {{=}} f<sub>max</sub>}} '''then''' {{math|R ← R ⋃ {p}}}<br />
<br />
{{pad|3em}}'''Else if''' {{math|f > f<sub>max</sub>}} '''then''' {{math|R ← {p}}}; {{math|f<sub>max</sub> ← f}}<br />
<br />
{{pad|3em}}'''End'''<br />
<br />
{{pad|2em}}'''Else'''<br />
<br />
{{pad|3em}}'''If''' {{math|F {{=}} F<sub>1</sub>}} '''or''' {{math|f &ge; f<sub>max</sub>}} '''then''' {{math|P ← P ⋃ {p}}}<br />
<br />
{{pad|3em}}'''End'''<br />
<br />
{{pad|2em}}'''End'''<br />
<br />
{{pad|1em}}'''End'''<br />
<br />
'''End'''<br />
|}<br />
<br />
<br />
{|class="wikitable"<br />
|+ Mavisto<br />
|-<br />
!rowspan="1"|数据: 图 <math>G</math>, 目标模式规模 <math>t</math>, 频率概念 <math>F</math>。<br><br />
结果: 以最大频率设置大小为 <math>t</math>的模式 <math>R</math>.<br><br />
|-<br />
|rowspan="20"| <math>R \leftarrow \Phi , f_{max}\leftarrow 0</math><br><br />
<math>P \leftarrow</math> 开始于大小为1的模式 <math>p_{1}</math><br />
<br />
<math>M_{p_{1}} \leftarrow </math> 图 <math>G</math> 中模式 <math>p_{1}</math> 的所有匹配<br />
<br />
当 <math>P \neq \Phi </math> 时,执行:<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;<math>P_{max} \leftarrow</math> 从 <math>P</math> 中选择最大规模的所有模式<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;<math>P\leftarrow</math> 从 <math>P_{max}</math> 中选择最大频率的模式<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;<math>E = ExtensionLoop(G, p, M_{p})</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;对于 <math>p \in E </math> 的所有模式:<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>F = F_{1}</math> ,那么 <math>f \leftarrow size(M_{p})</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他<math>f \leftarrow</math> 最大独立集 <math>(F, M_{p})</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>size(p) = t</math> ,那么<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>f = f_{max}</math> ,那么 <math>R \leftarrow R \cup \{p\}</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他 如果 <math>f > f_{max}</math> ,那么 <math>R \leftarrow \{p\}</math>; <math>f_{max} \leftarrow f</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>F = F_{1} or f \geq f_{max}</math> ,那么 <math> P \leftarrow P \cup \{p\}</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
结束<br />
|}<br />
<br />
===ESU (FANMOD)算法及对应的软件===<br />
The sampling bias of Kashtan ''et al.'' <ref name="kas1" /> provided great impetus for designing better algorithms for the NM discovery problem. Although Kashtan ''et al.'' tried to settle this drawback by means of a weighting scheme, this method imposed an undesired overhead on the running time as well a more complicated implementation. This tool is one of the most useful ones, as it supports visual options and also is an efficient algorithm with respect to time. But, it has a limitation on motif size as it does not allow searching for motifs of size 9 or higher because of the way the tool is implemented.<br />
<br />
由于Kashtan等学者发现的采样偏差问题,所以针对NM discovery problem需要设计更好的算法。虽然Kashtan等人尝试用加权法来解决这个弊端,但这个方法在运行上,消耗了过多的运行时间,且实现起来也变得更加复杂。但这个工具还是最好用的工具之一,因为它支持可视化选项,同时也『是个节约时间的算法』。但是,它在所支持的模体的规模大小还是有局限性。由于该工具在具体实施中,不允许搜索规模大小为9或者更大的模体。<br />
<br />
Wernicke <ref name="wer1" /> introduced an algorithm named ''RAND-ESU'' that provides a significant improvement over ''mfinder''.<ref name="kas1" /> This algorithm, which is based on the exact enumeration algorithm ''ESU'', has been implemented as an application called ''FANMOD''.<ref name="wer1" /> ''RAND-ESU'' is a NM discovery algorithm applicable for both directed and undirected networks, effectively exploits an unbiased node sampling throughout the network, and prevents overcounting sub-graphs more than once. Furthermore, ''RAND-ESU'' uses a novel analytical approach called ''DIRECT'' for determining sub-graph significance instead of using an ensemble of random networks as a Null-model. The ''DIRECT'' method estimates the sub-graph concentration without explicitly generating random networks.<ref name="wer1" /> Empirically, the DIRECT method is more efficient in comparison with the random network ensemble in case of sub-graphs with a very low concentration; however, the classical Null-model is faster than the ''DIRECT'' method for highly concentrated sub-graphs.<ref name="mil1" /><ref name="wer1" /> In the following, we detail the ''ESU'' algorithm and then we show how this exact algorithm can be modified efficiently to ''RAND-ESU'' that estimates sub-graphs concentrations.<br />
<br />
Weinicke引入了一种叫RAND-ESU的算法,这个新引入的算法比Mfinder软件有着更显著的提升。RAND-ESU基于精准的ESU算法,已有对应的软件FANMOD。RAND-ESU是一种[NM算法],可应用于定向的或者不定向的网络中,能够有效的在网络中利用无偏差节点进行采样,以及保证了一个子图仅仅被搜索一次,且不会产生无意义的子图。并且,RAND-ESU采用了一个叫做DIRECT的全新的分析方式,从而来确定子图的重要性,而不是用随机网络的组合来建立『Null模型』。DIRECT方法可以不用大量生成随机网络就能估计子图的浓度。实际上,相较于用随机网络组合分析比较低集中度的子图来说,DIRECT这个方法更加的高效。但是,传统的『Null模型』又比DIRECT这个算法能更加快速地解决高度集中的子图。接下来,我们将详细讲述ESU算法和展示如何把这种精确的算法调整为RAND-ESU算法去估计子图的浓度。<br />
<br />
The algorithms ''ESU'' and ''RAND-ESU'' are fairly simple, and hence easy to implement. ''ESU'' first finds the set of all induced sub-graphs of size {{math|k}}, let {{math|S<sub>k</sub>}} be this set. ''ESU'' can be implemented as a recursive function; the running of this function can be displayed as a tree-like structure of depth {{math|k}}, called the ESU-Tree (see figure). Each of the ESU-Tree nodes indicate the status of the recursive function that entails two consecutive sets SUB and EXT. SUB refers to nodes in the target network that are adjacent and establish a partial sub-graph of size {{math|{{!}}SUB{{!}} ≤ k}}. If {{math|{{!}}SUB{{!}} {{=}} k}}, the algorithm has found an induced complete sub-graph, so {{math|S<sub>k</sub> {{=}} SUB ∪ S<sub>k</sub>}}. However, if {{math|{{!}}SUB{{!}} < k}}, the algorithm must expand SUB to achieve cardinality {{math|k}}. This is done by the EXT set that contains all the nodes that satisfy two conditions: First, each of the nodes in EXT must be adjacent to at least one of the nodes in SUB; second, their numerical labels must be larger than the label of first element in SUB. The first condition makes sure that the expansion of SUB nodes yields a connected graph and the second condition causes ESU-Tree leaves (see figure) to be distinct; as a result, it prevents overcounting. Note that, the EXT set is not a static set, so in each step it may expand by some new nodes that do not breach the two conditions. The next step of ESU involves classification of sub-graphs placed in the ESU-Tree leaves into non-isomorphic size-{{math|k}} graph classes; consequently, ESU determines sub-graphs frequencies and concentrations. This stage has been implemented simply by employing McKay's ''nauty'' algorithm,<ref name="mck1">{{cite journal |author=McKay BD |title=Practical graph isomorphism |journal=Congressus Numerantium |year=1981 |volume=30 |pages=45–87|bibcode=2013arXiv1301.1493M |arxiv=1301.1493 }}</ref><ref name="mck2">{{cite journal |author=McKay BD |title=Isomorph-free exhaustive generation |journal=Journal of Algorithms |year=1998 |volume=26 |issue=2 |pages=306–324 |doi=10.1006/jagm.1997.0898}}</ref> which classifies each sub-graph by performing a graph isomorphism test. Therefore, ESU finds the set of all induced {{math|k}}-size sub-graphs in a target graph by a recursive algorithm and then determines their frequency using an efficient tool.<br />
<br />
ESU和RAND-ESU两种算法都比较简捷,所以实现起来都很容易。『ESU首先找到大小为k的所有诱导子图的集合』,并命名这个集合为Sk。因为EUS以递归函数的形式实现,该函数的运行可以演示为『k级』的树状结构,称为ESU-Tree(见图)。每一个在ESU-Tree上的节点都表示递归函数的状态,这个递归函数需要两个连续集合的SUB和EXT。『SUB指的是在目标网络的相邻节点上,并且是一部分的层级绝对值大小小于等于k的子图集合。』如果SUB集合层级的绝对值等于k,那么这个算法可以找到一个『完整的诱导子图』,所以在此情况下Sk等于SUB与Sk的并集。相反,如果它的绝对值小于k,那么这个算法必须把SUB扩大,才能实现基数为k。『EXT这个集合包含了所有的满足以下两个情况的节点。第一,每个在EXT的节点必须至少与在SUB的一个节点相邻。第二,他们的下标必须比在SUB的第一个元素大。』???第一个条件保证了『SUB节点的展开产生相关的图』,第二个条件能使ESU-Tree树状图上的分支变得离散。所以,这个方法可以避免过度计算。注意,EXT集合不是一个固定的集合。所以每一步都有可能扩展满足于以上两个条件的新节点。下一步包含了在ESU-Tree分支上的子图的分类,『将它们分为非同构的大小为k的图类』。因此,ESU决定了子图的『频率以及浓度』。这一阶段的实施仅通过运用McKay的nauty算法,这一算法可以通过图的同构测试来把每个子图进行分类。所以,ESU能够在目标图中通过递归算法,找到所有规模大小为k的诱导子图集合,且使用高效的工具来确定他们的『频率』。<br />
<br />
The procedure of implementing ''RAND-ESU'' is quite straightforward and is one of the main advantages of ''FANMOD''. One can change the ''ESU'' algorithm to explore just a portion of the ESU-Tree leaves by applying a probability value {{math|0 ≤ p<sub>d</sub> ≤ 1}} for each level of the ESU-Tree and oblige ''ESU'' to traverse each child node of a node in level {{math|d-1}} with probability {{math|p<sub>d</sub>}}. This new algorithm is called ''RAND-ESU''. Evidently, when {{math|p<sub>d</sub> {{=}} 1}} for all levels, ''RAND-ESU'' acts like ''ESU''. For {{math|p<sub>d</sub> {{=}} 0}} the algorithm finds nothing. Note that, this procedure ensures that the chances of visiting each leaf of the ESU-Tree are the same, resulting in ''unbiased'' sampling of sub-graphs through the network. The probability of visiting each leaf is {{math|∏<sub>d</sub>p<sub>d</sub>}} and this is identical for all of the ESU-Tree leaves; therefore, this method guarantees unbiased sampling of sub-graphs from the network. Nonetheless, determining the value of {{math|p<sub>d</sub>}} for {{math|1 ≤ d ≤ k}} is another issue that must be determined manually by an expert to get precise results of sub-graph concentrations.<ref name="cir1" /> While there is no lucid prescript for this matter, the Wernicke provides some general observations that may help in determining p_d values. In summary, ''RAND-ESU'' is a very fast algorithm for NM discovery in the case of induced sub-graphs supporting unbiased sampling method. Although, the main ''ESU'' algorithm and so the ''FANMOD'' tool is known for discovering induced sub-graphs, there is trivial modification to ''ESU'' which makes it possible for finding non-induced sub-graphs, too. The pseudo code of ''ESU (FANMOD)'' is shown below:<br />
运用RAND-ESU的过程十分的简单,这也是FANMOD的一个主要的优点。可以通过对ESU-Tree『树状图』的每个级别应用概率{{math|0 ≤ p<sub>d</sub> ≤ 1}}并强制ESU以概率{{math|p<sub>d</sub>}}遍历{{math|d-1}}级别中节点的每个子节点,来更改ESU算法使其仅搜索ESU-Tree分支的一部分。 这种新的演算方式叫RAND-ESU。显然,当所有阶段{{math|p<sub>d</sub> {{=}} 1}}时,RAND-ESU等同于ESU。当{{math|p<sub>d</sub> {{=}} 0}}时,在这个算法下没有任何意义。注意,这个过程只是确保了可以找到ESU-Tree上的每一分支的机会都是相同的,从而使网络中的子图采样无偏差。访问每个分支的概率为{{math|∏<sub>d</sub>p<sub>d</sub>}},这对于所有ESU-Tree中的分支都是相同的; 因此,该方法可确保从网络中对子图进行无偏采样。但是,设置{{math|1 ≤ d ≤ k}}的{{math|p<sub>d</sub>}}参数是另一个问题,必须由专家人工确定才能获得子图『浓度』的精确结果。尽管对此没有明确的规定,但是Wrenucke提出了一些一般性的观察结论,这些结论有可能可以帮助我们确定p_d值。总的来说,在诱导子图支持无偏采样方法的情况下,RAND-ESU是一个能快速解决『NM discovery problem』的算法。 尽管,ESU算法的主要部分和FANMOD工具是以用来寻找诱导子图而著称的,但只需对ESU进行细小的改动,就可以用来寻找诱导子图。ESU(FANMOD)的伪代码如下:<br />
[[File:ESU-Tree.jpg|thumb|(a) ''A target graph of size 5'', (b) ''the ESU-tree of depth k that is associated to the extraction of sub-graphs of size 3 in the target graph''. Leaves correspond to set S3 or all of the size-3 induced sub-graphs of the target graph (a). Nodes in the ESU-tree include two adjoining sets, the first set contains adjacent nodes called SUB and the second set named EXT holds all nodes that are adjacent to at least one of the SUB nodes and where their numerical labels are larger than the SUB nodes labels. The EXT set is utilized by the algorithm to expand a SUB set until it reaches a desired sub-graph size that are placed at the lowest level of ESU-Tree (or its leaves).]]<br />
<br />
{| class="wikitable"<br />
|-<br />
! Enumeration of ESU (FANMOD)<br />
|-<br />
|'''''EnumerateSubgraphs(G,k)'''''<br />
<br />
'''Input:''' A graph {{math|G {{=}} (V, E)}} and an integer {{math|1 ≤ k ≤ {{!}}V{{!}}}}.<br />
<br />
'''Output:''' All size-{{math|k}} subgraphs in {{math|G}}.<br />
<br />
'''for each''' vertex {{math|v ∈ V}} '''do'''<br />
<br />
{{pad|2em}}{{math|VExtension ← {u ∈ N({v}) {{!}} u > v}}}<br />
<br />
{{pad|2em}}'''call''' {{math|''ExtendSubgraph''({v}, VExtension, v)}}<br />
<br />
'''endfor'''<br />
|-<br />
|'''''ExtendSubgraph(VSubgraph, VExtension, v)'''''<br />
<br />
'''if''' {{math|{{!}}VSubgraph{{!}} {{=}} k}} '''then''' output {{math|G[VSubgraph]}} and '''return'''<br />
<br />
'''while''' {{math|VExtension ≠ ∅}} '''do'''<br />
<br />
{{pad|2em}}Remove an arbitrarily chosen vertex {{math|w}} from {{math|VExtension}}<br />
<br />
{{pad|2em}}{{math|VExtension&prime; ← VExtension ∪ {u ∈ N<sub>excl</sub>(w, VSubgraph) {{!}} u > v}}}<br />
<br />
{{pad|2em}}'''call''' {{math|''ExtendSubgraph''(VSubgraph ∪ {w}, VExtension&prime;, v)}}<br />
<br />
'''return'''<br />
|}<br />
<br />
{| class="wikitable"<br />
|-<br />
! ESU子图搜索算法(FANMOD软件实现)<br />
|-<br />
|'''''枚举子图(G,k)'''''<br />
<br />
'''输入:''' 图 {{math|G {{=}} (V, E)}} 和 一个 整数 {{math|1 ≤ k ≤ {{!}}V{{!}}}}.<br />
<br />
'''输出:''' 所有size-{{math|k}} 子图 in {{math|G}}.<br />
<br />
'''for each'''顶点v{{math|v ∈ V}} '''执行'''<br />
<br />
{{pad|2em}}{{math|VExtension(集合EXT) ← {u ∈ N({v}) {{!}} u > v}}}<br />
<br />
{{pad|2em}}'''调用''' {{math|''ExtendSubgraph''({v}, VExtension, v)}}<br />
<br />
'''结束for循环'''<br />
|-<br />
|'''''ExtendSubgraph(VSubgraph, VExtension, v)'''''<br />
<br />
'''若''' {{math|{{!}}VSubgraph{{!}} {{=}} k}} '''则''' 输出 {{math|G[VSubgraph]}} and '''返回主函数'''<br />
<br />
'''当''' {{math|VExtension ≠ ∅}} '''执行'''<br />
<br />
{{pad|2em}}删除一个任意选择的顶点 {{math|w}} 源于 {{math|VExtension}} 中<br />
<br />
{{pad|2em}}{{math|VExtension&prime; ← VExtension ∪ {u ∈ N<sub>excl</sub>(w, VSubgraph) {{!}} u > v}}}<br />
<br />
{{pad|2em}}'''call''' {{math|''ExtendSubgraph''(VSubgraph ∪ {w}, VExtension&prime;, v)}}<br />
<br />
'''返回'''<br />
|}<br />
<br />
===NeMoFinder===<br />
Chen ''et al.'' <ref name="che1">{{cite conference |vauthors=Chen J, Hsu W, Li Lee M, etal |title=NeMoFinder: dissecting genome-wide protein-protein interactions with meso-scale network motifs |conference=the 12th ACM SIGKDD international conference on Knowledge discovery and data mining |year=2006 |location=Philadelphia, Pennsylvania, USA |pages=106–115}}</ref> introduced a new NM discovery algorithm called ''NeMoFinder'', which adapts the idea in ''SPIN'' <ref name="hua1">{{cite conference |vauthors=Huan J, Wang W, Prins J, etal |title=SPIN: mining maximal frequent sub-graphs from graph databases |conference=the 10th ACM SIGKDD international conference on Knowledge discovery and data mining |year=2004 |pages=581–586}}</ref> to extract frequent trees and after that expands them into non-isomorphic graphs.<ref name="cir1" /> ''NeMoFinder'' utilizes frequent size-n trees to partition the input network into a collection of size-{{math|n}} graphs, afterward finding frequent size-n sub-graphs by expansion of frequent trees edge-by-edge until getting a complete size-{{math|n}} graph {{math|K<sub>n</sub>}}. The algorithm finds NMs in undirected networks and is not limited to extracting only induced sub-graphs. Furthermore, ''NeMoFinder'' is an exact enumeration algorithm and is not based on a sampling method. As Chen ''et al.'' claim, ''NeMoFinder'' is applicable for detecting relatively large NMs, for instance, finding NMs up to size-12 from the whole ''S. cerevisiae'' (yeast) PPI network as the authors claimed.<ref name="uet1">{{cite journal |vauthors=Uetz P, Giot L, Cagney G, etal |title=A comprehensive analysis of protein-protein interactions in Saccharomyces cerevisiae |journal=Nature |year=2000 |volume=403 |issue=6770 |pages=623–627 |doi=10.1038/35001009 |pmid=10688190|bibcode=2000Natur.403..623U }}</ref><br />
<br />
''NeMoFinder'' consists of three main steps. First, finding frequent size-{{math|n}} trees, then utilizing repeated size-n trees to divide the entire network into a collection of size-{{math|n}} graphs, finally, performing sub-graph join operations to find frequent size-n sub-graphs.<ref name="che1" /> In the first step, the algorithm detects all non-isomorphic size-{{math|n}} trees and mappings from a tree to the network. In the second step, the ranges of these mappings are employed to partition the network into size-n graphs. Up to this step, there is no distinction between ''NeMoFinder'' and an exact enumeration method. However, a large portion of non-isomorphic size-n graphs still remain. ''NeMoFinder'' exploits a heuristic to enumerate non-tree size-n graphs by the obtained information from the preceding steps. The main advantage of the algorithm is in the third step, which generates candidate sub-graphs from previously enumerated sub-graphs. This generation of new size-{{math|n}} sub-graphs is done by joining each previous sub-graph with derivative sub-graphs from itself called ''cousin sub-graphs''. These new sub-graphs contain one additional edge in comparison to the previous sub-graphs. However, there exist some problems in generating new sub-graphs: There is no clear method to derive cousins from a graph, joining a sub-graph with its cousins leads to redundancy in generating particular sub-graph more than once, and cousin determination is done by a canonical representation of the adjacency matrix which is not closed under join operation. ''NeMoFinder'' is an efficient network motif finding algorithm for motifs up to size 12 only for protein-protein interaction networks, which are presented as undirected graphs. And it is not able to work on directed networks which are so important in the field of complex and biological networks. The pseudocode of ''NeMoFinder'' is shown below:<br />
<br />
{| class="wikitable"<br />
|-<br />
! NeMoFinder<br />
|-<br />
|'''Input:'''<br />
<br />
{{math|G}} - PPI network;<br />
<br />
{{math|N}} - Number of randomized networks;<br />
<br />
{{math|K}} - Maximal network motif size;<br />
<br />
{{math|F}} - Frequency threshold;<br />
<br />
{{math|S}} - Uniqueness threshold;<br />
<br />
'''Output:'''<br />
<br />
{{math|U}} - Repeated and unique network motif set;<br />
<br />
{{math|D ← ∅}};<br />
<br />
'''for''' motif-size {{math|k}} '''from''' 3 '''to''' {{math|K}} '''do'''<br />
<br />
{{pad|1em}}{{math|T ← ''FindRepeatedTrees''(k)}};<br />
<br />
{{pad|1em}}{{math|GD<sub>k</sub> ← ''GraphPartition''(G, T)}}<br />
<br />
{{pad|1em}}{{math|D ← D ∪ T}};<br />
<br />
{{pad|1em}}{{math|D&prime; ← T}};<br />
<br />
{{pad|1em}}{{math|i ← k}};<br />
<br />
{{pad|1em}}'''while''' {{math|D&prime; ≠ ∅}} '''and''' {{math|i ≤ k &times; (k - 1) / 2}} '''do'''<br />
<br />
{{pad|2em}}{{math|D&prime; ← ''FindRepeatedGraphs''(k, i, D&prime;)}};<br />
<br />
{{pad|2em}}{{math|D ← D ∪ D&prime;}};<br />
<br />
{{pad|2em}}{{math|i ← i + 1}};<br />
<br />
{{pad|1em}}'''end while'''<br />
<br />
'''end for'''<br />
<br />
'''for''' counter {{math|i}} '''from''' 1 '''to''' {{math|N}} '''do'''<br />
<br />
{{pad|1em}}{{math|G<sub>rand</sub> ← ''RandomizedNetworkGeneration''()}};<br />
<br />
{{pad|1em}}'''for each''' {{math|g ∈ D}} '''do'''<br />
<br />
{{pad|2em}}{{math|''GetRandFrequency''(g, G<sub>rand</sub>)}};<br />
<br />
{{pad|1em}}'''end for'''<br />
<br />
'''end for'''<br />
<br />
{{math|U ← ∅}};<br />
<br />
'''for each''' {{math|g ∈ D}} '''do'''<br />
<br />
{{pad|1em}}{{math|s ← ''GetUniqunessValue''(g)}};<br />
<br />
{{pad|1em}}'''if''' {{math|s ≥ S}} '''then'''<br />
<br />
{{pad|2em}}{{math|U ← U ∪ {g}}};<br />
<br />
{{pad|1em}}'''end if'''<br />
<br />
'''end for'''<br />
<br />
'''return''' {{math|U}};<br />
|}<br />
<br />
===Grochow–Kellis===<br />
Grochow and Kellis <ref name="gro1">{{cite conference|vauthors=Grochow JA, Kellis M |title=Network Motif Discovery Using Sub-graph Enumeration and Symmetry-Breaking |conference=RECOMB |year=2007 |pages=92–106| doi=10.1007/978-3-540-71681-5_7| url=http://www.cs.colorado.edu/~jgrochow/Grochow_Kellis_RECOMB_07_Network_Motifs.pdf}}</ref> proposed an ''exact'' algorithm for enumerating sub-graph appearances. The algorithm is based on a ''motif-centric'' approach, which means that the frequency of a given sub-graph,called the ''query graph'', is exhaustively determined by searching for all possible mappings from the query graph into the larger network. It is claimed <ref name="gro1" /> that a ''motif-centric'' method in comparison to ''network-centric'' methods has some beneficial features. First of all it avoids the increased complexity of sub-graph enumeration. Also, by using mapping instead of enumerating, it enables an improvement in the isomorphism test. To improve the performance of the algorithm, since it is an inefficient exact enumeration algorithm, the authors introduced a fast method which is called ''symmetry-breaking conditions''. During straightforward sub-graph isomorphism tests, a sub-graph may be mapped to the same sub-graph of the query graph multiple times. In the Grochow–Kellis (GK) algorithm symmetry-breaking is used to avoid such multiple mappings. Here we introduce the GK algorithm and the symmetry-breaking condition which eliminates redundant isomorphism tests.<br />
<br />
[[File:Automorphisms of a subgraph.jpg|thumb|(a) ''graph G'', (b) ''illustration of all automorphisms of G that is showed in (a)''. From set AutG we can obtain a set of symmetry-breaking conditions of G given by SymG in (c). Only the first mapping in AutG satisfies the SynG conditions; as a result, by applying SymG in the Isomorphism Extension module the algorithm only enumerate each match-able sub-graph in the network to G once. Note that SynG is not necessarily a unique set for an arbitrary graph G.]]<br />
<br />
The GK algorithm discovers the whole set of mappings of a given query graph to the network in two major steps. It starts with the computation of symmetry-breaking conditions of the query graph. Next, by means of a branch-and-bound method, the algorithm tries to find every possible mapping from the query graph to the network that meets the associated symmetry-breaking conditions. An example of the usage of symmetry-breaking conditions in GK algorithm is demonstrated in figure.<br />
<br />
As it is mentioned above, the symmetry-breaking technique is a simple mechanism that precludes spending time finding a sub-graph more than once due to its symmetries.<ref name="gro1" /><ref name="gro2">{{cite conference|author=Grochow JA |title=On the structure and evolution of protein interaction networks |conference=Thesis M. Eng., Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science|year=2006| url=http://www.cs.toronto.edu/~jgrochow/Grochow_MIT_Masters_06_PPI_Networks.pdf}}</ref> Note that, computing symmetry-breaking conditions requires finding all automorphisms of a given query graph. Even though, there is no efficient (or polynomial time) algorithm for the graph automorphism problem, this problem can be tackled efficiently in practice by McKay's tools.<ref name="mck1" /><ref name="mck2" /> As it is claimed, using symmetry-breaking conditions in NM detection lead to save a great deal of running time. Moreover, it can be inferred from the results in <ref name="gro1" /><ref name="gro2" /> that using the symmetry-breaking conditions results in high efficiency particularly for directed networks in comparison to undirected networks. The symmetry-breaking conditions used in the GK algorithm are similar to the restriction which ''ESU'' algorithm applies to the labels in EXT and SUB sets. In conclusion, the GK algorithm computes the exact number of appearance of a given query graph in a large complex network and exploiting symmetry-breaking conditions improves the algorithm performance. Also, GK algorithm is one of the known algorithms having no limitation for motif size in implementation and potentially it can find motifs of any size.<br />
<br />
===Color-coding approach===<br />
Most algorithms in the field of NM discovery are used to find induced sub-graphs of a network. In 2008, Noga Alon ''et al.'' <ref name="alo1">{{cite journal|author1=Alon N |author2=Dao P |author3=Hajirasouliha I |author4=Hormozdiari F |author5=Sahinalp S.C |title=Biomolecular network motif counting and discovery by color coding |journal=Bioinformatics |year=2008 |volume=24 |issue=13 |pages=i241–i249 |doi=10.1093/bioinformatics/btn163|pmid=18586721 |pmc=2718641 }}</ref> introduced an approach for finding non-induced sub-graphs too. Their technique works on undirected networks such as PPI ones. Also, it counts non-induced trees and bounded treewidth sub-graphs. This method is applied for sub-graphs of size up to 10.<br />
<br />
This algorithm counts the number of non-induced occurrences of a tree {{math|T}} with {{math|k {{=}} O(logn)}} vertices in a network {{math|G}} with {{math|n}} vertices as follows:<br />
<br />
# '''Color coding.''' Color each vertex of input network G independently and uniformly at random with one of the {{math|k}} colors.<br />
# '''Counting.''' Apply a dynamic programming routine to count the number of non-induced occurrences of {{math|T}} in which each vertex has a unique color. For more details on this step, see.<ref name="alo1" /><br />
# Repeat the above two steps {{math|O(e<sup>k</sup>)}} times and add up the number of occurrences of {{math|T}} to get an estimate on the number of its occurrences in {{math|G}}.<br />
<br />
As available PPI networks are far from complete and error free, this approach is suitable for NM discovery for such networks. As Grochow–Kellis Algorithm and this one are the ones popular for non-induced sub-graphs, it is worth to mention that the algorithm introduced by Alon ''et al.'' is less time-consuming than the Grochow–Kellis Algorithm.<ref name="alo1" /><br />
<br />
===MODA===<br />
Omidi ''et al.'' <ref name="omi1">{{cite journal|vauthors=Omidi S, Schreiber F, Masoudi-Nejad A |title=MODA: an efficient algorithm for network motif discovery in biological networks |journal=Genes Genet Syst |year=2009 |volume=84 |issue=5 |pages=385–395 |doi=10.1266/ggs.84.385|pmid=20154426 |doi-access=free }}</ref> introduced a new algorithm for motif detection named ''MODA'' which is applicable for induced and non-induced NM discovery in undirected networks. It is based on the motif-centric approach discussed in the Grochow–Kellis algorithm section. It is very important to distinguish motif-centric algorithms such as MODA and GK algorithm because of their ability to work as query-finding algorithms. This feature allows such algorithms to be able to find a single motif query or a small number of motif queries (not all possible sub-graphs of a given size) with larger sizes. As the number of possible non-isomorphic sub-graphs increases exponentially with sub-graph size, for large size motifs (even larger than 10), the network-centric algorithms, those looking for all possible sub-graphs, face a problem. Although motif-centric algorithms also have problems in discovering all possible large size sub-graphs, but their ability to find small numbers of them is sometimes a significant property.<br />
<br />
Using a hierarchical structure called an ''expansion tree'', the ''MODA'' algorithm is able to extract NMs of a given size systematically and similar to ''FPF'' that avoids enumerating unpromising sub-graphs; ''MODA'' takes into consideration potential queries (or candidate sub-graphs) that would result in frequent sub-graphs. Despite the fact that ''MODA'' resembles ''FPF'' in using a tree like structure, the expansion tree is applicable merely for computing frequency concept {{math|F<sub>1</sub>}}. As we will discuss next, the advantage of this algorithm is that it does not carry out the sub-graph isomorphism test for ''non-tree'' query graphs. Additionally, it utilizes a sampling method in order to speed up the running time of the algorithm.<br />
<br />
Here is the main idea: by a simple criterion one can generalize a mapping of a k-size graph into the network to its same size supergraphs. For example, suppose there is mapping {{math|f(G)}} of graph {{math|G}} with {{math|k}} nodes into the network and we have a same size graph {{math|G&prime;}} with one more edge {{math|&langu, v&rang;}}; {{math|f<sub>G</sub>}} will map {{math|G&prime;}} into the network, if there is an edge {{math|&lang;f<sub>G</sub>(u), f<sub>G</sub>(v)&rang;}} in the network. As a result, we can exploit the mapping set of a graph to determine the frequencies of its same order supergraphs simply in {{math|O(1)}} time without carrying out sub-graph isomorphism testing. The algorithm starts ingeniously with minimally connected query graphs of size k and finds their mappings in the network via sub-graph isomorphism. After that, with conservation of the graph size, it expands previously considered query graphs edge-by-edge and computes the frequency of these expanded graphs as mentioned above. The expansion process continues until reaching a complete graph {{math|K<sub>k</sub>}} (fully connected with {{math|{{frac|k(k-1)|2}}}} edge).<br />
<br />
As discussed above, the algorithm starts by computing sub-tree frequencies in the network and then expands sub-trees edge by edge. One way to implement this idea is called the expansion tree {{math|T<sub>k</sub>}} for each {{math|k}}. Figure shows the expansion tree for size-4 sub-graphs. {{math|T<sub>k</sub>}} organizes the running process and provides query graphs in a hierarchical manner. Strictly speaking, the expansion tree {{math|T<sub>k</sub>}} is simply a [[directed acyclic graph]] or DAG, with its root number {{math|k}} indicating the graph size existing in the expansion tree and each of its other nodes containing the adjacency matrix of a distinct {{math|k}}-size query graph. Nodes in the first level of {{math|T<sub>k</sub>}} are all distinct {{math|k}}-size trees and by traversing {{math|T<sub>k</sub>}} in depth query graphs expand with one edge at each level. A query graph in a node is a sub-graph of the query graph in a node's child with one edge difference. The longest path in {{math|T<sub>k</sub>}} consists of {{math|(k<sup>2</sup>-3k+4)/2}} edges and is the path from the root to the leaf node holding the complete graph. Generating expansion trees can be done by a simple routine which is explained in.<ref name="omi1" /><br />
<br />
''MODA'' traverses {{math|T<sub>k</sub>}} and when it extracts query trees from the first level of {{math|T<sub>k</sub>}} it computes their mapping sets and saves these mappings for the next step. For non-tree queries from {{math|T<sub>k</sub>}}, the algorithm extracts the mappings associated with the parent node in {{math|T<sub>k</sub>}} and determines which of these mappings can support the current query graphs. The process will continue until the algorithm gets the complete query graph. The query tree mappings are extracted using the Grochow–Kellis algorithm. For computing the frequency of non-tree query graphs, the algorithm employs a simple routine that takes {{math|O(1)}} steps. In addition, ''MODA'' exploits a sampling method where the sampling of each node in the network is linearly proportional to the node degree, the probability distribution is exactly similar to the well-known Barabási-Albert preferential attachment model in the field of complex networks.<ref name="bar1">{{cite journal|vauthors=Barabasi AL, Albert R |title=Emergence of scaling in random networks |journal=Science |year=1999 |volume=286 |issue=5439 |pages=509–512 |doi=10.1126/science.286.5439.509 |pmid=10521342|bibcode=1999Sci...286..509B |arxiv=cond-mat/9910332 }}</ref> This approach generates approximations; however, the results are almost stable in different executions since sub-graphs aggregate around highly connected nodes.<ref name="vaz1">{{cite journal |vauthors=Vázquez A, Dobrin R, Sergi D, etal |title=The topological relationship between the large-scale attributes and local interaction patterns of complex networks |journal=PNAS |year=2004 |volume=101 |issue=52 |pages=17940–17945 |doi=10.1073/pnas.0406024101|pmid=15598746 |pmc=539752 |bibcode=2004PNAS..10117940V |arxiv=cond-mat/0408431 }}</ref> The pseudocode of ''MODA'' is shown below:<br />
<br />
[[File:Expansion Tree.jpg|thumb|''Illustration of the expansion tree T4 for 4-node query graphs''. At the first level, there are non-isomorphic k-size trees and at each level, an edge is added to the parent graph to form a child graph. In the second level, there is a graph with two alternative edges that is shown by a dashed red edge. In fact, this node represents two expanded graphs that are isomorphic.<ref name="omi1" />]]<br />
<br />
{| class="wikitable"<br />
|-<br />
! MODA<br />
|-<br />
|'''Input:''' {{math|G}}: Input graph, {{math|k}}: sub-graph size, {{math|Δ}}: threshold value<br />
<br />
'''Output:''' Frequent Subgraph List: List of all frequent {{math|k}}-size sub-graphs<br />
<br />
'''Note:''' {{math|F<sub>G</sub>}}: set of mappings from {{math|G}} in the input graph {{math|G}}<br />
<br />
'''fetch''' {{math|T<sub>k</sub>}}<br />
<br />
'''do'''<br />
<br />
{{pad|1em}}{{math|G&prime; {{=}} ''Get-Next-BFS''(T<sub>k</sub>)}} // {{math|G&prime;}} is a query graph<br />
<br />
{{pad|1em}}if {{math|{{!}}E(G&prime;){{!}} {{=}} (k – 1)}}<br />
<br />
{{pad|1em}}'''call''' {{math|''Mapping-Module''(G&prime;, G)}}<br />
<br />
{{pad|1em}}'''else'''<br />
<br />
{{pad|2em}}'''call''' {{math|''Enumerating-Module''(G&prime;, G, T<sub>k</sub>)}}<br />
<br />
{{pad|1em}}'''end if'''<br />
<br />
{{pad|1em}}'''save''' {{math|F<sub>2</sub>}}<br />
<br />
{{pad|1em}}'''if''' {{math|{{!}}F<sub>G</sub>{{!}} > Δ}} '''then'''<br />
<br />
{{pad|2em}}add {{math|G&prime;}} into Frequent Subgraph List<br />
<br />
{{pad|1em}}'''end if'''<br />
<br />
'''Until''' {{math|{{!}}E(G'){{!}} {{=}} (k – 1)/2}}<br />
<br />
'''return''' Frequent Subgraph List<br />
|}<br />
<br />
===Kavosh===<br />
A recently introduced algorithm named ''Kavosh'' <ref name="kash1">{{cite journal|vauthors=Kashani ZR, Ahrabian H, Elahi E, Nowzari-Dalini A, Ansari ES, Asadi S, Mohammadi S, Schreiber F, Masoudi-Nejad A |title=Kavosh: a new algorithm for finding network motifs |journal=BMC Bioinformatics |year=2009 |volume=10 |issue=318|pages=318 |doi=10.1186/1471-2105-10-318 |pmid=19799800 |pmc=2765973}} </ref> aims at improved main memory usage. ''Kavosh'' is usable to detect NM in both directed and undirected networks. The main idea of the enumeration is similar to the ''GK'' and ''MODA'' algorithms, which first find all {{math|k}}-size sub-graphs that a particular node participated in, then remove the node, and subsequently repeat this process for the remaining nodes.<ref name="kash1" /><br />
<br />
For counting the sub-graphs of size {{math|k}} that include a particular node, trees with maximum depth of k, rooted at this node and based on neighborhood relationship are implicitly built. Children of each node include both incoming and outgoing adjacent nodes. To descend the tree, a child is chosen at each level with the restriction that a particular child can be included only if it has not been included at any upper level. After having descended to the lowest level possible, the tree is again ascended and the process is repeated with the stipulation that nodes visited in earlier paths of a descendant are now considered unvisited nodes. A final restriction in building trees is that all children in a particular tree must have numerical labels larger than the label of the root of the tree. The restrictions on the labels of the children are similar to the conditions which ''GK'' and ''ESU'' algorithm use to avoid overcounting sub-graphs.<br />
<br />
The protocol for extracting sub-graphs makes use of the compositions of an integer. For the extraction of sub-graphs of size {{math|k}}, all possible compositions of the integer {{math|k-1}} must be considered. The compositions of {{math|k-1}} consist of all possible manners of expressing {{math|k-1}} as a sum of positive integers. Summations in which the order of the summands differs are considered distinct. A composition can be expressed as {{math|k<sub>2</sub>,k<sub>3</sub>,…,k<sub>m</sub>}} where {{math|k<sub>2</sub> + k<sub>3</sub> + … + k<sub>m</sub> {{=}} k-1}}. To count sub-graphs based on the composition, {{math|k<sub>i</sub>}} nodes are selected from the {{math|i}}-th level of the tree to be nodes of the sub-graphs ({{math|i {{=}} 2,3,…,m}}). The {{math|k-1}} selected nodes along with the node at the root define a sub-graph within the network. After discovering a sub-graph involved as a match in the target network, in order to be able to evaluate the size of each class according to the target network, ''Kavosh'' employs the ''nauty'' algorithm <ref name="mck1" /><ref name="mck2" /> in the same way as ''FANMOD''. The enumeration part of Kavosh algorithm is shown below:<br />
<br />
{| class="wikitable"<br />
|-<br />
! Enumeration of Kavosh<br />
|-<br />
|'''''Enumerate_Vertex(G, u, S, Remainder, i)'''''<br />
<br />
'''Input:''' {{math|G}}: Input graph<br><br />
{{pad|3em}}{{math|u}}: Root vertex<br><br />
{{pad|3em}}{{math|S}}: selection ({{math|S {{=}} { S<sub>0</sub>,S<sub>1</sub>,...,S<sub>k-1</sub>}}} is an array of the set of all {{math|S<sub>i</sub>}})<br><br />
{{pad|3em}}{{math|Remainder}}: number of remaining vertices to be selected<br><br />
{{pad|3em}}{{math|i}}: Current depth of the tree.<br><br />
'''Output:''' all {{math|k}}-size sub-graphs of graph {{math|G}} rooted in {{math|u}}.<br />
<br />
'''if''' {{math|Remainder {{=}} 0}} '''then'''<br><br />
{{pad|1em}}'''return'''<br><br />
'''else'''<br><br />
{{pad|1em}}{{math|ValList ← ''Validate''(G, S<sub>i-1</sub>, u)}}<br><br />
{{pad|1em}}{{math|n<sub>i</sub> ← ''Min''({{!}}ValList{{!}}, Remainder)}}<br><br />
{{pad|1em}}'''for''' {{math|k<sub>i</sub> {{=}} 1}} '''to''' {{math|n<sub>i</sub>}} '''do'''<br><br />
{{pad|2em}}{{math|C ← ''Initial_Comb''(ValList, k<sub>i</sub>)}}<br><br />
{{pad|2em}}(Make the first vertex combination selection according)<br><br />
{{pad|2em}}'''repeat'''<br><br />
{{pad|3em}}{{math|S<sub>i</sub> ← C}}<br><br />
{{pad|3em}}{{math|''Enumerate_Vertex''(G, u, S, Remainder-k<sub>i</sub>, i+1)}}<br><br />
{{pad|3em}}{{math|''Next_Comb''(ValList, k<sub>i</sub>)}}<br><br />
{{pad|3em}}(Make the next vertex combination selection according)<br><br />
{{pad|2em}}'''until''' {{math|C {{=}} NILL}}<br><br />
{{pad|2em}}'''end for'''<br><br />
{{pad|1em}}'''for each''' {{math|v ∈ ValList}} '''do'''<br><br />
{{pad|2em}}{{math|Visited[v] ← false}}<br><br />
{{pad|1em}}'''end for'''<br><br />
'''end if'''<br />
|-<br />
|'''''Validate(G, Parents, u)'''''<br><br />
'''Input:''' {{math|G}}: input graph, {{math|Parents}}: selected vertices of last layer, {{math|u}}: Root vertex.<br><br />
'''Output:''' Valid vertices of the current level.<br />
<br />
{{math|ValList ← NILL}}<br><br />
'''for each''' {{math|v ∈ Parents}} '''do'''<br><br />
{{pad|1em}}'''for each''' {{math|w ∈ Neighbor[u]}} '''do'''<br><br />
{{pad|2em}}'''if''' {{math|label[u] < label[w]}} '''AND NOT''' {{math|Visited[w]}} '''then'''<br><br />
{{pad|3em}}{{math|Visited[w] ← true}}<br><br />
{{pad|3em}}{{math|ValList {{=}} ValList + w}}<br><br />
{{pad|2em}}'''end if'''<br><br />
{{pad|1em}}'''end for'''<br><br />
'''end for'''<br><br />
'''return''' {{math|ValList}}<br><br />
|}<br />
<br />
Recently a ''Cytoscape'' plugin called ''CytoKavosh'' <ref name="mas2">{{cite journal|author1=Ali Masoudi-Nejad |author2=Mitra Anasariola |author3=Ali Salehzadeh-Yazdi |author4=Sahand Khakabimamaghani |title=CytoKavosh: a Cytoscape Plug-in for Finding Network Motifs in Large Biological Networks |journal=PLoS ONE |volume=7 |issue=8 |pages=e43287 |year=2012 |doi=10.1371/journal.pone.0043287|pmid=22952659 |pmc=3430699 |bibcode=2012PLoSO...743287M }} </ref> is developed for this software. It is available via ''Cytoscape'' web page [http://apps.cytoscape.org/apps/cytokavosh].<br />
<br />
===G-Tries===<br />
2010年, Pedro Ribeiro 和 Fernando Silva 提出了一个叫做''g-trie''的新数据结构,用来存储一组子图。<ref name="rib1">{{cite conference|vauthors=Ribeiro P, Silva F |title=G-Tries: an efficient data structure for discovering network motifs |conference=ACM 25th Symposium On Applied Computing - Bioinformatics Track |location=Sierre, Switzerland |year=2010 |pages=1559–1566 |url=http://www.nrcbioinformatics.ca/acmsac2010/}}</ref>这个在概念上类似前缀树的数据结构,根据子图结构来进行存储,并找出了每个子图在一个更大的图中出现的次数。这个数据结构有一个突出的方面:在应用于模体发现算法时,主网络中的子图需要进行评估。因此,在随机网络中寻找那些在不在主网络中的子图,这个消耗时间的步骤就不再需要执行了。<br />
<br />
''g-trie'' 是一个存储一组图的多叉树。每一个树节点都存储着一个'''图节点'''及其'''对应的到前一个节点的边'''的信息。从根节点到叶节点的一条路径对应一个图。一个 g-trie 节点的子孙节点共享一个子图(即每一次路径的分叉意味着从一个子图结构中扩展出不同的图结构,而这些扩展出来的图结构自然有着相同的子图结构)。如何构造一个 ''g-trie'' 在<ref name="rib1" />中有详细描述。构造好一个 ''g-trie'' 以后,需要进行计数步骤。计数流程的主要思想是回溯所有可能的子图,同时进行同构性测试。这种回溯技术本质上和其他以模体为中心的方法,比如''MODA'' 和 ''GK'' 算法中使用的技术是一样的。这种技术利用了共同的子结构,亦即在一定时间内,几个不同的候选子图中存在部分是同构的。<br />
<br />
在上述算法中,''G-Tries'' 是最快的。然而,它的一个缺点是内存的超量使用,这局限了它在个人电脑运行时所能发现的模体的大小<br />
<br />
===对比===<br />
<br />
下面的表格和数据显示了在各种标准网络中运行上述算法所获得的结果。这些结果皆获取于各自相应的来源<ref name="omi1" /><ref name="kash1" /><ref name="rib1" /> ,因此需要独立地对待它们。<br />
<br />
[[Image:Runtimes of algorithms.jpg|thumb|''Runtimes of Grochow–Kellis, mfinder, FANMOD, FPF and MODA for subgraphs from three nodes up to nine nodes''.<ref name="omi1" />]]<br />
<br />
{|class="wikitable"<br />
|+ Grochow–Kellis, FANMOD, 和 G-Trie 在5个不同网络上生成含3到9个节点子图所用的运行时间 <ref name="rib1" /><br />
|-<br />
!rowspan="2"|网络<br />
!rowspan="2"|子图大小<br />
!colspan="3"|原始网络数据<br />
!colspan="3"|随机网络平均数据<br />
|-<br />
!FANMOD<br />
!GK<br />
!G-Trie<br />
!FANMOD<br />
!GK<br />
!G-Trie<br />
|-<br />
|rowspan="5"|Dolphins<br />
|5 || 0.07 || 0.03 || 0.01 || 0.13 || 0.04 || 0.01<br />
|-<br />
|6||0.48||0.28||0.04||1.14||0.35||0.07<br />
|-<br />
|7||3.02||3.44||0.23||8.34||3.55||0.46<br />
|-<br />
|8||19.44||73.16||1.69||67.94||37.31||4.03<br />
|-<br />
|9||100.86||2984.22||6.98||493.98||366.79||24.84<br />
|-<br />
|rowspan="3"|Circuit<br />
|6||0.49||0.41||0.03||0.55||0.24||0.03<br />
|-<br />
|7||3.28||3.73||0.22||3.53||1.34||0.17<br />
|-<br />
|8||17.78||48.00||1.52||21.42||7.91||1.06<br />
|-<br />
|rowspan="3"|Social<br />
|3||0.31||0.11||0.02||0.35||0.11||0.02<br />
|-<br />
|4||7.78||1.37||0.56||13.27||1.86||0.57<br />
|-<br />
|5||208.30||31.85||14.88||531.65||62.66||22.11<br />
|-<br />
|rowspan="3"|Yeast<br />
|3||0.47||0.33||0.02||0.57||0.35||0.02<br />
|-<br />
|4||10.07||2.04||0.36||12.90||2.25||0.41<br />
|-<br />
|5||268.51||34.10||12.73||400.13||47.16||14.98<br />
|-<br />
|rowspan="5"|Power<br />
|3||0.51||1.46||0.00||0.91||1.37||0.01<br />
|-<br />
|4||1.38||4.34||0.02||3.01||4.40||0.03<br />
|-<br />
|5||4.68||16.95||0.10||12.38||17.54||0.14<br />
|-<br />
|6||20.36||95.58||0.55||67.65||92.74||0.88<br />
|-<br />
|7||101.04||765.91||3.36||408.15||630.65||5.17<br />
|}<br />
<br />
{|class="wikitable"<br />
|+ mfinder, FANMOD, Mavisto 和 Kavosh 在3个不同网络上生成含3到10个节点子图所用的运行时间<ref name="kash1" /><br />
|-<br />
!&nbsp;<br />
!子图大小→<br />
!rowspan="2"|3<br />
!rowspan="2"|4<br />
!rowspan="2"|5<br />
!rowspan="2"|6<br />
!rowspan="2"|7<br />
!rowspan="2"|8<br />
!rowspan="2"|9<br />
!rowspan="2"|10<br />
|-<br />
!网络↓<br />
!算法↓<br />
|-<br />
|rowspan="4"|E. coli<br />
|Kavosh||0.30||1.84||14.91||141.98||1374.0||13173.7||121110.3||1120560.1<br />
|-<br />
|FANMOD||0.81||2.53||15.71||132.24||1205.9||9256.6||-||-<br />
|-<br />
|Mavisto||13532||-||-||-||-||-||-||-<br />
|-<br />
|Mfinder||31.0||297||23671||-||-||-||-||-<br />
|-<br />
|rowspan="4"|Electronic<br />
|Kavosh||0.08||0.36||8.02||11.39||77.22||422.6||2823.7||18037.5<br />
|-<br />
|FANMOD||0.53||1.06||4.34||24.24||160||967.99||-||-<br />
|-<br />
|Mavisto||210.0||1727||-||-||-||-||-||-<br />
|-<br />
|Mfinder||7||14||109.8||2020.2||-||-||-||-<br />
|-<br />
|rowspan="4"|Social<br />
|Kavosh||0.04||0.23||1.63||10.48||69.43||415.66||2594.19||14611.23<br />
|-<br />
|FANMOD||0.46||0.84||3.07||17.63||117.43||845.93||-||-<br />
|-<br />
|Mavisto||393||1492||-||-||-||-||-||-<br />
|-<br />
|Mfinder||12||49||798||181077||-||-||-||-<br />
|}<br />
<br />
===算法的分类===<br />
正如表格所示,模体发现算法可以分为两大类:基于精确计数的算法,以及使用统计采样以及估计的算法。因为后者并不计数所有子图在主网络中出现的次数,所以第二类算法会更快,却也可能产生带有偏向性的,甚至不现实的结果。<br />
<br />
更深一层地,基于精确计数的算法可以分为'''以网络为中心'''的方法以及以'''子图为中心'''的方法。前者在给定网络中搜索给定大小的子图,而后者首先根据给定大小生成各种可能的非同构图,然后在网络中分别搜索这些生成的图。这两种方法都有各自的优缺点,这些在上文有讨论。<br />
<br />
另一方面,基于估计的方法可能会利用如前面描述过的颜色编码手段,其它的手段则通常会在枚举过程中忽略一些子图(比如,像在 FANMOD 中做的那样),然后只在枚举出来的子图上做估计。<br />
<br />
此外,表格还指出了一个算法能否应用于有向网络或无向网络,以及导出子图或非导出子图。更多信息请参考下方提供的网页和实验室地址及联系方式。<br />
{|class="wikitable"<br />
|+ 模体发现算法的分类<br />
|-<br />
!计数方式<br />
!基础<br />
!算法名称<br />
!有向 / 无向<br />
!导出/ 非导出<br />
|-<br />
| rowspan="9" |精确基数<br />
| rowspan="5" |以网络为中心<br />
|[http://www.weizmann.ac.il/mcb/UriAlon/ mfinder]||皆可||导出<br />
|-<br />
|[http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ ESU (FANMOD)]||皆可||导出<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/Kavosh/ Kavosh] (used in [http://apps.cytoscape.org/apps/cytokavosh CytoKavosh])||皆可||导出<br />
|-<br />
|[http://www.dcc.fc.up.pt/gtries/ G-Tries]||皆可||导出<br />
|-<br />
|[http://nesreenahmed.com/graphlets PGD]<br />
|无向<br />
|导出<br />
|-<br />
|rowspan="4"|以子图为中心<br />
|[http://mavisto.ipk-gatersleben.de/ FPF (Mavisto)]||皆可||导出<br />
|-<br />
|[https://www.msu.edu/~jinchen/ NeMoFinder]||无向||导出<br />
|-<br />
|[http://people.cs.uchicago.edu/~joshuag/index.html Grochow–Kellis]||皆可||Both<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/MODA/ MODA]||皆可||皆可<br />
|-<br />
|rowspan="3"|采样估计<br />
|颜色编码<br />
|[http://www.math.tau.ac.il/~nogaa/ N. Alon] ''et al.''’s Algorithm||无向||非导出<br />
|-<br />
|rowspan="2"|其他手段<br />
|[http://www.weizmann.ac.il/mcb/UriAlon/ mfinder]||皆可||导出<br />
|-<br />
|[http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ ESU (FANMOD)]||皆可||导出<br />
|}<br />
<br />
{|class="wikitable"<br />
|+ 算法提出者的地址和联系方式<br />
|-<br />
!算法<br />
!实验室/研究组<br />
!学院<br />
!大学/研究所<br />
!地址<br />
!电子邮件<br />
|-<br />
|[http://www.weizmann.ac.il/mcb/UriAlon/ mfinder]||Uri Alon's Group||Department of Molecular Cell Biology||Weizmann Institute of Science||Rehovot, Israel, Wolfson, Rm. 607||urialon at weizmann.ac.il<br />
|-<br />
|[http://mavisto.ipk-gatersleben.de/ FPF (Mavisto)]||----||----||Leibniz-Institut für Pflanzengenetik und Kulturpflanzenforschung (IPK)||Corrensstraße 3, D-06466 Stadt Seeland, OT Gatersleben, Deutschland||schreibe at ipk-gatersleben.de<br />
|-<br />
|[http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ ESU (FANMOD)]||Lehrstuhl Theoretische Informatik I||Institut für Informatik||Friedrich-Schiller-Universität Jena||Ernst-Abbe-Platz 2,D-07743 Jena, Deutschland||sebastian.wernicke at gmail.com<br />
|-<br />
|[https://www.msu.edu/~jinchen/ NeMoFinder]||----||School of Computing||National University of Singapore||Singapore 119077||chenjin at comp.nus.edu.sg<br />
|-<br />
|[http://www.cs.colorado.edu/~jgrochow/ Grochow–Kellis]||CS Theory Group & Complex Systems Group||Computer Science||University of Colorado, Boulder||1111 Engineering Dr. ECOT 717, 430 UCB Boulder, CO 80309-0430 USA||jgrochow at colorado.edu<br />
|-<br />
|[http://www.math.tau.ac.il/~nogaa/ N. Alon] ''et al.''’s Algorithm||Department of Pure Mathematics||School of Mathematical Sciences||Tel Aviv University||Tel Aviv 69978, Israel||nogaa at post.tau.ac.il<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/MODA/ MODA]||Laboratory of Systems Biology and Bioinformatics (LBB)||Institute of Biochemistry and Biophysics (IBB)||University of Tehran||Enghelab Square, Enghelab Ave, Tehran, Iran||amasoudin at ibb.ut.ac.ir<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/Kavosh/ Kavosh] (used in [http://apps.cytoscape.org/apps/cytokavosh CytoKavosh])||Laboratory of Systems Biology and Bioinformatics (LBB)||Institute of Biochemistry and Biophysics (IBB)||University of Tehran||Enghelab Square, Enghelab Ave, Tehran, Iran||amasoudin at ibb.ut.ac.ir<br />
|-<br />
|[http://www.dcc.fc.up.pt/gtries/ G-Tries]||Center for Research in Advanced Computing Systems||Computer Science||University of Porto||Rua Campo Alegre 1021/1055, Porto, Portugal||pribeiro at dcc.fc.up.pt<br />
|-<br />
|[http://nesreenahmed.com/graphlets PGD]<br />
|Network Learning and Discovery Lab<br />
|Department of Computer Science<br />
|Purdue University<br />
|Purdue University, 305 N University St, West Lafayette, IN 47907<br />
|nkahmed@purdue.edu<br />
|}<br />
<br />
==Well-established motifs and their functions==<br />
Much experimental work has been devoted to understanding network motifs in [[gene regulatory networks]]. These networks control which genes are expressed in the cell in response to biological signals. The network is defined such that genes are nodes, and directed edges represent the control of one gene by a transcription factor (regulatory protein that binds DNA) encoded by another gene. Thus, network motifs are patterns of genes regulating each other's transcription rate. When analyzing transcription networks, it is seen that the same network motifs appear again and again in diverse organisms from bacteria to human. The transcription network of ''[[Escherichia coli|E. coli]]'' and yeast, for example, is made of three main motif families, that make up almost the entire network. The leading hypothesis is that the network motif were independently selected by evolutionary processes in a converging manner,<ref name="bab1">{{cite journal |vauthors=Babu MM, Luscombe NM, Aravind L, Gerstein M, Teichmann SA |title=Structure and evolution of transcriptional regulatory networks |journal=Current Opinion in Structural Biology |volume=14 |issue=3 |pages=283–91 |date=June 2004 |pmid=15193307 |doi=10.1016/j.sbi.2004.05.004 |citeseerx=10.1.1.471.9692 }}</ref><ref name="con1">{{cite journal |vauthors=Conant GC, Wagner A |title=Convergent evolution of gene circuits |journal=Nat. Genet. |volume=34 |issue=3 |pages=264–6 |date=July 2003 |pmid=12819781 |doi=10.1038/ng1181}}</ref> since the creation or elimination of regulatory interactions is fast on evolutionary time scale, relative to the rate at which genes change,<ref name="bab1"/><ref name="con1"/><ref name="dek1">{{cite journal |vauthors=Dekel E, Alon U |title=Optimality and evolutionary tuning of the expression level of a protein |journal=Nature |volume=436 |issue=7050 |pages=588–92 |date=July 2005 |pmid=16049495 |doi=10.1038/nature03842 |bibcode=2005Natur.436..588D }}</ref> Furthermore, experiments on the dynamics generated by network motifs in living cells indicate that they have characteristic dynamical functions. This suggests that the network motif serve as building blocks in gene regulatory networks that are beneficial to the organism.<br />
<br />
The functions associated with common network motifs in transcription networks were explored and demonstrated by several research projects both theoretically and experimentally. Below are some of the most common network motifs and their associated function.<br />
<br />
===Negative auto-regulation (NAR)===<br />
[[Image:Autoregulation motif.png|thumb|Schematic representation of an auto-regulation motif]]<br />
One of simplest and most abundant network motifs in ''[[Escherichia coli|E. coli]]'' is negative auto-regulation in which a transcription factor (TF) represses its own transcription. This motif was shown to perform two important functions. The first function is response acceleration. NAR was shown to speed-up the response to signals both theoretically <ref name="zab1">{{cite journal |doi=10.1016/j.jtbi.2011.06.021 |author=Zabet NR |title=Negative feedback and physical limits of genes |journal=Journal of Theoretical Biology |volume= 284|issue=1 |pages=82–91 |date=September 2011 |pmid=21723295 |arxiv=1408.1869 |citeseerx=10.1.1.759.5418 }}</ref> and experimentally. This was first shown in a synthetic transcription network<ref name="ros1">{{cite journal |doi=10.1016/S0022-2836(02)00994-4 |vauthors=Rosenfeld N, Elowitz MB, Alon U |title=Negative autoregulation speeds the response times of transcription networks |journal=J. Mol. Biol. |volume=323 |issue=5 |pages=785–93 |date=November 2002 |pmid=12417193 |citeseerx=10.1.1.126.2604 }}</ref> and later on in the natural context in the SOS DNA repair system of E .coli.<ref name="cam1">{{cite journal |vauthors=Camas FM, Blázquez J, Poyatos JF |title=Autogenous and nonautogenous control of response in a genetic network |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=103 |issue=34 |pages=12718–23 |date=August 2006 |pmid=16908855 |pmc=1568915 |doi=10.1073/pnas.0602119103 |bibcode=2006PNAS..10312718C }}</ref> The second function is increased stability of the auto-regulated gene product concentration against stochastic noise, thus reducing variations in protein levels between different cells.<ref name="bec1">{{cite journal |vauthors=Becskei A, Serrano L |title=Engineering stability in gene networks by autoregulation |journal=Nature |volume=405 |issue=6786 |pages=590–3 |date=June 2000 |pmid=10850721 |doi=10.1038/35014651}}</ref><ref name="dub1">{{cite journal |vauthors=Dublanche Y, Michalodimitrakis K, Kümmerer N, Foglierini M, Serrano L |title=Noise in transcription negative feedback loops: simulation and experimental analysis |journal=Mol. Syst. Biol. |volume=2 |pages=41 |year=2006 |pmid=16883354 |pmc=1681513 |doi=10.1038/msb4100081 |issue=1}}</ref><ref name="shi1">{{cite journal |vauthors=Shimoga V, White J, Li Y, Sontag E, Bleris L |title= Synthetic mammalian transgene negative autoregulation |journal=Mol. Syst. Biol. |volume=9 |pages=670 |year=2013|doi=10.1038/msb.2013.27|pmid= 23736683 |pmc= 3964311 }}</ref><br />
<br />
<br />
<br />
===Positive auto-regulation (PAR)===<br />
Positive auto-regulation (PAR) occurs when a transcription factor enhances its own rate of production. Opposite to the NAR motif this motif slows the response time compared to simple regulation.<ref name="mae1">{{cite journal |vauthors=Maeda YT, Sano M |title=Regulatory dynamics of synthetic gene networks with positive feedback |journal=J. Mol. Biol. |volume=359 |issue=4 |pages=1107–24 |date=June 2006 |pmid=16701695 |doi=10.1016/j.jmb.2006.03.064 }}</ref> In the case of a strong PAR the motif may lead to a bimodal distribution of protein levels in cell populations.<ref name="bec2">{{cite journal |vauthors=Becskei A, Séraphin B, Serrano L |title=Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion |journal=EMBO J. |volume=20 |issue=10 |pages=2528–35 |date=May 2001 |pmid=11350942 |pmc=125456 |doi=10.1093/emboj/20.10.2528}}</ref><br />
<br />
===Feed-forward loops (FFL)===<br />
[[Image:Feed-forward motif.GIF|thumb|Schematic representation of a Feed-forward motif]]<br />
This motif is commonly found in many gene systems and organisms. The motif consists of three genes and three regulatory interactions. The target gene C is regulated by 2 TFs A and B and in addition TF B is also regulated by TF A . Since each of the regulatory interactions may either be positive or negative there are possibly eight types of FFL motifs.<ref name="man1">{{cite journal |vauthors=Mangan S, Alon U |title=Structure and function of the feed-forward loop network motif |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=100 |issue=21 |pages=11980–5 |date=October 2003 |pmid=14530388 |pmc=218699 |doi=10.1073/pnas.2133841100 |bibcode=2003PNAS..10011980M }}</ref> Two of those eight types: the coherent type 1 FFL (C1-FFL) (where all interactions are positive) and the incoherent type 1 FFL (I1-FFL) (A activates C and also activates B which represses C) are found much more frequently in the transcription network of ''[[Escherichia coli|E. coli]]'' and yeast than the other six types.<ref name="man1"/><ref name="ma1">{{cite journal |vauthors=Ma HW, Kumar B, Ditges U, Gunzer F, Buer J, Zeng AP |title=An extended transcriptional regulatory network of ''Escherichia coli'' and analysis of its hierarchical structure and network motifs |journal=Nucleic Acids Res. |volume=32 |issue=22 |pages=6643–9 |year=2004 |pmid=15604458 |pmc=545451 |doi=10.1093/nar/gkh1009 |url=http://nar.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=15604458}}</ref> In addition to the structure of the circuitry the way in which the signals from A and B are integrated by the C promoter should also be considered. In most of the cases the FFL is either an AND gate (A and B are required for C activation) or OR gate (either A or B are sufficient for C activation) but other input function are also possible.<br />
<br />
===Coherent type 1 FFL (C1-FFL)===<br />
The C1-FFL with an AND gate was shown to have a function of a ‘sign-sensitive delay’ element and a persistence detector both theoretically <ref name="man1"/> and experimentally<ref name="man2">{{cite journal |doi=10.1016/j.jmb.2003.09.049 |vauthors=Mangan S, Zaslaver A, Alon U |title=The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks |journal=J. Mol. Biol. |volume=334 |issue=2 |pages=197–204 |date=November 2003 |pmid=14607112 |citeseerx=10.1.1.110.4629 }}</ref> with the arabinose system of ''[[Escherichia coli|E. coli]]''. This means that this motif can provide pulse filtration in which short pulses of signal will not generate a response but persistent signals will generate a response after short delay. The shut off of the output when a persistent pulse is ended will be fast. The opposite behavior emerges in the case of a sum gate with fast response and delayed shut off as was demonstrated in the flagella system of ''[[Escherichia coli|E. coli]]''.<ref name="kal1">{{cite journal |vauthors=Kalir S, Mangan S, Alon U |title=A coherent feed-forward loop with a SUM input function prolongs flagella expression in ''Escherichia coli'' |journal=Mol. Syst. Biol. |volume=1 |pages=E1–E6 |year=2005 |pmid=16729041 |pmc=1681456 |doi=10.1038/msb4100010 |issue=1}}</ref> De novo evolution of C1-FFLs in [[gene regulatory network]]s has been demonstrated computationally in response to selection to filter out an idealized short signal pulse, but for non-idealized noise, a dynamics-based system of feed-forward regulation with different topology was instead favored.<ref>{{cite journal |last1=Xiong |first1=Kun |last2=Lancaster |first2=Alex K. |last3=Siegal |first3=Mark L. |last4=Masel |first4=Joanna |title=Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise |journal=Nature Communications |date=3 June 2019 |volume=10 |issue=1 |pages=2418 |doi=10.1038/s41467-019-10388-6|pmid=31160574 |pmc=6546794 }}</ref><br />
<br />
===Incoherent type 1 FFL (I1-FFL)===<br />
The I1-FFL is a pulse generator and response accelerator. The two signal pathways of the I1-FFL act in opposite directions where one pathway activates Z and the other represses it. When the repression is complete this leads to a pulse-like dynamics. It was also demonstrated experimentally that the I1-FFL can serve as response accelerator in a way which is similar to the NAR motif. The difference is that the I1-FFL can speed-up the response of any gene and not necessarily a transcription factor gene.<ref name="man3">{{cite journal |vauthors=Mangan S, Itzkovitz S, Zaslaver A, Alon U |title=The incoherent feed-forward loop accelerates the response-time of the gal system of ''Escherichia coli'' |journal=J. Mol. Biol. |volume=356 |issue=5 |pages=1073–81 |date=March 2006 |pmid=16406067 |doi=10.1016/j.jmb.2005.12.003 |citeseerx=10.1.1.184.8360 }}</ref> An additional function was assigned to the I1-FFL network motif: it was shown both theoretically and experimentally that the I1-FFL can generate non-monotonic input function in both a synthetic <ref name="ent1">{{cite journal |vauthors=Entus R, Aufderheide B, Sauro HM |title=Design and implementation of three incoherent feed-forward motif based biological concentration sensors |journal=Syst Synth Biol |volume=1 |issue=3 |pages=119–28 |date=August 2007 |pmid=19003446 |pmc=2398716 |doi=10.1007/s11693-007-9008-6 }}</ref> and native systems.<ref name="kap1">{{cite journal |vauthors=Kaplan S, Bren A, Dekel E, Alon U |title=The incoherent feed-forward loop can generate non-monotonic input functions for genes |journal=Mol. Syst. Biol. |volume=4 |pages=203 |year=2008 |pmid=18628744 |pmc=2516365 |doi=10.1038/msb.2008.43 |issue=1}}</ref> Finally, expression units that incorporate incoherent feedforward control of the gene product provide adaptation to the amount of DNA template and can be superior to simple combinations of constitutive promoters.<ref name="ble1">{{cite journal |vauthors=Bleris L, Xie Z, Glass D, Adadey A, Sontag E, Benenson Y |title=Synthetic incoherent feedforward circuits show adaptation to the amount of their genetic template |journal=Mol. Syst. Biol. |volume=7 |pages=519|year=2011 |doi=10.1038/msb.2011.49 |issue=1 |pmid=21811230 |pmc=3202791}}</ref> Feedforward regulation displayed better adaptation than negative feedback, and circuits based on RNA interference were the most robust to variation in DNA template amounts.<ref name="ble1"/><br />
<br />
===Multi-output FFLs===<br />
In some cases the same regulators X and Y regulate several Z genes of the same system. By adjusting the strength of the interactions this motif was shown to determine the temporal order of gene activation. This was demonstrated experimentally in the flagella system of ''[[Escherichia coli|E. coli]]''.<ref name="kal2">{{cite journal |vauthors=Kalir S, McClure J, Pabbaraju K, etal |title=Ordering genes in a flagella pathway by analysis of expression kinetics from living bacteria |journal=Science |volume=292 |issue=5524 |pages=2080–3 |date=June 2001 |pmid=11408658 |doi=10.1126/science.1058758 }}</ref><br />
<br />
===Single-input modules (SIM)===<br />
This motif occurs when a single regulator regulates a set of genes with no additional regulation. This is useful when the genes are cooperatively carrying out a specific function and therefore always need to be activated in a synchronized manner. By adjusting the strength of the interactions it can create temporal expression program of the genes it regulates.<ref name="zas1">{{cite journal |vauthors=Zaslaver A, Mayo AE, Rosenberg R, etal |title=Just-in-time transcription program in metabolic pathways |journal=Nat. Genet. |volume=36 |issue=5 |pages=486–91 |date=May 2004 |pmid=15107854 |doi=10.1038/ng1348|doi-access=free }}</ref><br />
<br />
In the literature, Multiple-input modules (MIM) arose as a generalization of SIM. However, the precise definitions of SIM and MIM have been a source of inconsistency. There are attempts to provide orthogonal definitions for canonical motifs in biological networks and algorithms to enumerate them, especially SIM, MIM and Bi-Fan (2x2 MIM).<ref>{{cite journal |vauthors=Konagurthu AS, Lesk AM |title=Single and Multiple Input Modules in regulatory networks |journal=Proteins |volume=73 |issue=2 |pages=320–324 |year=2008 |doi=10.1002/prot.22053|pmid=18433061 }}</ref><br />
<br />
===Dense overlapping regulons (DOR)===<br />
This motif occurs in the case that several regulators combinatorially control a set of genes with diverse regulatory combinations. This motif was found in ''[[Escherichia coli|E. coli]]'' in various systems such as carbon utilization, anaerobic growth, stress response and others.<ref name="she1"/><ref name="boy1"/> In order to better understand the function of this motif one has to obtain more information about the way the multiple inputs are integrated by the genes. Kaplan ''et al.''<ref name="kap2">{{cite journal |vauthors=Kaplan S, Bren A, Zaslaver A, Dekel E, Alon U |title=Diverse two-dimensional input functions control bacterial sugar genes |journal=Mol. Cell |volume=29 |issue=6 |pages=786–92 |date=March 2008 |pmid=18374652 |pmc=2366073 |doi=10.1016/j.molcel.2008.01.021 }}</ref> has mapped the input functions of the sugar utilization genes in ''[[Escherichia coli|E. coli]]'', showing diverse shapes.<br />
<br />
==已知的模体及其功能==<br />
许多实验工作致力于理解[[基因调控网络]]中的网络模体。在响应生物信号的过程中,这些网络控制细胞中需要表达的基因。这样的网络以基因作为节点,有向边代表对某个基因的调控,基因调控通过其他基因编码的转录因子[[结合在DNA上的调控蛋白]]来实现。因此,网络模体是基因之间相互调控转录速率的模式。在分析转录调控网络的时候,人们发现某些相同的网络模体在不同的物种中不断地出现,从细菌到人类。例如,''[[大肠杆菌]]''和酵母的转录网络由三种主要的网络模体家族组成,它们可以构建几乎整个网络。主要的假设是在进化的过程中,网络模体是被以收敛的方式独立选择出来的。<ref name="bab1">{{cite journal |vauthors=Babu MM, Luscombe NM, Aravind L, Gerstein M, Teichmann SA |title=Structure and evolution of transcriptional regulatory networks |journal=Current Opinion in Structural Biology |volume=14 |issue=3 |pages=283–91 |date=June 2004 |pmid=15193307 |doi=10.1016/j.sbi.2004.05.004 |citeseerx=10.1.1.471.9692 }}</ref><ref name="con1">{{cite journal |vauthors=Conant GC, Wagner A |title=Convergent evolution of gene circuits |journal=Nat. Genet. |volume=34 |issue=3 |pages=264–6 |date=July 2003 |pmid=12819781 |doi=10.1038/ng1181}}</ref> 因为相对于基因改变的速率,转录相互作用产生和消失的时间尺度在进化上是很快的。<ref name="bab1"/><ref name="con1"/><ref name="dek1">{{cite journal |vauthors=Dekel E, Alon U |title=Optimality and evolutionary tuning of the expression level of a protein |journal=Nature |volume=436 |issue=7050 |pages=588–92 |date=July 2005 |pmid=16049495 |doi=10.1038/nature03842 |bibcode=2005Natur.436..588D }}</ref> 此外,对活细胞中网络模体所产生的动力学行为的实验表明,它们具有典型的动力学功能。这表明,网络模体是基因调控网络中对生物体有益的基本单元。<br />
<br />
一些研究从理论和实验两方面探讨和论证了转录网络中与共同网络模体相关的功能。下面是一些最常见的网络模体及其相关功能。<br />
<br />
===负自反馈调控(NAR)===<br />
[[Image:Autoregulation motif.png|thumb|Schematic representation of an auto-regulation motif]]<br />
负自反馈调控是[[大肠杆菌]]中最简单和最冗余的网络模体之一,其中一个转录因子抑制它自身的转录。这种网络模体有两个重要的功能,其中第一个是加速响应。人们发现在实验和理论上, <ref name="zab1">{{cite journal |doi=10.1016/j.jtbi.2011.06.021 |author=Zabet NR |title=Negative feedback and physical limits of genes |journal=Journal of Theoretical Biology |volume= 284|issue=1 |pages=82–91 |date=September 2011 |pmid=21723295 |arxiv=1408.1869 |citeseerx=10.1.1.759.5418 }}</ref>NAR都可以加快对信号的响应。这个功能首先在一个人工合成的转录网络中被发现,<ref name="ros1">{{cite journal |doi=10.1016/S0022-2836(02)00994-4 |vauthors=Rosenfeld N, Elowitz MB, Alon U |title=Negative autoregulation speeds the response times of transcription networks |journal=J. Mol. Biol. |volume=323 |issue=5 |pages=785–93 |date=November 2002 |pmid=12417193 |citeseerx=10.1.1.126.2604 }}</ref> 然后在大肠杆菌SOS DAN修复系统这个自然体系中也被发现。<ref name="cam1">{{cite journal |vauthors=Camas FM, Blázquez J, Poyatos JF |title=Autogenous and nonautogenous control of response in a genetic network |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=103 |issue=34 |pages=12718–23 |date=August 2006 |pmid=16908855 |pmc=1568915 |doi=10.1073/pnas.0602119103 |bibcode=2006PNAS..10312718C }}</ref> 负自反馈网络的第二个功能是增强自调控基因的产物浓度的稳定性,从而抵抗随机的噪声,减少该蛋白含量在不同细胞中的差异。<ref name="bec1">{{cite journal |vauthors=Becskei A, Serrano L |title=Engineering stability in gene networks by autoregulation |journal=Nature |volume=405 |issue=6786 |pages=590–3 |date=June 2000 |pmid=10850721 |doi=10.1038/35014651}}</ref><ref name="dub1">{{cite journal |vauthors=Dublanche Y, Michalodimitrakis K, Kümmerer N, Foglierini M, Serrano L |title=Noise in transcription negative feedback loops: simulation and experimental analysis |journal=Mol. Syst. Biol. |volume=2 |pages=41 |year=2006 |pmid=16883354 |pmc=1681513 |doi=10.1038/msb4100081 |issue=1}}</ref><ref name="shi1">{{cite journal |vauthors=Shimoga V, White J, Li Y, Sontag E, Bleris L |title= Synthetic mammalian transgene negative autoregulation |journal=Mol. Syst. Biol. |volume=9 |pages=670 |year=2013|doi=10.1038/msb.2013.27|pmid= 23736683 |pmc= 3964311 }}</ref><br />
<br />
===正自反馈调控(PAR)===<br />
正自反馈调控是指转录因子增强它自身转录速率的调控。和负自反馈调节相反,NAR模体相比于简单的调控能够延长反应时间。<ref name="mae1">{{cite journal |vauthors=Maeda YT, Sano M |title=Regulatory dynamics of synthetic gene networks with positive feedback |journal=J. Mol. Biol. |volume=359 |issue=4 |pages=1107–24 |date=June 2006 |pmid=16701695 |doi=10.1016/j.jmb.2006.03.064 }}</ref> 在强PAR的情况下,模体可能导致蛋白质水平在细胞群中呈现双峰分布。<ref name="bec2">{{cite journal |vauthors=Becskei A, Séraphin B, Serrano L |title=Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion |journal=EMBO J. |volume=20 |issue=10 |pages=2528–35 |date=May 2001 |pmid=11350942 |pmc=125456 |doi=10.1093/emboj/20.10.2528}}</ref><br />
<br />
===前馈回路 (FFL)===<br />
[[Image:Feed-forward motif.GIF|thumb|Schematic representation of a Feed-forward motif]]<br />
前馈回路普遍存在于许多基因系统和生物体中。这种模体包括三个基因以及三个相互作用。目标基因C被两个转录因子(TFs)A和B调控,并且TF B同时被TF A调控。由于每个调控相互作用可以是正的或者负的,所以总共可能有八种类型的FFL模体。<ref name="man1">{{cite journal |vauthors=Mangan S, Alon U |title=Structure and function of the feed-forward loop network motif |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=100 |issue=21 |pages=11980–5 |date=October 2003 |pmid=14530388 |pmc=218699 |doi=10.1073/pnas.2133841100 |bibcode=2003PNAS..10011980M }}</ref> 其中的两种:一致前馈回路的类型一(C1-FFL)(所有相互作用都是正的)和非一致前馈回路的类型一(I1-FFL)(A激活C和B,B抑制C)在[[大肠杆菌]]和酵母中相比于其他六种更频繁的出现。<ref name="man1"/><ref name="ma1">{{cite journal |vauthors=Ma HW, Kumar B, Ditges U, Gunzer F, Buer J, Zeng AP |title=An extended transcriptional regulatory network of ''Escherichia coli'' and analysis of its hierarchical structure and network motifs |journal=Nucleic Acids Res. |volume=32 |issue=22 |pages=6643–9 |year=2004 |pmid=15604458 |pmc=545451 |doi=10.1093/nar/gkh1009 |url=http://nar.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=15604458}}</ref> 除了网络的结构外,还应该考虑来自A和B的信号被C的启动子集成的方式。在大多数情况下,FFL要么是一个与门(激活C需要A和B),要么是或门(激活C需要A或B),但也可以是其他输入函数。<br />
<br />
===一致前馈回路类型一(C1-FFL)===<br />
具有与门的C1-FFL有“符号-敏感延迟”单元和持久性探测器的功能,这一点在[[大肠杆菌]]阿拉伯糖系系统的理论<ref name="man1"/>和实验上<ref name="man2">{{cite journal |doi=10.1016/j.jmb.2003.09.049 |vauthors=Mangan S, Zaslaver A, Alon U |title=The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks |journal=J. Mol. Biol. |volume=334 |issue=2 |pages=197–204 |date=November 2003 |pmid=14607112 |citeseerx=10.1.1.110.4629 }}</ref> 都有发现。这意味着该模体可以提供脉冲过滤,短脉冲信号不会产生响应,而持久信号在短延迟后会产生响应。当持久脉冲结束时,输出的关闭将很快。与此相反的行为出现在具有快速响应和延迟关闭特性的加和门的情况下,这在[[大肠杆菌]]的鞭毛系统中得到了证明。<ref name="kal1">{{cite journal |vauthors=Kalir S, Mangan S, Alon U |title=A coherent feed-forward loop with a SUM input function prolongs flagella expression in ''Escherichia coli'' |journal=Mol. Syst. Biol. |volume=1 |pages=E1–E6 |year=2005 |pmid=16729041 |pmc=1681456 |doi=10.1038/msb4100010 |issue=1}}</ref>在[[基因调控网络]]的重头进化中,对于滤除理想化的短信号脉冲作为进化压,C1-FFLs已经在计算上被证明可以进化出来。但是对于非理想化的噪声,不同拓扑结构前馈调节的动态系统将被优先考虑。 <ref>{{cite journal |last1=Xiong |first1=Kun |last2=Lancaster |first2=Alex K. |last3=Siegal |first3=Mark L. |last4=Masel |first4=Joanna |title=Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise |journal=Nature Communications |date=3 June 2019 |volume=10 |issue=1 |pages=2418 |doi=10.1038/s41467-019-10388-6|pmid=31160574 |pmc=6546794 }}</ref><br />
<br />
===非一致前馈回路类型一(I1-FFL)===<br />
I1-FFL是一个脉冲生成器和响应加速器。I1-FFL的两种信号通路作用方向相反,一种通路激活Z,而另一种抑制Z。完全的抑制会导致类似脉冲的动力学行为。另外有实验证明,它可以类似于NAR模体起到响应加速器的作用。与NAR模体的不同之处在于,它可以加速任何基因的响应,而不必是转录因子。<ref name="man3">{{cite journal |vauthors=Mangan S, Itzkovitz S, Zaslaver A, Alon U |title=The incoherent feed-forward loop accelerates the response-time of the gal system of ''Escherichia coli'' |journal=J. Mol. Biol. |volume=356 |issue=5 |pages=1073–81 |date=March 2006 |pmid=16406067 |doi=10.1016/j.jmb.2005.12.003 |citeseerx=10.1.1.184.8360 }}</ref>I1-FFL网络还有另外一个功能:在理论和实验上都有证明I1-FFL可以生成非单调的输入函数,无论在人工合成的<ref name="ent1">{{cite journal |vauthors=Entus R, Aufderheide B, Sauro HM |title=Design and implementation of three incoherent feed-forward motif based biological concentration sensors |journal=Syst Synth Biol |volume=1 |issue=3 |pages=119–28 |date=August 2007 |pmid=19003446 |pmc=2398716 |doi=10.1007/s11693-007-9008-6 }}</ref>还是自然的系统中。 <ref name="kap1">{{cite journal |vauthors=Kaplan S, Bren A, Dekel E, Alon U |title=The incoherent feed-forward loop can generate non-monotonic input functions for genes |journal=Mol. Syst. Biol. |volume=4 |pages=203 |year=2008 |pmid=18628744 |pmc=2516365 |doi=10.1038/msb.2008.43 |issue=1}}</ref> 最后,包含非一致前馈调控的基因生成物的表达单元对DNA模板的数量具有适应性,可以优于简单的组合本构启动子。<ref name="ble1">{{cite journal |vauthors=Bleris L, Xie Z, Glass D, Adadey A, Sontag E, Benenson Y |title=Synthetic incoherent feedforward circuits show adaptation to the amount of their genetic template |journal=Mol. Syst. Biol. |volume=7 |pages=519|year=2011 |doi=10.1038/msb.2011.49 |issue=1 |pmid=21811230 |pmc=3202791}}</ref> 前馈调控比负反馈具有更好的适应性,并且基于RNA干扰的网络对DNA模板数具有最高的鲁棒性。<ref name="ble1"/><br />
<br />
===多输出前馈回路===<br />
在某些情况,相同的调控子X和Y可以调控同一系统中的多个Z基因。通过调节相互作用的强度,这些网络可以决定基因激活的时间顺序。这一点在[[大肠杆菌]]的鞭毛系统中有实验证据。<ref name="kal2">{{cite journal |vauthors=Kalir S, McClure J, Pabbaraju K, etal |title=Ordering genes in a flagella pathway by analysis of expression kinetics from living bacteria |journal=Science |volume=292 |issue=5524 |pages=2080–3 |date=June 2001 |pmid=11408658 |doi=10.1126/science.1058758 }}</ref><br />
<br />
===单一输入模块(SIM)===<br />
当单个调控子调控一组基因,并且没有其他的调控因素时,这样的模体叫做单一输入模块(SIM)。当很多基因合作执行某个功能时这是有用的,因为这些基因需要同步地被激活。通过调节相互作用的强度,可以编排它所调控的基因表达的时间顺序。<ref name="zas1">{{cite journal |vauthors=Zaslaver A, Mayo AE, Rosenberg R, etal |title=Just-in-time transcription program in metabolic pathways |journal=Nat. Genet. |volume=36 |issue=5 |pages=486–91 |date=May 2004 |pmid=15107854 |doi=10.1038/ng1348|doi-access=free }}</ref><br />
<br />
在文献中,多输入模块(MIM)来自于SIM的扩展。但是二者的精确定义并不太一致。有一些尝试给出生物网络中规范模体的正交定义,也有一些算法去枚举它们,特别是SIM,MIM和2x2 MIM等。<ref>{{cite journal |vauthors=Konagurthu AS, Lesk AM |title=Single and Multiple Input Modules in regulatory networks |journal=Proteins |volume=73 |issue=2 |pages=320–324 |year=2008 |doi=10.1002/prot.22053|pmid=18433061 }}</ref><br />
<br />
===密集交盖调节网(DOR)===<br />
这种类型的网络存在于多个调节子结合起来控制一组基因的情形,并且有多种调控的组合。这种模体出现在[[大肠杆菌]]的多种系统中,例如碳利用、厌氧生长、应激反应等。<ref name="she1"/><ref name="boy1"/> 为了更好地理解这种网络,我们必须得到关于基因集成多种输入的方式的信息。Kaplan ''et al.''<ref name="kap2">{{cite journal |vauthors=Kaplan S, Bren A, Zaslaver A, Dekel E, Alon U |title=Diverse two-dimensional input functions control bacterial sugar genes |journal=Mol. Cell |volume=29 |issue=6 |pages=786–92 |date=March 2008 |pmid=18374652 |pmc=2366073 |doi=10.1016/j.molcel.2008.01.021 }}</ref>绘制了[[大肠杆菌]]糖利用基因的输入函数,表现出各种各样的形状。<br />
<br />
==活动模体==<br />
<br />
有一个对网络模体的有趣概括:'''活动模体'''是在对节点和边都被量化标注的网络中可发现的【反复】斑图。例如,当新城代谢的边以相应基因的表达量或【时间】来标注时,一些斑图在'''给定的'''底层网络结构里【是反复的】。<ref name="agc">{{cite journal |vauthors=Chechik G, Oh E, Rando O, Weissman J, Regev A, Koller D |title=Activity motifs reveal principles of timing in transcriptional control of the yeast metabolic network |journal=Nat. Biotechnol. |volume=26 |issue=11 |pages=1251–9 |date=November 2008 |pmid=18953355 |pmc=2651818 |doi=10.1038/nbt.1499}}</ref><br />
<br />
==批判==<br />
<br />
对拓扑子结构有一个(某种程度上隐含的)前提性假设是其具有特定的功能重要性。但该假设最近遭到质疑,有人提出在不同的网络环境下模体可能表现出多样性,例如双扇模体,故<ref name="ad">{{cite journal |vauthors=Ingram PJ, Stumpf MP, Stark J |title=Network motifs: structure does not determine function |journal=BMC Genomics |volume=7 |pages=108 |year=2006 |pmid=16677373 |pmc=1488845 |doi=10.1186/1471-2164-7-108 }} </ref>模体的结构不必然决定功能,网络结构也不当然能揭示其功能;这种见解由来已久,可参见【Sin 操纵子】</font>。<ref>{{cite journal |vauthors=Voigt CA, Wolf DM, Arkin AP |title=The ''Bacillus subtilis'' sin operon: an evolvable network motif |journal=Genetics |volume=169 |issue=3 |pages=1187–202 |date=March 2005 |pmid=15466432 |pmc=1449569 |doi=10.1534/genetics.104.031955 |url=http://www.genetics.org/cgi/pmidlookup?view=long&pmid=15466432}}</ref><br />
<br />
<br />
大多数模体功能分析是基于模体孤立运行的情形。最近的研究<ref>{{cite journal |vauthors=Knabe JF, Nehaniv CL, Schilstra MJ |title=Do motifs reflect evolved function?—No convergent evolution of genetic regulatory network subgraph topologies |journal=BioSystems |volume=94 |issue=1–2 |pages=68–74 |year=2008 |pmid=18611431 |doi=10.1016/j.biosystems.2008.05.012 }}</ref>表明网络环境至关重要,不能忽视网络环境而仅从本地结构来对其功能进行推论——引用的论文还回顾了对观测数据的批判及其他可能的解释。人们研究了单个模体模组对网络全局的动力学影响及其分析<ref>{{cite journal |vauthors=Taylor D, Restrepo JG |title=Network connectivity during mergers and growth: Optimizing the addition of a module |journal=Physical Review E |volume=83 |issue=6 |year=2011 |page=66112 |doi=10.1103/PhysRevE.83.066112 |pmid=21797446 |bibcode=2011PhRvE..83f6112T |arxiv=1102.4876 }}</ref>。而另一项近期的研究工作提出生物网络的某些拓扑特征能自然地引起经典模体的常见形态,让人不禁疑问:这样的发生频率是否能证明模体的结构是出于其对所在网络运行的功能性贡献而被选择保留下的结果?<ref>{{cite journal|last1=Konagurthu|first1=Arun S.|last2=Lesk|first2=Arthur M.|title=Single and multiple input modules in regulatory networks|journal=Proteins: Structure, Function, and Bioinformatics|date=23 April 2008|volume=73|issue=2|pages=320–324|doi=10.1002/prot.22053|pmid=18433061}}</ref><ref>{{cite journal |vauthors=Konagurthu AS, Lesk AM |title=On the origin of distribution patterns of motifs in biological networks |journal=BMC Syst Biol |volume=2 |pages=73 |year=2008 |pmid=18700017 |pmc=2538512 |doi=10.1186/1752-0509-2-73 }} </ref><br />
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模体的研究主要应用于静态复杂网络,而时变复杂网络的研究<ref>Braha, D., & Bar‐Yam, Y. (2006). [https://static1.squarespace.com/static/5b68a4e4a2772c2a206180a1/t/5c5de3faf4e1fc43e7b3d21e/1549657083988/Complexity_Braha_Original_w_Cover.pdf From centrality to temporary fame: Dynamic centrality in complex networks]. Complexity, 12(2), 59-63. </ref>就网络模体提出了重大的新解释,并介绍了'''时变网络模体'''的概念。Braha和Bar-Yam<ref> Braha D., Bar-Yam Y. (2009) [https://s3.amazonaws.com/academia.edu.documents/4892116/Adaptive_Networks__Theory__Models_and_Applications__Understanding_Complex_Systems_.pdf?response-content-disposition=inline%3B%20filename%3DRedes_teoria.pdf&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAIWOWYYGZ2Y53UL3A%2F20191111%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20191111T173250Z&X-Amz-Expires=3600&X-Amz-SignedHeaders=host&X-Amz-Signature=89d08c9e92b88ed817e4eb0f87c480757ef79c4b865919a5e0890cbefa164c61#page=55 Time-Dependent Complex Networks: Dynamic Centrality, Dynamic Motifs, and Cycles of Social Interactions]. In: Gross T., Sayama H. (eds) Adaptive Networks. Understanding Complex Systems. Springer, Berlin, Heidelberg </ref>研究了本地模体结构在时间依赖网络/时变网络的动力学,发现的一些反复模式有望成为社会互动周期的经验论据。他们证明了对于时变网络,其本地结构是时间依赖的且可能随时间演变,可作为对复杂网络中稳定模体观及模体表达观的反论,Braha和Bar-Yam还进一步提出,对时变本地结构的分析有可能揭示系统级任务和功能方面的动力学的重要信息。<br />
<br />
==See also==<br />
* [[Clique (graph theory)]]<br />
* [[Graphical model]]<br />
<br />
==References==<br />
{{reflist|2}}<br />
<br />
==External links==<br />
<br />
* [http://www.weizmann.ac.il/mcb/UriAlon/groupNetworkMotifSW.html A software tool that can detect network motifs]<br />
* [http://www.bio-physics.at/wiki/index.php?title=Network_Motifs bio-physics-wiki NETWORK MOTIFS]<br />
* [http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ FANMOD: a tool for fast network motif detection]<br />
* [http://mavisto.ipk-gatersleben.de/ MAVisto: network motif analysis and visualisation tool]<br />
* [https://www.msu.edu/~jinchen/ NeMoFinder]<br />
* [http://people.cs.uchicago.edu/~joshuag/index.html Grochow–Kellis]<br />
* [http://lbb.ut.ac.ir/Download/LBBsoft/MODA/ MODA]<br />
* [http://lbb.ut.ac.ir/Download/LBBsoft/Kavosh/ Kavosh]<br />
* [http://apps.cytoscape.org/apps/cytokavosh CytoKavosh]<br />
* [http://www.dcc.fc.up.pt/gtries/ G-Tries]<br />
* [http://www.ft.unicamp.br/docentes/meira/accmotifs/ acc-MOTIF detection tool]<br />
<br />
[[Category:Gene expression]]<br />
[[Category:Networks]]</div>Imphttps://wiki.swarma.org/index.php?title=%E7%BD%91%E7%BB%9C%E6%A8%A1%E4%BD%93_Network_motifs&diff=7156网络模体 Network motifs2020-05-07T07:54:05Z<p>Imp:/* ESU (FANMOD)算法及对应的软件 */</p>
<hr />
<div>大家好,我们的公众号计划要推送一篇关于网络模体的综述文章,我们希望可以配套建议该重要概念:网络模体。现在希望可以大家一起协作完成这个词条。<br />
翻译任务主要分为以下5个内容:<br />
* 网络定义和历史 ---许菁 <br />
* 网络模体的发现算法 mfinder和FPF算法---李鹏<br />
* 网络模体的发现算法 ESU和对应的软件FANMOD---Imp<br />
* 网络模体的发现算法 G-Trie、算法对比和算法分类——Ricky(中英对照[[用户讨论:Qige96|初稿在这里]])<br />
* 已有网络模体及其函数表示 --周佳欣<br />
* 活动模体+批判 --- 孙宇<br />
* 代码实现<br />
<br />
大家可以在对应感兴趣的部分下面,写上姓名。我们的协作方式是石墨文档上翻译,最后再编辑成文。<br />
对应的词条链接:https://en.wikipedia.org/wiki/Network_motif#Well-established_motifs_and_their_functions<br />
<br />
截止时间:今晚12:00<br />
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<br />
All networks, including [[biological network]]s, social networks, technological networks (e.g., computer networks and electrical circuits) and more, can be represented as [[complex network|graphs]], which include a wide variety of subgraphs. One important local property of networks are so-called '''network motifs''', which are defined as recurrent and [[statistically significant]] sub-graphs or patterns.<br />
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所有网络,包括生物网络(biological networks)、社会网络(social networks)、技术网络(例如计算机网络和电路)等,都可以用图的形式来表示,这些图中会包括各种各样的子图(subgraphs)。网络的一个重要的局部性质是所谓的网络基序,即重复且具有统计意义的子图或模式(patterns)。<br />
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Network motifs are sub-graphs that repeat themselves in a specific network or even among various networks. Each of these sub-graphs, defined by a particular pattern of interactions between vertices, may reflect a framework in which particular functions are achieved efficiently. Indeed, motifs are of notable importance largely because they may reflect functional properties. They have recently gathered much attention as a useful concept to uncover structural design principles of complex networks.<ref name="mas1">{{cite journal |vauthors=Masoudi-Nejad A, Schreiber F, Razaghi MK Z |title=Building Blocks of Biological Networks: A Review on Major Network Motif Discovery Algorithms |journal=IET Systems Biology |volume=6 |issue=5 |pages=164–74 |year=2012|doi=10.1049/iet-syb.2011.0011 |pmid=23101871 }}</ref> Although network motifs may provide a deep insight into the network's functional abilities, their detection is computationally challenging.<br />
网络模体(Network motifs)是指在特定网络或各种网络中重复出现的相同的子图。这些子图由顶点之间特定的交互模式定义,一个子图便可以反映一个框架,这个框架可以有效地实现某个特定的功能。事实上,之所以说模体是一个重要的特性,正是因为它们可能反映出对应网络功能的这一性质。近年来这一概念作为揭示复杂网络结构设计原理的一个有用概念而受到了广泛的关注。<ref name="mas1">{{cite journal |vauthors=Masoudi-Nejad A, Schreiber F, Razaghi MK Z |title=Building Blocks of Biological Networks: A Review on Major Network Motif Discovery Algorithms |journal=IET Systems Biology |volume=6 |issue=5 |pages=164–74 |year=2012|doi=10.1049/iet-syb.2011.0011 |pmid=23101871 }}</ref> 但是,虽然通过研究网络模体可以深入了解网络的功能,但是对于模体的检测在计算上是具有挑战性的。<br />
<br />
==Definition==<br />
Let {{math|G {{=}} (V, E)}} and {{math|G&prime; {{=}} (V&prime;, E&prime;)}} be two graphs. Graph {{math|G&prime;}} is a ''sub-graph'' of graph {{math|G}} (written as {{math|G&prime; ⊆ G}}) if {{math|V&prime; ⊆ V}} and {{math|E&prime; ⊆ E ∩ (V&prime; &times; V&prime;)}}. If {{math|G&prime; ⊆ G}} and {{math|G&prime;}} contains all of the edges {{math|&lang;u, v&rang; ∈ E}} with {{math|u, v ∈ V&prime;}}, then {{math|G&prime;}} is an ''induced sub-graph'' of {{math|G}}. We call {{math|G&prime;}} and {{math|G}} isomorphic (written as {{math|G&prime; ↔ G}}), if there exists a bijection (one-to-one) {{math|f:V&prime; → V}} with {{math|&lang;u, v&rang; ∈ E&prime; ⇔ &lang;f(u), f(v)&rang; ∈ E}} for all {{math|u, v ∈ V&prime;}}. The mapping {{math|f}} is called an isomorphism between {{math|G}} and {{math|G&prime;}}.<ref name="die1">{{cite journal |author=Diestel R |title=Graph Theory (Graduate Texts in Mathematics) |volume=173 |year=2005|publisher=New York: Springer-Verlag Heidelberg}}</ref><br />
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设{{math|G {{=}} (V, E)}} 和 {{math|G&prime; {{=}} (V&prime;, E&prime;)}} 是两个图。若{{math|V&prime; ⊆ V}}且满足{{math|E&prime; ⊆ E ∩ (V&prime; &times; V&prime;)}})(即图{{math|G&prime; ⊆ G}的所有边和点都属于图{{math|G}})则称图{{math|G&prime; ⊆ G}是图{{math|G}}的一个子图<ref name="die1">{{cite journal |author=Diestel R |title=Graph Theory (Graduate Texts in Mathematics) |volume=173 |year=2005|publisher=New York: Springer-Verlag Heidelberg}}</ref><br />
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若{{math|G&prime; ⊆ G}},且对于顶点{{math|u}}、{{math|v}}及其连边,只要{{math|u}}和{{math|v}}存在于{{math|G&prime;}}(即若{{math|U}}, {{math|V&prime; ⊆ V}}),那么{{math|G&prime; ⊆ G}}中就应该包含原图{{math|G}}中的所有{{math|u}}和{{math|V}}的对应连边(即{{math|&lang;u, v&rang; ∈ E}}),则称此时图{{math|G&prime;}}就是图{{math|G}}的导出子图。<br />
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如果存在一个双射(一对一){{math|f:V&prime; → V}},且对所有{{math|u, v ∈ V&prime;}}都有{{math|&lang;u, v&rang; ∈ E&prime; ⇔ &lang;f(u), f(v)&rang; ∈ E}} ,则称{{math|G&prime }}是{{math|G}}的同构图(记作:{{math|G&prime; → G}}),映射f则称为{{math|G}}与{{math|G&prime;}}之间的同构(isomorphism)。[2]<br />
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When {{math|G&Prime; ⊂ G}} and there exists an isomorphism between the sub-graph {{math|G&Prime;}} and a graph {{math|G&prime;}}, this mapping represents an ''appearance'' of {{math|G&prime;}} in {{math|G}}. The number of appearances of graph {{math|G&prime;}} in {{math|G}} is called the frequency {{math|F<sub>G</sub>}} of {{math|G&prime;}} in {{math|G}}. A graph is called ''recurrent'' (or ''frequent'') in {{math|G}}, when its ''frequency'' {{math|F<sub>G</sub>(G&prime;)}} is above a predefined threshold or cut-off value. We use terms ''pattern'' and ''frequent sub-graph'' in this review interchangeably. There is an [[Statistical ensemble (mathematical physics)|ensemble]] {{math|Ω(G)}} of random graphs corresponding to the [[Null model|null-model]] associated to {{math|G}}. We should choose {{math|N}} random graphs uniformly from {{math|Ω(G)}} and calculate the frequency for a particular frequent sub-graph {{math|G&prime;}} in {{math|G}}. If the frequency of {{math|G&prime;}} in {{math|G}} is higher than its arithmetic mean frequency in {{math|N}} random graphs {{math|R<sub>i</sub>}}, where {{math|1 ≤ i ≤ N}}, we call this recurrent pattern ''significant'' and hence treat {{math|G&prime;}} as a ''network motif'' for {{math|G}}. For a small graph {{math|G&prime;}}, the network {{math|G}} and a set of randomized networks {{math|R(G) ⊆ Ω(R)}}, where {{math|1=R(G) {{=}} N}}, the ''Z-Score'' that has been defined by the following formula:<br />
<br />
<math>Z(G^\prime) = \frac{F_G(G^\prime) - \mu_R(G^\prime)}{\sigma_R(G^\prime)}</math><br />
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当{{math|G&Prime; ⊂ G}},且{{math|G&Prime;}}与图{{math|G&prime;}}之间存在同构时,该映射表示{{math|G&prime;}}对于{{math|G}}存在。图{{math|G&prime;}}在{{math|G}}的出现次数称为{{math|G&prime;}}出现在{{math|G}}的频率{{math|F<sub>G</sub>}}。当一个子图的频率{{math|F<sub>G</sub>}}高于预定的阈值或截止值时,则称{{math|G&prime;}}是{{math|G}}中的递归(或频繁)子图。<br />
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在接下来的内容中,我们交替使用术语“模式(motifs)”和“频繁子图(frequent sub-graph)”。<br />
<br />
设从与{{math|G}}相关联的零模型(the null-model)获得的随机图集合为{{math|Ω(G)}},我们从{{math|Ω(G)}}中均匀地选择N个随机图,并计算其特定频繁子图的频率。如果{{math|G&prime;}}出现在{{math|G}}的频率高于N个随机图Ri的算术平均频率,其中{{math|1 ≤ i ≤ N}},我们称此递归模式是有意义的,因此可以将{{math|G&prime;}}视为{{math|G}}的网络模体。<br />
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对于一个小图{{math|G&prime;}},网络{{math|G}}和一组随机网络{{math|R(G) ⊆ Ω(R)}},当{{math|1=R(G) {{=}} N}}时,由其Z分数(Z-score)的定义如下式:<br />
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<math>Z(G^\prime) = \frac{F_G(G^\prime) - \mu_R(G^\prime)}{\sigma_R(G^\prime)}</math><br />
<br />
where {{math|μ<sub>R</sub>(G&prime;)}} and {{math|σ<sub>R</sub>(G&prime;)}} stand for mean and standard deviation frequency in set {{math|R(G)}}, respectively.<ref name="mil1">{{cite journal |vauthors=Milo R, Shen-Orr SS, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |volume=298 |year=2002|journal=Science|issue=5594|pages=824–827 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="alb1">{{cite journal |vauthors=Albert R, Barabási AL |title=Statistical mechanics of complex networks |journal=Reviews of Modern Physics |volume=74 |issue=1 |year=2002 |pages=47–49 |doi=10.1103/RevModPhys.74.47 |bibcode=2002RvMP...74...47A|arxiv=cond-mat/0106096 |citeseerx=10.1.1.242.4753 }}</ref><ref name="mil2">{{cite journal |vauthors=Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheffer M, Alon U |title=Superfamilies of designed and evolved networks |journal=Science |volume=303 |issue=5663 |year=2004 |pages=1538–1542 |pmid=15001784 |doi=10.1126/science.1089167 |bibcode=2004Sci...303.1538M |url=https://semanticscholar.org/paper/87ad24efd5329046d37cd704f970323e878710ca }}</ref><ref name="sch1">{{cite encyclopedia|last=Schwöbbermeyer |first=H |title=Network Motifs |encyclopedia=Analysis of Biological Networks |editor=Junker BH, Schreiber F |publisher=Hoboken, New Jersey: John Wiley & Sons |year=2008 |pages=85–108}}</ref><ref name="bor1">{{cite encyclopedia |last1=Bornholdt |first1=S |last2=Schuster |first2=HG |title=Handbook of graphs and networks : from the genome to the Internet |journal=Handbook of Graphs and Networks: From the Genome to the Internet |pages=417 |year=2003|bibcode=2003hgnf.book.....B }}</ref><ref name="cir1">{{cite journal |vauthors=Ciriello G, Guerra C |title=A review on models and algorithms for motif discovery in protein-protein interaction networks |journal=Briefings in Functional Genomics and Proteomics |year=2008 |volume=7 |issue=2 |pages=147–156 |doi=10.1093/bfgp/eln015|pmid=18443014 |doi-access=free }}</ref> The larger the {{math|Z(G&prime;)}}, the more significant is the sub-graph {{math|G&prime;}} as a motif. Alternatively, another measurement in statistical hypothesis testing that can be considered in motif detection is the P-Value, given as the probability of {{math|F<sub>R</sub>(G&prime;) ≥ F<sub>G</sub>(G&prime;)}} (as its null-hypothesis), where {{math|F<sub>R</sub>(G&prime;)}} indicates the frequency of G' in a randomized network.<ref name="sch1" /> A sub-graph with P-value less than a threshold (commonly 0.01 or 0.05) will be treated as a significant pattern. The P-value is defined as<br />
<br />
<math>P(G^\prime) = \frac{1}{N}\sum_{i=1}^N \delta(c(i)) ; c(i): F_R^i(G^\prime) \ge F_G(G^\prime)</math><br />
<br />
式中,{{math|μ<sub>R</sub>(G&prime;)}} 和 {{math|σ<sub>R</sub>(G&prime;)}}分别代表集合{{math|R(G)}}中的平均和标准偏差频率。.<ref name="mil1">{{cite journal |vauthors=Milo R, Shen-Orr SS, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |volume=298 |year=2002|journal=Science|issue=5594|pages=824–827 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="alb1">{{cite journal |vauthors=Albert R, Barabási AL |title=Statistical mechanics of complex networks |journal=Reviews of Modern Physics |volume=74 |issue=1 |year=2002 |pages=47–49 |doi=10.1103/RevModPhys.74.47 |bibcode=2002RvMP...74...47A|arxiv=cond-mat/0106096 |citeseerx=10.1.1.242.4753 }}</ref><ref name="mil2">{{cite journal |vauthors=Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheffer M, Alon U |title=Superfamilies of designed and evolved networks |journal=Science |volume=303 |issue=5663 |year=2004 |pages=1538–1542 |pmid=15001784 |doi=10.1126/science.1089167 |bibcode=2004Sci...303.1538M |url=https://semanticscholar.org/paper/87ad24efd5329046d37cd704f970323e878710ca }}</ref><ref name="sch1">{{cite encyclopedia|last=Schwöbbermeyer |first=H |title=Network Motifs |encyclopedia=Analysis of Biological Networks |editor=Junker BH, Schreiber F |publisher=Hoboken, New Jersey: John Wiley & Sons |year=2008 |pages=85–108}}</ref><ref name="bor1">{{cite encyclopedia |last1=Bornholdt |first1=S |last2=Schuster |first2=HG |title=Handbook of graphs and networks : from the genome to the Internet |journal=Handbook of Graphs and Networks: From the Genome to the Internet |pages=417 |year=2003|bibcode=2003hgnf.book.....B }}</ref><ref name="cir1">{{cite journal |vauthors=Ciriello G, Guerra C |title=A review on models and algorithms for motif discovery in protein-protein interaction networks |journal=Briefings in Functional Genomics and Proteomics |year=2008 |volume=7 |issue=2 |pages=147–156 |doi=10.1093/bfgp/eln015|pmid=18443014 |doi-access=free }}</ref> {{math|Z(G&prime;)}}越大,子图{{math|G&prime;}}作为模体的意义也就越大。<br />
<br />
此外还可以使用统计假设检验中的另一个测量方法,可以作为模体检测中的一种方法,即P值(P-value),以 {{math|F<sub>R</sub>(G&prime;) ≥ F<sub>G</sub>(G&prime;)}}的概率给出(作为其零假设null-hypothesis),其中{{math|F<sub>R</sub>(G&prime;)}}表示随机网络中{{math|G&prime;}}的频率。<ref name="sch1" /> 当P值小于阈值(通常为0.01或0.05)时,该子图可以被称为显著模式。该P值定义为:<br />
<br />
<math>P(G^\prime) = \frac{1}{N}\sum_{i=1}^N \delta(c(i)) ; c(i): F_R^i(G^\prime) \ge F_G(G^\prime)</math><br />
<br />
[[File:Different occurrences of a sub-graph in a graph.jpg|thumb|''Different occurrences of a sub-graph in a graph''. (M1 – M4) are different occurrences of sub-graph (b) in graph (a). For frequency concept {{math|F<sub>1</sub>}}, the set M1, M2, M3, M4 represent all matches, so {{math|F<sub>1</sub> {{=}} 4}}. For {{math|F<sub>2</sub>}}, one of the two set M1, M4 or M2, M3 are possible matches, {{math|F<sub>2</sub> {{=}} 2}}. Finally, for frequency concept {{math|F<sub>3</sub>}}, merely one of the matches (M1 to M4) is allowed, therefore {{math|F<sub>3</sub> {{=}} 1}}. The frequency of these three frequency concepts decrease as the usage of network elements are restricted.]]<br />
<br />
Where {{math|N}} indicates number of randomized networks, {{math|i}} is defined over an ensemble of randomized networks and the Kronecker delta function {{math|δ(c(i))}} is one if the condition {{math|c(i)}} holds. The concentration <ref name="kas1">{{cite journal |vauthors=Kashtan N, Itzkovitz S, Milo R, Alon U |title=Efficient sampling algorithm for estimating sub-graph concentrations and detecting network motifs |journal=Bioinformatics |year=2004 |volume=20 |issue=11 |pages=1746–1758 |doi=10.1093/bioinformatics/bth163|pmid=15001476 |doi-access=free }}</ref><ref name="wer1">{{cite journal |author=Wernicke S |title=Efficient detection of network motifs |journal=IEEE/ACM Transactions on Computational Biology and Bioinformatics |year=2006 |volume=3 |issue=4 |pages=347–359 |doi=10.1109/tcbb.2006.51|pmid=17085844 |citeseerx=10.1.1.304.2576 }}</ref> of a particular n-size sub-graph {{math|G&prime;}} in network {{math|G}} refers to the ratio of the sub-graph appearance in the network to the total ''n''-size non-isomorphic sub-graphs’ frequencies, which is formulated by<br />
<br />
<math>C_G(G^\prime) = \frac{F_G(G^\prime)}{\sum_i F_G(G_i)}</math><br />
<br />
where index {{math|i}} is defined over the set of all non-isomorphic n-size graphs. Another statistical measurement is defined for evaluating network motifs, but it is rarely used in known algorithms. This measurement is introduced by Picard ''et al.'' in 2008 and used the Poisson distribution, rather than the Gaussian normal distribution that is implicitly being used above.<ref name="pic1">{{cite journal |vauthors=Picard F, Daudin JJ, Schbath S, Robin S |title=Assessing the Exceptionality of Network Motifs |journal=J. Comp. Bio. |year=2005 |volume=15 |issue=1 |pages=1–20|doi=10.1089/cmb.2007.0137 |pmid=18257674 |citeseerx=10.1.1.475.4300 }}</ref><br />
<br />
其中索引 i 定义在所有非同构 n 大小图的集合上。 另一种统计测量是用来评估网络主题的,但在已知的算法中很少使用。 这种测量方法是由 Picard 等人在2008年提出的,使用的是泊松分佈分布,而不是上面隐含使用的高斯正态分布。<ref name="pic1">{{cite journal |vauthors=Picard F, Daudin JJ, Schbath S, Robin S |title=Assessing the Exceptionality of Network Motifs |journal=J. Comp. Bio. |year=2005 |volume=15 |issue=1 |pages=1–20|doi=10.1089/cmb.2007.0137 |pmid=18257674 |citeseerx=10.1.1.475.4300 }}</ref>其中{{math|N}}表示随机网络的数目,{{math|i}}定义在随机网络的集合上,若条件{{math|c(i)}}成立,则Kroneckerδ函数{{math|δ(c(i))}}是1。在网络{{math|G}}中,一个特定的n维子图{{math|N&prime;}}的集中度是指子图在网络中出现频率与n维非同构子图的总频率之比,其计算公式如下:<br />
<br />
<math>C_G(G^\prime) = \frac{F_G(G^\prime)}{\sum_i F_G(G_i)}</math><br />
<br />
<br />
In addition, three specific concepts of sub-graph frequency have been proposed.<ref name="schr1">{{cite book |vauthors=Schreiber F, Schwöbbermeyer H |title=Frequency concepts and pattern detection for the analysis of motifs in networks |journal=Transactions on Computational Systems Biology III |volume=3737 |year=2005 |pages=89–104|doi=10.1007/11599128_7 |citeseerx=10.1.1.73.1130 |series=Lecture Notes in Computer Science |isbn=978-3-540-30883-6 }}</ref> As the figure illustrates, the first frequency concept {{math|F<sub>1</sub>}} considers all matches of a graph in original network. This definition is similar to what we have introduced above. The second concept {{math|F<sub>2</sub>}} is defined as the maximum number of edge-disjoint instances of a given graph in original network. And finally, the frequency concept {{math|F<sub>3</sub>}} entails matches with disjoint edges and nodes. Therefore, the two concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}} restrict the usage of elements of the graph, and as can be inferred, the frequency of a sub-graph declines by imposing restrictions on network element usage. As a result, a network motif detection algorithm would pass over more candidate sub-graphs if we insist on frequency concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}}.<br />
<br />
此外,他们还提出了子图频率的三个具体概念。<ref name="schr1">{{cite book |vauthors=Schreiber F, Schwöbbermeyer H |title=Frequency concepts and pattern detection for the analysis of motifs in networks |journal=Transactions on Computational Systems Biology III |volume=3737 |year=2005 |pages=89–104|doi=10.1007/11599128_7 |citeseerx=10.1.1.73.1130 |series=Lecture Notes in Computer Science |isbn=978-3-540-30883-6 }}</ref> 如图所示,第一频率概念 {{math|F<sub>1</sub>}}考虑原始网络中图的所有匹配,这与我们前面介绍过的类似。第二个概念{{math|F<sub>2</sub>}}定义为原始网络中给定图的最大不相交边的数量。最后,频率概念{{math|F<sub>3</sub>}}包含与不相交边(disjoint edges)和节点的匹配。因此,两个概念F2和F3限制了图元素的使用,并且可以看出,通过对网络元素的使用施加限制,子图的频率下降。因此,如果我们坚持使用频率概念{{math|F<sub>2</sub>}}和{{math|F<sub>3</sub>}},网络模体检测算法将可以筛选出更多的候选子图。<br />
<br />
==History==<br />
The study of network motifs was pioneered by Holland and Leinhardt<ref>Holland, P. W., & Leinhardt, S. (1974). The statistical analysis of local structure in social networks. Working Paper No. 44, National Bureau of Economic Research.</ref><ref>Hollandi, P., & Leinhardt, S. (1975). The Statistical Analysis of Local. Structure in Social Networks. Sociological Methodology, David Heise, ed. San Francisco: Josey-Bass.</ref><ref> Holland, P. W., & Leinhardt, S. (1976). Local structure in social networks. Sociological methodology, 7, 1-45.</ref><ref>Holland, P. W., & Leinhardt, S. (1977). A method for detecting structure in sociometric data. In Social Networks (pp. 411-432). Academic Press.</ref> who introduced the concept of a triad census of networks. They introduced methods to enumerate various types of subgraph configurations, and test whether the subgraph counts are statistically different from those expected in random networks. <br />
霍兰(Holland)和莱因哈特(Leinhardt)率先提出了'''网络三合会普查'''(a triad census of networks)的概念,开创了网络模体研究的先河。<ref>Holland, P. W., & Leinhardt, S. (1974). The statistical analysis of local structure in social networks. Working Paper No. 44, National Bureau of Economic Research.</ref><ref>Hollandi, P., & Leinhardt, S. (1975). The Statistical Analysis of Local. Structure in Social Networks. Sociological Methodology, David Heise, ed. San Francisco: Josey-Bass.</ref><ref> Holland, P. W., & Leinhardt, S. (1976). Local structure in social networks. Sociological methodology, 7, 1-45.</ref><ref>Holland, P. W., & Leinhardt, S. (1977). A method for detecting structure in sociometric data. In Social Networks (pp. 411-432). Academic Press.</ref> 他们介绍了枚举各种子图配置的方法,并测试子图计数是否与随机网络中的期望值存在统计学上的差异。<br />
<br />
这里对于'''网络三合会普查'''(a triad census of networks)这一概念的翻译存疑<br />
<br />
<br />
This idea was further generalized in 2002 by [[Uri Alon]] and his group <ref name="she1">{{cite journal |vauthors=Shen-Orr SS, Milo R, Mangan S, Alon U |title=Network motifs in the transcriptional regulation network of ''Escherichia coli'' |journal=Nat. Genet. |volume=31 |issue=1 |pages=64–8 |date=May 2002 |pmid=11967538 |doi=10.1038/ng881}}</ref> when network motifs were discovered in the gene regulation (transcription) network of the bacteria ''[[Escherichia coli|E. coli]]'' and then in a large set of natural networks. Since then, a considerable number of studies have been conducted on the subject. Some of these studies focus on the biological applications, while others focus on the computational theory of network motifs.<br />
<br />
2002年,Uri Alon和他的团队[17]在大肠杆菌的基因调控(gene regulation network)(转录 transcription)网络中发现了网络模体,随后在大量的自然网络中也发现了网络模体,从而进一步推广了这一观点。自那时起,许多科学家都对这一问题进行了大量的研究。其中一些研究集中在生物学应用上,而另一些则集中在网络模体的计算理论上。<ref name="she1">{{cite journal |vauthors=Shen-Orr SS, Milo R, Mangan S, Alon U |title=Network motifs in the transcriptional regulation network of ''Escherichia coli'' |journal=Nat. Genet. |volume=31 |issue=1 |pages=64–8 |date=May 2002 |pmid=11967538 |doi=10.1038/ng881}}</ref> <br />
<br />
<br />
The biological studies endeavor to interpret the motifs detected for biological networks. For example, in work following,<ref name="she1" /> the network motifs found in ''[[Escherichia coli|E. coli]]'' were discovered in the transcription networks of other bacteria<ref name="eic1">{{cite journal |vauthors=Eichenberger P, Fujita M, Jensen ST, etal |title=The program of gene transcription for a single differentiating cell type during sporulation in ''Bacillus subtilis'' |journal=PLOS Biology |volume=2 |issue=10 |pages=e328 |date=October 2004 |pmid=15383836 |pmc=517825 |doi=10.1371/journal.pbio.0020328 }} </ref> as well as yeast<ref name="mil3">{{cite journal |vauthors=Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |journal=Science |volume=298 |issue=5594 |pages=824–7 |date=October 2002 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="lee1">{{cite journal |vauthors=Lee TI, Rinaldi NJ, Robert F, etal |title=Transcriptional regulatory networks in Saccharomyces cerevisiae |journal=Science |volume=298 |issue=5594 |pages=799–804 |date=October 2002 |pmid=12399584 |doi=10.1126/science.1075090 |bibcode=2002Sci...298..799L }}</ref> and higher organisms.<ref name="odo1">{{cite journal |vauthors=Odom DT, Zizlsperger N, Gordon DB, etal |title=Control of pancreas and liver gene expression by HNF transcription factors |journal=Science |volume=303 |issue=5662 |pages=1378–81 |date=February 2004 |pmid=14988562 |pmc=3012624 |doi=10.1126/science.1089769 |bibcode=2004Sci...303.1378O }}</ref><ref name="boy1">{{cite journal |vauthors=Boyer LA, Lee TI, Cole MF, etal |title=Core transcriptional regulatory circuitry in human embryonic stem cells |journal=Cell |volume=122 |issue=6 |pages=947–56 |date=September 2005 |pmid=16153702 |pmc=3006442 |doi=10.1016/j.cell.2005.08.020 }}</ref><ref name="ira1">{{cite journal |vauthors=Iranfar N, Fuller D, Loomis WF |title=Transcriptional regulation of post-aggregation genes in Dictyostelium by a feed-forward loop involving GBF and LagC |journal=Dev. Biol. |volume=290 |issue=2 |pages=460–9 |date=February 2006 |pmid=16386729 |doi=10.1016/j.ydbio.2005.11.035 |doi-access=free }}</ref> A distinct set of network motifs were identified in other types of biological networks such as neuronal networks and protein interaction networks.<ref name="mil2" /><ref name="maa1">{{cite journal |vauthors=Ma'ayan A, Jenkins SL, Neves S, etal |title=Formation of regulatory patterns during signal propagation in a Mammalian cellular network |journal=Science |volume=309 |issue=5737 |pages=1078–83 |date=August 2005 |pmid=16099987 |pmc=3032439 |doi=10.1126/science.1108876 |bibcode=2005Sci...309.1078M }}</ref><ref name="pta1">{{cite journal |vauthors=Ptacek J, Devgan G, Michaud G, etal |title=Global analysis of protein phosphorylation in yeast |journal=Nature |volume=438 |issue=7068 |pages=679–84 |date=December 2005 |pmid=16319894 |doi=10.1038/nature04187|bibcode=2005Natur.438..679P |url=https://authors.library.caltech.edu/56271/2/Tables.pdf |type=Submitted manuscript }}</ref><br />
<br />
生物学研究试图解释为生物网络检测到的模体。例如,在接下来的工作中,文献[17]在大肠杆菌中发现的网络模体存在于其他细菌<ref name="eic1">{{cite journal |vauthors=Eichenberger P, Fujita M, Jensen ST, etal |title=The program of gene transcription for a single differentiating cell type during sporulation in ''Bacillus subtilis'' |journal=PLOS Biology |volume=2 |issue=10 |pages=e328 |date=October 2004 |pmid=15383836 |pmc=517825 |doi=10.1371/journal.pbio.0020328 }} </ref>以及酵母<ref name="mil3">{{cite journal |vauthors=Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |journal=Science |volume=298 |issue=5594 |pages=824–7 |date=October 2002 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="lee1">{{cite journal |vauthors=Lee TI, Rinaldi NJ, Robert F, etal |title=Transcriptional regulatory networks in Saccharomyces cerevisiae |journal=Science |volume=298 |issue=5594 |pages=799–804 |date=October 2002 |pmid=12399584 |doi=10.1126/science.1075090 |bibcode=2002Sci...298..799L }}</ref>和高等生物的转录网络中。文献<ref name="odo1">{{cite journal |vauthors=Odom DT, Zizlsperger N, Gordon DB, etal |title=Control of pancreas and liver gene expression by HNF transcription factors |journal=Science |volume=303 |issue=5662 |pages=1378–81 |date=February 2004 |pmid=14988562 |pmc=3012624 |doi=10.1126/science.1089769 |bibcode=2004Sci...303.1378O }}</ref><ref name="boy1">{{cite journal |vauthors=Boyer LA, Lee TI, Cole MF, etal |title=Core transcriptional regulatory circuitry in human embryonic stem cells |journal=Cell |volume=122 |issue=6 |pages=947–56 |date=September 2005 |pmid=16153702 |pmc=3006442 |doi=10.1016/j.cell.2005.08.020 }}</ref><ref name="ira1">{{cite journal |vauthors=Iranfar N, Fuller D, Loomis WF |title=Transcriptional regulation of post-aggregation genes in Dictyostelium by a feed-forward loop involving GBF and LagC |journal=Dev. Biol. |volume=290 |issue=2 |pages=460–9 |date=February 2006 |pmid=16386729 |doi=10.1016/j.ydbio.2005.11.035 |doi-access=free }}</ref>在其他类型的生物网络中发现了一组不同的网络模体,如神经元网络和蛋白质相互作用网络。<ref name="mil2" /><ref name="maa1">{{cite journal |vauthors=Ma'ayan A, Jenkins SL, Neves S, etal |title=Formation of regulatory patterns during signal propagation in a Mammalian cellular network |journal=Science |volume=309 |issue=5737 |pages=1078–83 |date=August 2005 |pmid=16099987 |pmc=3032439 |doi=10.1126/science.1108876 |bibcode=2005Sci...309.1078M }}</ref><ref name="pta1">{{cite journal |vauthors=Ptacek J, Devgan G, Michaud G, etal |title=Global analysis of protein phosphorylation in yeast |journal=Nature |volume=438 |issue=7068 |pages=679–84 |date=December 2005 |pmid=16319894 |doi=10.1038/nature04187|bibcode=2005Natur.438..679P |url=https://authors.library.caltech.edu/56271/2/Tables.pdf |type=Submitted manuscript }}</ref><br />
<br />
<br />
The computational research has focused on improving existing motif detection tools to assist the biological investigations and allow larger networks to be analyzed. Several different algorithms have been provided so far, which are elaborated in the next section in chronological order.<br />
<br />
另一方面,对于计算研究的重点则是改进现有的模体检测工具,以协助生物学研究,并允许对更大的网络进行分析。到目前为止,已经提供了几种不同的算法,这些算法将在下一节按时间顺序进行阐述。<br />
<br />
Most recently, the acc-MOTIF tool to detect network motifs was released.<ref>{{Cite web | url=http://www.ft.unicamp.br/docentes/meira/accmotifs/ |title = Acc-Motif: Accelerated Motif Detection}}</ref><br />
<br />
最近,还发布了用于检测网络基序的acc基序工具。<ref>{{Cite web | url=http://www.ft.unicamp.br/docentes/meira/accmotifs/ |title = Acc-Motif: Accelerated Motif Detection}}</ref><br />
<br />
<br />
==模体发现算法 Motif discovery algorithms==<br />
<br />
Various solutions have been proposed for the challenging problem of motif discovery. These algorithms can be classified under various paradigms such as exact counting methods, sampling methods, pattern growth methods and so on. However, motif discovery problem comprises two main steps: first, calculating the number of occurrences of a sub-graph and then, evaluating the sub-graph significance. The recurrence is significant if it is detectably far more than expected. Roughly speaking, the expected number of appearances of a sub-graph can be determined by a Null-model, which is defined by an ensemble of random networks with some of the same properties as the original network.<br />
<br />
针对模体发现这一问题存在多种解决方案。这些算法可以归纳为不同的范式:例如精确计数方法,采样方法,模式增长方法等。但模体发现问题包括两个主要步骤:首先,计算子图的出现次数,然后评估子图的重要性。如果检测到的重现性远超过预期,那么这种重现性是很显著的。粗略地讲,子图的预期出现次数可以由'''零模型 Null-model''' 确定,该模型定义为具有与原始网络某些属性相同的随机网络的集合。<br />
<br />
<br />
Here, a review on computational aspects of major algorithms is given and their related benefits and drawbacks from an algorithmic perspective are discussed.<br />
<br />
接下来,对下列算法的计算原理进行简要回顾,并从算法的角度讨论了它们的优缺点。<br />
<br />
===mfinder 算法===<br />
<br />
''mfinder'', the first motif-mining tool, implements two kinds of motif finding algorithms: a full enumeration and a sampling method. Until 2004, the only exact counting method for NM (network motif) detection was the brute-force one proposed by Milo ''et al.''.<ref name="mil1" /> This algorithm was successful for discovering small motifs, but using this method for finding even size 5 or 6 motifs was not computationally feasible. Hence, a new approach to this problem was needed.<br />
<br />
'''mfinder'''是第一个模体挖掘工具,它主要有两种模体查找算法:完全枚举 full enumeration 和采样方法 sampling method。直到2004年,用于NM('''网络模体 networkmotif''')检测的唯一精确计数方法是'''Milo'''等人提出的暴力穷举方法。<ref name="mil1" />该算法成功地发现了小规模的模体,但是这种方法甚至对于发现规模为5个或6个的模体在计算上都不可行的。因此,需要一种解决该问题的新方法。<br />
<br />
<br />
Kashtan ''et al.'' <ref name="kas1" /> presented the first sampling NM discovery algorithm, which was based on ''edge sampling'' throughout the network. This algorithm estimates concentrations of induced sub-graphs and can be utilized for motif discovery in directed or undirected networks. The sampling procedure of the algorithm starts from an arbitrary edge of the network that leads to a sub-graph of size two, and then expands the sub-graph by choosing a random edge that is incident to the current sub-graph. After that, it continues choosing random neighboring edges until a sub-graph of size n is obtained. Finally, the sampled sub-graph is expanded to include all of the edges that exist in the network between these n nodes. When an algorithm uses a sampling approach, taking unbiased samples is the most important issue that the algorithm might address. The sampling procedure, however, does not take samples uniformly and therefore Kashtan ''et al.'' proposed a weighting scheme that assigns different weights to the different sub-graphs within network.<ref name="kas1" /> The underlying principle of weight allocation is exploiting the information of the [[sampling probability]] for each sub-graph, i.e. the probable sub-graphs will obtain comparatively less weights in comparison to the improbable sub-graphs; hence, the algorithm must calculate the sampling probability of each sub-graph that has been sampled. This weighting technique assists ''mfinder'' to determine sub-graph concentrations impartially.<br />
<br />
'''Kashtan''' 等人<ref name="kas1" />首次提出了一种基于边缘采样的网络模体(NM)采样发现算法。该算法估计了<font color="red">所含子图 induced sub-graphs 的集中度 concentrations </font>,可用于有向或无向网络中的模体发现。该算法的采样过程从网络的任意一条边开始,该边连向大小为2的子图,然后选择一条与当前子图相关的随机边对子图进行扩展。之后,它将继续选择随机的相邻边,直到获得大小为n的子图为止。最后,采样得到的子图扩展为包括这n个节点在内的网络中存在的所有边。当使用采样方法时,获取无偏样本是这类算法可能面临的最重要问题。而且,采样过程并不能保证采到所有的样本(也就是不能保证得到所有的子图,译者注),因此,Kashtan 等人又提出了一种加权方案,为网络中的不同子图分配不同的权重。<ref name="kas1" /> 权重分配的基本原理是利用每个子图的抽样概率信息,即,与不可能的子图相比,可能的子图将获得相对较少的权重;因此,该算法必须计算已采样的每个子图的采样概率。这种加权技术有助于mfinder公正地确定子图的<font color="red">集中度 concentrations </font>。<br />
<br />
<br />
In expanded to include sharp contrast to exhaustive search, the computational time of the algorithm surprisingly is asymptotically independent of the network size. An analysis of the computational time of the algorithm has shown that it takes {{math|O(n<sup>n</sup>)}} for each sample of a sub-graph of size {{math|n}} from the network. On the other hand, there is no analysis in <ref name="kas1" /> on the classification time of sampled sub-graphs that requires solving the ''graph isomorphism'' problem for each sub-graph sample. Additionally, an extra computational effort is imposed on the algorithm by the sub-graph weight calculation. But it is unavoidable to say that the algorithm may sample the same sub-graph multiple times – spending time without gathering any information.<ref name="wer1" /> In conclusion, by taking the advantages of sampling, the algorithm performs more efficiently than an exhaustive search algorithm; however, it only determines sub-graphs concentrations approximately. This algorithm can find motifs up to size 6 because of its main implementation, and as result it gives the most significant motif, not all the others too. Also, it is necessary to mention that this tool has no option of visual presentation. The sampling algorithm is shown briefly:<br />
<br />
与穷举搜索形成鲜明对比的是,该算法的计算时间竟然与网络大小渐近无关。对算法时间复杂度的分析表明,对于网络中大小为n的子图的每个样本,它的时间复杂度为<math>O(n^n)</math>。另一方面,<font color="red">并没有对已采样子图的每一个子图样本判断图同构问题的分类时间进行分析</font><ref name="kas1" />。另外,子图权重计算将额外增加该算法的计算负担。但是不得不指出的是,该算法可能会多次采样相同的子图——花费时间而不收集任何有用信息。<ref name="wer1" />总之,通过利用采样的优势,该算法的性能比穷举搜索算法更有效;但是,它只能大致确定子图的<font color="red">集中度 concentrations </font>。由于该算法的实现方式,使得它可以找到最大为6的模体,并且它会给出的最重要的模体,而不是其他所有模体。另外,有必要提到此工具没有可视化的呈现。采样算法简要显示如下:<br />
<br />
<br />
{| class="wikitable"<br />
|-<br />
! mfinder<br />
|-<br />
| '''Definitions:''' {{math|E<sub>s</sub>}}is the set of picked edges. {{math|V<sub>s</sub>}} is the set of all nodes that are touched by the edges in {{math|E}}.<br />
|-<br />
| Init {{math|V<sub>s</sub>}} and {{math|E<sub>s</sub>}} to be empty sets.<br />
1. Pick a random edge {{math|e<sub>1</sub> {{=}} (v<sub>i</sub>, v<sub>j</sub>)}}. Update {{math|E<sub>s</sub> {{=}} {e<sub>1</sub>}}}, {{math|V<sub>s</sub> {{=}} {v<sub>i</sub>, v<sub>j</sub>}}}<br />
<br />
2. Make a list {{math|L}} of all neighbor edges of {{math|E<sub>s</sub>}}. Omit from {{math|L}} all edges between members of {{math|V<sub>s</sub>}}.<br />
<br />
3. Pick a random edge {{math|e {{=}} {v<sub>k</sub>,v<sub>l</sub>}}} from {{math|L}}. Update {{math|E<sub>s</sub> {{=}} E<sub>s</sub> ⋃ {e}}}, {{math|V<sub>s</sub> {{=}} V<sub>s</sub> ⋃ {v<sub>k</sub>, v<sub>l</sub>}}}.<br />
<br />
4. Repeat steps 2-3 until completing an ''n''-node subgraph (until {{math|{{!}}V<sub>s</sub>{{!}} {{=}} n}}).<br />
<br />
5. Calculate the probability to sample the picked ''n''-node subgraph.<br />
|}<br />
<br />
<br />
{|class="wikitable"<br />
|+ mfinder<br />
|-<br />
!rowspan="1"|定义:<math>E_{s}</math>是采集的边集合。<math>V_{s}</math>是<math>E</math>中所有边的顶点的集合。<br />
|-<br />
|rowspan="5"|初始化<math>V_{s}</math>和<math>E_{s}</math>为空集。<br><br />
1. 随机选择一条边<math> e_{1} = (v_{i}, v_{j}) </math>,更新 <math>E_{s} = \{e_{1}\}, V{s} = \{v_{i}, v_{j}\}</math><br />
<br />
2. 列出<math>E{s}</math>的所有邻边列表<math> L </math>,从<math> L </math>中删除<math>V{s}</math>中所有元素组成的边。<br />
<br />
3. 从<math> L </math>中随机选择一条边<math> e = \{v_{k},v_{l}\} </math>, 更新<math>E_{s} = E_{s} \cup \{e\} , V_{s} = V_{s} \cup \{v_{k}, v_{l}\}</math>。<br />
<br />
4. 重复步骤2-3,直到完成包含n个节点的子图 (<math>\left | V_{s} \right | = n</math>)。<br />
<br />
5. 计算对选取的n节点子图进行采样的概率。<br />
|}<br />
<br />
<br />
===FPF (Mavisto)算法===<br />
<br />
Schreiber and Schwöbbermeyer <ref name="schr1" /> proposed an algorithm named ''flexible pattern finder (FPF)'' for extracting frequent sub-graphs of an input network and implemented it in a system named ''Mavisto''.<ref name="schr2">{{cite journal |vauthors=Schreiber F, Schwobbermeyer H |title=MAVisto: a tool for the exploration of network motifs |journal=Bioinformatics |volume=21 |issue=17|pages=3572–3574 |year=2005 |doi=10.1093/bioinformatics/bti556|pmid=16020473 |doi-access=free }}</ref> Their algorithm exploits the ''downward closure'' property which is applicable for frequency concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}}. The downward closure property asserts that the frequency for sub-graphs decrease monotonically by increasing the size of sub-graphs; however, this property does not hold necessarily for frequency concept {{math|F<sub>1</sub>}}. FPF is based on a ''pattern tree'' (see figure) consisting of nodes that represents different graphs (or patterns), where the parent of each node is a sub-graph of its children nodes; in other words, the corresponding graph of each pattern tree's node is expanded by adding a new edge to the graph of its parent node.<br />
<br />
Schreiber和Schwöbbermeyer <ref name="schr1" />提出了一种称为灵活模式查找器(FPF)的算法,用于提取输入网络的频繁子图,并将其在名为Mavisto的系统中加以实现。<ref name="schr2">{{cite journal |vauthors=Schreiber F, Schwobbermeyer H |title=MAVisto: a tool for the exploration of network motifs |journal=Bioinformatics |volume=21 |issue=17|pages=3572–3574 |year=2005 |doi=10.1093/bioinformatics/bti556|pmid=16020473 |doi-access=free }}</ref> 他们的算法利用了向下闭包特性,该特性适用于频率概念<math>F_{2}</math>和<math>F_{3}</math>。向下闭包性质表明,子图的频率随着子图的大小而单调下降;但这一性质并不一定适用于频率概念<math>F_{1}</math>。FPF算法基于模式树(见右图),由代表不同图形(或模式)的节点组成,其中每个节点的父节点是其子节点的子图;换句话说,每个模式树节点的对应图通过向其父节点图添加新边来扩展。<br />
<br />
<br />
[[Image:The pattern tree in FPF algorithm.jpg|right|thumb|''FPF算法中的模式树展示''.<ref name="schr1" />]]<br />
<br />
<br />
At first, the FPF algorithm enumerates and maintains the information of all matches of a sub-graph located at the root of the pattern tree. Then, one-by-one it builds child nodes of the previous node in the pattern tree by adding one edge supported by a matching edge in the target graph, and tries to expand all of the previous information about matches to the new sub-graph (child node). In next step, it decides whether the frequency of the current pattern is lower than a predefined threshold or not. If it is lower and if downward closure holds, FPF can abandon that path and not traverse further in this part of the tree; as a result, unnecessary computation is avoided. This procedure is continued until there is no remaining path to traverse.<br />
<br />
首先,FPF算法枚举并维护位于模式树根部的子图的所有匹配信息。然后,它通过在目标图中添加匹配边缘支持的一条边缘,在模式树中一一建立前一节点的子节点,然后通过在目标图中添加匹配边支持的一条边,逐个构建模式树中前一个节点的子节点,并尝试将以前关于匹配的所有信息拓展到新的子图(子节点)中。下一步,它判断当前模式的频率是否低于预定义的阈值。如果它低于阈值且保持向下闭包,则FPF算法会放弃该路径,而不会在树的此部分进一步遍历;这样就避免了不必要的计算。重复此过程,直到没有剩余可遍历的路径为止。<br />
<br />
<br />
The advantage of the algorithm is that it does not consider infrequent sub-graphs and tries to finish the enumeration process as soon as possible; therefore, it only spends time for promising nodes in the pattern tree and discards all other nodes. As an added bonus, the pattern tree notion permits FPF to be implemented and executed in a parallel manner since it is possible to traverse each path of the pattern tree independently. However, FPF is most useful for frequency concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}}, because downward closure is not applicable to {{math|F<sub>1</sub>}}. Nevertheless, the pattern tree is still practical for {{math|F<sub>1</sub>}} if the algorithm runs in parallel. Another advantage of the algorithm is that the implementation of this algorithm has no limitation on motif size, which makes it more amenable to improvements. The pseudocode of FPF (Mavisto) is shown below:<br />
<br />
该算法的优点是它不会考虑不频繁的子图,并尝试尽快完成枚举过程;因此,它只花时间在模式树中用于有希望的节点上,而放弃所有其他节点。还有一点额外的好处,模式树概念允许 FPF 以并行方式实现和执行,因为它可以独立地遍历模式树的每个路径。但是,FPF对于频率概念<math>F_{2}</math>和<math>F_{3}</math>最为有用,因为向下闭包不适用于<math>F_{1}</math>。尽管如此,如果算法并行运行,那么模式树对于<math>F_{1}</math>仍然是可行的。该算法的另一个优点是它的实现对模体大小没有限制,这使其更易于改进。FPF(Mavisto)的伪代码如下所示:<br />
<br />
<br />
{| class="wikitable"<br />
|-<br />
! Mavisto<br />
|-<br />
| '''Data:''' Graph {{math|G}}, target pattern size {{math|t}}, frequency concept {{math|F}}<br />
<br />
'''Result:''' Set {{math|R}} of patterns of size {{math|t}} with maximum frequency.<br />
|-<br />
| {{math|R ← φ}}, {{math|f<sub>max</sub> ← 0}}<br />
<br />
{{math|P ←}}start pattern {{math|p1}} of size 1<br />
<br />
{{math|M<sub>p<sub>1</sub></sub> ←}}all matches of {{math|p<sub>1</sub>}} in {{math|G}}<br />
<br />
'''While''' {{math|P &ne; φ}} '''do'''<br />
<br />
{{pad|1em}}{{math|P<sub>max</sub> ←}}select all patterns from {{math|P}} with maximum size.<br />
<br />
{{pad|1em}}{{math|P ←}} select pattern with maximum frequency from {{math|P<sub>max</sub>}}<br />
<br />
{{pad|1em}}{{math|Ε {{=}} ''ExtensionLoop''(G, p, M<sub>p</sub>)}}<br />
<br />
{{pad|1em}}'''Foreach''' pattern {{math|p &isin; E}}<br />
<br />
{{pad|2em}}'''If''' {{math|F {{=}} F<sub>1</sub>}} '''then''' {{math|f ← ''size''(M<sub>p</sub>)}}<br />
<br />
{{pad|2em}}'''Else''' {{math|f ←}} ''Maximum Independent set''{{math|(F, M<sub>p</sub>)}}<br />
<br />
{{pad|2em}}'''End'''<br />
<br />
{{pad|2em}}'''If''' {{math|''size''(p) {{=}} t}} '''then'''<br />
<br />
{{pad|3em}}'''If''' {{math|f {{=}} f<sub>max</sub>}} '''then''' {{math|R ← R ⋃ {p}}}<br />
<br />
{{pad|3em}}'''Else if''' {{math|f > f<sub>max</sub>}} '''then''' {{math|R ← {p}}}; {{math|f<sub>max</sub> ← f}}<br />
<br />
{{pad|3em}}'''End'''<br />
<br />
{{pad|2em}}'''Else'''<br />
<br />
{{pad|3em}}'''If''' {{math|F {{=}} F<sub>1</sub>}} '''or''' {{math|f &ge; f<sub>max</sub>}} '''then''' {{math|P ← P ⋃ {p}}}<br />
<br />
{{pad|3em}}'''End'''<br />
<br />
{{pad|2em}}'''End'''<br />
<br />
{{pad|1em}}'''End'''<br />
<br />
'''End'''<br />
|}<br />
<br />
<br />
{|class="wikitable"<br />
|+ Mavisto<br />
|-<br />
!rowspan="1"|数据: 图 <math>G</math>, 目标模式规模 <math>t</math>, 频率概念 <math>F</math>。<br><br />
结果: 以最大频率设置大小为 <math>t</math>的模式 <math>R</math>.<br><br />
|-<br />
|rowspan="20"| <math>R \leftarrow \Phi , f_{max}\leftarrow 0</math><br><br />
<math>P \leftarrow</math> 开始于大小为1的模式 <math>p_{1}</math><br />
<br />
<math>M_{p_{1}} \leftarrow </math> 图 <math>G</math> 中模式 <math>p_{1}</math> 的所有匹配<br />
<br />
当 <math>P \neq \Phi </math> 时,执行:<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;<math>P_{max} \leftarrow</math> 从 <math>P</math> 中选择最大规模的所有模式<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;<math>P\leftarrow</math> 从 <math>P_{max}</math> 中选择最大频率的模式<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;<math>E = ExtensionLoop(G, p, M_{p})</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;对于 <math>p \in E </math> 的所有模式:<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>F = F_{1}</math> ,那么 <math>f \leftarrow size(M_{p})</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他<math>f \leftarrow</math> 最大独立集 <math>(F, M_{p})</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>size(p) = t</math> ,那么<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>f = f_{max}</math> ,那么 <math>R \leftarrow R \cup \{p\}</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他 如果 <math>f > f_{max}</math> ,那么 <math>R \leftarrow \{p\}</math>; <math>f_{max} \leftarrow f</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>F = F_{1} or f \geq f_{max}</math> ,那么 <math> P \leftarrow P \cup \{p\}</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
结束<br />
|}<br />
<br />
===ESU (FANMOD)算法及对应的软件===<br />
The sampling bias of Kashtan ''et al.'' <ref name="kas1" /> provided great impetus for designing better algorithms for the NM discovery problem. Although Kashtan ''et al.'' tried to settle this drawback by means of a weighting scheme, this method imposed an undesired overhead on the running time as well a more complicated implementation. This tool is one of the most useful ones, as it supports visual options and also is an efficient algorithm with respect to time. But, it has a limitation on motif size as it does not allow searching for motifs of size 9 or higher because of the way the tool is implemented.<br />
<br />
由于Kashtan等学者发现的采样偏差问题,所以针对NM discovery problem需要设计更好的算法。虽然Kashtan等人尝试用加权法来解决这个弊端,但这个方法在运行上,消耗了过多的运行时间,且实现起来也变得更加复杂。但这个工具还是最好用的工具之一,因为它支持可视化选项,同时也『是个节约时间的算法』。但是,它在所支持的模体的规模大小还是有局限性。由于该工具在具体实施中,不允许搜索规模大小为9或者更大的模体。<br />
<br />
Wernicke <ref name="wer1" /> introduced an algorithm named ''RAND-ESU'' that provides a significant improvement over ''mfinder''.<ref name="kas1" /> This algorithm, which is based on the exact enumeration algorithm ''ESU'', has been implemented as an application called ''FANMOD''.<ref name="wer1" /> ''RAND-ESU'' is a NM discovery algorithm applicable for both directed and undirected networks, effectively exploits an unbiased node sampling throughout the network, and prevents overcounting sub-graphs more than once. Furthermore, ''RAND-ESU'' uses a novel analytical approach called ''DIRECT'' for determining sub-graph significance instead of using an ensemble of random networks as a Null-model. The ''DIRECT'' method estimates the sub-graph concentration without explicitly generating random networks.<ref name="wer1" /> Empirically, the DIRECT method is more efficient in comparison with the random network ensemble in case of sub-graphs with a very low concentration; however, the classical Null-model is faster than the ''DIRECT'' method for highly concentrated sub-graphs.<ref name="mil1" /><ref name="wer1" /> In the following, we detail the ''ESU'' algorithm and then we show how this exact algorithm can be modified efficiently to ''RAND-ESU'' that estimates sub-graphs concentrations.<br />
<br />
Weinicke引入了一种叫RAND-ESU的算法,这个新引入的算法比Mfinder软件有着更显著的提升。RAND-ESU基于精准的ESU算法,已有对应的软件FANMOD。RAND-ESU是一种[NM算法],可应用于定向的或者不定向的网络中,能够有效的在网络中利用无偏差节点进行采样,以及保证了一个子图仅仅被搜索一次,且不会产生无意义的子图。并且,RAND-ESU采用了一个叫做DIRECT的全新的分析方式,从而来确定子图的重要性,而不是用随机网络的组合来建立『Null模型』。DIRECT方法可以不用大量生成随机网络就能估计子图的浓度。实际上,相较于用随机网络组合分析比较低集中度的子图来说,DIRECT这个方法更加的高效。但是,传统的『Null模型』又比DIRECT这个算法能更加快速地解决高度集中的子图。接下来,我们将详细讲述ESU算法和展示如何把这种精确的算法调整为RAND-ESU算法去估计子图的浓度。<br />
<br />
The algorithms ''ESU'' and ''RAND-ESU'' are fairly simple, and hence easy to implement. ''ESU'' first finds the set of all induced sub-graphs of size {{math|k}}, let {{math|S<sub>k</sub>}} be this set. ''ESU'' can be implemented as a recursive function; the running of this function can be displayed as a tree-like structure of depth {{math|k}}, called the ESU-Tree (see figure). Each of the ESU-Tree nodes indicate the status of the recursive function that entails two consecutive sets SUB and EXT. SUB refers to nodes in the target network that are adjacent and establish a partial sub-graph of size {{math|{{!}}SUB{{!}} ≤ k}}. If {{math|{{!}}SUB{{!}} {{=}} k}}, the algorithm has found an induced complete sub-graph, so {{math|S<sub>k</sub> {{=}} SUB ∪ S<sub>k</sub>}}. However, if {{math|{{!}}SUB{{!}} < k}}, the algorithm must expand SUB to achieve cardinality {{math|k}}. This is done by the EXT set that contains all the nodes that satisfy two conditions: First, each of the nodes in EXT must be adjacent to at least one of the nodes in SUB; second, their numerical labels must be larger than the label of first element in SUB. The first condition makes sure that the expansion of SUB nodes yields a connected graph and the second condition causes ESU-Tree leaves (see figure) to be distinct; as a result, it prevents overcounting. Note that, the EXT set is not a static set, so in each step it may expand by some new nodes that do not breach the two conditions. The next step of ESU involves classification of sub-graphs placed in the ESU-Tree leaves into non-isomorphic size-{{math|k}} graph classes; consequently, ESU determines sub-graphs frequencies and concentrations. This stage has been implemented simply by employing McKay's ''nauty'' algorithm,<ref name="mck1">{{cite journal |author=McKay BD |title=Practical graph isomorphism |journal=Congressus Numerantium |year=1981 |volume=30 |pages=45–87|bibcode=2013arXiv1301.1493M |arxiv=1301.1493 }}</ref><ref name="mck2">{{cite journal |author=McKay BD |title=Isomorph-free exhaustive generation |journal=Journal of Algorithms |year=1998 |volume=26 |issue=2 |pages=306–324 |doi=10.1006/jagm.1997.0898}}</ref> which classifies each sub-graph by performing a graph isomorphism test. Therefore, ESU finds the set of all induced {{math|k}}-size sub-graphs in a target graph by a recursive algorithm and then determines their frequency using an efficient tool.<br />
<br />
ESU和RAND-ESU两种算法都比较简捷,所以实现起来都很容易。『ESU首先找到大小为k的所有诱导子图的集合』,并命名这个集合为Sk。因为EUS以递归函数的形式实现,该函数的运行可以演示为『k级』的树状结构,称为ESU-Tree(见图)。每一个在ESU-Tree上的节点都表示递归函数的状态,这个递归函数需要两个连续集合的SUB和EXT。『SUB指的是在目标网络的相邻节点上,并且是一部分的层级绝对值大小小于等于k的子图集合。』如果SUB集合层级的绝对值等于k,那么这个算法可以找到一个『完整的诱导子图』,所以在此情况下Sk等于SUB与Sk的并集。相反,如果它的绝对值小于k,那么这个算法必须把SUB扩大,才能实现基数为k。『EXT这个集合包含了所有的满足以下两个情况的节点。第一,每个在EXT的节点必须至少与在SUB的一个节点相邻。第二,他们的下标必须比在SUB的第一个元素大。』???第一个条件保证了『SUB节点的展开产生相关的图』,第二个条件能使ESU-Tree树状图上的分支变得离散。所以,这个方法可以避免过度计算。注意,EXT集合不是一个固定的集合。所以每一步都有可能扩展满足于以上两个条件的新节点。下一步包含了在ESU-Tree分支上的子图的分类,『将它们分为非同构的大小为k的图类』。因此,ESU决定了子图的『频率以及浓度』。这一阶段的实施仅通过运用McKay的nauty算法,这一算法可以通过图的同构测试来把每个子图进行分类。所以,ESU能够在目标图中通过递归算法,找到所有规模大小为k的诱导子图集合,且使用高效的工具来确定他们的『频率』。<br />
<br />
The procedure of implementing ''RAND-ESU'' is quite straightforward and is one of the main advantages of ''FANMOD''. One can change the ''ESU'' algorithm to explore just a portion of the ESU-Tree leaves by applying a probability value {{math|0 ≤ p<sub>d</sub> ≤ 1}} for each level of the ESU-Tree and oblige ''ESU'' to traverse each child node of a node in level {{math|d-1}} with probability {{math|p<sub>d</sub>}}. This new algorithm is called ''RAND-ESU''. Evidently, when {{math|p<sub>d</sub> {{=}} 1}} for all levels, ''RAND-ESU'' acts like ''ESU''. For {{math|p<sub>d</sub> {{=}} 0}} the algorithm finds nothing. Note that, this procedure ensures that the chances of visiting each leaf of the ESU-Tree are the same, resulting in ''unbiased'' sampling of sub-graphs through the network. The probability of visiting each leaf is {{math|∏<sub>d</sub>p<sub>d</sub>}} and this is identical for all of the ESU-Tree leaves; therefore, this method guarantees unbiased sampling of sub-graphs from the network. Nonetheless, determining the value of {{math|p<sub>d</sub>}} for {{math|1 ≤ d ≤ k}} is another issue that must be determined manually by an expert to get precise results of sub-graph concentrations.<ref name="cir1" /> While there is no lucid prescript for this matter, the Wernicke provides some general observations that may help in determining p_d values. In summary, ''RAND-ESU'' is a very fast algorithm for NM discovery in the case of induced sub-graphs supporting unbiased sampling method. Although, the main ''ESU'' algorithm and so the ''FANMOD'' tool is known for discovering induced sub-graphs, there is trivial modification to ''ESU'' which makes it possible for finding non-induced sub-graphs, too. The pseudo code of ''ESU (FANMOD)'' is shown below:<br />
运用RAND-ESU的过程十分的简单,这也是FANMOD的一个主要的优点。可以通过对ESU-Tree『树状图』的每个级别应用概率{{math|0 ≤ p<sub>d</sub> ≤ 1}}并强制ESU以概率{{math|p<sub>d</sub>}}遍历{{math|d-1}}级别中节点的每个子节点,来更改ESU算法使其仅搜索ESU-Tree分支的一部分。 这种新的演算方式叫RAND-ESU。显然,当所有阶段{{math|p<sub>d</sub> {{=}} 1}}时,RAND-ESU等同于ESU。当{{math|p<sub>d</sub> {{=}} 0}}时,在这个算法下没有任何意义。注意,这个过程只是确保了可以找到ESU-Tree上的每一分支的机会都是相同的,从而使网络中的子图采样无偏差。访问每个分支的概率为{{math|∏<sub>d</sub>p<sub>d</sub>}},这对于所有ESU-Tree中的分支都是相同的; 因此,该方法可确保从网络中对子图进行无偏采样。但是,设置{{math|1 ≤ d ≤ k}}的{{math|p<sub>d</sub>}}参数是另一个问题,必须由专家人工确定才能获得子图『浓度』的精确结果。尽管对此没有明确的规定,但是Wrenucke提出了一些一般性的观察结论,这些结论有可能可以帮助我们确定p_d值。总的来说,在诱导子图支持无偏采样方法的情况下,RAND-ESU是一个能快速解决『NM discovery problem』的算法。 尽管,ESU算法的主要部分和FANMOD工具是以用来寻找诱导子图而著称的,但只需对ESU进行细小的改动,就可以用来寻找诱导子图。ESU(FANMOD)的伪代码如下:<br />
[[File:ESU-Tree.jpg|thumb|(a) ''A target graph of size 5'', (b) ''the ESU-tree of depth k that is associated to the extraction of sub-graphs of size 3 in the target graph''. Leaves correspond to set S3 or all of the size-3 induced sub-graphs of the target graph (a). Nodes in the ESU-tree include two adjoining sets, the first set contains adjacent nodes called SUB and the second set named EXT holds all nodes that are adjacent to at least one of the SUB nodes and where their numerical labels are larger than the SUB nodes labels. The EXT set is utilized by the algorithm to expand a SUB set until it reaches a desired sub-graph size that are placed at the lowest level of ESU-Tree (or its leaves).]]<br />
<br />
{| class="wikitable"<br />
|-<br />
! Enumeration of ESU (FANMOD)<br />
|-<br />
|'''''EnumerateSubgraphs(G,k)'''''<br />
<br />
'''Input:''' A graph {{math|G {{=}} (V, E)}} and an integer {{math|1 ≤ k ≤ {{!}}V{{!}}}}.<br />
<br />
'''Output:''' All size-{{math|k}} subgraphs in {{math|G}}.<br />
<br />
'''for each''' vertex {{math|v ∈ V}} '''do'''<br />
<br />
{{pad|2em}}{{math|VExtension ← {u ∈ N({v}) {{!}} u > v}}}<br />
<br />
{{pad|2em}}'''call''' {{math|''ExtendSubgraph''({v}, VExtension, v)}}<br />
<br />
'''endfor'''<br />
|-<br />
|'''''ExtendSubgraph(VSubgraph, VExtension, v)'''''<br />
<br />
'''if''' {{math|{{!}}VSubgraph{{!}} {{=}} k}} '''then''' output {{math|G[VSubgraph]}} and '''return'''<br />
<br />
'''while''' {{math|VExtension ≠ ∅}} '''do'''<br />
<br />
{{pad|2em}}Remove an arbitrarily chosen vertex {{math|w}} from {{math|VExtension}}<br />
<br />
{{pad|2em}}{{math|VExtension&prime; ← VExtension ∪ {u ∈ N<sub>excl</sub>(w, VSubgraph) {{!}} u > v}}}<br />
<br />
{{pad|2em}}'''call''' {{math|''ExtendSubgraph''(VSubgraph ∪ {w}, VExtension&prime;, v)}}<br />
<br />
'''return'''<br />
|}<br />
<br />
===NeMoFinder===<br />
Chen ''et al.'' <ref name="che1">{{cite conference |vauthors=Chen J, Hsu W, Li Lee M, etal |title=NeMoFinder: dissecting genome-wide protein-protein interactions with meso-scale network motifs |conference=the 12th ACM SIGKDD international conference on Knowledge discovery and data mining |year=2006 |location=Philadelphia, Pennsylvania, USA |pages=106–115}}</ref> introduced a new NM discovery algorithm called ''NeMoFinder'', which adapts the idea in ''SPIN'' <ref name="hua1">{{cite conference |vauthors=Huan J, Wang W, Prins J, etal |title=SPIN: mining maximal frequent sub-graphs from graph databases |conference=the 10th ACM SIGKDD international conference on Knowledge discovery and data mining |year=2004 |pages=581–586}}</ref> to extract frequent trees and after that expands them into non-isomorphic graphs.<ref name="cir1" /> ''NeMoFinder'' utilizes frequent size-n trees to partition the input network into a collection of size-{{math|n}} graphs, afterward finding frequent size-n sub-graphs by expansion of frequent trees edge-by-edge until getting a complete size-{{math|n}} graph {{math|K<sub>n</sub>}}. The algorithm finds NMs in undirected networks and is not limited to extracting only induced sub-graphs. Furthermore, ''NeMoFinder'' is an exact enumeration algorithm and is not based on a sampling method. As Chen ''et al.'' claim, ''NeMoFinder'' is applicable for detecting relatively large NMs, for instance, finding NMs up to size-12 from the whole ''S. cerevisiae'' (yeast) PPI network as the authors claimed.<ref name="uet1">{{cite journal |vauthors=Uetz P, Giot L, Cagney G, etal |title=A comprehensive analysis of protein-protein interactions in Saccharomyces cerevisiae |journal=Nature |year=2000 |volume=403 |issue=6770 |pages=623–627 |doi=10.1038/35001009 |pmid=10688190|bibcode=2000Natur.403..623U }}</ref><br />
<br />
''NeMoFinder'' consists of three main steps. First, finding frequent size-{{math|n}} trees, then utilizing repeated size-n trees to divide the entire network into a collection of size-{{math|n}} graphs, finally, performing sub-graph join operations to find frequent size-n sub-graphs.<ref name="che1" /> In the first step, the algorithm detects all non-isomorphic size-{{math|n}} trees and mappings from a tree to the network. In the second step, the ranges of these mappings are employed to partition the network into size-n graphs. Up to this step, there is no distinction between ''NeMoFinder'' and an exact enumeration method. However, a large portion of non-isomorphic size-n graphs still remain. ''NeMoFinder'' exploits a heuristic to enumerate non-tree size-n graphs by the obtained information from the preceding steps. The main advantage of the algorithm is in the third step, which generates candidate sub-graphs from previously enumerated sub-graphs. This generation of new size-{{math|n}} sub-graphs is done by joining each previous sub-graph with derivative sub-graphs from itself called ''cousin sub-graphs''. These new sub-graphs contain one additional edge in comparison to the previous sub-graphs. However, there exist some problems in generating new sub-graphs: There is no clear method to derive cousins from a graph, joining a sub-graph with its cousins leads to redundancy in generating particular sub-graph more than once, and cousin determination is done by a canonical representation of the adjacency matrix which is not closed under join operation. ''NeMoFinder'' is an efficient network motif finding algorithm for motifs up to size 12 only for protein-protein interaction networks, which are presented as undirected graphs. And it is not able to work on directed networks which are so important in the field of complex and biological networks. The pseudocode of ''NeMoFinder'' is shown below:<br />
<br />
{| class="wikitable"<br />
|-<br />
! NeMoFinder<br />
|-<br />
|'''Input:'''<br />
<br />
{{math|G}} - PPI network;<br />
<br />
{{math|N}} - Number of randomized networks;<br />
<br />
{{math|K}} - Maximal network motif size;<br />
<br />
{{math|F}} - Frequency threshold;<br />
<br />
{{math|S}} - Uniqueness threshold;<br />
<br />
'''Output:'''<br />
<br />
{{math|U}} - Repeated and unique network motif set;<br />
<br />
{{math|D ← ∅}};<br />
<br />
'''for''' motif-size {{math|k}} '''from''' 3 '''to''' {{math|K}} '''do'''<br />
<br />
{{pad|1em}}{{math|T ← ''FindRepeatedTrees''(k)}};<br />
<br />
{{pad|1em}}{{math|GD<sub>k</sub> ← ''GraphPartition''(G, T)}}<br />
<br />
{{pad|1em}}{{math|D ← D ∪ T}};<br />
<br />
{{pad|1em}}{{math|D&prime; ← T}};<br />
<br />
{{pad|1em}}{{math|i ← k}};<br />
<br />
{{pad|1em}}'''while''' {{math|D&prime; ≠ ∅}} '''and''' {{math|i ≤ k &times; (k - 1) / 2}} '''do'''<br />
<br />
{{pad|2em}}{{math|D&prime; ← ''FindRepeatedGraphs''(k, i, D&prime;)}};<br />
<br />
{{pad|2em}}{{math|D ← D ∪ D&prime;}};<br />
<br />
{{pad|2em}}{{math|i ← i + 1}};<br />
<br />
{{pad|1em}}'''end while'''<br />
<br />
'''end for'''<br />
<br />
'''for''' counter {{math|i}} '''from''' 1 '''to''' {{math|N}} '''do'''<br />
<br />
{{pad|1em}}{{math|G<sub>rand</sub> ← ''RandomizedNetworkGeneration''()}};<br />
<br />
{{pad|1em}}'''for each''' {{math|g ∈ D}} '''do'''<br />
<br />
{{pad|2em}}{{math|''GetRandFrequency''(g, G<sub>rand</sub>)}};<br />
<br />
{{pad|1em}}'''end for'''<br />
<br />
'''end for'''<br />
<br />
{{math|U ← ∅}};<br />
<br />
'''for each''' {{math|g ∈ D}} '''do'''<br />
<br />
{{pad|1em}}{{math|s ← ''GetUniqunessValue''(g)}};<br />
<br />
{{pad|1em}}'''if''' {{math|s ≥ S}} '''then'''<br />
<br />
{{pad|2em}}{{math|U ← U ∪ {g}}};<br />
<br />
{{pad|1em}}'''end if'''<br />
<br />
'''end for'''<br />
<br />
'''return''' {{math|U}};<br />
|}<br />
<br />
===Grochow–Kellis===<br />
Grochow and Kellis <ref name="gro1">{{cite conference|vauthors=Grochow JA, Kellis M |title=Network Motif Discovery Using Sub-graph Enumeration and Symmetry-Breaking |conference=RECOMB |year=2007 |pages=92–106| doi=10.1007/978-3-540-71681-5_7| url=http://www.cs.colorado.edu/~jgrochow/Grochow_Kellis_RECOMB_07_Network_Motifs.pdf}}</ref> proposed an ''exact'' algorithm for enumerating sub-graph appearances. The algorithm is based on a ''motif-centric'' approach, which means that the frequency of a given sub-graph,called the ''query graph'', is exhaustively determined by searching for all possible mappings from the query graph into the larger network. It is claimed <ref name="gro1" /> that a ''motif-centric'' method in comparison to ''network-centric'' methods has some beneficial features. First of all it avoids the increased complexity of sub-graph enumeration. Also, by using mapping instead of enumerating, it enables an improvement in the isomorphism test. To improve the performance of the algorithm, since it is an inefficient exact enumeration algorithm, the authors introduced a fast method which is called ''symmetry-breaking conditions''. During straightforward sub-graph isomorphism tests, a sub-graph may be mapped to the same sub-graph of the query graph multiple times. In the Grochow–Kellis (GK) algorithm symmetry-breaking is used to avoid such multiple mappings. Here we introduce the GK algorithm and the symmetry-breaking condition which eliminates redundant isomorphism tests.<br />
<br />
[[File:Automorphisms of a subgraph.jpg|thumb|(a) ''graph G'', (b) ''illustration of all automorphisms of G that is showed in (a)''. From set AutG we can obtain a set of symmetry-breaking conditions of G given by SymG in (c). Only the first mapping in AutG satisfies the SynG conditions; as a result, by applying SymG in the Isomorphism Extension module the algorithm only enumerate each match-able sub-graph in the network to G once. Note that SynG is not necessarily a unique set for an arbitrary graph G.]]<br />
<br />
The GK algorithm discovers the whole set of mappings of a given query graph to the network in two major steps. It starts with the computation of symmetry-breaking conditions of the query graph. Next, by means of a branch-and-bound method, the algorithm tries to find every possible mapping from the query graph to the network that meets the associated symmetry-breaking conditions. An example of the usage of symmetry-breaking conditions in GK algorithm is demonstrated in figure.<br />
<br />
As it is mentioned above, the symmetry-breaking technique is a simple mechanism that precludes spending time finding a sub-graph more than once due to its symmetries.<ref name="gro1" /><ref name="gro2">{{cite conference|author=Grochow JA |title=On the structure and evolution of protein interaction networks |conference=Thesis M. Eng., Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science|year=2006| url=http://www.cs.toronto.edu/~jgrochow/Grochow_MIT_Masters_06_PPI_Networks.pdf}}</ref> Note that, computing symmetry-breaking conditions requires finding all automorphisms of a given query graph. Even though, there is no efficient (or polynomial time) algorithm for the graph automorphism problem, this problem can be tackled efficiently in practice by McKay's tools.<ref name="mck1" /><ref name="mck2" /> As it is claimed, using symmetry-breaking conditions in NM detection lead to save a great deal of running time. Moreover, it can be inferred from the results in <ref name="gro1" /><ref name="gro2" /> that using the symmetry-breaking conditions results in high efficiency particularly for directed networks in comparison to undirected networks. The symmetry-breaking conditions used in the GK algorithm are similar to the restriction which ''ESU'' algorithm applies to the labels in EXT and SUB sets. In conclusion, the GK algorithm computes the exact number of appearance of a given query graph in a large complex network and exploiting symmetry-breaking conditions improves the algorithm performance. Also, GK algorithm is one of the known algorithms having no limitation for motif size in implementation and potentially it can find motifs of any size.<br />
<br />
===Color-coding approach===<br />
Most algorithms in the field of NM discovery are used to find induced sub-graphs of a network. In 2008, Noga Alon ''et al.'' <ref name="alo1">{{cite journal|author1=Alon N |author2=Dao P |author3=Hajirasouliha I |author4=Hormozdiari F |author5=Sahinalp S.C |title=Biomolecular network motif counting and discovery by color coding |journal=Bioinformatics |year=2008 |volume=24 |issue=13 |pages=i241–i249 |doi=10.1093/bioinformatics/btn163|pmid=18586721 |pmc=2718641 }}</ref> introduced an approach for finding non-induced sub-graphs too. Their technique works on undirected networks such as PPI ones. Also, it counts non-induced trees and bounded treewidth sub-graphs. This method is applied for sub-graphs of size up to 10.<br />
<br />
This algorithm counts the number of non-induced occurrences of a tree {{math|T}} with {{math|k {{=}} O(logn)}} vertices in a network {{math|G}} with {{math|n}} vertices as follows:<br />
<br />
# '''Color coding.''' Color each vertex of input network G independently and uniformly at random with one of the {{math|k}} colors.<br />
# '''Counting.''' Apply a dynamic programming routine to count the number of non-induced occurrences of {{math|T}} in which each vertex has a unique color. For more details on this step, see.<ref name="alo1" /><br />
# Repeat the above two steps {{math|O(e<sup>k</sup>)}} times and add up the number of occurrences of {{math|T}} to get an estimate on the number of its occurrences in {{math|G}}.<br />
<br />
As available PPI networks are far from complete and error free, this approach is suitable for NM discovery for such networks. As Grochow–Kellis Algorithm and this one are the ones popular for non-induced sub-graphs, it is worth to mention that the algorithm introduced by Alon ''et al.'' is less time-consuming than the Grochow–Kellis Algorithm.<ref name="alo1" /><br />
<br />
===MODA===<br />
Omidi ''et al.'' <ref name="omi1">{{cite journal|vauthors=Omidi S, Schreiber F, Masoudi-Nejad A |title=MODA: an efficient algorithm for network motif discovery in biological networks |journal=Genes Genet Syst |year=2009 |volume=84 |issue=5 |pages=385–395 |doi=10.1266/ggs.84.385|pmid=20154426 |doi-access=free }}</ref> introduced a new algorithm for motif detection named ''MODA'' which is applicable for induced and non-induced NM discovery in undirected networks. It is based on the motif-centric approach discussed in the Grochow–Kellis algorithm section. It is very important to distinguish motif-centric algorithms such as MODA and GK algorithm because of their ability to work as query-finding algorithms. This feature allows such algorithms to be able to find a single motif query or a small number of motif queries (not all possible sub-graphs of a given size) with larger sizes. As the number of possible non-isomorphic sub-graphs increases exponentially with sub-graph size, for large size motifs (even larger than 10), the network-centric algorithms, those looking for all possible sub-graphs, face a problem. Although motif-centric algorithms also have problems in discovering all possible large size sub-graphs, but their ability to find small numbers of them is sometimes a significant property.<br />
<br />
Using a hierarchical structure called an ''expansion tree'', the ''MODA'' algorithm is able to extract NMs of a given size systematically and similar to ''FPF'' that avoids enumerating unpromising sub-graphs; ''MODA'' takes into consideration potential queries (or candidate sub-graphs) that would result in frequent sub-graphs. Despite the fact that ''MODA'' resembles ''FPF'' in using a tree like structure, the expansion tree is applicable merely for computing frequency concept {{math|F<sub>1</sub>}}. As we will discuss next, the advantage of this algorithm is that it does not carry out the sub-graph isomorphism test for ''non-tree'' query graphs. Additionally, it utilizes a sampling method in order to speed up the running time of the algorithm.<br />
<br />
Here is the main idea: by a simple criterion one can generalize a mapping of a k-size graph into the network to its same size supergraphs. For example, suppose there is mapping {{math|f(G)}} of graph {{math|G}} with {{math|k}} nodes into the network and we have a same size graph {{math|G&prime;}} with one more edge {{math|&langu, v&rang;}}; {{math|f<sub>G</sub>}} will map {{math|G&prime;}} into the network, if there is an edge {{math|&lang;f<sub>G</sub>(u), f<sub>G</sub>(v)&rang;}} in the network. As a result, we can exploit the mapping set of a graph to determine the frequencies of its same order supergraphs simply in {{math|O(1)}} time without carrying out sub-graph isomorphism testing. The algorithm starts ingeniously with minimally connected query graphs of size k and finds their mappings in the network via sub-graph isomorphism. After that, with conservation of the graph size, it expands previously considered query graphs edge-by-edge and computes the frequency of these expanded graphs as mentioned above. The expansion process continues until reaching a complete graph {{math|K<sub>k</sub>}} (fully connected with {{math|{{frac|k(k-1)|2}}}} edge).<br />
<br />
As discussed above, the algorithm starts by computing sub-tree frequencies in the network and then expands sub-trees edge by edge. One way to implement this idea is called the expansion tree {{math|T<sub>k</sub>}} for each {{math|k}}. Figure shows the expansion tree for size-4 sub-graphs. {{math|T<sub>k</sub>}} organizes the running process and provides query graphs in a hierarchical manner. Strictly speaking, the expansion tree {{math|T<sub>k</sub>}} is simply a [[directed acyclic graph]] or DAG, with its root number {{math|k}} indicating the graph size existing in the expansion tree and each of its other nodes containing the adjacency matrix of a distinct {{math|k}}-size query graph. Nodes in the first level of {{math|T<sub>k</sub>}} are all distinct {{math|k}}-size trees and by traversing {{math|T<sub>k</sub>}} in depth query graphs expand with one edge at each level. A query graph in a node is a sub-graph of the query graph in a node's child with one edge difference. The longest path in {{math|T<sub>k</sub>}} consists of {{math|(k<sup>2</sup>-3k+4)/2}} edges and is the path from the root to the leaf node holding the complete graph. Generating expansion trees can be done by a simple routine which is explained in.<ref name="omi1" /><br />
<br />
''MODA'' traverses {{math|T<sub>k</sub>}} and when it extracts query trees from the first level of {{math|T<sub>k</sub>}} it computes their mapping sets and saves these mappings for the next step. For non-tree queries from {{math|T<sub>k</sub>}}, the algorithm extracts the mappings associated with the parent node in {{math|T<sub>k</sub>}} and determines which of these mappings can support the current query graphs. The process will continue until the algorithm gets the complete query graph. The query tree mappings are extracted using the Grochow–Kellis algorithm. For computing the frequency of non-tree query graphs, the algorithm employs a simple routine that takes {{math|O(1)}} steps. In addition, ''MODA'' exploits a sampling method where the sampling of each node in the network is linearly proportional to the node degree, the probability distribution is exactly similar to the well-known Barabási-Albert preferential attachment model in the field of complex networks.<ref name="bar1">{{cite journal|vauthors=Barabasi AL, Albert R |title=Emergence of scaling in random networks |journal=Science |year=1999 |volume=286 |issue=5439 |pages=509–512 |doi=10.1126/science.286.5439.509 |pmid=10521342|bibcode=1999Sci...286..509B |arxiv=cond-mat/9910332 }}</ref> This approach generates approximations; however, the results are almost stable in different executions since sub-graphs aggregate around highly connected nodes.<ref name="vaz1">{{cite journal |vauthors=Vázquez A, Dobrin R, Sergi D, etal |title=The topological relationship between the large-scale attributes and local interaction patterns of complex networks |journal=PNAS |year=2004 |volume=101 |issue=52 |pages=17940–17945 |doi=10.1073/pnas.0406024101|pmid=15598746 |pmc=539752 |bibcode=2004PNAS..10117940V |arxiv=cond-mat/0408431 }}</ref> The pseudocode of ''MODA'' is shown below:<br />
<br />
[[File:Expansion Tree.jpg|thumb|''Illustration of the expansion tree T4 for 4-node query graphs''. At the first level, there are non-isomorphic k-size trees and at each level, an edge is added to the parent graph to form a child graph. In the second level, there is a graph with two alternative edges that is shown by a dashed red edge. In fact, this node represents two expanded graphs that are isomorphic.<ref name="omi1" />]]<br />
<br />
{| class="wikitable"<br />
|-<br />
! MODA<br />
|-<br />
|'''Input:''' {{math|G}}: Input graph, {{math|k}}: sub-graph size, {{math|Δ}}: threshold value<br />
<br />
'''Output:''' Frequent Subgraph List: List of all frequent {{math|k}}-size sub-graphs<br />
<br />
'''Note:''' {{math|F<sub>G</sub>}}: set of mappings from {{math|G}} in the input graph {{math|G}}<br />
<br />
'''fetch''' {{math|T<sub>k</sub>}}<br />
<br />
'''do'''<br />
<br />
{{pad|1em}}{{math|G&prime; {{=}} ''Get-Next-BFS''(T<sub>k</sub>)}} // {{math|G&prime;}} is a query graph<br />
<br />
{{pad|1em}}if {{math|{{!}}E(G&prime;){{!}} {{=}} (k – 1)}}<br />
<br />
{{pad|1em}}'''call''' {{math|''Mapping-Module''(G&prime;, G)}}<br />
<br />
{{pad|1em}}'''else'''<br />
<br />
{{pad|2em}}'''call''' {{math|''Enumerating-Module''(G&prime;, G, T<sub>k</sub>)}}<br />
<br />
{{pad|1em}}'''end if'''<br />
<br />
{{pad|1em}}'''save''' {{math|F<sub>2</sub>}}<br />
<br />
{{pad|1em}}'''if''' {{math|{{!}}F<sub>G</sub>{{!}} > Δ}} '''then'''<br />
<br />
{{pad|2em}}add {{math|G&prime;}} into Frequent Subgraph List<br />
<br />
{{pad|1em}}'''end if'''<br />
<br />
'''Until''' {{math|{{!}}E(G'){{!}} {{=}} (k – 1)/2}}<br />
<br />
'''return''' Frequent Subgraph List<br />
|}<br />
<br />
===Kavosh===<br />
A recently introduced algorithm named ''Kavosh'' <ref name="kash1">{{cite journal|vauthors=Kashani ZR, Ahrabian H, Elahi E, Nowzari-Dalini A, Ansari ES, Asadi S, Mohammadi S, Schreiber F, Masoudi-Nejad A |title=Kavosh: a new algorithm for finding network motifs |journal=BMC Bioinformatics |year=2009 |volume=10 |issue=318|pages=318 |doi=10.1186/1471-2105-10-318 |pmid=19799800 |pmc=2765973}} </ref> aims at improved main memory usage. ''Kavosh'' is usable to detect NM in both directed and undirected networks. The main idea of the enumeration is similar to the ''GK'' and ''MODA'' algorithms, which first find all {{math|k}}-size sub-graphs that a particular node participated in, then remove the node, and subsequently repeat this process for the remaining nodes.<ref name="kash1" /><br />
<br />
For counting the sub-graphs of size {{math|k}} that include a particular node, trees with maximum depth of k, rooted at this node and based on neighborhood relationship are implicitly built. Children of each node include both incoming and outgoing adjacent nodes. To descend the tree, a child is chosen at each level with the restriction that a particular child can be included only if it has not been included at any upper level. After having descended to the lowest level possible, the tree is again ascended and the process is repeated with the stipulation that nodes visited in earlier paths of a descendant are now considered unvisited nodes. A final restriction in building trees is that all children in a particular tree must have numerical labels larger than the label of the root of the tree. The restrictions on the labels of the children are similar to the conditions which ''GK'' and ''ESU'' algorithm use to avoid overcounting sub-graphs.<br />
<br />
The protocol for extracting sub-graphs makes use of the compositions of an integer. For the extraction of sub-graphs of size {{math|k}}, all possible compositions of the integer {{math|k-1}} must be considered. The compositions of {{math|k-1}} consist of all possible manners of expressing {{math|k-1}} as a sum of positive integers. Summations in which the order of the summands differs are considered distinct. A composition can be expressed as {{math|k<sub>2</sub>,k<sub>3</sub>,…,k<sub>m</sub>}} where {{math|k<sub>2</sub> + k<sub>3</sub> + … + k<sub>m</sub> {{=}} k-1}}. To count sub-graphs based on the composition, {{math|k<sub>i</sub>}} nodes are selected from the {{math|i}}-th level of the tree to be nodes of the sub-graphs ({{math|i {{=}} 2,3,…,m}}). The {{math|k-1}} selected nodes along with the node at the root define a sub-graph within the network. After discovering a sub-graph involved as a match in the target network, in order to be able to evaluate the size of each class according to the target network, ''Kavosh'' employs the ''nauty'' algorithm <ref name="mck1" /><ref name="mck2" /> in the same way as ''FANMOD''. The enumeration part of Kavosh algorithm is shown below:<br />
<br />
{| class="wikitable"<br />
|-<br />
! Enumeration of Kavosh<br />
|-<br />
|'''''Enumerate_Vertex(G, u, S, Remainder, i)'''''<br />
<br />
'''Input:''' {{math|G}}: Input graph<br><br />
{{pad|3em}}{{math|u}}: Root vertex<br><br />
{{pad|3em}}{{math|S}}: selection ({{math|S {{=}} { S<sub>0</sub>,S<sub>1</sub>,...,S<sub>k-1</sub>}}} is an array of the set of all {{math|S<sub>i</sub>}})<br><br />
{{pad|3em}}{{math|Remainder}}: number of remaining vertices to be selected<br><br />
{{pad|3em}}{{math|i}}: Current depth of the tree.<br><br />
'''Output:''' all {{math|k}}-size sub-graphs of graph {{math|G}} rooted in {{math|u}}.<br />
<br />
'''if''' {{math|Remainder {{=}} 0}} '''then'''<br><br />
{{pad|1em}}'''return'''<br><br />
'''else'''<br><br />
{{pad|1em}}{{math|ValList ← ''Validate''(G, S<sub>i-1</sub>, u)}}<br><br />
{{pad|1em}}{{math|n<sub>i</sub> ← ''Min''({{!}}ValList{{!}}, Remainder)}}<br><br />
{{pad|1em}}'''for''' {{math|k<sub>i</sub> {{=}} 1}} '''to''' {{math|n<sub>i</sub>}} '''do'''<br><br />
{{pad|2em}}{{math|C ← ''Initial_Comb''(ValList, k<sub>i</sub>)}}<br><br />
{{pad|2em}}(Make the first vertex combination selection according)<br><br />
{{pad|2em}}'''repeat'''<br><br />
{{pad|3em}}{{math|S<sub>i</sub> ← C}}<br><br />
{{pad|3em}}{{math|''Enumerate_Vertex''(G, u, S, Remainder-k<sub>i</sub>, i+1)}}<br><br />
{{pad|3em}}{{math|''Next_Comb''(ValList, k<sub>i</sub>)}}<br><br />
{{pad|3em}}(Make the next vertex combination selection according)<br><br />
{{pad|2em}}'''until''' {{math|C {{=}} NILL}}<br><br />
{{pad|2em}}'''end for'''<br><br />
{{pad|1em}}'''for each''' {{math|v ∈ ValList}} '''do'''<br><br />
{{pad|2em}}{{math|Visited[v] ← false}}<br><br />
{{pad|1em}}'''end for'''<br><br />
'''end if'''<br />
|-<br />
|'''''Validate(G, Parents, u)'''''<br><br />
'''Input:''' {{math|G}}: input graph, {{math|Parents}}: selected vertices of last layer, {{math|u}}: Root vertex.<br><br />
'''Output:''' Valid vertices of the current level.<br />
<br />
{{math|ValList ← NILL}}<br><br />
'''for each''' {{math|v ∈ Parents}} '''do'''<br><br />
{{pad|1em}}'''for each''' {{math|w ∈ Neighbor[u]}} '''do'''<br><br />
{{pad|2em}}'''if''' {{math|label[u] < label[w]}} '''AND NOT''' {{math|Visited[w]}} '''then'''<br><br />
{{pad|3em}}{{math|Visited[w] ← true}}<br><br />
{{pad|3em}}{{math|ValList {{=}} ValList + w}}<br><br />
{{pad|2em}}'''end if'''<br><br />
{{pad|1em}}'''end for'''<br><br />
'''end for'''<br><br />
'''return''' {{math|ValList}}<br><br />
|}<br />
<br />
Recently a ''Cytoscape'' plugin called ''CytoKavosh'' <ref name="mas2">{{cite journal|author1=Ali Masoudi-Nejad |author2=Mitra Anasariola |author3=Ali Salehzadeh-Yazdi |author4=Sahand Khakabimamaghani |title=CytoKavosh: a Cytoscape Plug-in for Finding Network Motifs in Large Biological Networks |journal=PLoS ONE |volume=7 |issue=8 |pages=e43287 |year=2012 |doi=10.1371/journal.pone.0043287|pmid=22952659 |pmc=3430699 |bibcode=2012PLoSO...743287M }} </ref> is developed for this software. It is available via ''Cytoscape'' web page [http://apps.cytoscape.org/apps/cytokavosh].<br />
<br />
===G-Tries===<br />
2010年, Pedro Ribeiro 和 Fernando Silva 提出了一个叫做''g-trie''的新数据结构,用来存储一组子图。<ref name="rib1">{{cite conference|vauthors=Ribeiro P, Silva F |title=G-Tries: an efficient data structure for discovering network motifs |conference=ACM 25th Symposium On Applied Computing - Bioinformatics Track |location=Sierre, Switzerland |year=2010 |pages=1559–1566 |url=http://www.nrcbioinformatics.ca/acmsac2010/}}</ref>这个在概念上类似前缀树的数据结构,根据子图结构来进行存储,并找出了每个子图在一个更大的图中出现的次数。这个数据结构有一个突出的方面:在应用于模体发现算法时,主网络中的子图需要进行评估。因此,在随机网络中寻找那些在不在主网络中的子图,这个消耗时间的步骤就不再需要执行了。<br />
<br />
''g-trie'' 是一个存储一组图的多叉树。每一个树节点都存储着一个'''图节点'''及其'''对应的到前一个节点的边'''的信息。从根节点到叶节点的一条路径对应一个图。一个 g-trie 节点的子孙节点共享一个子图(即每一次路径的分叉意味着从一个子图结构中扩展出不同的图结构,而这些扩展出来的图结构自然有着相同的子图结构)。如何构造一个 ''g-trie'' 在<ref name="rib1" />中有详细描述。构造好一个 ''g-trie'' 以后,需要进行计数步骤。计数流程的主要思想是回溯所有可能的子图,同时进行同构性测试。这种回溯技术本质上和其他以模体为中心的方法,比如''MODA'' 和 ''GK'' 算法中使用的技术是一样的。这种技术利用了共同的子结构,亦即在一定时间内,几个不同的候选子图中存在部分是同构的。<br />
<br />
在上述算法中,''G-Tries'' 是最快的。然而,它的一个缺点是内存的超量使用,这局限了它在个人电脑运行时所能发现的模体的大小<br />
<br />
===对比===<br />
<br />
下面的表格和数据显示了在各种标准网络中运行上述算法所获得的结果。这些结果皆获取于各自相应的来源<ref name="omi1" /><ref name="kash1" /><ref name="rib1" /> ,因此需要独立地对待它们。<br />
<br />
[[Image:Runtimes of algorithms.jpg|thumb|''Runtimes of Grochow–Kellis, mfinder, FANMOD, FPF and MODA for subgraphs from three nodes up to nine nodes''.<ref name="omi1" />]]<br />
<br />
{|class="wikitable"<br />
|+ Grochow–Kellis, FANMOD, 和 G-Trie 在5个不同网络上生成含3到9个节点子图所用的运行时间 <ref name="rib1" /><br />
|-<br />
!rowspan="2"|网络<br />
!rowspan="2"|子图大小<br />
!colspan="3"|原始网络数据<br />
!colspan="3"|随机网络平均数据<br />
|-<br />
!FANMOD<br />
!GK<br />
!G-Trie<br />
!FANMOD<br />
!GK<br />
!G-Trie<br />
|-<br />
|rowspan="5"|Dolphins<br />
|5 || 0.07 || 0.03 || 0.01 || 0.13 || 0.04 || 0.01<br />
|-<br />
|6||0.48||0.28||0.04||1.14||0.35||0.07<br />
|-<br />
|7||3.02||3.44||0.23||8.34||3.55||0.46<br />
|-<br />
|8||19.44||73.16||1.69||67.94||37.31||4.03<br />
|-<br />
|9||100.86||2984.22||6.98||493.98||366.79||24.84<br />
|-<br />
|rowspan="3"|Circuit<br />
|6||0.49||0.41||0.03||0.55||0.24||0.03<br />
|-<br />
|7||3.28||3.73||0.22||3.53||1.34||0.17<br />
|-<br />
|8||17.78||48.00||1.52||21.42||7.91||1.06<br />
|-<br />
|rowspan="3"|Social<br />
|3||0.31||0.11||0.02||0.35||0.11||0.02<br />
|-<br />
|4||7.78||1.37||0.56||13.27||1.86||0.57<br />
|-<br />
|5||208.30||31.85||14.88||531.65||62.66||22.11<br />
|-<br />
|rowspan="3"|Yeast<br />
|3||0.47||0.33||0.02||0.57||0.35||0.02<br />
|-<br />
|4||10.07||2.04||0.36||12.90||2.25||0.41<br />
|-<br />
|5||268.51||34.10||12.73||400.13||47.16||14.98<br />
|-<br />
|rowspan="5"|Power<br />
|3||0.51||1.46||0.00||0.91||1.37||0.01<br />
|-<br />
|4||1.38||4.34||0.02||3.01||4.40||0.03<br />
|-<br />
|5||4.68||16.95||0.10||12.38||17.54||0.14<br />
|-<br />
|6||20.36||95.58||0.55||67.65||92.74||0.88<br />
|-<br />
|7||101.04||765.91||3.36||408.15||630.65||5.17<br />
|}<br />
<br />
{|class="wikitable"<br />
|+ mfinder, FANMOD, Mavisto 和 Kavosh 在3个不同网络上生成含3到10个节点子图所用的运行时间<ref name="kash1" /><br />
|-<br />
!&nbsp;<br />
!子图大小→<br />
!rowspan="2"|3<br />
!rowspan="2"|4<br />
!rowspan="2"|5<br />
!rowspan="2"|6<br />
!rowspan="2"|7<br />
!rowspan="2"|8<br />
!rowspan="2"|9<br />
!rowspan="2"|10<br />
|-<br />
!网络↓<br />
!算法↓<br />
|-<br />
|rowspan="4"|E. coli<br />
|Kavosh||0.30||1.84||14.91||141.98||1374.0||13173.7||121110.3||1120560.1<br />
|-<br />
|FANMOD||0.81||2.53||15.71||132.24||1205.9||9256.6||-||-<br />
|-<br />
|Mavisto||13532||-||-||-||-||-||-||-<br />
|-<br />
|Mfinder||31.0||297||23671||-||-||-||-||-<br />
|-<br />
|rowspan="4"|Electronic<br />
|Kavosh||0.08||0.36||8.02||11.39||77.22||422.6||2823.7||18037.5<br />
|-<br />
|FANMOD||0.53||1.06||4.34||24.24||160||967.99||-||-<br />
|-<br />
|Mavisto||210.0||1727||-||-||-||-||-||-<br />
|-<br />
|Mfinder||7||14||109.8||2020.2||-||-||-||-<br />
|-<br />
|rowspan="4"|Social<br />
|Kavosh||0.04||0.23||1.63||10.48||69.43||415.66||2594.19||14611.23<br />
|-<br />
|FANMOD||0.46||0.84||3.07||17.63||117.43||845.93||-||-<br />
|-<br />
|Mavisto||393||1492||-||-||-||-||-||-<br />
|-<br />
|Mfinder||12||49||798||181077||-||-||-||-<br />
|}<br />
<br />
===算法的分类===<br />
正如表格所示,模体发现算法可以分为两大类:基于精确计数的算法,以及使用统计采样以及估计的算法。因为后者并不计数所有子图在主网络中出现的次数,所以第二类算法会更快,却也可能产生带有偏向性的,甚至不现实的结果。<br />
<br />
更深一层地,基于精确计数的算法可以分为'''以网络为中心'''的方法以及以'''子图为中心'''的方法。前者在给定网络中搜索给定大小的子图,而后者首先根据给定大小生成各种可能的非同构图,然后在网络中分别搜索这些生成的图。这两种方法都有各自的优缺点,这些在上文有讨论。<br />
<br />
另一方面,基于估计的方法可能会利用如前面描述过的颜色编码手段,其它的手段则通常会在枚举过程中忽略一些子图(比如,像在 FANMOD 中做的那样),然后只在枚举出来的子图上做估计。<br />
<br />
此外,表格还指出了一个算法能否应用于有向网络或无向网络,以及导出子图或非导出子图。更多信息请参考下方提供的网页和实验室地址及联系方式。<br />
{|class="wikitable"<br />
|+ 模体发现算法的分类<br />
|-<br />
!计数方式<br />
!基础<br />
!算法名称<br />
!有向 / 无向<br />
!导出/ 非导出<br />
|-<br />
| rowspan="9" |精确基数<br />
| rowspan="5" |以网络为中心<br />
|[http://www.weizmann.ac.il/mcb/UriAlon/ mfinder]||皆可||导出<br />
|-<br />
|[http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ ESU (FANMOD)]||皆可||导出<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/Kavosh/ Kavosh] (used in [http://apps.cytoscape.org/apps/cytokavosh CytoKavosh])||皆可||导出<br />
|-<br />
|[http://www.dcc.fc.up.pt/gtries/ G-Tries]||皆可||导出<br />
|-<br />
|[http://nesreenahmed.com/graphlets PGD]<br />
|无向<br />
|导出<br />
|-<br />
|rowspan="4"|以子图为中心<br />
|[http://mavisto.ipk-gatersleben.de/ FPF (Mavisto)]||皆可||导出<br />
|-<br />
|[https://www.msu.edu/~jinchen/ NeMoFinder]||无向||导出<br />
|-<br />
|[http://people.cs.uchicago.edu/~joshuag/index.html Grochow–Kellis]||皆可||Both<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/MODA/ MODA]||皆可||皆可<br />
|-<br />
|rowspan="3"|采样估计<br />
|颜色编码<br />
|[http://www.math.tau.ac.il/~nogaa/ N. Alon] ''et al.''’s Algorithm||无向||非导出<br />
|-<br />
|rowspan="2"|其他手段<br />
|[http://www.weizmann.ac.il/mcb/UriAlon/ mfinder]||皆可||导出<br />
|-<br />
|[http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ ESU (FANMOD)]||皆可||导出<br />
|}<br />
<br />
{|class="wikitable"<br />
|+ 算法提出者的地址和联系方式<br />
|-<br />
!算法<br />
!实验室/研究组<br />
!学院<br />
!大学/研究所<br />
!地址<br />
!电子邮件<br />
|-<br />
|[http://www.weizmann.ac.il/mcb/UriAlon/ mfinder]||Uri Alon's Group||Department of Molecular Cell Biology||Weizmann Institute of Science||Rehovot, Israel, Wolfson, Rm. 607||urialon at weizmann.ac.il<br />
|-<br />
|[http://mavisto.ipk-gatersleben.de/ FPF (Mavisto)]||----||----||Leibniz-Institut für Pflanzengenetik und Kulturpflanzenforschung (IPK)||Corrensstraße 3, D-06466 Stadt Seeland, OT Gatersleben, Deutschland||schreibe at ipk-gatersleben.de<br />
|-<br />
|[http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ ESU (FANMOD)]||Lehrstuhl Theoretische Informatik I||Institut für Informatik||Friedrich-Schiller-Universität Jena||Ernst-Abbe-Platz 2,D-07743 Jena, Deutschland||sebastian.wernicke at gmail.com<br />
|-<br />
|[https://www.msu.edu/~jinchen/ NeMoFinder]||----||School of Computing||National University of Singapore||Singapore 119077||chenjin at comp.nus.edu.sg<br />
|-<br />
|[http://www.cs.colorado.edu/~jgrochow/ Grochow–Kellis]||CS Theory Group & Complex Systems Group||Computer Science||University of Colorado, Boulder||1111 Engineering Dr. ECOT 717, 430 UCB Boulder, CO 80309-0430 USA||jgrochow at colorado.edu<br />
|-<br />
|[http://www.math.tau.ac.il/~nogaa/ N. Alon] ''et al.''’s Algorithm||Department of Pure Mathematics||School of Mathematical Sciences||Tel Aviv University||Tel Aviv 69978, Israel||nogaa at post.tau.ac.il<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/MODA/ MODA]||Laboratory of Systems Biology and Bioinformatics (LBB)||Institute of Biochemistry and Biophysics (IBB)||University of Tehran||Enghelab Square, Enghelab Ave, Tehran, Iran||amasoudin at ibb.ut.ac.ir<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/Kavosh/ Kavosh] (used in [http://apps.cytoscape.org/apps/cytokavosh CytoKavosh])||Laboratory of Systems Biology and Bioinformatics (LBB)||Institute of Biochemistry and Biophysics (IBB)||University of Tehran||Enghelab Square, Enghelab Ave, Tehran, Iran||amasoudin at ibb.ut.ac.ir<br />
|-<br />
|[http://www.dcc.fc.up.pt/gtries/ G-Tries]||Center for Research in Advanced Computing Systems||Computer Science||University of Porto||Rua Campo Alegre 1021/1055, Porto, Portugal||pribeiro at dcc.fc.up.pt<br />
|-<br />
|[http://nesreenahmed.com/graphlets PGD]<br />
|Network Learning and Discovery Lab<br />
|Department of Computer Science<br />
|Purdue University<br />
|Purdue University, 305 N University St, West Lafayette, IN 47907<br />
|nkahmed@purdue.edu<br />
|}<br />
<br />
==Well-established motifs and their functions==<br />
Much experimental work has been devoted to understanding network motifs in [[gene regulatory networks]]. These networks control which genes are expressed in the cell in response to biological signals. The network is defined such that genes are nodes, and directed edges represent the control of one gene by a transcription factor (regulatory protein that binds DNA) encoded by another gene. Thus, network motifs are patterns of genes regulating each other's transcription rate. When analyzing transcription networks, it is seen that the same network motifs appear again and again in diverse organisms from bacteria to human. The transcription network of ''[[Escherichia coli|E. coli]]'' and yeast, for example, is made of three main motif families, that make up almost the entire network. The leading hypothesis is that the network motif were independently selected by evolutionary processes in a converging manner,<ref name="bab1">{{cite journal |vauthors=Babu MM, Luscombe NM, Aravind L, Gerstein M, Teichmann SA |title=Structure and evolution of transcriptional regulatory networks |journal=Current Opinion in Structural Biology |volume=14 |issue=3 |pages=283–91 |date=June 2004 |pmid=15193307 |doi=10.1016/j.sbi.2004.05.004 |citeseerx=10.1.1.471.9692 }}</ref><ref name="con1">{{cite journal |vauthors=Conant GC, Wagner A |title=Convergent evolution of gene circuits |journal=Nat. Genet. |volume=34 |issue=3 |pages=264–6 |date=July 2003 |pmid=12819781 |doi=10.1038/ng1181}}</ref> since the creation or elimination of regulatory interactions is fast on evolutionary time scale, relative to the rate at which genes change,<ref name="bab1"/><ref name="con1"/><ref name="dek1">{{cite journal |vauthors=Dekel E, Alon U |title=Optimality and evolutionary tuning of the expression level of a protein |journal=Nature |volume=436 |issue=7050 |pages=588–92 |date=July 2005 |pmid=16049495 |doi=10.1038/nature03842 |bibcode=2005Natur.436..588D }}</ref> Furthermore, experiments on the dynamics generated by network motifs in living cells indicate that they have characteristic dynamical functions. This suggests that the network motif serve as building blocks in gene regulatory networks that are beneficial to the organism.<br />
<br />
The functions associated with common network motifs in transcription networks were explored and demonstrated by several research projects both theoretically and experimentally. Below are some of the most common network motifs and their associated function.<br />
<br />
===Negative auto-regulation (NAR)===<br />
[[Image:Autoregulation motif.png|thumb|Schematic representation of an auto-regulation motif]]<br />
One of simplest and most abundant network motifs in ''[[Escherichia coli|E. coli]]'' is negative auto-regulation in which a transcription factor (TF) represses its own transcription. This motif was shown to perform two important functions. The first function is response acceleration. NAR was shown to speed-up the response to signals both theoretically <ref name="zab1">{{cite journal |doi=10.1016/j.jtbi.2011.06.021 |author=Zabet NR |title=Negative feedback and physical limits of genes |journal=Journal of Theoretical Biology |volume= 284|issue=1 |pages=82–91 |date=September 2011 |pmid=21723295 |arxiv=1408.1869 |citeseerx=10.1.1.759.5418 }}</ref> and experimentally. This was first shown in a synthetic transcription network<ref name="ros1">{{cite journal |doi=10.1016/S0022-2836(02)00994-4 |vauthors=Rosenfeld N, Elowitz MB, Alon U |title=Negative autoregulation speeds the response times of transcription networks |journal=J. Mol. Biol. |volume=323 |issue=5 |pages=785–93 |date=November 2002 |pmid=12417193 |citeseerx=10.1.1.126.2604 }}</ref> and later on in the natural context in the SOS DNA repair system of E .coli.<ref name="cam1">{{cite journal |vauthors=Camas FM, Blázquez J, Poyatos JF |title=Autogenous and nonautogenous control of response in a genetic network |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=103 |issue=34 |pages=12718–23 |date=August 2006 |pmid=16908855 |pmc=1568915 |doi=10.1073/pnas.0602119103 |bibcode=2006PNAS..10312718C }}</ref> The second function is increased stability of the auto-regulated gene product concentration against stochastic noise, thus reducing variations in protein levels between different cells.<ref name="bec1">{{cite journal |vauthors=Becskei A, Serrano L |title=Engineering stability in gene networks by autoregulation |journal=Nature |volume=405 |issue=6786 |pages=590–3 |date=June 2000 |pmid=10850721 |doi=10.1038/35014651}}</ref><ref name="dub1">{{cite journal |vauthors=Dublanche Y, Michalodimitrakis K, Kümmerer N, Foglierini M, Serrano L |title=Noise in transcription negative feedback loops: simulation and experimental analysis |journal=Mol. Syst. Biol. |volume=2 |pages=41 |year=2006 |pmid=16883354 |pmc=1681513 |doi=10.1038/msb4100081 |issue=1}}</ref><ref name="shi1">{{cite journal |vauthors=Shimoga V, White J, Li Y, Sontag E, Bleris L |title= Synthetic mammalian transgene negative autoregulation |journal=Mol. Syst. Biol. |volume=9 |pages=670 |year=2013|doi=10.1038/msb.2013.27|pmid= 23736683 |pmc= 3964311 }}</ref><br />
<br />
<br />
<br />
===Positive auto-regulation (PAR)===<br />
Positive auto-regulation (PAR) occurs when a transcription factor enhances its own rate of production. Opposite to the NAR motif this motif slows the response time compared to simple regulation.<ref name="mae1">{{cite journal |vauthors=Maeda YT, Sano M |title=Regulatory dynamics of synthetic gene networks with positive feedback |journal=J. Mol. Biol. |volume=359 |issue=4 |pages=1107–24 |date=June 2006 |pmid=16701695 |doi=10.1016/j.jmb.2006.03.064 }}</ref> In the case of a strong PAR the motif may lead to a bimodal distribution of protein levels in cell populations.<ref name="bec2">{{cite journal |vauthors=Becskei A, Séraphin B, Serrano L |title=Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion |journal=EMBO J. |volume=20 |issue=10 |pages=2528–35 |date=May 2001 |pmid=11350942 |pmc=125456 |doi=10.1093/emboj/20.10.2528}}</ref><br />
<br />
===Feed-forward loops (FFL)===<br />
[[Image:Feed-forward motif.GIF|thumb|Schematic representation of a Feed-forward motif]]<br />
This motif is commonly found in many gene systems and organisms. The motif consists of three genes and three regulatory interactions. The target gene C is regulated by 2 TFs A and B and in addition TF B is also regulated by TF A . Since each of the regulatory interactions may either be positive or negative there are possibly eight types of FFL motifs.<ref name="man1">{{cite journal |vauthors=Mangan S, Alon U |title=Structure and function of the feed-forward loop network motif |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=100 |issue=21 |pages=11980–5 |date=October 2003 |pmid=14530388 |pmc=218699 |doi=10.1073/pnas.2133841100 |bibcode=2003PNAS..10011980M }}</ref> Two of those eight types: the coherent type 1 FFL (C1-FFL) (where all interactions are positive) and the incoherent type 1 FFL (I1-FFL) (A activates C and also activates B which represses C) are found much more frequently in the transcription network of ''[[Escherichia coli|E. coli]]'' and yeast than the other six types.<ref name="man1"/><ref name="ma1">{{cite journal |vauthors=Ma HW, Kumar B, Ditges U, Gunzer F, Buer J, Zeng AP |title=An extended transcriptional regulatory network of ''Escherichia coli'' and analysis of its hierarchical structure and network motifs |journal=Nucleic Acids Res. |volume=32 |issue=22 |pages=6643–9 |year=2004 |pmid=15604458 |pmc=545451 |doi=10.1093/nar/gkh1009 |url=http://nar.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=15604458}}</ref> In addition to the structure of the circuitry the way in which the signals from A and B are integrated by the C promoter should also be considered. In most of the cases the FFL is either an AND gate (A and B are required for C activation) or OR gate (either A or B are sufficient for C activation) but other input function are also possible.<br />
<br />
===Coherent type 1 FFL (C1-FFL)===<br />
The C1-FFL with an AND gate was shown to have a function of a ‘sign-sensitive delay’ element and a persistence detector both theoretically <ref name="man1"/> and experimentally<ref name="man2">{{cite journal |doi=10.1016/j.jmb.2003.09.049 |vauthors=Mangan S, Zaslaver A, Alon U |title=The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks |journal=J. Mol. Biol. |volume=334 |issue=2 |pages=197–204 |date=November 2003 |pmid=14607112 |citeseerx=10.1.1.110.4629 }}</ref> with the arabinose system of ''[[Escherichia coli|E. coli]]''. This means that this motif can provide pulse filtration in which short pulses of signal will not generate a response but persistent signals will generate a response after short delay. The shut off of the output when a persistent pulse is ended will be fast. The opposite behavior emerges in the case of a sum gate with fast response and delayed shut off as was demonstrated in the flagella system of ''[[Escherichia coli|E. coli]]''.<ref name="kal1">{{cite journal |vauthors=Kalir S, Mangan S, Alon U |title=A coherent feed-forward loop with a SUM input function prolongs flagella expression in ''Escherichia coli'' |journal=Mol. Syst. Biol. |volume=1 |pages=E1–E6 |year=2005 |pmid=16729041 |pmc=1681456 |doi=10.1038/msb4100010 |issue=1}}</ref> De novo evolution of C1-FFLs in [[gene regulatory network]]s has been demonstrated computationally in response to selection to filter out an idealized short signal pulse, but for non-idealized noise, a dynamics-based system of feed-forward regulation with different topology was instead favored.<ref>{{cite journal |last1=Xiong |first1=Kun |last2=Lancaster |first2=Alex K. |last3=Siegal |first3=Mark L. |last4=Masel |first4=Joanna |title=Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise |journal=Nature Communications |date=3 June 2019 |volume=10 |issue=1 |pages=2418 |doi=10.1038/s41467-019-10388-6|pmid=31160574 |pmc=6546794 }}</ref><br />
<br />
===Incoherent type 1 FFL (I1-FFL)===<br />
The I1-FFL is a pulse generator and response accelerator. The two signal pathways of the I1-FFL act in opposite directions where one pathway activates Z and the other represses it. When the repression is complete this leads to a pulse-like dynamics. It was also demonstrated experimentally that the I1-FFL can serve as response accelerator in a way which is similar to the NAR motif. The difference is that the I1-FFL can speed-up the response of any gene and not necessarily a transcription factor gene.<ref name="man3">{{cite journal |vauthors=Mangan S, Itzkovitz S, Zaslaver A, Alon U |title=The incoherent feed-forward loop accelerates the response-time of the gal system of ''Escherichia coli'' |journal=J. Mol. Biol. |volume=356 |issue=5 |pages=1073–81 |date=March 2006 |pmid=16406067 |doi=10.1016/j.jmb.2005.12.003 |citeseerx=10.1.1.184.8360 }}</ref> An additional function was assigned to the I1-FFL network motif: it was shown both theoretically and experimentally that the I1-FFL can generate non-monotonic input function in both a synthetic <ref name="ent1">{{cite journal |vauthors=Entus R, Aufderheide B, Sauro HM |title=Design and implementation of three incoherent feed-forward motif based biological concentration sensors |journal=Syst Synth Biol |volume=1 |issue=3 |pages=119–28 |date=August 2007 |pmid=19003446 |pmc=2398716 |doi=10.1007/s11693-007-9008-6 }}</ref> and native systems.<ref name="kap1">{{cite journal |vauthors=Kaplan S, Bren A, Dekel E, Alon U |title=The incoherent feed-forward loop can generate non-monotonic input functions for genes |journal=Mol. Syst. Biol. |volume=4 |pages=203 |year=2008 |pmid=18628744 |pmc=2516365 |doi=10.1038/msb.2008.43 |issue=1}}</ref> Finally, expression units that incorporate incoherent feedforward control of the gene product provide adaptation to the amount of DNA template and can be superior to simple combinations of constitutive promoters.<ref name="ble1">{{cite journal |vauthors=Bleris L, Xie Z, Glass D, Adadey A, Sontag E, Benenson Y |title=Synthetic incoherent feedforward circuits show adaptation to the amount of their genetic template |journal=Mol. Syst. Biol. |volume=7 |pages=519|year=2011 |doi=10.1038/msb.2011.49 |issue=1 |pmid=21811230 |pmc=3202791}}</ref> Feedforward regulation displayed better adaptation than negative feedback, and circuits based on RNA interference were the most robust to variation in DNA template amounts.<ref name="ble1"/><br />
<br />
===Multi-output FFLs===<br />
In some cases the same regulators X and Y regulate several Z genes of the same system. By adjusting the strength of the interactions this motif was shown to determine the temporal order of gene activation. This was demonstrated experimentally in the flagella system of ''[[Escherichia coli|E. coli]]''.<ref name="kal2">{{cite journal |vauthors=Kalir S, McClure J, Pabbaraju K, etal |title=Ordering genes in a flagella pathway by analysis of expression kinetics from living bacteria |journal=Science |volume=292 |issue=5524 |pages=2080–3 |date=June 2001 |pmid=11408658 |doi=10.1126/science.1058758 }}</ref><br />
<br />
===Single-input modules (SIM)===<br />
This motif occurs when a single regulator regulates a set of genes with no additional regulation. This is useful when the genes are cooperatively carrying out a specific function and therefore always need to be activated in a synchronized manner. By adjusting the strength of the interactions it can create temporal expression program of the genes it regulates.<ref name="zas1">{{cite journal |vauthors=Zaslaver A, Mayo AE, Rosenberg R, etal |title=Just-in-time transcription program in metabolic pathways |journal=Nat. Genet. |volume=36 |issue=5 |pages=486–91 |date=May 2004 |pmid=15107854 |doi=10.1038/ng1348|doi-access=free }}</ref><br />
<br />
In the literature, Multiple-input modules (MIM) arose as a generalization of SIM. However, the precise definitions of SIM and MIM have been a source of inconsistency. There are attempts to provide orthogonal definitions for canonical motifs in biological networks and algorithms to enumerate them, especially SIM, MIM and Bi-Fan (2x2 MIM).<ref>{{cite journal |vauthors=Konagurthu AS, Lesk AM |title=Single and Multiple Input Modules in regulatory networks |journal=Proteins |volume=73 |issue=2 |pages=320–324 |year=2008 |doi=10.1002/prot.22053|pmid=18433061 }}</ref><br />
<br />
===Dense overlapping regulons (DOR)===<br />
This motif occurs in the case that several regulators combinatorially control a set of genes with diverse regulatory combinations. This motif was found in ''[[Escherichia coli|E. coli]]'' in various systems such as carbon utilization, anaerobic growth, stress response and others.<ref name="she1"/><ref name="boy1"/> In order to better understand the function of this motif one has to obtain more information about the way the multiple inputs are integrated by the genes. Kaplan ''et al.''<ref name="kap2">{{cite journal |vauthors=Kaplan S, Bren A, Zaslaver A, Dekel E, Alon U |title=Diverse two-dimensional input functions control bacterial sugar genes |journal=Mol. Cell |volume=29 |issue=6 |pages=786–92 |date=March 2008 |pmid=18374652 |pmc=2366073 |doi=10.1016/j.molcel.2008.01.021 }}</ref> has mapped the input functions of the sugar utilization genes in ''[[Escherichia coli|E. coli]]'', showing diverse shapes.<br />
<br />
==已知的模体及其功能==<br />
许多实验工作致力于理解[[基因调控网络]]中的网络模体。在响应生物信号的过程中,这些网络控制细胞中需要表达的基因。这样的网络以基因作为节点,有向边代表对某个基因的调控,基因调控通过其他基因编码的转录因子[[结合在DNA上的调控蛋白]]来实现。因此,网络模体是基因之间相互调控转录速率的模式。在分析转录调控网络的时候,人们发现某些相同的网络模体在不同的物种中不断地出现,从细菌到人类。例如,''[[大肠杆菌]]''和酵母的转录网络由三种主要的网络模体家族组成,它们可以构建几乎整个网络。主要的假设是在进化的过程中,网络模体是被以收敛的方式独立选择出来的。<ref name="bab1">{{cite journal |vauthors=Babu MM, Luscombe NM, Aravind L, Gerstein M, Teichmann SA |title=Structure and evolution of transcriptional regulatory networks |journal=Current Opinion in Structural Biology |volume=14 |issue=3 |pages=283–91 |date=June 2004 |pmid=15193307 |doi=10.1016/j.sbi.2004.05.004 |citeseerx=10.1.1.471.9692 }}</ref><ref name="con1">{{cite journal |vauthors=Conant GC, Wagner A |title=Convergent evolution of gene circuits |journal=Nat. Genet. |volume=34 |issue=3 |pages=264–6 |date=July 2003 |pmid=12819781 |doi=10.1038/ng1181}}</ref> 因为相对于基因改变的速率,转录相互作用产生和消失的时间尺度在进化上是很快的。<ref name="bab1"/><ref name="con1"/><ref name="dek1">{{cite journal |vauthors=Dekel E, Alon U |title=Optimality and evolutionary tuning of the expression level of a protein |journal=Nature |volume=436 |issue=7050 |pages=588–92 |date=July 2005 |pmid=16049495 |doi=10.1038/nature03842 |bibcode=2005Natur.436..588D }}</ref> 此外,对活细胞中网络模体所产生的动力学行为的实验表明,它们具有典型的动力学功能。这表明,网络模体是基因调控网络中对生物体有益的基本单元。<br />
<br />
一些研究从理论和实验两方面探讨和论证了转录网络中与共同网络模体相关的功能。下面是一些最常见的网络模体及其相关功能。<br />
<br />
===负自反馈调控(NAR)===<br />
[[Image:Autoregulation motif.png|thumb|Schematic representation of an auto-regulation motif]]<br />
负自反馈调控是[[大肠杆菌]]中最简单和最冗余的网络模体之一,其中一个转录因子抑制它自身的转录。这种网络模体有两个重要的功能,其中第一个是加速响应。人们发现在实验和理论上, <ref name="zab1">{{cite journal |doi=10.1016/j.jtbi.2011.06.021 |author=Zabet NR |title=Negative feedback and physical limits of genes |journal=Journal of Theoretical Biology |volume= 284|issue=1 |pages=82–91 |date=September 2011 |pmid=21723295 |arxiv=1408.1869 |citeseerx=10.1.1.759.5418 }}</ref>NAR都可以加快对信号的响应。这个功能首先在一个人工合成的转录网络中被发现,<ref name="ros1">{{cite journal |doi=10.1016/S0022-2836(02)00994-4 |vauthors=Rosenfeld N, Elowitz MB, Alon U |title=Negative autoregulation speeds the response times of transcription networks |journal=J. Mol. Biol. |volume=323 |issue=5 |pages=785–93 |date=November 2002 |pmid=12417193 |citeseerx=10.1.1.126.2604 }}</ref> 然后在大肠杆菌SOS DAN修复系统这个自然体系中也被发现。<ref name="cam1">{{cite journal |vauthors=Camas FM, Blázquez J, Poyatos JF |title=Autogenous and nonautogenous control of response in a genetic network |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=103 |issue=34 |pages=12718–23 |date=August 2006 |pmid=16908855 |pmc=1568915 |doi=10.1073/pnas.0602119103 |bibcode=2006PNAS..10312718C }}</ref> 负自反馈网络的第二个功能是增强自调控基因的产物浓度的稳定性,从而抵抗随机的噪声,减少该蛋白含量在不同细胞中的差异。<ref name="bec1">{{cite journal |vauthors=Becskei A, Serrano L |title=Engineering stability in gene networks by autoregulation |journal=Nature |volume=405 |issue=6786 |pages=590–3 |date=June 2000 |pmid=10850721 |doi=10.1038/35014651}}</ref><ref name="dub1">{{cite journal |vauthors=Dublanche Y, Michalodimitrakis K, Kümmerer N, Foglierini M, Serrano L |title=Noise in transcription negative feedback loops: simulation and experimental analysis |journal=Mol. Syst. Biol. |volume=2 |pages=41 |year=2006 |pmid=16883354 |pmc=1681513 |doi=10.1038/msb4100081 |issue=1}}</ref><ref name="shi1">{{cite journal |vauthors=Shimoga V, White J, Li Y, Sontag E, Bleris L |title= Synthetic mammalian transgene negative autoregulation |journal=Mol. Syst. Biol. |volume=9 |pages=670 |year=2013|doi=10.1038/msb.2013.27|pmid= 23736683 |pmc= 3964311 }}</ref><br />
<br />
===正自反馈调控(PAR)===<br />
正自反馈调控是指转录因子增强它自身转录速率的调控。和负自反馈调节相反,NAR模体相比于简单的调控能够延长反应时间。<ref name="mae1">{{cite journal |vauthors=Maeda YT, Sano M |title=Regulatory dynamics of synthetic gene networks with positive feedback |journal=J. Mol. Biol. |volume=359 |issue=4 |pages=1107–24 |date=June 2006 |pmid=16701695 |doi=10.1016/j.jmb.2006.03.064 }}</ref> 在强PAR的情况下,模体可能导致蛋白质水平在细胞群中呈现双峰分布。<ref name="bec2">{{cite journal |vauthors=Becskei A, Séraphin B, Serrano L |title=Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion |journal=EMBO J. |volume=20 |issue=10 |pages=2528–35 |date=May 2001 |pmid=11350942 |pmc=125456 |doi=10.1093/emboj/20.10.2528}}</ref><br />
<br />
===前馈回路 (FFL)===<br />
[[Image:Feed-forward motif.GIF|thumb|Schematic representation of a Feed-forward motif]]<br />
前馈回路普遍存在于许多基因系统和生物体中。这种模体包括三个基因以及三个相互作用。目标基因C被两个转录因子(TFs)A和B调控,并且TF B同时被TF A调控。由于每个调控相互作用可以是正的或者负的,所以总共可能有八种类型的FFL模体。<ref name="man1">{{cite journal |vauthors=Mangan S, Alon U |title=Structure and function of the feed-forward loop network motif |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=100 |issue=21 |pages=11980–5 |date=October 2003 |pmid=14530388 |pmc=218699 |doi=10.1073/pnas.2133841100 |bibcode=2003PNAS..10011980M }}</ref> 其中的两种:一致前馈回路的类型一(C1-FFL)(所有相互作用都是正的)和非一致前馈回路的类型一(I1-FFL)(A激活C和B,B抑制C)在[[大肠杆菌]]和酵母中相比于其他六种更频繁的出现。<ref name="man1"/><ref name="ma1">{{cite journal |vauthors=Ma HW, Kumar B, Ditges U, Gunzer F, Buer J, Zeng AP |title=An extended transcriptional regulatory network of ''Escherichia coli'' and analysis of its hierarchical structure and network motifs |journal=Nucleic Acids Res. |volume=32 |issue=22 |pages=6643–9 |year=2004 |pmid=15604458 |pmc=545451 |doi=10.1093/nar/gkh1009 |url=http://nar.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=15604458}}</ref> 除了网络的结构外,还应该考虑来自A和B的信号被C的启动子集成的方式。在大多数情况下,FFL要么是一个与门(激活C需要A和B),要么是或门(激活C需要A或B),但也可以是其他输入函数。<br />
<br />
===一致前馈回路类型一(C1-FFL)===<br />
具有与门的C1-FFL有“符号-敏感延迟”单元和持久性探测器的功能,这一点在[[大肠杆菌]]阿拉伯糖系系统的理论<ref name="man1"/>和实验上<ref name="man2">{{cite journal |doi=10.1016/j.jmb.2003.09.049 |vauthors=Mangan S, Zaslaver A, Alon U |title=The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks |journal=J. Mol. Biol. |volume=334 |issue=2 |pages=197–204 |date=November 2003 |pmid=14607112 |citeseerx=10.1.1.110.4629 }}</ref> 都有发现。这意味着该模体可以提供脉冲过滤,短脉冲信号不会产生响应,而持久信号在短延迟后会产生响应。当持久脉冲结束时,输出的关闭将很快。与此相反的行为出现在具有快速响应和延迟关闭特性的加和门的情况下,这在[[大肠杆菌]]的鞭毛系统中得到了证明。<ref name="kal1">{{cite journal |vauthors=Kalir S, Mangan S, Alon U |title=A coherent feed-forward loop with a SUM input function prolongs flagella expression in ''Escherichia coli'' |journal=Mol. Syst. Biol. |volume=1 |pages=E1–E6 |year=2005 |pmid=16729041 |pmc=1681456 |doi=10.1038/msb4100010 |issue=1}}</ref>在[[基因调控网络]]的重头进化中,对于滤除理想化的短信号脉冲作为进化压,C1-FFLs已经在计算上被证明可以进化出来。但是对于非理想化的噪声,不同拓扑结构前馈调节的动态系统将被优先考虑。 <ref>{{cite journal |last1=Xiong |first1=Kun |last2=Lancaster |first2=Alex K. |last3=Siegal |first3=Mark L. |last4=Masel |first4=Joanna |title=Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise |journal=Nature Communications |date=3 June 2019 |volume=10 |issue=1 |pages=2418 |doi=10.1038/s41467-019-10388-6|pmid=31160574 |pmc=6546794 }}</ref><br />
<br />
===非一致前馈回路类型一(I1-FFL)===<br />
I1-FFL是一个脉冲生成器和响应加速器。I1-FFL的两种信号通路作用方向相反,一种通路激活Z,而另一种抑制Z。完全的抑制会导致类似脉冲的动力学行为。另外有实验证明,它可以类似于NAR模体起到响应加速器的作用。与NAR模体的不同之处在于,它可以加速任何基因的响应,而不必是转录因子。<ref name="man3">{{cite journal |vauthors=Mangan S, Itzkovitz S, Zaslaver A, Alon U |title=The incoherent feed-forward loop accelerates the response-time of the gal system of ''Escherichia coli'' |journal=J. Mol. Biol. |volume=356 |issue=5 |pages=1073–81 |date=March 2006 |pmid=16406067 |doi=10.1016/j.jmb.2005.12.003 |citeseerx=10.1.1.184.8360 }}</ref>I1-FFL网络还有另外一个功能:在理论和实验上都有证明I1-FFL可以生成非单调的输入函数,无论在人工合成的<ref name="ent1">{{cite journal |vauthors=Entus R, Aufderheide B, Sauro HM |title=Design and implementation of three incoherent feed-forward motif based biological concentration sensors |journal=Syst Synth Biol |volume=1 |issue=3 |pages=119–28 |date=August 2007 |pmid=19003446 |pmc=2398716 |doi=10.1007/s11693-007-9008-6 }}</ref>还是自然的系统中。 <ref name="kap1">{{cite journal |vauthors=Kaplan S, Bren A, Dekel E, Alon U |title=The incoherent feed-forward loop can generate non-monotonic input functions for genes |journal=Mol. Syst. Biol. |volume=4 |pages=203 |year=2008 |pmid=18628744 |pmc=2516365 |doi=10.1038/msb.2008.43 |issue=1}}</ref> 最后,包含非一致前馈调控的基因生成物的表达单元对DNA模板的数量具有适应性,可以优于简单的组合本构启动子。<ref name="ble1">{{cite journal |vauthors=Bleris L, Xie Z, Glass D, Adadey A, Sontag E, Benenson Y |title=Synthetic incoherent feedforward circuits show adaptation to the amount of their genetic template |journal=Mol. Syst. Biol. |volume=7 |pages=519|year=2011 |doi=10.1038/msb.2011.49 |issue=1 |pmid=21811230 |pmc=3202791}}</ref> 前馈调控比负反馈具有更好的适应性,并且基于RNA干扰的网络对DNA模板数具有最高的鲁棒性。<ref name="ble1"/><br />
<br />
===多输出前馈回路===<br />
在某些情况,相同的调控子X和Y可以调控同一系统中的多个Z基因。通过调节相互作用的强度,这些网络可以决定基因激活的时间顺序。这一点在[[大肠杆菌]]的鞭毛系统中有实验证据。<ref name="kal2">{{cite journal |vauthors=Kalir S, McClure J, Pabbaraju K, etal |title=Ordering genes in a flagella pathway by analysis of expression kinetics from living bacteria |journal=Science |volume=292 |issue=5524 |pages=2080–3 |date=June 2001 |pmid=11408658 |doi=10.1126/science.1058758 }}</ref><br />
<br />
===单一输入模块(SIM)===<br />
当单个调控子调控一组基因,并且没有其他的调控因素时,这样的模体叫做单一输入模块(SIM)。当很多基因合作执行某个功能时这是有用的,因为这些基因需要同步地被激活。通过调节相互作用的强度,可以编排它所调控的基因表达的时间顺序。<ref name="zas1">{{cite journal |vauthors=Zaslaver A, Mayo AE, Rosenberg R, etal |title=Just-in-time transcription program in metabolic pathways |journal=Nat. Genet. |volume=36 |issue=5 |pages=486–91 |date=May 2004 |pmid=15107854 |doi=10.1038/ng1348|doi-access=free }}</ref><br />
<br />
在文献中,多输入模块(MIM)来自于SIM的扩展。但是二者的精确定义并不太一致。有一些尝试给出生物网络中规范模体的正交定义,也有一些算法去枚举它们,特别是SIM,MIM和2x2 MIM等。<ref>{{cite journal |vauthors=Konagurthu AS, Lesk AM |title=Single and Multiple Input Modules in regulatory networks |journal=Proteins |volume=73 |issue=2 |pages=320–324 |year=2008 |doi=10.1002/prot.22053|pmid=18433061 }}</ref><br />
<br />
===密集交盖调节网(DOR)===<br />
这种类型的网络存在于多个调节子结合起来控制一组基因的情形,并且有多种调控的组合。这种模体出现在[[大肠杆菌]]的多种系统中,例如碳利用、厌氧生长、应激反应等。<ref name="she1"/><ref name="boy1"/> 为了更好地理解这种网络,我们必须得到关于基因集成多种输入的方式的信息。Kaplan ''et al.''<ref name="kap2">{{cite journal |vauthors=Kaplan S, Bren A, Zaslaver A, Dekel E, Alon U |title=Diverse two-dimensional input functions control bacterial sugar genes |journal=Mol. Cell |volume=29 |issue=6 |pages=786–92 |date=March 2008 |pmid=18374652 |pmc=2366073 |doi=10.1016/j.molcel.2008.01.021 }}</ref>绘制了[[大肠杆菌]]糖利用基因的输入函数,表现出各种各样的形状。<br />
<br />
==活动模体==<br />
<br />
有一个对网络模体的有趣概括:'''活动模体'''是在对节点和边都被量化标注的网络中可发现的【反复】斑图。例如,当新城代谢的边以相应基因的表达量或【时间】来标注时,一些斑图在'''给定的'''底层网络结构里【是反复的】。<ref name="agc">{{cite journal |vauthors=Chechik G, Oh E, Rando O, Weissman J, Regev A, Koller D |title=Activity motifs reveal principles of timing in transcriptional control of the yeast metabolic network |journal=Nat. Biotechnol. |volume=26 |issue=11 |pages=1251–9 |date=November 2008 |pmid=18953355 |pmc=2651818 |doi=10.1038/nbt.1499}}</ref><br />
<br />
==批判==<br />
<br />
对拓扑子结构有一个(某种程度上隐含的)前提性假设是其具有特定的功能重要性。但该假设最近遭到质疑,有人提出在不同的网络环境下模体可能表现出多样性,例如双扇模体,故<ref name="ad">{{cite journal |vauthors=Ingram PJ, Stumpf MP, Stark J |title=Network motifs: structure does not determine function |journal=BMC Genomics |volume=7 |pages=108 |year=2006 |pmid=16677373 |pmc=1488845 |doi=10.1186/1471-2164-7-108 }} </ref>模体的结构不必然决定功能,网络结构也不当然能揭示其功能;这种见解由来已久,可参见【Sin 操纵子】</font>。<ref>{{cite journal |vauthors=Voigt CA, Wolf DM, Arkin AP |title=The ''Bacillus subtilis'' sin operon: an evolvable network motif |journal=Genetics |volume=169 |issue=3 |pages=1187–202 |date=March 2005 |pmid=15466432 |pmc=1449569 |doi=10.1534/genetics.104.031955 |url=http://www.genetics.org/cgi/pmidlookup?view=long&pmid=15466432}}</ref><br />
<br />
<br />
大多数模体功能分析是基于模体孤立运行的情形。最近的研究<ref>{{cite journal |vauthors=Knabe JF, Nehaniv CL, Schilstra MJ |title=Do motifs reflect evolved function?—No convergent evolution of genetic regulatory network subgraph topologies |journal=BioSystems |volume=94 |issue=1–2 |pages=68–74 |year=2008 |pmid=18611431 |doi=10.1016/j.biosystems.2008.05.012 }}</ref>表明网络环境至关重要,不能忽视网络环境而仅从本地结构来对其功能进行推论——引用的论文还回顾了对观测数据的批判及其他可能的解释。人们研究了单个模体模组对网络全局的动力学影响及其分析<ref>{{cite journal |vauthors=Taylor D, Restrepo JG |title=Network connectivity during mergers and growth: Optimizing the addition of a module |journal=Physical Review E |volume=83 |issue=6 |year=2011 |page=66112 |doi=10.1103/PhysRevE.83.066112 |pmid=21797446 |bibcode=2011PhRvE..83f6112T |arxiv=1102.4876 }}</ref>。而另一项近期的研究工作提出生物网络的某些拓扑特征能自然地引起经典模体的常见形态,让人不禁疑问:这样的发生频率是否能证明模体的结构是出于其对所在网络运行的功能性贡献而被选择保留下的结果?<ref>{{cite journal|last1=Konagurthu|first1=Arun S.|last2=Lesk|first2=Arthur M.|title=Single and multiple input modules in regulatory networks|journal=Proteins: Structure, Function, and Bioinformatics|date=23 April 2008|volume=73|issue=2|pages=320–324|doi=10.1002/prot.22053|pmid=18433061}}</ref><ref>{{cite journal |vauthors=Konagurthu AS, Lesk AM |title=On the origin of distribution patterns of motifs in biological networks |journal=BMC Syst Biol |volume=2 |pages=73 |year=2008 |pmid=18700017 |pmc=2538512 |doi=10.1186/1752-0509-2-73 }} </ref><br />
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模体的研究主要应用于静态复杂网络,而时变复杂网络的研究<ref>Braha, D., & Bar‐Yam, Y. (2006). [https://static1.squarespace.com/static/5b68a4e4a2772c2a206180a1/t/5c5de3faf4e1fc43e7b3d21e/1549657083988/Complexity_Braha_Original_w_Cover.pdf From centrality to temporary fame: Dynamic centrality in complex networks]. Complexity, 12(2), 59-63. </ref>就网络模体提出了重大的新解释,并介绍了'''时变网络模体'''的概念。Braha和Bar-Yam<ref> Braha D., Bar-Yam Y. (2009) [https://s3.amazonaws.com/academia.edu.documents/4892116/Adaptive_Networks__Theory__Models_and_Applications__Understanding_Complex_Systems_.pdf?response-content-disposition=inline%3B%20filename%3DRedes_teoria.pdf&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAIWOWYYGZ2Y53UL3A%2F20191111%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20191111T173250Z&X-Amz-Expires=3600&X-Amz-SignedHeaders=host&X-Amz-Signature=89d08c9e92b88ed817e4eb0f87c480757ef79c4b865919a5e0890cbefa164c61#page=55 Time-Dependent Complex Networks: Dynamic Centrality, Dynamic Motifs, and Cycles of Social Interactions]. In: Gross T., Sayama H. (eds) Adaptive Networks. Understanding Complex Systems. Springer, Berlin, Heidelberg </ref>研究了本地模体结构在时间依赖网络/时变网络的动力学,发现的一些反复模式有望成为社会互动周期的经验论据。他们证明了对于时变网络,其本地结构是时间依赖的且可能随时间演变,可作为对复杂网络中稳定模体观及模体表达观的反论,Braha和Bar-Yam还进一步提出,对时变本地结构的分析有可能揭示系统级任务和功能方面的动力学的重要信息。<br />
<br />
==See also==<br />
* [[Clique (graph theory)]]<br />
* [[Graphical model]]<br />
<br />
==References==<br />
{{reflist|2}}<br />
<br />
==External links==<br />
<br />
* [http://www.weizmann.ac.il/mcb/UriAlon/groupNetworkMotifSW.html A software tool that can detect network motifs]<br />
* [http://www.bio-physics.at/wiki/index.php?title=Network_Motifs bio-physics-wiki NETWORK MOTIFS]<br />
* [http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ FANMOD: a tool for fast network motif detection]<br />
* [http://mavisto.ipk-gatersleben.de/ MAVisto: network motif analysis and visualisation tool]<br />
* [https://www.msu.edu/~jinchen/ NeMoFinder]<br />
* [http://people.cs.uchicago.edu/~joshuag/index.html Grochow–Kellis]<br />
* [http://lbb.ut.ac.ir/Download/LBBsoft/MODA/ MODA]<br />
* [http://lbb.ut.ac.ir/Download/LBBsoft/Kavosh/ Kavosh]<br />
* [http://apps.cytoscape.org/apps/cytokavosh CytoKavosh]<br />
* [http://www.dcc.fc.up.pt/gtries/ G-Tries]<br />
* [http://www.ft.unicamp.br/docentes/meira/accmotifs/ acc-MOTIF detection tool]<br />
<br />
[[Category:Gene expression]]<br />
[[Category:Networks]]</div>Imphttps://wiki.swarma.org/index.php?title=%E7%BD%91%E7%BB%9C%E6%A8%A1%E4%BD%93_Network_motifs&diff=7120网络模体 Network motifs2020-05-07T06:16:18Z<p>Imp:/* ESU (FANMOD)算法及对应的软件 */</p>
<hr />
<div>大家好,我们的公众号计划要推送一篇关于网络模体的综述文章,我们希望可以配套建议该重要概念:网络模体。现在希望可以大家一起协作完成这个词条。<br />
翻译任务主要分为以下5个内容:<br />
* 网络定义和历史 ---许菁 <br />
* 网络模体的发现算法 mfinder和FPF算法---李鹏<br />
* 网络模体的发现算法 ESU和对应的软件FANMOD---Imp<br />
* 网络模体的发现算法 G-Trie、算法对比和算法分类——Ricky(中英对照[[用户讨论:Qige96|初稿在这里]])<br />
* 已有网络模体及其函数表示 --周佳欣<br />
* 活动模体+批判 --- 孙宇<br />
* 代码实现<br />
<br />
大家可以在对应感兴趣的部分下面,写上姓名。我们的协作方式是石墨文档上翻译,最后再编辑成文。<br />
对应的词条链接:https://en.wikipedia.org/wiki/Network_motif#Well-established_motifs_and_their_functions<br />
<br />
截止时间:今晚12:00<br />
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<br />
All networks, including [[biological network]]s, social networks, technological networks (e.g., computer networks and electrical circuits) and more, can be represented as [[complex network|graphs]], which include a wide variety of subgraphs. One important local property of networks are so-called '''network motifs''', which are defined as recurrent and [[statistically significant]] sub-graphs or patterns.<br />
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所有网络,包括生物网络(biological networks)、社会网络(social networks)、技术网络(例如计算机网络和电路)等,都可以用图的形式来表示,这些图中会包括各种各样的子图(subgraphs)。网络的一个重要的局部性质是所谓的网络基序,即重复且具有统计意义的子图或模式(patterns)。<br />
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Network motifs are sub-graphs that repeat themselves in a specific network or even among various networks. Each of these sub-graphs, defined by a particular pattern of interactions between vertices, may reflect a framework in which particular functions are achieved efficiently. Indeed, motifs are of notable importance largely because they may reflect functional properties. They have recently gathered much attention as a useful concept to uncover structural design principles of complex networks.<ref name="mas1">{{cite journal |vauthors=Masoudi-Nejad A, Schreiber F, Razaghi MK Z |title=Building Blocks of Biological Networks: A Review on Major Network Motif Discovery Algorithms |journal=IET Systems Biology |volume=6 |issue=5 |pages=164–74 |year=2012|doi=10.1049/iet-syb.2011.0011 |pmid=23101871 }}</ref> Although network motifs may provide a deep insight into the network's functional abilities, their detection is computationally challenging.<br />
网络模体(Network motifs)是指在特定网络或各种网络中重复出现的相同的子图。这些子图由顶点之间特定的交互模式定义,一个子图便可以反映一个框架,这个框架可以有效地实现某个特定的功能。事实上,之所以说模体是一个重要的特性,正是因为它们可能反映出对应网络功能的这一性质。近年来这一概念作为揭示复杂网络结构设计原理的一个有用概念而受到了广泛的关注。<ref name="mas1">{{cite journal |vauthors=Masoudi-Nejad A, Schreiber F, Razaghi MK Z |title=Building Blocks of Biological Networks: A Review on Major Network Motif Discovery Algorithms |journal=IET Systems Biology |volume=6 |issue=5 |pages=164–74 |year=2012|doi=10.1049/iet-syb.2011.0011 |pmid=23101871 }}</ref> 但是,虽然通过研究网络模体可以深入了解网络的功能,但是对于模体的检测在计算上是具有挑战性的。<br />
<br />
==Definition==<br />
Let {{math|G {{=}} (V, E)}} and {{math|G&prime; {{=}} (V&prime;, E&prime;)}} be two graphs. Graph {{math|G&prime;}} is a ''sub-graph'' of graph {{math|G}} (written as {{math|G&prime; ⊆ G}}) if {{math|V&prime; ⊆ V}} and {{math|E&prime; ⊆ E ∩ (V&prime; &times; V&prime;)}}. If {{math|G&prime; ⊆ G}} and {{math|G&prime;}} contains all of the edges {{math|&lang;u, v&rang; ∈ E}} with {{math|u, v ∈ V&prime;}}, then {{math|G&prime;}} is an ''induced sub-graph'' of {{math|G}}. We call {{math|G&prime;}} and {{math|G}} isomorphic (written as {{math|G&prime; ↔ G}}), if there exists a bijection (one-to-one) {{math|f:V&prime; → V}} with {{math|&lang;u, v&rang; ∈ E&prime; ⇔ &lang;f(u), f(v)&rang; ∈ E}} for all {{math|u, v ∈ V&prime;}}. The mapping {{math|f}} is called an isomorphism between {{math|G}} and {{math|G&prime;}}.<ref name="die1">{{cite journal |author=Diestel R |title=Graph Theory (Graduate Texts in Mathematics) |volume=173 |year=2005|publisher=New York: Springer-Verlag Heidelberg}}</ref><br />
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设{{math|G {{=}} (V, E)}} 和 {{math|G&prime; {{=}} (V&prime;, E&prime;)}} 是两个图。若{{math|V&prime; ⊆ V}}且满足{{math|E&prime; ⊆ E ∩ (V&prime; &times; V&prime;)}})(即图{{math|G&prime; ⊆ G}的所有边和点都属于图{{math|G}})则称图{{math|G&prime; ⊆ G}是图{{math|G}}的一个子图<ref name="die1">{{cite journal |author=Diestel R |title=Graph Theory (Graduate Texts in Mathematics) |volume=173 |year=2005|publisher=New York: Springer-Verlag Heidelberg}}</ref><br />
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若{{math|G&prime; ⊆ G}},且对于顶点{{math|u}}、{{math|v}}及其连边,只要{{math|u}}和{{math|v}}存在于{{math|G&prime;}}(即若{{math|U}}, {{math|V&prime; ⊆ V}}),那么{{math|G&prime; ⊆ G}}中就应该包含原图{{math|G}}中的所有{{math|u}}和{{math|V}}的对应连边(即{{math|&lang;u, v&rang; ∈ E}}),则称此时图{{math|G&prime;}}就是图{{math|G}}的导出子图。<br />
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如果存在一个双射(一对一){{math|f:V&prime; → V}},且对所有{{math|u, v ∈ V&prime;}}都有{{math|&lang;u, v&rang; ∈ E&prime; ⇔ &lang;f(u), f(v)&rang; ∈ E}} ,则称{{math|G&prime }}是{{math|G}}的同构图(记作:{{math|G&prime; → G}}),映射f则称为{{math|G}}与{{math|G&prime;}}之间的同构(isomorphism)。[2]<br />
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When {{math|G&Prime; ⊂ G}} and there exists an isomorphism between the sub-graph {{math|G&Prime;}} and a graph {{math|G&prime;}}, this mapping represents an ''appearance'' of {{math|G&prime;}} in {{math|G}}. The number of appearances of graph {{math|G&prime;}} in {{math|G}} is called the frequency {{math|F<sub>G</sub>}} of {{math|G&prime;}} in {{math|G}}. A graph is called ''recurrent'' (or ''frequent'') in {{math|G}}, when its ''frequency'' {{math|F<sub>G</sub>(G&prime;)}} is above a predefined threshold or cut-off value. We use terms ''pattern'' and ''frequent sub-graph'' in this review interchangeably. There is an [[Statistical ensemble (mathematical physics)|ensemble]] {{math|Ω(G)}} of random graphs corresponding to the [[Null model|null-model]] associated to {{math|G}}. We should choose {{math|N}} random graphs uniformly from {{math|Ω(G)}} and calculate the frequency for a particular frequent sub-graph {{math|G&prime;}} in {{math|G}}. If the frequency of {{math|G&prime;}} in {{math|G}} is higher than its arithmetic mean frequency in {{math|N}} random graphs {{math|R<sub>i</sub>}}, where {{math|1 ≤ i ≤ N}}, we call this recurrent pattern ''significant'' and hence treat {{math|G&prime;}} as a ''network motif'' for {{math|G}}. For a small graph {{math|G&prime;}}, the network {{math|G}} and a set of randomized networks {{math|R(G) ⊆ Ω(R)}}, where {{math|1=R(G) {{=}} N}}, the ''Z-Score'' that has been defined by the following formula:<br />
<br />
<math>Z(G^\prime) = \frac{F_G(G^\prime) - \mu_R(G^\prime)}{\sigma_R(G^\prime)}</math><br />
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当{{math|G&Prime; ⊂ G}},且{{math|G&Prime;}}与图{{math|G&prime;}}之间存在同构时,该映射表示{{math|G&prime;}}对于{{math|G}}存在。图{{math|G&prime;}}在{{math|G}}的出现次数称为{{math|G&prime;}}出现在{{math|G}}的频率{{math|F<sub>G</sub>}}。当一个子图的频率{{math|F<sub>G</sub>}}高于预定的阈值或截止值时,则称{{math|G&prime;}}是{{math|G}}中的递归(或频繁)子图。<br />
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在接下来的内容中,我们交替使用术语“模式(motifs)”和“频繁子图(frequent sub-graph)”。<br />
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设从与{{math|G}}相关联的零模型(the null-model)获得的随机图集合为{{math|Ω(G)}},我们从{{math|Ω(G)}}中均匀地选择N个随机图,并计算其特定频繁子图的频率。如果{{math|G&prime;}}出现在{{math|G}}的频率高于N个随机图Ri的算术平均频率,其中{{math|1 ≤ i ≤ N}},我们称此递归模式是有意义的,因此可以将{{math|G&prime;}}视为{{math|G}}的网络模体。<br />
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对于一个小图{{math|G&prime;}},网络{{math|G}}和一组随机网络{{math|R(G) ⊆ Ω(R)}},当{{math|1=R(G) {{=}} N}}时,由其Z分数(Z-score)的定义如下式:<br />
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<math>Z(G^\prime) = \frac{F_G(G^\prime) - \mu_R(G^\prime)}{\sigma_R(G^\prime)}</math><br />
<br />
where {{math|μ<sub>R</sub>(G&prime;)}} and {{math|σ<sub>R</sub>(G&prime;)}} stand for mean and standard deviation frequency in set {{math|R(G)}}, respectively.<ref name="mil1">{{cite journal |vauthors=Milo R, Shen-Orr SS, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |volume=298 |year=2002|journal=Science|issue=5594|pages=824–827 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="alb1">{{cite journal |vauthors=Albert R, Barabási AL |title=Statistical mechanics of complex networks |journal=Reviews of Modern Physics |volume=74 |issue=1 |year=2002 |pages=47–49 |doi=10.1103/RevModPhys.74.47 |bibcode=2002RvMP...74...47A|arxiv=cond-mat/0106096 |citeseerx=10.1.1.242.4753 }}</ref><ref name="mil2">{{cite journal |vauthors=Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheffer M, Alon U |title=Superfamilies of designed and evolved networks |journal=Science |volume=303 |issue=5663 |year=2004 |pages=1538–1542 |pmid=15001784 |doi=10.1126/science.1089167 |bibcode=2004Sci...303.1538M |url=https://semanticscholar.org/paper/87ad24efd5329046d37cd704f970323e878710ca }}</ref><ref name="sch1">{{cite encyclopedia|last=Schwöbbermeyer |first=H |title=Network Motifs |encyclopedia=Analysis of Biological Networks |editor=Junker BH, Schreiber F |publisher=Hoboken, New Jersey: John Wiley & Sons |year=2008 |pages=85–108}}</ref><ref name="bor1">{{cite encyclopedia |last1=Bornholdt |first1=S |last2=Schuster |first2=HG |title=Handbook of graphs and networks : from the genome to the Internet |journal=Handbook of Graphs and Networks: From the Genome to the Internet |pages=417 |year=2003|bibcode=2003hgnf.book.....B }}</ref><ref name="cir1">{{cite journal |vauthors=Ciriello G, Guerra C |title=A review on models and algorithms for motif discovery in protein-protein interaction networks |journal=Briefings in Functional Genomics and Proteomics |year=2008 |volume=7 |issue=2 |pages=147–156 |doi=10.1093/bfgp/eln015|pmid=18443014 |doi-access=free }}</ref> The larger the {{math|Z(G&prime;)}}, the more significant is the sub-graph {{math|G&prime;}} as a motif. Alternatively, another measurement in statistical hypothesis testing that can be considered in motif detection is the P-Value, given as the probability of {{math|F<sub>R</sub>(G&prime;) ≥ F<sub>G</sub>(G&prime;)}} (as its null-hypothesis), where {{math|F<sub>R</sub>(G&prime;)}} indicates the frequency of G' in a randomized network.<ref name="sch1" /> A sub-graph with P-value less than a threshold (commonly 0.01 or 0.05) will be treated as a significant pattern. The P-value is defined as<br />
<br />
<math>P(G^\prime) = \frac{1}{N}\sum_{i=1}^N \delta(c(i)) ; c(i): F_R^i(G^\prime) \ge F_G(G^\prime)</math><br />
<br />
式中,{{math|μ<sub>R</sub>(G&prime;)}} 和 {{math|σ<sub>R</sub>(G&prime;)}}分别代表集合{{math|R(G)}}中的平均和标准偏差频率。.<ref name="mil1">{{cite journal |vauthors=Milo R, Shen-Orr SS, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |volume=298 |year=2002|journal=Science|issue=5594|pages=824–827 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="alb1">{{cite journal |vauthors=Albert R, Barabási AL |title=Statistical mechanics of complex networks |journal=Reviews of Modern Physics |volume=74 |issue=1 |year=2002 |pages=47–49 |doi=10.1103/RevModPhys.74.47 |bibcode=2002RvMP...74...47A|arxiv=cond-mat/0106096 |citeseerx=10.1.1.242.4753 }}</ref><ref name="mil2">{{cite journal |vauthors=Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheffer M, Alon U |title=Superfamilies of designed and evolved networks |journal=Science |volume=303 |issue=5663 |year=2004 |pages=1538–1542 |pmid=15001784 |doi=10.1126/science.1089167 |bibcode=2004Sci...303.1538M |url=https://semanticscholar.org/paper/87ad24efd5329046d37cd704f970323e878710ca }}</ref><ref name="sch1">{{cite encyclopedia|last=Schwöbbermeyer |first=H |title=Network Motifs |encyclopedia=Analysis of Biological Networks |editor=Junker BH, Schreiber F |publisher=Hoboken, New Jersey: John Wiley & Sons |year=2008 |pages=85–108}}</ref><ref name="bor1">{{cite encyclopedia |last1=Bornholdt |first1=S |last2=Schuster |first2=HG |title=Handbook of graphs and networks : from the genome to the Internet |journal=Handbook of Graphs and Networks: From the Genome to the Internet |pages=417 |year=2003|bibcode=2003hgnf.book.....B }}</ref><ref name="cir1">{{cite journal |vauthors=Ciriello G, Guerra C |title=A review on models and algorithms for motif discovery in protein-protein interaction networks |journal=Briefings in Functional Genomics and Proteomics |year=2008 |volume=7 |issue=2 |pages=147–156 |doi=10.1093/bfgp/eln015|pmid=18443014 |doi-access=free }}</ref> {{math|Z(G&prime;)}}越大,子图{{math|G&prime;}}作为模体的意义也就越大。<br />
<br />
此外还可以使用统计假设检验中的另一个测量方法,可以作为模体检测中的一种方法,即P值(P-value),以 {{math|F<sub>R</sub>(G&prime;) ≥ F<sub>G</sub>(G&prime;)}}的概率给出(作为其零假设null-hypothesis),其中{{math|F<sub>R</sub>(G&prime;)}}表示随机网络中{{math|G&prime;}}的频率。<ref name="sch1" /> 当P值小于阈值(通常为0.01或0.05)时,该子图可以被称为显著模式。该P值定义为:<br />
<br />
<math>P(G^\prime) = \frac{1}{N}\sum_{i=1}^N \delta(c(i)) ; c(i): F_R^i(G^\prime) \ge F_G(G^\prime)</math><br />
<br />
[[File:Different occurrences of a sub-graph in a graph.jpg|thumb|''Different occurrences of a sub-graph in a graph''. (M1 – M4) are different occurrences of sub-graph (b) in graph (a). For frequency concept {{math|F<sub>1</sub>}}, the set M1, M2, M3, M4 represent all matches, so {{math|F<sub>1</sub> {{=}} 4}}. For {{math|F<sub>2</sub>}}, one of the two set M1, M4 or M2, M3 are possible matches, {{math|F<sub>2</sub> {{=}} 2}}. Finally, for frequency concept {{math|F<sub>3</sub>}}, merely one of the matches (M1 to M4) is allowed, therefore {{math|F<sub>3</sub> {{=}} 1}}. The frequency of these three frequency concepts decrease as the usage of network elements are restricted.]]<br />
<br />
Where {{math|N}} indicates number of randomized networks, {{math|i}} is defined over an ensemble of randomized networks and the Kronecker delta function {{math|δ(c(i))}} is one if the condition {{math|c(i)}} holds. The concentration <ref name="kas1">{{cite journal |vauthors=Kashtan N, Itzkovitz S, Milo R, Alon U |title=Efficient sampling algorithm for estimating sub-graph concentrations and detecting network motifs |journal=Bioinformatics |year=2004 |volume=20 |issue=11 |pages=1746–1758 |doi=10.1093/bioinformatics/bth163|pmid=15001476 |doi-access=free }}</ref><ref name="wer1">{{cite journal |author=Wernicke S |title=Efficient detection of network motifs |journal=IEEE/ACM Transactions on Computational Biology and Bioinformatics |year=2006 |volume=3 |issue=4 |pages=347–359 |doi=10.1109/tcbb.2006.51|pmid=17085844 |citeseerx=10.1.1.304.2576 }}</ref> of a particular n-size sub-graph {{math|G&prime;}} in network {{math|G}} refers to the ratio of the sub-graph appearance in the network to the total ''n''-size non-isomorphic sub-graphs’ frequencies, which is formulated by<br />
<br />
<math>C_G(G^\prime) = \frac{F_G(G^\prime)}{\sum_i F_G(G_i)}</math><br />
<br />
where index {{math|i}} is defined over the set of all non-isomorphic n-size graphs. Another statistical measurement is defined for evaluating network motifs, but it is rarely used in known algorithms. This measurement is introduced by Picard ''et al.'' in 2008 and used the Poisson distribution, rather than the Gaussian normal distribution that is implicitly being used above.<ref name="pic1">{{cite journal |vauthors=Picard F, Daudin JJ, Schbath S, Robin S |title=Assessing the Exceptionality of Network Motifs |journal=J. Comp. Bio. |year=2005 |volume=15 |issue=1 |pages=1–20|doi=10.1089/cmb.2007.0137 |pmid=18257674 |citeseerx=10.1.1.475.4300 }}</ref><br />
<br />
其中索引 i 定义在所有非同构 n 大小图的集合上。 另一种统计测量是用来评估网络主题的,但在已知的算法中很少使用。 这种测量方法是由 Picard 等人在2008年提出的,使用的是泊松分佈分布,而不是上面隐含使用的高斯正态分布。<ref name="pic1">{{cite journal |vauthors=Picard F, Daudin JJ, Schbath S, Robin S |title=Assessing the Exceptionality of Network Motifs |journal=J. Comp. Bio. |year=2005 |volume=15 |issue=1 |pages=1–20|doi=10.1089/cmb.2007.0137 |pmid=18257674 |citeseerx=10.1.1.475.4300 }}</ref>其中{{math|N}}表示随机网络的数目,{{math|i}}定义在随机网络的集合上,若条件{{math|c(i)}}成立,则Kroneckerδ函数{{math|δ(c(i))}}是1。在网络{{math|G}}中,一个特定的n维子图{{math|N&prime;}}的集中度是指子图在网络中出现频率与n维非同构子图的总频率之比,其计算公式如下:<br />
<br />
<math>C_G(G^\prime) = \frac{F_G(G^\prime)}{\sum_i F_G(G_i)}</math><br />
<br />
<br />
In addition, three specific concepts of sub-graph frequency have been proposed.<ref name="schr1">{{cite book |vauthors=Schreiber F, Schwöbbermeyer H |title=Frequency concepts and pattern detection for the analysis of motifs in networks |journal=Transactions on Computational Systems Biology III |volume=3737 |year=2005 |pages=89–104|doi=10.1007/11599128_7 |citeseerx=10.1.1.73.1130 |series=Lecture Notes in Computer Science |isbn=978-3-540-30883-6 }}</ref> As the figure illustrates, the first frequency concept {{math|F<sub>1</sub>}} considers all matches of a graph in original network. This definition is similar to what we have introduced above. The second concept {{math|F<sub>2</sub>}} is defined as the maximum number of edge-disjoint instances of a given graph in original network. And finally, the frequency concept {{math|F<sub>3</sub>}} entails matches with disjoint edges and nodes. Therefore, the two concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}} restrict the usage of elements of the graph, and as can be inferred, the frequency of a sub-graph declines by imposing restrictions on network element usage. As a result, a network motif detection algorithm would pass over more candidate sub-graphs if we insist on frequency concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}}.<br />
<br />
此外,他们还提出了子图频率的三个具体概念。<ref name="schr1">{{cite book |vauthors=Schreiber F, Schwöbbermeyer H |title=Frequency concepts and pattern detection for the analysis of motifs in networks |journal=Transactions on Computational Systems Biology III |volume=3737 |year=2005 |pages=89–104|doi=10.1007/11599128_7 |citeseerx=10.1.1.73.1130 |series=Lecture Notes in Computer Science |isbn=978-3-540-30883-6 }}</ref> 如图所示,第一频率概念 {{math|F<sub>1</sub>}}考虑原始网络中图的所有匹配,这与我们前面介绍过的类似。第二个概念{{math|F<sub>2</sub>}}定义为原始网络中给定图的最大不相交边的数量。最后,频率概念{{math|F<sub>3</sub>}}包含与不相交边(disjoint edges)和节点的匹配。因此,两个概念F2和F3限制了图元素的使用,并且可以看出,通过对网络元素的使用施加限制,子图的频率下降。因此,如果我们坚持使用频率概念{{math|F<sub>2</sub>}}和{{math|F<sub>3</sub>}},网络模体检测算法将可以筛选出更多的候选子图。<br />
<br />
==History==<br />
The study of network motifs was pioneered by Holland and Leinhardt<ref>Holland, P. W., & Leinhardt, S. (1974). The statistical analysis of local structure in social networks. Working Paper No. 44, National Bureau of Economic Research.</ref><ref>Hollandi, P., & Leinhardt, S. (1975). The Statistical Analysis of Local. Structure in Social Networks. Sociological Methodology, David Heise, ed. San Francisco: Josey-Bass.</ref><ref> Holland, P. W., & Leinhardt, S. (1976). Local structure in social networks. Sociological methodology, 7, 1-45.</ref><ref>Holland, P. W., & Leinhardt, S. (1977). A method for detecting structure in sociometric data. In Social Networks (pp. 411-432). Academic Press.</ref> who introduced the concept of a triad census of networks. They introduced methods to enumerate various types of subgraph configurations, and test whether the subgraph counts are statistically different from those expected in random networks. <br />
霍兰(Holland)和莱因哈特(Leinhardt)率先提出了'''网络三合会普查'''(a triad census of networks)的概念,开创了网络模体研究的先河。<ref>Holland, P. W., & Leinhardt, S. (1974). The statistical analysis of local structure in social networks. Working Paper No. 44, National Bureau of Economic Research.</ref><ref>Hollandi, P., & Leinhardt, S. (1975). The Statistical Analysis of Local. Structure in Social Networks. Sociological Methodology, David Heise, ed. San Francisco: Josey-Bass.</ref><ref> Holland, P. W., & Leinhardt, S. (1976). Local structure in social networks. Sociological methodology, 7, 1-45.</ref><ref>Holland, P. W., & Leinhardt, S. (1977). A method for detecting structure in sociometric data. In Social Networks (pp. 411-432). Academic Press.</ref> 他们介绍了枚举各种子图配置的方法,并测试子图计数是否与随机网络中的期望值存在统计学上的差异。<br />
<br />
这里对于'''网络三合会普查'''(a triad census of networks)这一概念的翻译存疑<br />
<br />
<br />
This idea was further generalized in 2002 by [[Uri Alon]] and his group <ref name="she1">{{cite journal |vauthors=Shen-Orr SS, Milo R, Mangan S, Alon U |title=Network motifs in the transcriptional regulation network of ''Escherichia coli'' |journal=Nat. Genet. |volume=31 |issue=1 |pages=64–8 |date=May 2002 |pmid=11967538 |doi=10.1038/ng881}}</ref> when network motifs were discovered in the gene regulation (transcription) network of the bacteria ''[[Escherichia coli|E. coli]]'' and then in a large set of natural networks. Since then, a considerable number of studies have been conducted on the subject. Some of these studies focus on the biological applications, while others focus on the computational theory of network motifs.<br />
<br />
2002年,Uri Alon和他的团队[17]在大肠杆菌的基因调控(gene regulation network)(转录 transcription)网络中发现了网络模体,随后在大量的自然网络中也发现了网络模体,从而进一步推广了这一观点。自那时起,许多科学家都对这一问题进行了大量的研究。其中一些研究集中在生物学应用上,而另一些则集中在网络模体的计算理论上。<ref name="she1">{{cite journal |vauthors=Shen-Orr SS, Milo R, Mangan S, Alon U |title=Network motifs in the transcriptional regulation network of ''Escherichia coli'' |journal=Nat. Genet. |volume=31 |issue=1 |pages=64–8 |date=May 2002 |pmid=11967538 |doi=10.1038/ng881}}</ref> <br />
<br />
<br />
The biological studies endeavor to interpret the motifs detected for biological networks. For example, in work following,<ref name="she1" /> the network motifs found in ''[[Escherichia coli|E. coli]]'' were discovered in the transcription networks of other bacteria<ref name="eic1">{{cite journal |vauthors=Eichenberger P, Fujita M, Jensen ST, etal |title=The program of gene transcription for a single differentiating cell type during sporulation in ''Bacillus subtilis'' |journal=PLOS Biology |volume=2 |issue=10 |pages=e328 |date=October 2004 |pmid=15383836 |pmc=517825 |doi=10.1371/journal.pbio.0020328 }} </ref> as well as yeast<ref name="mil3">{{cite journal |vauthors=Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |journal=Science |volume=298 |issue=5594 |pages=824–7 |date=October 2002 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="lee1">{{cite journal |vauthors=Lee TI, Rinaldi NJ, Robert F, etal |title=Transcriptional regulatory networks in Saccharomyces cerevisiae |journal=Science |volume=298 |issue=5594 |pages=799–804 |date=October 2002 |pmid=12399584 |doi=10.1126/science.1075090 |bibcode=2002Sci...298..799L }}</ref> and higher organisms.<ref name="odo1">{{cite journal |vauthors=Odom DT, Zizlsperger N, Gordon DB, etal |title=Control of pancreas and liver gene expression by HNF transcription factors |journal=Science |volume=303 |issue=5662 |pages=1378–81 |date=February 2004 |pmid=14988562 |pmc=3012624 |doi=10.1126/science.1089769 |bibcode=2004Sci...303.1378O }}</ref><ref name="boy1">{{cite journal |vauthors=Boyer LA, Lee TI, Cole MF, etal |title=Core transcriptional regulatory circuitry in human embryonic stem cells |journal=Cell |volume=122 |issue=6 |pages=947–56 |date=September 2005 |pmid=16153702 |pmc=3006442 |doi=10.1016/j.cell.2005.08.020 }}</ref><ref name="ira1">{{cite journal |vauthors=Iranfar N, Fuller D, Loomis WF |title=Transcriptional regulation of post-aggregation genes in Dictyostelium by a feed-forward loop involving GBF and LagC |journal=Dev. Biol. |volume=290 |issue=2 |pages=460–9 |date=February 2006 |pmid=16386729 |doi=10.1016/j.ydbio.2005.11.035 |doi-access=free }}</ref> A distinct set of network motifs were identified in other types of biological networks such as neuronal networks and protein interaction networks.<ref name="mil2" /><ref name="maa1">{{cite journal |vauthors=Ma'ayan A, Jenkins SL, Neves S, etal |title=Formation of regulatory patterns during signal propagation in a Mammalian cellular network |journal=Science |volume=309 |issue=5737 |pages=1078–83 |date=August 2005 |pmid=16099987 |pmc=3032439 |doi=10.1126/science.1108876 |bibcode=2005Sci...309.1078M }}</ref><ref name="pta1">{{cite journal |vauthors=Ptacek J, Devgan G, Michaud G, etal |title=Global analysis of protein phosphorylation in yeast |journal=Nature |volume=438 |issue=7068 |pages=679–84 |date=December 2005 |pmid=16319894 |doi=10.1038/nature04187|bibcode=2005Natur.438..679P |url=https://authors.library.caltech.edu/56271/2/Tables.pdf |type=Submitted manuscript }}</ref><br />
<br />
生物学研究试图解释为生物网络检测到的模体。例如,在接下来的工作中,文献[17]在大肠杆菌中发现的网络模体存在于其他细菌<ref name="eic1">{{cite journal |vauthors=Eichenberger P, Fujita M, Jensen ST, etal |title=The program of gene transcription for a single differentiating cell type during sporulation in ''Bacillus subtilis'' |journal=PLOS Biology |volume=2 |issue=10 |pages=e328 |date=October 2004 |pmid=15383836 |pmc=517825 |doi=10.1371/journal.pbio.0020328 }} </ref>以及酵母<ref name="mil3">{{cite journal |vauthors=Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |journal=Science |volume=298 |issue=5594 |pages=824–7 |date=October 2002 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="lee1">{{cite journal |vauthors=Lee TI, Rinaldi NJ, Robert F, etal |title=Transcriptional regulatory networks in Saccharomyces cerevisiae |journal=Science |volume=298 |issue=5594 |pages=799–804 |date=October 2002 |pmid=12399584 |doi=10.1126/science.1075090 |bibcode=2002Sci...298..799L }}</ref>和高等生物的转录网络中。文献<ref name="odo1">{{cite journal |vauthors=Odom DT, Zizlsperger N, Gordon DB, etal |title=Control of pancreas and liver gene expression by HNF transcription factors |journal=Science |volume=303 |issue=5662 |pages=1378–81 |date=February 2004 |pmid=14988562 |pmc=3012624 |doi=10.1126/science.1089769 |bibcode=2004Sci...303.1378O }}</ref><ref name="boy1">{{cite journal |vauthors=Boyer LA, Lee TI, Cole MF, etal |title=Core transcriptional regulatory circuitry in human embryonic stem cells |journal=Cell |volume=122 |issue=6 |pages=947–56 |date=September 2005 |pmid=16153702 |pmc=3006442 |doi=10.1016/j.cell.2005.08.020 }}</ref><ref name="ira1">{{cite journal |vauthors=Iranfar N, Fuller D, Loomis WF |title=Transcriptional regulation of post-aggregation genes in Dictyostelium by a feed-forward loop involving GBF and LagC |journal=Dev. Biol. |volume=290 |issue=2 |pages=460–9 |date=February 2006 |pmid=16386729 |doi=10.1016/j.ydbio.2005.11.035 |doi-access=free }}</ref>在其他类型的生物网络中发现了一组不同的网络模体,如神经元网络和蛋白质相互作用网络。<ref name="mil2" /><ref name="maa1">{{cite journal |vauthors=Ma'ayan A, Jenkins SL, Neves S, etal |title=Formation of regulatory patterns during signal propagation in a Mammalian cellular network |journal=Science |volume=309 |issue=5737 |pages=1078–83 |date=August 2005 |pmid=16099987 |pmc=3032439 |doi=10.1126/science.1108876 |bibcode=2005Sci...309.1078M }}</ref><ref name="pta1">{{cite journal |vauthors=Ptacek J, Devgan G, Michaud G, etal |title=Global analysis of protein phosphorylation in yeast |journal=Nature |volume=438 |issue=7068 |pages=679–84 |date=December 2005 |pmid=16319894 |doi=10.1038/nature04187|bibcode=2005Natur.438..679P |url=https://authors.library.caltech.edu/56271/2/Tables.pdf |type=Submitted manuscript }}</ref><br />
<br />
<br />
The computational research has focused on improving existing motif detection tools to assist the biological investigations and allow larger networks to be analyzed. Several different algorithms have been provided so far, which are elaborated in the next section in chronological order.<br />
<br />
另一方面,对于计算研究的重点则是改进现有的模体检测工具,以协助生物学研究,并允许对更大的网络进行分析。到目前为止,已经提供了几种不同的算法,这些算法将在下一节按时间顺序进行阐述。<br />
<br />
Most recently, the acc-MOTIF tool to detect network motifs was released.<ref>{{Cite web | url=http://www.ft.unicamp.br/docentes/meira/accmotifs/ |title = Acc-Motif: Accelerated Motif Detection}}</ref><br />
<br />
最近,还发布了用于检测网络基序的acc基序工具。<ref>{{Cite web | url=http://www.ft.unicamp.br/docentes/meira/accmotifs/ |title = Acc-Motif: Accelerated Motif Detection}}</ref><br />
<br />
<br />
==模体发现算法 Motif discovery algorithms==<br />
<br />
Various solutions have been proposed for the challenging problem of motif discovery. These algorithms can be classified under various paradigms such as exact counting methods, sampling methods, pattern growth methods and so on. However, motif discovery problem comprises two main steps: first, calculating the number of occurrences of a sub-graph and then, evaluating the sub-graph significance. The recurrence is significant if it is detectably far more than expected. Roughly speaking, the expected number of appearances of a sub-graph can be determined by a Null-model, which is defined by an ensemble of random networks with some of the same properties as the original network.<br />
<br />
针对模体发现这一问题存在多种解决方案。这些算法可以归纳为不同的范式:例如精确计数方法,采样方法,模式增长方法等。但模体发现问题包括两个主要步骤:首先,计算子图的出现次数,然后评估子图的重要性。如果检测到的重现性远超过预期,那么这种重现性是很显著的。粗略地讲,子图的预期出现次数可以由'''零模型 Null-model''' 确定,该模型定义为具有与原始网络某些属性相同的随机网络的集合。<br />
<br />
<br />
Here, a review on computational aspects of major algorithms is given and their related benefits and drawbacks from an algorithmic perspective are discussed.<br />
<br />
接下来,对下列算法的计算原理进行简要回顾,并从算法的角度讨论了它们的优缺点。<br />
<br />
===mfinder 算法===<br />
<br />
''mfinder'', the first motif-mining tool, implements two kinds of motif finding algorithms: a full enumeration and a sampling method. Until 2004, the only exact counting method for NM (network motif) detection was the brute-force one proposed by Milo ''et al.''.<ref name="mil1" /> This algorithm was successful for discovering small motifs, but using this method for finding even size 5 or 6 motifs was not computationally feasible. Hence, a new approach to this problem was needed.<br />
<br />
'''mfinder'''是第一个模体挖掘工具,它主要有两种模体查找算法:完全枚举 full enumeration 和采样方法 sampling method。直到2004年,用于NM('''网络模体 networkmotif''')检测的唯一精确计数方法是'''Milo'''等人提出的暴力穷举方法。<ref name="mil1" />该算法成功地发现了小规模的模体,但是这种方法甚至对于发现规模为5个或6个的模体在计算上都不可行的。因此,需要一种解决该问题的新方法。<br />
<br />
<br />
Kashtan ''et al.'' <ref name="kas1" /> presented the first sampling NM discovery algorithm, which was based on ''edge sampling'' throughout the network. This algorithm estimates concentrations of induced sub-graphs and can be utilized for motif discovery in directed or undirected networks. The sampling procedure of the algorithm starts from an arbitrary edge of the network that leads to a sub-graph of size two, and then expands the sub-graph by choosing a random edge that is incident to the current sub-graph. After that, it continues choosing random neighboring edges until a sub-graph of size n is obtained. Finally, the sampled sub-graph is expanded to include all of the edges that exist in the network between these n nodes. When an algorithm uses a sampling approach, taking unbiased samples is the most important issue that the algorithm might address. The sampling procedure, however, does not take samples uniformly and therefore Kashtan ''et al.'' proposed a weighting scheme that assigns different weights to the different sub-graphs within network.<ref name="kas1" /> The underlying principle of weight allocation is exploiting the information of the [[sampling probability]] for each sub-graph, i.e. the probable sub-graphs will obtain comparatively less weights in comparison to the improbable sub-graphs; hence, the algorithm must calculate the sampling probability of each sub-graph that has been sampled. This weighting technique assists ''mfinder'' to determine sub-graph concentrations impartially.<br />
<br />
'''Kashtan''' 等人<ref name="kas1" />首次提出了一种基于边缘采样的网络模体(NM)采样发现算法。该算法估计了<font color="red">所含子图 induced sub-graphs 的集中度 concentrations </font>,可用于有向或无向网络中的模体发现。该算法的采样过程从网络的任意一条边开始,该边连向大小为2的子图,然后选择一条与当前子图相关的随机边对子图进行扩展。之后,它将继续选择随机的相邻边,直到获得大小为n的子图为止。最后,采样得到的子图扩展为包括这n个节点在内的网络中存在的所有边。当使用采样方法时,获取无偏样本是这类算法可能面临的最重要问题。而且,采样过程并不能保证采到所有的样本(也就是不能保证得到所有的子图,译者注),因此,Kashtan 等人又提出了一种加权方案,为网络中的不同子图分配不同的权重。<ref name="kas1" /> 权重分配的基本原理是利用每个子图的抽样概率信息,即,与不可能的子图相比,可能的子图将获得相对较少的权重;因此,该算法必须计算已采样的每个子图的采样概率。这种加权技术有助于mfinder公正地确定子图的<font color="red">集中度 concentrations </font>。<br />
<br />
<br />
In expanded to include sharp contrast to exhaustive search, the computational time of the algorithm surprisingly is asymptotically independent of the network size. An analysis of the computational time of the algorithm has shown that it takes {{math|O(n<sup>n</sup>)}} for each sample of a sub-graph of size {{math|n}} from the network. On the other hand, there is no analysis in <ref name="kas1" /> on the classification time of sampled sub-graphs that requires solving the ''graph isomorphism'' problem for each sub-graph sample. Additionally, an extra computational effort is imposed on the algorithm by the sub-graph weight calculation. But it is unavoidable to say that the algorithm may sample the same sub-graph multiple times – spending time without gathering any information.<ref name="wer1" /> In conclusion, by taking the advantages of sampling, the algorithm performs more efficiently than an exhaustive search algorithm; however, it only determines sub-graphs concentrations approximately. This algorithm can find motifs up to size 6 because of its main implementation, and as result it gives the most significant motif, not all the others too. Also, it is necessary to mention that this tool has no option of visual presentation. The sampling algorithm is shown briefly:<br />
<br />
与穷举搜索形成鲜明对比的是,该算法的计算时间竟然与网络大小渐近无关。对算法时间复杂度的分析表明,对于网络中大小为n的子图的每个样本,它的时间复杂度为<math>O(n^n)</math>。另一方面,<font color="red">并没有对已采样子图的每一个子图样本判断图同构问题的分类时间进行分析</font><ref name="kas1" />。另外,子图权重计算将额外增加该算法的计算负担。但是不得不指出的是,该算法可能会多次采样相同的子图——花费时间而不收集任何有用信息。<ref name="wer1" />总之,通过利用采样的优势,该算法的性能比穷举搜索算法更有效;但是,它只能大致确定子图的<font color="red">集中度 concentrations </font>。由于该算法的实现方式,使得它可以找到最大为6的模体,并且它会给出的最重要的模体,而不是其他所有模体。另外,有必要提到此工具没有可视化的呈现。采样算法简要显示如下:<br />
<br />
<br />
{| class="wikitable"<br />
|-<br />
! mfinder<br />
|-<br />
| '''Definitions:''' {{math|E<sub>s</sub>}}is the set of picked edges. {{math|V<sub>s</sub>}} is the set of all nodes that are touched by the edges in {{math|E}}.<br />
|-<br />
| Init {{math|V<sub>s</sub>}} and {{math|E<sub>s</sub>}} to be empty sets.<br />
1. Pick a random edge {{math|e<sub>1</sub> {{=}} (v<sub>i</sub>, v<sub>j</sub>)}}. Update {{math|E<sub>s</sub> {{=}} {e<sub>1</sub>}}}, {{math|V<sub>s</sub> {{=}} {v<sub>i</sub>, v<sub>j</sub>}}}<br />
<br />
2. Make a list {{math|L}} of all neighbor edges of {{math|E<sub>s</sub>}}. Omit from {{math|L}} all edges between members of {{math|V<sub>s</sub>}}.<br />
<br />
3. Pick a random edge {{math|e {{=}} {v<sub>k</sub>,v<sub>l</sub>}}} from {{math|L}}. Update {{math|E<sub>s</sub> {{=}} E<sub>s</sub> ⋃ {e}}}, {{math|V<sub>s</sub> {{=}} V<sub>s</sub> ⋃ {v<sub>k</sub>, v<sub>l</sub>}}}.<br />
<br />
4. Repeat steps 2-3 until completing an ''n''-node subgraph (until {{math|{{!}}V<sub>s</sub>{{!}} {{=}} n}}).<br />
<br />
5. Calculate the probability to sample the picked ''n''-node subgraph.<br />
|}<br />
<br />
<br />
{|class="wikitable"<br />
|+ mfinder<br />
|-<br />
!rowspan="1"|定义:<math>E_{s}</math>是采集的边集合。<math>V_{s}</math>是<math>E</math>中所有边的顶点的集合。<br />
|-<br />
|rowspan="5"|初始化<math>V_{s}</math>和<math>E_{s}</math>为空集。<br><br />
1. 随机选择一条边<math> e_{1} = (v_{i}, v_{j}) </math>,更新 <math>E_{s} = \{e_{1}\}, V{s} = \{v_{i}, v_{j}\}</math><br />
<br />
2. 列出<math>E{s}</math>的所有邻边列表<math> L </math>,从<math> L </math>中删除<math>V{s}</math>中所有元素组成的边。<br />
<br />
3. 从<math> L </math>中随机选择一条边<math> e = \{v_{k},v_{l}\} </math>, 更新<math>E_{s} = E_{s} \cup \{e\} , V_{s} = V_{s} \cup \{v_{k}, v_{l}\}</math>。<br />
<br />
4. 重复步骤2-3,直到完成包含n个节点的子图 (<math>\left | V_{s} \right | = n</math>)。<br />
<br />
5. 计算对选取的n节点子图进行采样的概率。<br />
|}<br />
<br />
<br />
===FPF (Mavisto)算法===<br />
<br />
Schreiber and Schwöbbermeyer <ref name="schr1" /> proposed an algorithm named ''flexible pattern finder (FPF)'' for extracting frequent sub-graphs of an input network and implemented it in a system named ''Mavisto''.<ref name="schr2">{{cite journal |vauthors=Schreiber F, Schwobbermeyer H |title=MAVisto: a tool for the exploration of network motifs |journal=Bioinformatics |volume=21 |issue=17|pages=3572–3574 |year=2005 |doi=10.1093/bioinformatics/bti556|pmid=16020473 |doi-access=free }}</ref> Their algorithm exploits the ''downward closure'' property which is applicable for frequency concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}}. The downward closure property asserts that the frequency for sub-graphs decrease monotonically by increasing the size of sub-graphs; however, this property does not hold necessarily for frequency concept {{math|F<sub>1</sub>}}. FPF is based on a ''pattern tree'' (see figure) consisting of nodes that represents different graphs (or patterns), where the parent of each node is a sub-graph of its children nodes; in other words, the corresponding graph of each pattern tree's node is expanded by adding a new edge to the graph of its parent node.<br />
<br />
Schreiber和Schwöbbermeyer <ref name="schr1" />提出了一种称为灵活模式查找器(FPF)的算法,用于提取输入网络的频繁子图,并将其在名为Mavisto的系统中加以实现。<ref name="schr2">{{cite journal |vauthors=Schreiber F, Schwobbermeyer H |title=MAVisto: a tool for the exploration of network motifs |journal=Bioinformatics |volume=21 |issue=17|pages=3572–3574 |year=2005 |doi=10.1093/bioinformatics/bti556|pmid=16020473 |doi-access=free }}</ref> 他们的算法利用了向下闭包特性,该特性适用于频率概念<math>F_{2}</math>和<math>F_{3}</math>。向下闭包性质表明,子图的频率随着子图的大小而单调下降;但这一性质并不一定适用于频率概念<math>F_{1}</math>。FPF算法基于模式树(见右图),由代表不同图形(或模式)的节点组成,其中每个节点的父节点是其子节点的子图;换句话说,每个模式树节点的对应图通过向其父节点图添加新边来扩展。<br />
<br />
<br />
[[Image:The pattern tree in FPF algorithm.jpg|right|thumb|''FPF算法中的模式树展示''.<ref name="schr1" />]]<br />
<br />
<br />
At first, the FPF algorithm enumerates and maintains the information of all matches of a sub-graph located at the root of the pattern tree. Then, one-by-one it builds child nodes of the previous node in the pattern tree by adding one edge supported by a matching edge in the target graph, and tries to expand all of the previous information about matches to the new sub-graph (child node). In next step, it decides whether the frequency of the current pattern is lower than a predefined threshold or not. If it is lower and if downward closure holds, FPF can abandon that path and not traverse further in this part of the tree; as a result, unnecessary computation is avoided. This procedure is continued until there is no remaining path to traverse.<br />
<br />
首先,FPF算法枚举并维护位于模式树根部的子图的所有匹配信息。然后,它通过在目标图中添加匹配边缘支持的一条边缘,在模式树中一一建立前一节点的子节点,然后通过在目标图中添加匹配边支持的一条边,逐个构建模式树中前一个节点的子节点,并尝试将以前关于匹配的所有信息拓展到新的子图(子节点)中。下一步,它判断当前模式的频率是否低于预定义的阈值。如果它低于阈值且保持向下闭包,则FPF算法会放弃该路径,而不会在树的此部分进一步遍历;这样就避免了不必要的计算。重复此过程,直到没有剩余可遍历的路径为止。<br />
<br />
<br />
The advantage of the algorithm is that it does not consider infrequent sub-graphs and tries to finish the enumeration process as soon as possible; therefore, it only spends time for promising nodes in the pattern tree and discards all other nodes. As an added bonus, the pattern tree notion permits FPF to be implemented and executed in a parallel manner since it is possible to traverse each path of the pattern tree independently. However, FPF is most useful for frequency concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}}, because downward closure is not applicable to {{math|F<sub>1</sub>}}. Nevertheless, the pattern tree is still practical for {{math|F<sub>1</sub>}} if the algorithm runs in parallel. Another advantage of the algorithm is that the implementation of this algorithm has no limitation on motif size, which makes it more amenable to improvements. The pseudocode of FPF (Mavisto) is shown below:<br />
<br />
该算法的优点是它不会考虑不频繁的子图,并尝试尽快完成枚举过程;因此,它只花时间在模式树中用于有希望的节点上,而放弃所有其他节点。还有一点额外的好处,模式树概念允许 FPF 以并行方式实现和执行,因为它可以独立地遍历模式树的每个路径。但是,FPF对于频率概念<math>F_{2}</math>和<math>F_{3}</math>最为有用,因为向下闭包不适用于<math>F_{1}</math>。尽管如此,如果算法并行运行,那么模式树对于<math>F_{1}</math>仍然是可行的。该算法的另一个优点是它的实现对模体大小没有限制,这使其更易于改进。FPF(Mavisto)的伪代码如下所示:<br />
<br />
<br />
{| class="wikitable"<br />
|-<br />
! Mavisto<br />
|-<br />
| '''Data:''' Graph {{math|G}}, target pattern size {{math|t}}, frequency concept {{math|F}}<br />
<br />
'''Result:''' Set {{math|R}} of patterns of size {{math|t}} with maximum frequency.<br />
|-<br />
| {{math|R ← φ}}, {{math|f<sub>max</sub> ← 0}}<br />
<br />
{{math|P ←}}start pattern {{math|p1}} of size 1<br />
<br />
{{math|M<sub>p<sub>1</sub></sub> ←}}all matches of {{math|p<sub>1</sub>}} in {{math|G}}<br />
<br />
'''While''' {{math|P &ne; φ}} '''do'''<br />
<br />
{{pad|1em}}{{math|P<sub>max</sub> ←}}select all patterns from {{math|P}} with maximum size.<br />
<br />
{{pad|1em}}{{math|P ←}} select pattern with maximum frequency from {{math|P<sub>max</sub>}}<br />
<br />
{{pad|1em}}{{math|Ε {{=}} ''ExtensionLoop''(G, p, M<sub>p</sub>)}}<br />
<br />
{{pad|1em}}'''Foreach''' pattern {{math|p &isin; E}}<br />
<br />
{{pad|2em}}'''If''' {{math|F {{=}} F<sub>1</sub>}} '''then''' {{math|f ← ''size''(M<sub>p</sub>)}}<br />
<br />
{{pad|2em}}'''Else''' {{math|f ←}} ''Maximum Independent set''{{math|(F, M<sub>p</sub>)}}<br />
<br />
{{pad|2em}}'''End'''<br />
<br />
{{pad|2em}}'''If''' {{math|''size''(p) {{=}} t}} '''then'''<br />
<br />
{{pad|3em}}'''If''' {{math|f {{=}} f<sub>max</sub>}} '''then''' {{math|R ← R ⋃ {p}}}<br />
<br />
{{pad|3em}}'''Else if''' {{math|f > f<sub>max</sub>}} '''then''' {{math|R ← {p}}}; {{math|f<sub>max</sub> ← f}}<br />
<br />
{{pad|3em}}'''End'''<br />
<br />
{{pad|2em}}'''Else'''<br />
<br />
{{pad|3em}}'''If''' {{math|F {{=}} F<sub>1</sub>}} '''or''' {{math|f &ge; f<sub>max</sub>}} '''then''' {{math|P ← P ⋃ {p}}}<br />
<br />
{{pad|3em}}'''End'''<br />
<br />
{{pad|2em}}'''End'''<br />
<br />
{{pad|1em}}'''End'''<br />
<br />
'''End'''<br />
|}<br />
<br />
<br />
{|class="wikitable"<br />
|+ Mavisto<br />
|-<br />
!rowspan="1"|数据: 图 <math>G</math>, 目标模式规模 <math>t</math>, 频率概念 <math>F</math>。<br><br />
结果: 以最大频率设置大小为 <math>t</math>的模式 <math>R</math>.<br><br />
|-<br />
|rowspan="20"| <math>R \leftarrow \Phi , f_{max}\leftarrow 0</math><br><br />
<math>P \leftarrow</math> 开始于大小为1的模式 <math>p_{1}</math><br />
<br />
<math>M_{p_{1}} \leftarrow </math> 图 <math>G</math> 中模式 <math>p_{1}</math> 的所有匹配<br />
<br />
当 <math>P \neq \Phi </math> 时,执行:<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;<math>P_{max} \leftarrow</math> 从 <math>P</math> 中选择最大规模的所有模式<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;<math>P\leftarrow</math> 从 <math>P_{max}</math> 中选择最大频率的模式<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;<math>E = ExtensionLoop(G, p, M_{p})</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;对于 <math>p \in E </math> 的所有模式:<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>F = F_{1}</math> ,那么 <math>f \leftarrow size(M_{p})</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他<math>f \leftarrow</math> 最大独立集 <math>(F, M_{p})</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>size(p) = t</math> ,那么<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>f = f_{max}</math> ,那么 <math>R \leftarrow R \cup \{p\}</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他 如果 <math>f > f_{max}</math> ,那么 <math>R \leftarrow \{p\}</math>; <math>f_{max} \leftarrow f</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>F = F_{1} or f \geq f_{max}</math> ,那么 <math> P \leftarrow P \cup \{p\}</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
结束<br />
|}<br />
<br />
===ESU (FANMOD)算法及对应的软件===<br />
The sampling bias of Kashtan ''et al.'' <ref name="kas1" /> provided great impetus for designing better algorithms for the NM discovery problem. Although Kashtan ''et al.'' tried to settle this drawback by means of a weighting scheme, this method imposed an undesired overhead on the running time as well a more complicated implementation. This tool is one of the most useful ones, as it supports visual options and also is an efficient algorithm with respect to time. But, it has a limitation on motif size as it does not allow searching for motifs of size 9 or higher because of the way the tool is implemented.<br />
<br />
由于Kashtan等学者发现的『采样偏差』问题为『the NM discovery problem』设计更好的算法提出了更高要求。虽然Kashtan等人尝试用加权法来解决这个弊端,但这个方法在运行上,消耗了过多的运行时间,且实现起来也变得更加复杂。但这个工具还是最好用的工具之一,因为它支持可视化选项,同时也『是个节约时间的算法』。但是,它在所支持的模体的规模大小还是有局限性。由于该工具在具体实施中,不允许搜索规模大小为9或者更大的模体。<br />
<br />
Wernicke <ref name="wer1" /> introduced an algorithm named ''RAND-ESU'' that provides a significant improvement over ''mfinder''.<ref name="kas1" /> This algorithm, which is based on the exact enumeration algorithm ''ESU'', has been implemented as an application called ''FANMOD''.<ref name="wer1" /> ''RAND-ESU'' is a NM discovery algorithm applicable for both directed and undirected networks, effectively exploits an unbiased node sampling throughout the network, and prevents overcounting sub-graphs more than once. Furthermore, ''RAND-ESU'' uses a novel analytical approach called ''DIRECT'' for determining sub-graph significance instead of using an ensemble of random networks as a Null-model. The ''DIRECT'' method estimates the sub-graph concentration without explicitly generating random networks.<ref name="wer1" /> Empirically, the DIRECT method is more efficient in comparison with the random network ensemble in case of sub-graphs with a very low concentration; however, the classical Null-model is faster than the ''DIRECT'' method for highly concentrated sub-graphs.<ref name="mil1" /><ref name="wer1" /> In the following, we detail the ''ESU'' algorithm and then we show how this exact algorithm can be modified efficiently to ''RAND-ESU'' that estimates sub-graphs concentrations.<br />
<br />
Weinicke引入了一种叫RAND-ESU的算法,这个新引入的算法比Mfinder软件有着更显著的提升。RAND-ESU基于精准的ESU算法,已有对应的软件FANMOD。RAND-ESU是一种[NM算法],可应用于定向的或者不定向的网络中,能够有效的在网络中利用无偏差节点进行采样,以及保证了一个子图仅仅被搜索一次,且不会产生无意义的子图。并且,RAND-ESU采用了一个叫做DIRECT的全新的分析方式,从而来确定子图的重要性,而不是用随机网络的组合来建立『Null模型』。DIRECT方法可以不用大量生成随机网络就能估计子图的浓度。实际上,相较于用随机网络组合分析比较低集中度的子图来说,DIRECT这个方法更加的高效。但是,传统的『Null模型』又比DIRECT这个算法能更加快速地解决高度集中的子图。接下来,我们将详细讲述ESU算法和展示如何把这种精确的算法调整为RAND-ESU算法去估计子图的浓度。<br />
<br />
The algorithms ''ESU'' and ''RAND-ESU'' are fairly simple, and hence easy to implement. ''ESU'' first finds the set of all induced sub-graphs of size {{math|k}}, let {{math|S<sub>k</sub>}} be this set. ''ESU'' can be implemented as a recursive function; the running of this function can be displayed as a tree-like structure of depth {{math|k}}, called the ESU-Tree (see figure). Each of the ESU-Tree nodes indicate the status of the recursive function that entails two consecutive sets SUB and EXT. SUB refers to nodes in the target network that are adjacent and establish a partial sub-graph of size {{math|{{!}}SUB{{!}} ≤ k}}. If {{math|{{!}}SUB{{!}} {{=}} k}}, the algorithm has found an induced complete sub-graph, so {{math|S<sub>k</sub> {{=}} SUB ∪ S<sub>k</sub>}}. However, if {{math|{{!}}SUB{{!}} < k}}, the algorithm must expand SUB to achieve cardinality {{math|k}}. This is done by the EXT set that contains all the nodes that satisfy two conditions: First, each of the nodes in EXT must be adjacent to at least one of the nodes in SUB; second, their numerical labels must be larger than the label of first element in SUB. The first condition makes sure that the expansion of SUB nodes yields a connected graph and the second condition causes ESU-Tree leaves (see figure) to be distinct; as a result, it prevents overcounting. Note that, the EXT set is not a static set, so in each step it may expand by some new nodes that do not breach the two conditions. The next step of ESU involves classification of sub-graphs placed in the ESU-Tree leaves into non-isomorphic size-{{math|k}} graph classes; consequently, ESU determines sub-graphs frequencies and concentrations. This stage has been implemented simply by employing McKay's ''nauty'' algorithm,<ref name="mck1">{{cite journal |author=McKay BD |title=Practical graph isomorphism |journal=Congressus Numerantium |year=1981 |volume=30 |pages=45–87|bibcode=2013arXiv1301.1493M |arxiv=1301.1493 }}</ref><ref name="mck2">{{cite journal |author=McKay BD |title=Isomorph-free exhaustive generation |journal=Journal of Algorithms |year=1998 |volume=26 |issue=2 |pages=306–324 |doi=10.1006/jagm.1997.0898}}</ref> which classifies each sub-graph by performing a graph isomorphism test. Therefore, ESU finds the set of all induced {{math|k}}-size sub-graphs in a target graph by a recursive algorithm and then determines their frequency using an efficient tool.<br />
<br />
ESU和RAND-ESU两种算法都比较简捷,所以实现起来都很容易。『ESU首先找到大小为k的所有诱导子图的集合』,并命名这个集合为Sk。因为EUS以递归函数的形式实现,该函数的运行可以演示为『k级』的树状结构,称为ESU-Tree(见图)。每一个在ESU-Tree上的节点都表示递归函数的状态,这个递归函数需要两个连续集合的SUB和EXT。『SUB指的是在目标网络的相邻节点上,并且是一部分的层级绝对值大小小于等于k的子图集合。』如果SUB集合层级的绝对值等于k,那么这个算法可以找到一个『完整的诱导子图』,所以在此情况下Sk等于SUB与Sk的并集。相反,如果它的绝对值小于k,那么这个算法必须把SUB扩大,才能实现基数为k。『EXT这个集合包含了所有的满足以下两个情况的节点。第一,每个在EXT的节点必须至少与在SUB的一个节点相邻。第二,他们的下标必须比在SUB的第一个元素大。』???第一个条件保证了『SUB节点的展开产生相关的图』,第二个条件能使ESU-Tree树状图上的分支变得离散。所以,这个方法可以避免过度计算。注意,EXT集合不是一个固定的集合。所以每一步都有可能扩展满足于以上两个条件的新节点。下一步包含了在ESU-Tree分支上的子图的分类,『将它们分为非同构的大小为k的图类』。因此,ESU决定了子图的『频率以及浓度』。这一阶段的实施仅通过运用McKay的nauty算法,这一算法可以通过图的同构测试来把每个子图进行分类。所以,ESU能够在目标图中通过递归算法,找到所有规模大小为k的诱导子图集合,且使用高效的工具来确定他们的『频率』。<br />
<br />
The procedure of implementing ''RAND-ESU'' is quite straightforward and is one of the main advantages of ''FANMOD''. One can change the ''ESU'' algorithm to explore just a portion of the ESU-Tree leaves by applying a probability value {{math|0 ≤ p<sub>d</sub> ≤ 1}} for each level of the ESU-Tree and oblige ''ESU'' to traverse each child node of a node in level {{math|d-1}} with probability {{math|p<sub>d</sub>}}. This new algorithm is called ''RAND-ESU''. Evidently, when {{math|p<sub>d</sub> {{=}} 1}} for all levels, ''RAND-ESU'' acts like ''ESU''. For {{math|p<sub>d</sub> {{=}} 0}} the algorithm finds nothing. Note that, this procedure ensures that the chances of visiting each leaf of the ESU-Tree are the same, resulting in ''unbiased'' sampling of sub-graphs through the network. The probability of visiting each leaf is {{math|∏<sub>d</sub>p<sub>d</sub>}} and this is identical for all of the ESU-Tree leaves; therefore, this method guarantees unbiased sampling of sub-graphs from the network. Nonetheless, determining the value of {{math|p<sub>d</sub>}} for {{math|1 ≤ d ≤ k}} is another issue that must be determined manually by an expert to get precise results of sub-graph concentrations.<ref name="cir1" /> While there is no lucid prescript for this matter, the Wernicke provides some general observations that may help in determining p_d values. In summary, ''RAND-ESU'' is a very fast algorithm for NM discovery in the case of induced sub-graphs supporting unbiased sampling method. Although, the main ''ESU'' algorithm and so the ''FANMOD'' tool is known for discovering induced sub-graphs, there is trivial modification to ''ESU'' which makes it possible for finding non-induced sub-graphs, too. The pseudo code of ''ESU (FANMOD)'' is shown below:<br />
运用RAND-ESU的过程十分的简单,这也是FANMOD的一个主要的优点。可以通过对ESU-Tree『树状图』的每个级别应用概率{{math|0 ≤ p<sub>d</sub> ≤ 1}}并强制ESU以概率{{math|p<sub>d</sub>}}遍历{{math|d-1}}级别中节点的每个子节点,来更改ESU算法使其仅搜索ESU-Tree分支的一部分。 这种新的演算方式叫RAND-ESU。显然,当所有阶段{{math|p<sub>d</sub> {{=}} 1}}时,RAND-ESU等同于ESU。当{{math|p<sub>d</sub> {{=}} 0}}时,在这个算法下没有任何意义。注意,这个过程只是确保了可以找到ESU-Tree上的每一分支的机会都是相同的,从而使网络中的子图采样无偏差。访问每个分支的概率为{{math|∏<sub>d</sub>p<sub>d</sub>}},这对于所有ESU-Tree中的分支都是相同的; 因此,该方法可确保从网络中对子图进行无偏采样。但是,设置{{math|1 ≤ d ≤ k}}的{{math|p<sub>d</sub>}}参数是另一个问题,必须由专家人工确定才能获得子图『浓度』的精确结果。尽管对此没有明确的规定,但是Wrenucke提出了一些一般性的观察结论,这些结论有可能可以帮助我们确定p_d值。总的来说,在诱导子图支持无偏采样方法的情况下,RAND-ESU是一个能快速解决『NM discovery problem』的算法。 尽管,ESU算法的主要部分和FANMOD工具是以用来寻找诱导子图而著称的,但只需对ESU进行细小的改动,就可以用来寻找诱导子图。ESU(FANMOD)的伪代码如下:<br />
[[File:ESU-Tree.jpg|thumb|(a) ''A target graph of size 5'', (b) ''the ESU-tree of depth k that is associated to the extraction of sub-graphs of size 3 in the target graph''. Leaves correspond to set S3 or all of the size-3 induced sub-graphs of the target graph (a). Nodes in the ESU-tree include two adjoining sets, the first set contains adjacent nodes called SUB and the second set named EXT holds all nodes that are adjacent to at least one of the SUB nodes and where their numerical labels are larger than the SUB nodes labels. The EXT set is utilized by the algorithm to expand a SUB set until it reaches a desired sub-graph size that are placed at the lowest level of ESU-Tree (or its leaves).]]<br />
<br />
{| class="wikitable"<br />
|-<br />
! Enumeration of ESU (FANMOD)<br />
|-<br />
|'''''EnumerateSubgraphs(G,k)'''''<br />
<br />
'''Input:''' A graph {{math|G {{=}} (V, E)}} and an integer {{math|1 ≤ k ≤ {{!}}V{{!}}}}.<br />
<br />
'''Output:''' All size-{{math|k}} subgraphs in {{math|G}}.<br />
<br />
'''for each''' vertex {{math|v ∈ V}} '''do'''<br />
<br />
{{pad|2em}}{{math|VExtension ← {u ∈ N({v}) {{!}} u > v}}}<br />
<br />
{{pad|2em}}'''call''' {{math|''ExtendSubgraph''({v}, VExtension, v)}}<br />
<br />
'''endfor'''<br />
|-<br />
|'''''ExtendSubgraph(VSubgraph, VExtension, v)'''''<br />
<br />
'''if''' {{math|{{!}}VSubgraph{{!}} {{=}} k}} '''then''' output {{math|G[VSubgraph]}} and '''return'''<br />
<br />
'''while''' {{math|VExtension ≠ ∅}} '''do'''<br />
<br />
{{pad|2em}}Remove an arbitrarily chosen vertex {{math|w}} from {{math|VExtension}}<br />
<br />
{{pad|2em}}{{math|VExtension&prime; ← VExtension ∪ {u ∈ N<sub>excl</sub>(w, VSubgraph) {{!}} u > v}}}<br />
<br />
{{pad|2em}}'''call''' {{math|''ExtendSubgraph''(VSubgraph ∪ {w}, VExtension&prime;, v)}}<br />
<br />
'''return'''<br />
|}<br />
<br />
===NeMoFinder===<br />
Chen ''et al.'' <ref name="che1">{{cite conference |vauthors=Chen J, Hsu W, Li Lee M, etal |title=NeMoFinder: dissecting genome-wide protein-protein interactions with meso-scale network motifs |conference=the 12th ACM SIGKDD international conference on Knowledge discovery and data mining |year=2006 |location=Philadelphia, Pennsylvania, USA |pages=106–115}}</ref> introduced a new NM discovery algorithm called ''NeMoFinder'', which adapts the idea in ''SPIN'' <ref name="hua1">{{cite conference |vauthors=Huan J, Wang W, Prins J, etal |title=SPIN: mining maximal frequent sub-graphs from graph databases |conference=the 10th ACM SIGKDD international conference on Knowledge discovery and data mining |year=2004 |pages=581–586}}</ref> to extract frequent trees and after that expands them into non-isomorphic graphs.<ref name="cir1" /> ''NeMoFinder'' utilizes frequent size-n trees to partition the input network into a collection of size-{{math|n}} graphs, afterward finding frequent size-n sub-graphs by expansion of frequent trees edge-by-edge until getting a complete size-{{math|n}} graph {{math|K<sub>n</sub>}}. The algorithm finds NMs in undirected networks and is not limited to extracting only induced sub-graphs. Furthermore, ''NeMoFinder'' is an exact enumeration algorithm and is not based on a sampling method. As Chen ''et al.'' claim, ''NeMoFinder'' is applicable for detecting relatively large NMs, for instance, finding NMs up to size-12 from the whole ''S. cerevisiae'' (yeast) PPI network as the authors claimed.<ref name="uet1">{{cite journal |vauthors=Uetz P, Giot L, Cagney G, etal |title=A comprehensive analysis of protein-protein interactions in Saccharomyces cerevisiae |journal=Nature |year=2000 |volume=403 |issue=6770 |pages=623–627 |doi=10.1038/35001009 |pmid=10688190|bibcode=2000Natur.403..623U }}</ref><br />
<br />
''NeMoFinder'' consists of three main steps. First, finding frequent size-{{math|n}} trees, then utilizing repeated size-n trees to divide the entire network into a collection of size-{{math|n}} graphs, finally, performing sub-graph join operations to find frequent size-n sub-graphs.<ref name="che1" /> In the first step, the algorithm detects all non-isomorphic size-{{math|n}} trees and mappings from a tree to the network. In the second step, the ranges of these mappings are employed to partition the network into size-n graphs. Up to this step, there is no distinction between ''NeMoFinder'' and an exact enumeration method. However, a large portion of non-isomorphic size-n graphs still remain. ''NeMoFinder'' exploits a heuristic to enumerate non-tree size-n graphs by the obtained information from the preceding steps. The main advantage of the algorithm is in the third step, which generates candidate sub-graphs from previously enumerated sub-graphs. This generation of new size-{{math|n}} sub-graphs is done by joining each previous sub-graph with derivative sub-graphs from itself called ''cousin sub-graphs''. These new sub-graphs contain one additional edge in comparison to the previous sub-graphs. However, there exist some problems in generating new sub-graphs: There is no clear method to derive cousins from a graph, joining a sub-graph with its cousins leads to redundancy in generating particular sub-graph more than once, and cousin determination is done by a canonical representation of the adjacency matrix which is not closed under join operation. ''NeMoFinder'' is an efficient network motif finding algorithm for motifs up to size 12 only for protein-protein interaction networks, which are presented as undirected graphs. And it is not able to work on directed networks which are so important in the field of complex and biological networks. The pseudocode of ''NeMoFinder'' is shown below:<br />
<br />
{| class="wikitable"<br />
|-<br />
! NeMoFinder<br />
|-<br />
|'''Input:'''<br />
<br />
{{math|G}} - PPI network;<br />
<br />
{{math|N}} - Number of randomized networks;<br />
<br />
{{math|K}} - Maximal network motif size;<br />
<br />
{{math|F}} - Frequency threshold;<br />
<br />
{{math|S}} - Uniqueness threshold;<br />
<br />
'''Output:'''<br />
<br />
{{math|U}} - Repeated and unique network motif set;<br />
<br />
{{math|D ← ∅}};<br />
<br />
'''for''' motif-size {{math|k}} '''from''' 3 '''to''' {{math|K}} '''do'''<br />
<br />
{{pad|1em}}{{math|T ← ''FindRepeatedTrees''(k)}};<br />
<br />
{{pad|1em}}{{math|GD<sub>k</sub> ← ''GraphPartition''(G, T)}}<br />
<br />
{{pad|1em}}{{math|D ← D ∪ T}};<br />
<br />
{{pad|1em}}{{math|D&prime; ← T}};<br />
<br />
{{pad|1em}}{{math|i ← k}};<br />
<br />
{{pad|1em}}'''while''' {{math|D&prime; ≠ ∅}} '''and''' {{math|i ≤ k &times; (k - 1) / 2}} '''do'''<br />
<br />
{{pad|2em}}{{math|D&prime; ← ''FindRepeatedGraphs''(k, i, D&prime;)}};<br />
<br />
{{pad|2em}}{{math|D ← D ∪ D&prime;}};<br />
<br />
{{pad|2em}}{{math|i ← i + 1}};<br />
<br />
{{pad|1em}}'''end while'''<br />
<br />
'''end for'''<br />
<br />
'''for''' counter {{math|i}} '''from''' 1 '''to''' {{math|N}} '''do'''<br />
<br />
{{pad|1em}}{{math|G<sub>rand</sub> ← ''RandomizedNetworkGeneration''()}};<br />
<br />
{{pad|1em}}'''for each''' {{math|g ∈ D}} '''do'''<br />
<br />
{{pad|2em}}{{math|''GetRandFrequency''(g, G<sub>rand</sub>)}};<br />
<br />
{{pad|1em}}'''end for'''<br />
<br />
'''end for'''<br />
<br />
{{math|U ← ∅}};<br />
<br />
'''for each''' {{math|g ∈ D}} '''do'''<br />
<br />
{{pad|1em}}{{math|s ← ''GetUniqunessValue''(g)}};<br />
<br />
{{pad|1em}}'''if''' {{math|s ≥ S}} '''then'''<br />
<br />
{{pad|2em}}{{math|U ← U ∪ {g}}};<br />
<br />
{{pad|1em}}'''end if'''<br />
<br />
'''end for'''<br />
<br />
'''return''' {{math|U}};<br />
|}<br />
<br />
===Grochow–Kellis===<br />
Grochow and Kellis <ref name="gro1">{{cite conference|vauthors=Grochow JA, Kellis M |title=Network Motif Discovery Using Sub-graph Enumeration and Symmetry-Breaking |conference=RECOMB |year=2007 |pages=92–106| doi=10.1007/978-3-540-71681-5_7| url=http://www.cs.colorado.edu/~jgrochow/Grochow_Kellis_RECOMB_07_Network_Motifs.pdf}}</ref> proposed an ''exact'' algorithm for enumerating sub-graph appearances. The algorithm is based on a ''motif-centric'' approach, which means that the frequency of a given sub-graph,called the ''query graph'', is exhaustively determined by searching for all possible mappings from the query graph into the larger network. It is claimed <ref name="gro1" /> that a ''motif-centric'' method in comparison to ''network-centric'' methods has some beneficial features. First of all it avoids the increased complexity of sub-graph enumeration. Also, by using mapping instead of enumerating, it enables an improvement in the isomorphism test. To improve the performance of the algorithm, since it is an inefficient exact enumeration algorithm, the authors introduced a fast method which is called ''symmetry-breaking conditions''. During straightforward sub-graph isomorphism tests, a sub-graph may be mapped to the same sub-graph of the query graph multiple times. In the Grochow–Kellis (GK) algorithm symmetry-breaking is used to avoid such multiple mappings. Here we introduce the GK algorithm and the symmetry-breaking condition which eliminates redundant isomorphism tests.<br />
<br />
[[File:Automorphisms of a subgraph.jpg|thumb|(a) ''graph G'', (b) ''illustration of all automorphisms of G that is showed in (a)''. From set AutG we can obtain a set of symmetry-breaking conditions of G given by SymG in (c). Only the first mapping in AutG satisfies the SynG conditions; as a result, by applying SymG in the Isomorphism Extension module the algorithm only enumerate each match-able sub-graph in the network to G once. Note that SynG is not necessarily a unique set for an arbitrary graph G.]]<br />
<br />
The GK algorithm discovers the whole set of mappings of a given query graph to the network in two major steps. It starts with the computation of symmetry-breaking conditions of the query graph. Next, by means of a branch-and-bound method, the algorithm tries to find every possible mapping from the query graph to the network that meets the associated symmetry-breaking conditions. An example of the usage of symmetry-breaking conditions in GK algorithm is demonstrated in figure.<br />
<br />
As it is mentioned above, the symmetry-breaking technique is a simple mechanism that precludes spending time finding a sub-graph more than once due to its symmetries.<ref name="gro1" /><ref name="gro2">{{cite conference|author=Grochow JA |title=On the structure and evolution of protein interaction networks |conference=Thesis M. Eng., Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science|year=2006| url=http://www.cs.toronto.edu/~jgrochow/Grochow_MIT_Masters_06_PPI_Networks.pdf}}</ref> Note that, computing symmetry-breaking conditions requires finding all automorphisms of a given query graph. Even though, there is no efficient (or polynomial time) algorithm for the graph automorphism problem, this problem can be tackled efficiently in practice by McKay's tools.<ref name="mck1" /><ref name="mck2" /> As it is claimed, using symmetry-breaking conditions in NM detection lead to save a great deal of running time. Moreover, it can be inferred from the results in <ref name="gro1" /><ref name="gro2" /> that using the symmetry-breaking conditions results in high efficiency particularly for directed networks in comparison to undirected networks. The symmetry-breaking conditions used in the GK algorithm are similar to the restriction which ''ESU'' algorithm applies to the labels in EXT and SUB sets. In conclusion, the GK algorithm computes the exact number of appearance of a given query graph in a large complex network and exploiting symmetry-breaking conditions improves the algorithm performance. Also, GK algorithm is one of the known algorithms having no limitation for motif size in implementation and potentially it can find motifs of any size.<br />
<br />
===Color-coding approach===<br />
Most algorithms in the field of NM discovery are used to find induced sub-graphs of a network. In 2008, Noga Alon ''et al.'' <ref name="alo1">{{cite journal|author1=Alon N |author2=Dao P |author3=Hajirasouliha I |author4=Hormozdiari F |author5=Sahinalp S.C |title=Biomolecular network motif counting and discovery by color coding |journal=Bioinformatics |year=2008 |volume=24 |issue=13 |pages=i241–i249 |doi=10.1093/bioinformatics/btn163|pmid=18586721 |pmc=2718641 }}</ref> introduced an approach for finding non-induced sub-graphs too. Their technique works on undirected networks such as PPI ones. Also, it counts non-induced trees and bounded treewidth sub-graphs. This method is applied for sub-graphs of size up to 10.<br />
<br />
This algorithm counts the number of non-induced occurrences of a tree {{math|T}} with {{math|k {{=}} O(logn)}} vertices in a network {{math|G}} with {{math|n}} vertices as follows:<br />
<br />
# '''Color coding.''' Color each vertex of input network G independently and uniformly at random with one of the {{math|k}} colors.<br />
# '''Counting.''' Apply a dynamic programming routine to count the number of non-induced occurrences of {{math|T}} in which each vertex has a unique color. For more details on this step, see.<ref name="alo1" /><br />
# Repeat the above two steps {{math|O(e<sup>k</sup>)}} times and add up the number of occurrences of {{math|T}} to get an estimate on the number of its occurrences in {{math|G}}.<br />
<br />
As available PPI networks are far from complete and error free, this approach is suitable for NM discovery for such networks. As Grochow–Kellis Algorithm and this one are the ones popular for non-induced sub-graphs, it is worth to mention that the algorithm introduced by Alon ''et al.'' is less time-consuming than the Grochow–Kellis Algorithm.<ref name="alo1" /><br />
<br />
===MODA===<br />
Omidi ''et al.'' <ref name="omi1">{{cite journal|vauthors=Omidi S, Schreiber F, Masoudi-Nejad A |title=MODA: an efficient algorithm for network motif discovery in biological networks |journal=Genes Genet Syst |year=2009 |volume=84 |issue=5 |pages=385–395 |doi=10.1266/ggs.84.385|pmid=20154426 |doi-access=free }}</ref> introduced a new algorithm for motif detection named ''MODA'' which is applicable for induced and non-induced NM discovery in undirected networks. It is based on the motif-centric approach discussed in the Grochow–Kellis algorithm section. It is very important to distinguish motif-centric algorithms such as MODA and GK algorithm because of their ability to work as query-finding algorithms. This feature allows such algorithms to be able to find a single motif query or a small number of motif queries (not all possible sub-graphs of a given size) with larger sizes. As the number of possible non-isomorphic sub-graphs increases exponentially with sub-graph size, for large size motifs (even larger than 10), the network-centric algorithms, those looking for all possible sub-graphs, face a problem. Although motif-centric algorithms also have problems in discovering all possible large size sub-graphs, but their ability to find small numbers of them is sometimes a significant property.<br />
<br />
Using a hierarchical structure called an ''expansion tree'', the ''MODA'' algorithm is able to extract NMs of a given size systematically and similar to ''FPF'' that avoids enumerating unpromising sub-graphs; ''MODA'' takes into consideration potential queries (or candidate sub-graphs) that would result in frequent sub-graphs. Despite the fact that ''MODA'' resembles ''FPF'' in using a tree like structure, the expansion tree is applicable merely for computing frequency concept {{math|F<sub>1</sub>}}. As we will discuss next, the advantage of this algorithm is that it does not carry out the sub-graph isomorphism test for ''non-tree'' query graphs. Additionally, it utilizes a sampling method in order to speed up the running time of the algorithm.<br />
<br />
Here is the main idea: by a simple criterion one can generalize a mapping of a k-size graph into the network to its same size supergraphs. For example, suppose there is mapping {{math|f(G)}} of graph {{math|G}} with {{math|k}} nodes into the network and we have a same size graph {{math|G&prime;}} with one more edge {{math|&langu, v&rang;}}; {{math|f<sub>G</sub>}} will map {{math|G&prime;}} into the network, if there is an edge {{math|&lang;f<sub>G</sub>(u), f<sub>G</sub>(v)&rang;}} in the network. As a result, we can exploit the mapping set of a graph to determine the frequencies of its same order supergraphs simply in {{math|O(1)}} time without carrying out sub-graph isomorphism testing. The algorithm starts ingeniously with minimally connected query graphs of size k and finds their mappings in the network via sub-graph isomorphism. After that, with conservation of the graph size, it expands previously considered query graphs edge-by-edge and computes the frequency of these expanded graphs as mentioned above. The expansion process continues until reaching a complete graph {{math|K<sub>k</sub>}} (fully connected with {{math|{{frac|k(k-1)|2}}}} edge).<br />
<br />
As discussed above, the algorithm starts by computing sub-tree frequencies in the network and then expands sub-trees edge by edge. One way to implement this idea is called the expansion tree {{math|T<sub>k</sub>}} for each {{math|k}}. Figure shows the expansion tree for size-4 sub-graphs. {{math|T<sub>k</sub>}} organizes the running process and provides query graphs in a hierarchical manner. Strictly speaking, the expansion tree {{math|T<sub>k</sub>}} is simply a [[directed acyclic graph]] or DAG, with its root number {{math|k}} indicating the graph size existing in the expansion tree and each of its other nodes containing the adjacency matrix of a distinct {{math|k}}-size query graph. Nodes in the first level of {{math|T<sub>k</sub>}} are all distinct {{math|k}}-size trees and by traversing {{math|T<sub>k</sub>}} in depth query graphs expand with one edge at each level. A query graph in a node is a sub-graph of the query graph in a node's child with one edge difference. The longest path in {{math|T<sub>k</sub>}} consists of {{math|(k<sup>2</sup>-3k+4)/2}} edges and is the path from the root to the leaf node holding the complete graph. Generating expansion trees can be done by a simple routine which is explained in.<ref name="omi1" /><br />
<br />
''MODA'' traverses {{math|T<sub>k</sub>}} and when it extracts query trees from the first level of {{math|T<sub>k</sub>}} it computes their mapping sets and saves these mappings for the next step. For non-tree queries from {{math|T<sub>k</sub>}}, the algorithm extracts the mappings associated with the parent node in {{math|T<sub>k</sub>}} and determines which of these mappings can support the current query graphs. The process will continue until the algorithm gets the complete query graph. The query tree mappings are extracted using the Grochow–Kellis algorithm. For computing the frequency of non-tree query graphs, the algorithm employs a simple routine that takes {{math|O(1)}} steps. In addition, ''MODA'' exploits a sampling method where the sampling of each node in the network is linearly proportional to the node degree, the probability distribution is exactly similar to the well-known Barabási-Albert preferential attachment model in the field of complex networks.<ref name="bar1">{{cite journal|vauthors=Barabasi AL, Albert R |title=Emergence of scaling in random networks |journal=Science |year=1999 |volume=286 |issue=5439 |pages=509–512 |doi=10.1126/science.286.5439.509 |pmid=10521342|bibcode=1999Sci...286..509B |arxiv=cond-mat/9910332 }}</ref> This approach generates approximations; however, the results are almost stable in different executions since sub-graphs aggregate around highly connected nodes.<ref name="vaz1">{{cite journal |vauthors=Vázquez A, Dobrin R, Sergi D, etal |title=The topological relationship between the large-scale attributes and local interaction patterns of complex networks |journal=PNAS |year=2004 |volume=101 |issue=52 |pages=17940–17945 |doi=10.1073/pnas.0406024101|pmid=15598746 |pmc=539752 |bibcode=2004PNAS..10117940V |arxiv=cond-mat/0408431 }}</ref> The pseudocode of ''MODA'' is shown below:<br />
<br />
[[File:Expansion Tree.jpg|thumb|''Illustration of the expansion tree T4 for 4-node query graphs''. At the first level, there are non-isomorphic k-size trees and at each level, an edge is added to the parent graph to form a child graph. In the second level, there is a graph with two alternative edges that is shown by a dashed red edge. In fact, this node represents two expanded graphs that are isomorphic.<ref name="omi1" />]]<br />
<br />
{| class="wikitable"<br />
|-<br />
! MODA<br />
|-<br />
|'''Input:''' {{math|G}}: Input graph, {{math|k}}: sub-graph size, {{math|Δ}}: threshold value<br />
<br />
'''Output:''' Frequent Subgraph List: List of all frequent {{math|k}}-size sub-graphs<br />
<br />
'''Note:''' {{math|F<sub>G</sub>}}: set of mappings from {{math|G}} in the input graph {{math|G}}<br />
<br />
'''fetch''' {{math|T<sub>k</sub>}}<br />
<br />
'''do'''<br />
<br />
{{pad|1em}}{{math|G&prime; {{=}} ''Get-Next-BFS''(T<sub>k</sub>)}} // {{math|G&prime;}} is a query graph<br />
<br />
{{pad|1em}}if {{math|{{!}}E(G&prime;){{!}} {{=}} (k – 1)}}<br />
<br />
{{pad|1em}}'''call''' {{math|''Mapping-Module''(G&prime;, G)}}<br />
<br />
{{pad|1em}}'''else'''<br />
<br />
{{pad|2em}}'''call''' {{math|''Enumerating-Module''(G&prime;, G, T<sub>k</sub>)}}<br />
<br />
{{pad|1em}}'''end if'''<br />
<br />
{{pad|1em}}'''save''' {{math|F<sub>2</sub>}}<br />
<br />
{{pad|1em}}'''if''' {{math|{{!}}F<sub>G</sub>{{!}} > Δ}} '''then'''<br />
<br />
{{pad|2em}}add {{math|G&prime;}} into Frequent Subgraph List<br />
<br />
{{pad|1em}}'''end if'''<br />
<br />
'''Until''' {{math|{{!}}E(G'){{!}} {{=}} (k – 1)/2}}<br />
<br />
'''return''' Frequent Subgraph List<br />
|}<br />
<br />
===Kavosh===<br />
A recently introduced algorithm named ''Kavosh'' <ref name="kash1">{{cite journal|vauthors=Kashani ZR, Ahrabian H, Elahi E, Nowzari-Dalini A, Ansari ES, Asadi S, Mohammadi S, Schreiber F, Masoudi-Nejad A |title=Kavosh: a new algorithm for finding network motifs |journal=BMC Bioinformatics |year=2009 |volume=10 |issue=318|pages=318 |doi=10.1186/1471-2105-10-318 |pmid=19799800 |pmc=2765973}} </ref> aims at improved main memory usage. ''Kavosh'' is usable to detect NM in both directed and undirected networks. The main idea of the enumeration is similar to the ''GK'' and ''MODA'' algorithms, which first find all {{math|k}}-size sub-graphs that a particular node participated in, then remove the node, and subsequently repeat this process for the remaining nodes.<ref name="kash1" /><br />
<br />
For counting the sub-graphs of size {{math|k}} that include a particular node, trees with maximum depth of k, rooted at this node and based on neighborhood relationship are implicitly built. Children of each node include both incoming and outgoing adjacent nodes. To descend the tree, a child is chosen at each level with the restriction that a particular child can be included only if it has not been included at any upper level. After having descended to the lowest level possible, the tree is again ascended and the process is repeated with the stipulation that nodes visited in earlier paths of a descendant are now considered unvisited nodes. A final restriction in building trees is that all children in a particular tree must have numerical labels larger than the label of the root of the tree. The restrictions on the labels of the children are similar to the conditions which ''GK'' and ''ESU'' algorithm use to avoid overcounting sub-graphs.<br />
<br />
The protocol for extracting sub-graphs makes use of the compositions of an integer. For the extraction of sub-graphs of size {{math|k}}, all possible compositions of the integer {{math|k-1}} must be considered. The compositions of {{math|k-1}} consist of all possible manners of expressing {{math|k-1}} as a sum of positive integers. Summations in which the order of the summands differs are considered distinct. A composition can be expressed as {{math|k<sub>2</sub>,k<sub>3</sub>,…,k<sub>m</sub>}} where {{math|k<sub>2</sub> + k<sub>3</sub> + … + k<sub>m</sub> {{=}} k-1}}. To count sub-graphs based on the composition, {{math|k<sub>i</sub>}} nodes are selected from the {{math|i}}-th level of the tree to be nodes of the sub-graphs ({{math|i {{=}} 2,3,…,m}}). The {{math|k-1}} selected nodes along with the node at the root define a sub-graph within the network. After discovering a sub-graph involved as a match in the target network, in order to be able to evaluate the size of each class according to the target network, ''Kavosh'' employs the ''nauty'' algorithm <ref name="mck1" /><ref name="mck2" /> in the same way as ''FANMOD''. The enumeration part of Kavosh algorithm is shown below:<br />
<br />
{| class="wikitable"<br />
|-<br />
! Enumeration of Kavosh<br />
|-<br />
|'''''Enumerate_Vertex(G, u, S, Remainder, i)'''''<br />
<br />
'''Input:''' {{math|G}}: Input graph<br><br />
{{pad|3em}}{{math|u}}: Root vertex<br><br />
{{pad|3em}}{{math|S}}: selection ({{math|S {{=}} { S<sub>0</sub>,S<sub>1</sub>,...,S<sub>k-1</sub>}}} is an array of the set of all {{math|S<sub>i</sub>}})<br><br />
{{pad|3em}}{{math|Remainder}}: number of remaining vertices to be selected<br><br />
{{pad|3em}}{{math|i}}: Current depth of the tree.<br><br />
'''Output:''' all {{math|k}}-size sub-graphs of graph {{math|G}} rooted in {{math|u}}.<br />
<br />
'''if''' {{math|Remainder {{=}} 0}} '''then'''<br><br />
{{pad|1em}}'''return'''<br><br />
'''else'''<br><br />
{{pad|1em}}{{math|ValList ← ''Validate''(G, S<sub>i-1</sub>, u)}}<br><br />
{{pad|1em}}{{math|n<sub>i</sub> ← ''Min''({{!}}ValList{{!}}, Remainder)}}<br><br />
{{pad|1em}}'''for''' {{math|k<sub>i</sub> {{=}} 1}} '''to''' {{math|n<sub>i</sub>}} '''do'''<br><br />
{{pad|2em}}{{math|C ← ''Initial_Comb''(ValList, k<sub>i</sub>)}}<br><br />
{{pad|2em}}(Make the first vertex combination selection according)<br><br />
{{pad|2em}}'''repeat'''<br><br />
{{pad|3em}}{{math|S<sub>i</sub> ← C}}<br><br />
{{pad|3em}}{{math|''Enumerate_Vertex''(G, u, S, Remainder-k<sub>i</sub>, i+1)}}<br><br />
{{pad|3em}}{{math|''Next_Comb''(ValList, k<sub>i</sub>)}}<br><br />
{{pad|3em}}(Make the next vertex combination selection according)<br><br />
{{pad|2em}}'''until''' {{math|C {{=}} NILL}}<br><br />
{{pad|2em}}'''end for'''<br><br />
{{pad|1em}}'''for each''' {{math|v ∈ ValList}} '''do'''<br><br />
{{pad|2em}}{{math|Visited[v] ← false}}<br><br />
{{pad|1em}}'''end for'''<br><br />
'''end if'''<br />
|-<br />
|'''''Validate(G, Parents, u)'''''<br><br />
'''Input:''' {{math|G}}: input graph, {{math|Parents}}: selected vertices of last layer, {{math|u}}: Root vertex.<br><br />
'''Output:''' Valid vertices of the current level.<br />
<br />
{{math|ValList ← NILL}}<br><br />
'''for each''' {{math|v ∈ Parents}} '''do'''<br><br />
{{pad|1em}}'''for each''' {{math|w ∈ Neighbor[u]}} '''do'''<br><br />
{{pad|2em}}'''if''' {{math|label[u] < label[w]}} '''AND NOT''' {{math|Visited[w]}} '''then'''<br><br />
{{pad|3em}}{{math|Visited[w] ← true}}<br><br />
{{pad|3em}}{{math|ValList {{=}} ValList + w}}<br><br />
{{pad|2em}}'''end if'''<br><br />
{{pad|1em}}'''end for'''<br><br />
'''end for'''<br><br />
'''return''' {{math|ValList}}<br><br />
|}<br />
<br />
Recently a ''Cytoscape'' plugin called ''CytoKavosh'' <ref name="mas2">{{cite journal|author1=Ali Masoudi-Nejad |author2=Mitra Anasariola |author3=Ali Salehzadeh-Yazdi |author4=Sahand Khakabimamaghani |title=CytoKavosh: a Cytoscape Plug-in for Finding Network Motifs in Large Biological Networks |journal=PLoS ONE |volume=7 |issue=8 |pages=e43287 |year=2012 |doi=10.1371/journal.pone.0043287|pmid=22952659 |pmc=3430699 |bibcode=2012PLoSO...743287M }} </ref> is developed for this software. It is available via ''Cytoscape'' web page [http://apps.cytoscape.org/apps/cytokavosh].<br />
<br />
===G-Tries===<br />
2010年, Pedro Ribeiro 和 Fernando Silva 提出了一个叫做''g-trie''的新数据结构,用来存储一组子图。<ref name="rib1">{{cite conference|vauthors=Ribeiro P, Silva F |title=G-Tries: an efficient data structure for discovering network motifs |conference=ACM 25th Symposium On Applied Computing - Bioinformatics Track |location=Sierre, Switzerland |year=2010 |pages=1559–1566 |url=http://www.nrcbioinformatics.ca/acmsac2010/}}</ref>这个在概念上类似前缀树的数据结构,根据子图结构来进行存储,并找出了每个子图在一个更大的图中出现的次数。这个数据结构有一个突出的方面:在应用于模体发现算法时,主网络中的子图需要进行评估。因此,在随机网络中寻找那些在不在主网络中的子图,这个消耗时间的步骤就不再需要执行了。<br />
<br />
''g-trie'' 是一个存储一组图的多叉树。每一个树节点都存储着一个'''图节点'''及其'''对应的到前一个节点的边'''的信息。从根节点到叶节点的一条路径对应一个图。一个 g-trie 节点的子孙节点共享一个子图(即每一次路径的分叉意味着从一个子图结构中扩展出不同的图结构,而这些扩展出来的图结构自然有着相同的子图结构)。如何构造一个 ''g-trie'' 在<ref name="rib1" />中有详细描述。构造好一个 ''g-trie'' 以后,需要进行计数步骤。计数流程的主要思想是回溯所有可能的子图,同时进行同构性测试。这种回溯技术本质上和其他以模体为中心的方法,比如''MODA'' 和 ''GK'' 算法中使用的技术是一样的。这种技术利用了共同的子结构,亦即在一定时间内,几个不同的候选子图中存在部分是同构的。<br />
<br />
在上述算法中,''G-Tries'' 是最快的。然而,它的一个缺点是内存的超量使用,这局限了它在个人电脑运行时所能发现的模体的大小<br />
<br />
===对比===<br />
<br />
下面的表格和数据显示了在各种标准网络中运行上述算法所获得的结果。这些结果皆获取于各自相应的来源<ref name="omi1" /><ref name="kash1" /><ref name="rib1" /> ,因此需要独立地对待它们。<br />
<br />
[[Image:Runtimes of algorithms.jpg|thumb|''Runtimes of Grochow–Kellis, mfinder, FANMOD, FPF and MODA for subgraphs from three nodes up to nine nodes''.<ref name="omi1" />]]<br />
<br />
{|class="wikitable"<br />
|+ Grochow–Kellis, FANMOD, 和 G-Trie 在5个不同网络上生成含3到9个节点子图所用的运行时间 <ref name="rib1" /><br />
|-<br />
!rowspan="2"|网络<br />
!rowspan="2"|子图大小<br />
!colspan="3"|原始网络数据<br />
!colspan="3"|随机网络平均数据<br />
|-<br />
!FANMOD<br />
!GK<br />
!G-Trie<br />
!FANMOD<br />
!GK<br />
!G-Trie<br />
|-<br />
|rowspan="5"|Dolphins<br />
|5 || 0.07 || 0.03 || 0.01 || 0.13 || 0.04 || 0.01<br />
|-<br />
|6||0.48||0.28||0.04||1.14||0.35||0.07<br />
|-<br />
|7||3.02||3.44||0.23||8.34||3.55||0.46<br />
|-<br />
|8||19.44||73.16||1.69||67.94||37.31||4.03<br />
|-<br />
|9||100.86||2984.22||6.98||493.98||366.79||24.84<br />
|-<br />
|rowspan="3"|Circuit<br />
|6||0.49||0.41||0.03||0.55||0.24||0.03<br />
|-<br />
|7||3.28||3.73||0.22||3.53||1.34||0.17<br />
|-<br />
|8||17.78||48.00||1.52||21.42||7.91||1.06<br />
|-<br />
|rowspan="3"|Social<br />
|3||0.31||0.11||0.02||0.35||0.11||0.02<br />
|-<br />
|4||7.78||1.37||0.56||13.27||1.86||0.57<br />
|-<br />
|5||208.30||31.85||14.88||531.65||62.66||22.11<br />
|-<br />
|rowspan="3"|Yeast<br />
|3||0.47||0.33||0.02||0.57||0.35||0.02<br />
|-<br />
|4||10.07||2.04||0.36||12.90||2.25||0.41<br />
|-<br />
|5||268.51||34.10||12.73||400.13||47.16||14.98<br />
|-<br />
|rowspan="5"|Power<br />
|3||0.51||1.46||0.00||0.91||1.37||0.01<br />
|-<br />
|4||1.38||4.34||0.02||3.01||4.40||0.03<br />
|-<br />
|5||4.68||16.95||0.10||12.38||17.54||0.14<br />
|-<br />
|6||20.36||95.58||0.55||67.65||92.74||0.88<br />
|-<br />
|7||101.04||765.91||3.36||408.15||630.65||5.17<br />
|}<br />
<br />
{|class="wikitable"<br />
|+ mfinder, FANMOD, Mavisto 和 Kavosh 在3个不同网络上生成含3到10个节点子图所用的运行时间<ref name="kash1" /><br />
|-<br />
!&nbsp;<br />
!子图大小→<br />
!rowspan="2"|3<br />
!rowspan="2"|4<br />
!rowspan="2"|5<br />
!rowspan="2"|6<br />
!rowspan="2"|7<br />
!rowspan="2"|8<br />
!rowspan="2"|9<br />
!rowspan="2"|10<br />
|-<br />
!网络↓<br />
!算法↓<br />
|-<br />
|rowspan="4"|E. coli<br />
|Kavosh||0.30||1.84||14.91||141.98||1374.0||13173.7||121110.3||1120560.1<br />
|-<br />
|FANMOD||0.81||2.53||15.71||132.24||1205.9||9256.6||-||-<br />
|-<br />
|Mavisto||13532||-||-||-||-||-||-||-<br />
|-<br />
|Mfinder||31.0||297||23671||-||-||-||-||-<br />
|-<br />
|rowspan="4"|Electronic<br />
|Kavosh||0.08||0.36||8.02||11.39||77.22||422.6||2823.7||18037.5<br />
|-<br />
|FANMOD||0.53||1.06||4.34||24.24||160||967.99||-||-<br />
|-<br />
|Mavisto||210.0||1727||-||-||-||-||-||-<br />
|-<br />
|Mfinder||7||14||109.8||2020.2||-||-||-||-<br />
|-<br />
|rowspan="4"|Social<br />
|Kavosh||0.04||0.23||1.63||10.48||69.43||415.66||2594.19||14611.23<br />
|-<br />
|FANMOD||0.46||0.84||3.07||17.63||117.43||845.93||-||-<br />
|-<br />
|Mavisto||393||1492||-||-||-||-||-||-<br />
|-<br />
|Mfinder||12||49||798||181077||-||-||-||-<br />
|}<br />
<br />
===算法的分类===<br />
正如表格所示,模体发现算法可以分为两大类:基于精确计数的算法,以及使用统计采样以及估计的算法。因为后者并不计数所有子图在主网络中出现的次数,所以第二类算法会更快,却也可能产生带有偏向性的,甚至不现实的结果。<br />
<br />
更深一层地,基于精确计数的算法可以分为'''以网络为中心'''的方法以及以'''子图为中心'''的方法。前者在给定网络中搜索给定大小的子图,而后者首先根据给定大小生成各种可能的非同构图,然后在网络中分别搜索这些生成的图。这两种方法都有各自的优缺点,这些在上文有讨论。<br />
<br />
另一方面,基于估计的方法可能会利用如前面描述过的颜色编码手段,其它的手段则通常会在枚举过程中忽略一些子图(比如,像在 FANMOD 中做的那样),然后只在枚举出来的子图上做估计。<br />
<br />
此外,表格还指出了一个算法能否应用于有向网络或无向网络,以及导出子图或非导出子图。更多信息请参考下方提供的网页和实验室地址及联系方式。<br />
{|class="wikitable"<br />
|+ 模体发现算法的分类<br />
|-<br />
!计数方式<br />
!基础<br />
!算法名称<br />
!有向 / 无向<br />
!导出/ 非导出<br />
|-<br />
| rowspan="9" |精确基数<br />
| rowspan="5" |以网络为中心<br />
|[http://www.weizmann.ac.il/mcb/UriAlon/ mfinder]||皆可||导出<br />
|-<br />
|[http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ ESU (FANMOD)]||皆可||导出<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/Kavosh/ Kavosh] (used in [http://apps.cytoscape.org/apps/cytokavosh CytoKavosh])||皆可||导出<br />
|-<br />
|[http://www.dcc.fc.up.pt/gtries/ G-Tries]||皆可||导出<br />
|-<br />
|[http://nesreenahmed.com/graphlets PGD]<br />
|无向<br />
|导出<br />
|-<br />
|rowspan="4"|以子图为中心<br />
|[http://mavisto.ipk-gatersleben.de/ FPF (Mavisto)]||皆可||导出<br />
|-<br />
|[https://www.msu.edu/~jinchen/ NeMoFinder]||无向||导出<br />
|-<br />
|[http://people.cs.uchicago.edu/~joshuag/index.html Grochow–Kellis]||皆可||Both<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/MODA/ MODA]||皆可||皆可<br />
|-<br />
|rowspan="3"|采样估计<br />
|颜色编码<br />
|[http://www.math.tau.ac.il/~nogaa/ N. Alon] ''et al.''’s Algorithm||无向||非导出<br />
|-<br />
|rowspan="2"|其他手段<br />
|[http://www.weizmann.ac.il/mcb/UriAlon/ mfinder]||皆可||导出<br />
|-<br />
|[http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ ESU (FANMOD)]||皆可||导出<br />
|}<br />
<br />
{|class="wikitable"<br />
|+ 算法提出者的地址和联系方式<br />
|-<br />
!算法<br />
!实验室/研究组<br />
!学院<br />
!大学/研究所<br />
!地址<br />
!电子邮件<br />
|-<br />
|[http://www.weizmann.ac.il/mcb/UriAlon/ mfinder]||Uri Alon's Group||Department of Molecular Cell Biology||Weizmann Institute of Science||Rehovot, Israel, Wolfson, Rm. 607||urialon at weizmann.ac.il<br />
|-<br />
|[http://mavisto.ipk-gatersleben.de/ FPF (Mavisto)]||----||----||Leibniz-Institut für Pflanzengenetik und Kulturpflanzenforschung (IPK)||Corrensstraße 3, D-06466 Stadt Seeland, OT Gatersleben, Deutschland||schreibe at ipk-gatersleben.de<br />
|-<br />
|[http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ ESU (FANMOD)]||Lehrstuhl Theoretische Informatik I||Institut für Informatik||Friedrich-Schiller-Universität Jena||Ernst-Abbe-Platz 2,D-07743 Jena, Deutschland||sebastian.wernicke at gmail.com<br />
|-<br />
|[https://www.msu.edu/~jinchen/ NeMoFinder]||----||School of Computing||National University of Singapore||Singapore 119077||chenjin at comp.nus.edu.sg<br />
|-<br />
|[http://www.cs.colorado.edu/~jgrochow/ Grochow–Kellis]||CS Theory Group & Complex Systems Group||Computer Science||University of Colorado, Boulder||1111 Engineering Dr. ECOT 717, 430 UCB Boulder, CO 80309-0430 USA||jgrochow at colorado.edu<br />
|-<br />
|[http://www.math.tau.ac.il/~nogaa/ N. Alon] ''et al.''’s Algorithm||Department of Pure Mathematics||School of Mathematical Sciences||Tel Aviv University||Tel Aviv 69978, Israel||nogaa at post.tau.ac.il<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/MODA/ MODA]||Laboratory of Systems Biology and Bioinformatics (LBB)||Institute of Biochemistry and Biophysics (IBB)||University of Tehran||Enghelab Square, Enghelab Ave, Tehran, Iran||amasoudin at ibb.ut.ac.ir<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/Kavosh/ Kavosh] (used in [http://apps.cytoscape.org/apps/cytokavosh CytoKavosh])||Laboratory of Systems Biology and Bioinformatics (LBB)||Institute of Biochemistry and Biophysics (IBB)||University of Tehran||Enghelab Square, Enghelab Ave, Tehran, Iran||amasoudin at ibb.ut.ac.ir<br />
|-<br />
|[http://www.dcc.fc.up.pt/gtries/ G-Tries]||Center for Research in Advanced Computing Systems||Computer Science||University of Porto||Rua Campo Alegre 1021/1055, Porto, Portugal||pribeiro at dcc.fc.up.pt<br />
|-<br />
|[http://nesreenahmed.com/graphlets PGD]<br />
|Network Learning and Discovery Lab<br />
|Department of Computer Science<br />
|Purdue University<br />
|Purdue University, 305 N University St, West Lafayette, IN 47907<br />
|nkahmed@purdue.edu<br />
|}<br />
<br />
==Well-established motifs and their functions==<br />
Much experimental work has been devoted to understanding network motifs in [[gene regulatory networks]]. These networks control which genes are expressed in the cell in response to biological signals. The network is defined such that genes are nodes, and directed edges represent the control of one gene by a transcription factor (regulatory protein that binds DNA) encoded by another gene. Thus, network motifs are patterns of genes regulating each other's transcription rate. When analyzing transcription networks, it is seen that the same network motifs appear again and again in diverse organisms from bacteria to human. The transcription network of ''[[Escherichia coli|E. coli]]'' and yeast, for example, is made of three main motif families, that make up almost the entire network. The leading hypothesis is that the network motif were independently selected by evolutionary processes in a converging manner,<ref name="bab1">{{cite journal |vauthors=Babu MM, Luscombe NM, Aravind L, Gerstein M, Teichmann SA |title=Structure and evolution of transcriptional regulatory networks |journal=Current Opinion in Structural Biology |volume=14 |issue=3 |pages=283–91 |date=June 2004 |pmid=15193307 |doi=10.1016/j.sbi.2004.05.004 |citeseerx=10.1.1.471.9692 }}</ref><ref name="con1">{{cite journal |vauthors=Conant GC, Wagner A |title=Convergent evolution of gene circuits |journal=Nat. Genet. |volume=34 |issue=3 |pages=264–6 |date=July 2003 |pmid=12819781 |doi=10.1038/ng1181}}</ref> since the creation or elimination of regulatory interactions is fast on evolutionary time scale, relative to the rate at which genes change,<ref name="bab1"/><ref name="con1"/><ref name="dek1">{{cite journal |vauthors=Dekel E, Alon U |title=Optimality and evolutionary tuning of the expression level of a protein |journal=Nature |volume=436 |issue=7050 |pages=588–92 |date=July 2005 |pmid=16049495 |doi=10.1038/nature03842 |bibcode=2005Natur.436..588D }}</ref> Furthermore, experiments on the dynamics generated by network motifs in living cells indicate that they have characteristic dynamical functions. This suggests that the network motif serve as building blocks in gene regulatory networks that are beneficial to the organism.<br />
<br />
The functions associated with common network motifs in transcription networks were explored and demonstrated by several research projects both theoretically and experimentally. Below are some of the most common network motifs and their associated function.<br />
<br />
===Negative auto-regulation (NAR)===<br />
[[Image:Autoregulation motif.png|thumb|Schematic representation of an auto-regulation motif]]<br />
One of simplest and most abundant network motifs in ''[[Escherichia coli|E. coli]]'' is negative auto-regulation in which a transcription factor (TF) represses its own transcription. This motif was shown to perform two important functions. The first function is response acceleration. NAR was shown to speed-up the response to signals both theoretically <ref name="zab1">{{cite journal |doi=10.1016/j.jtbi.2011.06.021 |author=Zabet NR |title=Negative feedback and physical limits of genes |journal=Journal of Theoretical Biology |volume= 284|issue=1 |pages=82–91 |date=September 2011 |pmid=21723295 |arxiv=1408.1869 |citeseerx=10.1.1.759.5418 }}</ref> and experimentally. This was first shown in a synthetic transcription network<ref name="ros1">{{cite journal |doi=10.1016/S0022-2836(02)00994-4 |vauthors=Rosenfeld N, Elowitz MB, Alon U |title=Negative autoregulation speeds the response times of transcription networks |journal=J. Mol. Biol. |volume=323 |issue=5 |pages=785–93 |date=November 2002 |pmid=12417193 |citeseerx=10.1.1.126.2604 }}</ref> and later on in the natural context in the SOS DNA repair system of E .coli.<ref name="cam1">{{cite journal |vauthors=Camas FM, Blázquez J, Poyatos JF |title=Autogenous and nonautogenous control of response in a genetic network |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=103 |issue=34 |pages=12718–23 |date=August 2006 |pmid=16908855 |pmc=1568915 |doi=10.1073/pnas.0602119103 |bibcode=2006PNAS..10312718C }}</ref> The second function is increased stability of the auto-regulated gene product concentration against stochastic noise, thus reducing variations in protein levels between different cells.<ref name="bec1">{{cite journal |vauthors=Becskei A, Serrano L |title=Engineering stability in gene networks by autoregulation |journal=Nature |volume=405 |issue=6786 |pages=590–3 |date=June 2000 |pmid=10850721 |doi=10.1038/35014651}}</ref><ref name="dub1">{{cite journal |vauthors=Dublanche Y, Michalodimitrakis K, Kümmerer N, Foglierini M, Serrano L |title=Noise in transcription negative feedback loops: simulation and experimental analysis |journal=Mol. Syst. Biol. |volume=2 |pages=41 |year=2006 |pmid=16883354 |pmc=1681513 |doi=10.1038/msb4100081 |issue=1}}</ref><ref name="shi1">{{cite journal |vauthors=Shimoga V, White J, Li Y, Sontag E, Bleris L |title= Synthetic mammalian transgene negative autoregulation |journal=Mol. Syst. Biol. |volume=9 |pages=670 |year=2013|doi=10.1038/msb.2013.27|pmid= 23736683 |pmc= 3964311 }}</ref><br />
<br />
<br />
<br />
===Positive auto-regulation (PAR)===<br />
Positive auto-regulation (PAR) occurs when a transcription factor enhances its own rate of production. Opposite to the NAR motif this motif slows the response time compared to simple regulation.<ref name="mae1">{{cite journal |vauthors=Maeda YT, Sano M |title=Regulatory dynamics of synthetic gene networks with positive feedback |journal=J. Mol. Biol. |volume=359 |issue=4 |pages=1107–24 |date=June 2006 |pmid=16701695 |doi=10.1016/j.jmb.2006.03.064 }}</ref> In the case of a strong PAR the motif may lead to a bimodal distribution of protein levels in cell populations.<ref name="bec2">{{cite journal |vauthors=Becskei A, Séraphin B, Serrano L |title=Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion |journal=EMBO J. |volume=20 |issue=10 |pages=2528–35 |date=May 2001 |pmid=11350942 |pmc=125456 |doi=10.1093/emboj/20.10.2528}}</ref><br />
<br />
===Feed-forward loops (FFL)===<br />
[[Image:Feed-forward motif.GIF|thumb|Schematic representation of a Feed-forward motif]]<br />
This motif is commonly found in many gene systems and organisms. The motif consists of three genes and three regulatory interactions. The target gene C is regulated by 2 TFs A and B and in addition TF B is also regulated by TF A . Since each of the regulatory interactions may either be positive or negative there are possibly eight types of FFL motifs.<ref name="man1">{{cite journal |vauthors=Mangan S, Alon U |title=Structure and function of the feed-forward loop network motif |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=100 |issue=21 |pages=11980–5 |date=October 2003 |pmid=14530388 |pmc=218699 |doi=10.1073/pnas.2133841100 |bibcode=2003PNAS..10011980M }}</ref> Two of those eight types: the coherent type 1 FFL (C1-FFL) (where all interactions are positive) and the incoherent type 1 FFL (I1-FFL) (A activates C and also activates B which represses C) are found much more frequently in the transcription network of ''[[Escherichia coli|E. coli]]'' and yeast than the other six types.<ref name="man1"/><ref name="ma1">{{cite journal |vauthors=Ma HW, Kumar B, Ditges U, Gunzer F, Buer J, Zeng AP |title=An extended transcriptional regulatory network of ''Escherichia coli'' and analysis of its hierarchical structure and network motifs |journal=Nucleic Acids Res. |volume=32 |issue=22 |pages=6643–9 |year=2004 |pmid=15604458 |pmc=545451 |doi=10.1093/nar/gkh1009 |url=http://nar.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=15604458}}</ref> In addition to the structure of the circuitry the way in which the signals from A and B are integrated by the C promoter should also be considered. In most of the cases the FFL is either an AND gate (A and B are required for C activation) or OR gate (either A or B are sufficient for C activation) but other input function are also possible.<br />
<br />
===Coherent type 1 FFL (C1-FFL)===<br />
The C1-FFL with an AND gate was shown to have a function of a ‘sign-sensitive delay’ element and a persistence detector both theoretically <ref name="man1"/> and experimentally<ref name="man2">{{cite journal |doi=10.1016/j.jmb.2003.09.049 |vauthors=Mangan S, Zaslaver A, Alon U |title=The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks |journal=J. Mol. Biol. |volume=334 |issue=2 |pages=197–204 |date=November 2003 |pmid=14607112 |citeseerx=10.1.1.110.4629 }}</ref> with the arabinose system of ''[[Escherichia coli|E. coli]]''. This means that this motif can provide pulse filtration in which short pulses of signal will not generate a response but persistent signals will generate a response after short delay. The shut off of the output when a persistent pulse is ended will be fast. The opposite behavior emerges in the case of a sum gate with fast response and delayed shut off as was demonstrated in the flagella system of ''[[Escherichia coli|E. coli]]''.<ref name="kal1">{{cite journal |vauthors=Kalir S, Mangan S, Alon U |title=A coherent feed-forward loop with a SUM input function prolongs flagella expression in ''Escherichia coli'' |journal=Mol. Syst. Biol. |volume=1 |pages=E1–E6 |year=2005 |pmid=16729041 |pmc=1681456 |doi=10.1038/msb4100010 |issue=1}}</ref> De novo evolution of C1-FFLs in [[gene regulatory network]]s has been demonstrated computationally in response to selection to filter out an idealized short signal pulse, but for non-idealized noise, a dynamics-based system of feed-forward regulation with different topology was instead favored.<ref>{{cite journal |last1=Xiong |first1=Kun |last2=Lancaster |first2=Alex K. |last3=Siegal |first3=Mark L. |last4=Masel |first4=Joanna |title=Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise |journal=Nature Communications |date=3 June 2019 |volume=10 |issue=1 |pages=2418 |doi=10.1038/s41467-019-10388-6|pmid=31160574 |pmc=6546794 }}</ref><br />
<br />
===Incoherent type 1 FFL (I1-FFL)===<br />
The I1-FFL is a pulse generator and response accelerator. The two signal pathways of the I1-FFL act in opposite directions where one pathway activates Z and the other represses it. When the repression is complete this leads to a pulse-like dynamics. It was also demonstrated experimentally that the I1-FFL can serve as response accelerator in a way which is similar to the NAR motif. The difference is that the I1-FFL can speed-up the response of any gene and not necessarily a transcription factor gene.<ref name="man3">{{cite journal |vauthors=Mangan S, Itzkovitz S, Zaslaver A, Alon U |title=The incoherent feed-forward loop accelerates the response-time of the gal system of ''Escherichia coli'' |journal=J. Mol. Biol. |volume=356 |issue=5 |pages=1073–81 |date=March 2006 |pmid=16406067 |doi=10.1016/j.jmb.2005.12.003 |citeseerx=10.1.1.184.8360 }}</ref> An additional function was assigned to the I1-FFL network motif: it was shown both theoretically and experimentally that the I1-FFL can generate non-monotonic input function in both a synthetic <ref name="ent1">{{cite journal |vauthors=Entus R, Aufderheide B, Sauro HM |title=Design and implementation of three incoherent feed-forward motif based biological concentration sensors |journal=Syst Synth Biol |volume=1 |issue=3 |pages=119–28 |date=August 2007 |pmid=19003446 |pmc=2398716 |doi=10.1007/s11693-007-9008-6 }}</ref> and native systems.<ref name="kap1">{{cite journal |vauthors=Kaplan S, Bren A, Dekel E, Alon U |title=The incoherent feed-forward loop can generate non-monotonic input functions for genes |journal=Mol. Syst. Biol. |volume=4 |pages=203 |year=2008 |pmid=18628744 |pmc=2516365 |doi=10.1038/msb.2008.43 |issue=1}}</ref> Finally, expression units that incorporate incoherent feedforward control of the gene product provide adaptation to the amount of DNA template and can be superior to simple combinations of constitutive promoters.<ref name="ble1">{{cite journal |vauthors=Bleris L, Xie Z, Glass D, Adadey A, Sontag E, Benenson Y |title=Synthetic incoherent feedforward circuits show adaptation to the amount of their genetic template |journal=Mol. Syst. Biol. |volume=7 |pages=519|year=2011 |doi=10.1038/msb.2011.49 |issue=1 |pmid=21811230 |pmc=3202791}}</ref> Feedforward regulation displayed better adaptation than negative feedback, and circuits based on RNA interference were the most robust to variation in DNA template amounts.<ref name="ble1"/><br />
<br />
===Multi-output FFLs===<br />
In some cases the same regulators X and Y regulate several Z genes of the same system. By adjusting the strength of the interactions this motif was shown to determine the temporal order of gene activation. This was demonstrated experimentally in the flagella system of ''[[Escherichia coli|E. coli]]''.<ref name="kal2">{{cite journal |vauthors=Kalir S, McClure J, Pabbaraju K, etal |title=Ordering genes in a flagella pathway by analysis of expression kinetics from living bacteria |journal=Science |volume=292 |issue=5524 |pages=2080–3 |date=June 2001 |pmid=11408658 |doi=10.1126/science.1058758 }}</ref><br />
<br />
===Single-input modules (SIM)===<br />
This motif occurs when a single regulator regulates a set of genes with no additional regulation. This is useful when the genes are cooperatively carrying out a specific function and therefore always need to be activated in a synchronized manner. By adjusting the strength of the interactions it can create temporal expression program of the genes it regulates.<ref name="zas1">{{cite journal |vauthors=Zaslaver A, Mayo AE, Rosenberg R, etal |title=Just-in-time transcription program in metabolic pathways |journal=Nat. Genet. |volume=36 |issue=5 |pages=486–91 |date=May 2004 |pmid=15107854 |doi=10.1038/ng1348|doi-access=free }}</ref><br />
<br />
In the literature, Multiple-input modules (MIM) arose as a generalization of SIM. However, the precise definitions of SIM and MIM have been a source of inconsistency. There are attempts to provide orthogonal definitions for canonical motifs in biological networks and algorithms to enumerate them, especially SIM, MIM and Bi-Fan (2x2 MIM).<ref>{{cite journal |vauthors=Konagurthu AS, Lesk AM |title=Single and Multiple Input Modules in regulatory networks |journal=Proteins |volume=73 |issue=2 |pages=320–324 |year=2008 |doi=10.1002/prot.22053|pmid=18433061 }}</ref><br />
<br />
===Dense overlapping regulons (DOR)===<br />
This motif occurs in the case that several regulators combinatorially control a set of genes with diverse regulatory combinations. This motif was found in ''[[Escherichia coli|E. coli]]'' in various systems such as carbon utilization, anaerobic growth, stress response and others.<ref name="she1"/><ref name="boy1"/> In order to better understand the function of this motif one has to obtain more information about the way the multiple inputs are integrated by the genes. Kaplan ''et al.''<ref name="kap2">{{cite journal |vauthors=Kaplan S, Bren A, Zaslaver A, Dekel E, Alon U |title=Diverse two-dimensional input functions control bacterial sugar genes |journal=Mol. Cell |volume=29 |issue=6 |pages=786–92 |date=March 2008 |pmid=18374652 |pmc=2366073 |doi=10.1016/j.molcel.2008.01.021 }}</ref> has mapped the input functions of the sugar utilization genes in ''[[Escherichia coli|E. coli]]'', showing diverse shapes.<br />
<br />
==已知的模体及其功能==<br />
许多实验工作致力于理解[[基因调控网络]]中的网络模体。在响应生物信号的过程中,这些网络控制细胞中需要表达的基因。这样的网络以基因作为节点,有向边代表对某个基因的调控,基因调控通过其他基因编码的转录因子[[结合在DNA上的调控蛋白]]来实现。因此,网络模体是基因之间相互调控转录速率的模式。在分析转录调控网络的时候,人们发现某些相同的网络模体在不同的物种中不断地出现,从细菌到人类。例如,''[[大肠杆菌]]''和酵母的转录网络由三种主要的网络模体家族组成,它们可以构建几乎整个网络。主要的假设是在进化的过程中,网络模体是被以收敛的方式独立选择出来的。<ref name="bab1">{{cite journal |vauthors=Babu MM, Luscombe NM, Aravind L, Gerstein M, Teichmann SA |title=Structure and evolution of transcriptional regulatory networks |journal=Current Opinion in Structural Biology |volume=14 |issue=3 |pages=283–91 |date=June 2004 |pmid=15193307 |doi=10.1016/j.sbi.2004.05.004 |citeseerx=10.1.1.471.9692 }}</ref><ref name="con1">{{cite journal |vauthors=Conant GC, Wagner A |title=Convergent evolution of gene circuits |journal=Nat. Genet. |volume=34 |issue=3 |pages=264–6 |date=July 2003 |pmid=12819781 |doi=10.1038/ng1181}}</ref> 因为相对于基因改变的速率,转录相互作用产生和消失的时间尺度在进化上是很快的。<ref name="bab1"/><ref name="con1"/><ref name="dek1">{{cite journal |vauthors=Dekel E, Alon U |title=Optimality and evolutionary tuning of the expression level of a protein |journal=Nature |volume=436 |issue=7050 |pages=588–92 |date=July 2005 |pmid=16049495 |doi=10.1038/nature03842 |bibcode=2005Natur.436..588D }}</ref> 此外,对活细胞中网络模体所产生的动力学行为的实验表明,它们具有典型的动力学功能。这表明,网络模体是基因调控网络中对生物体有益的基本单元。<br />
<br />
一些研究从理论和实验两方面探讨和论证了转录网络中与共同网络模体相关的功能。下面是一些最常见的网络模体及其相关功能。<br />
<br />
===负自反馈调控(NAR)===<br />
[[Image:Autoregulation motif.png|thumb|Schematic representation of an auto-regulation motif]]<br />
负自反馈调控是[[大肠杆菌]]中最简单和最冗余的网络模体之一,其中一个转录因子抑制它自身的转录。这种网络模体有两个重要的功能,其中第一个是加速响应。人们发现在实验和理论上, <ref name="zab1">{{cite journal |doi=10.1016/j.jtbi.2011.06.021 |author=Zabet NR |title=Negative feedback and physical limits of genes |journal=Journal of Theoretical Biology |volume= 284|issue=1 |pages=82–91 |date=September 2011 |pmid=21723295 |arxiv=1408.1869 |citeseerx=10.1.1.759.5418 }}</ref>NAR都可以加快对信号的响应。这个功能首先在一个人工合成的转录网络中被发现,<ref name="ros1">{{cite journal |doi=10.1016/S0022-2836(02)00994-4 |vauthors=Rosenfeld N, Elowitz MB, Alon U |title=Negative autoregulation speeds the response times of transcription networks |journal=J. Mol. Biol. |volume=323 |issue=5 |pages=785–93 |date=November 2002 |pmid=12417193 |citeseerx=10.1.1.126.2604 }}</ref> 然后在大肠杆菌SOS DAN修复系统这个自然体系中也被发现。<ref name="cam1">{{cite journal |vauthors=Camas FM, Blázquez J, Poyatos JF |title=Autogenous and nonautogenous control of response in a genetic network |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=103 |issue=34 |pages=12718–23 |date=August 2006 |pmid=16908855 |pmc=1568915 |doi=10.1073/pnas.0602119103 |bibcode=2006PNAS..10312718C }}</ref> 负自反馈网络的第二个功能是增强自调控基因的产物浓度的稳定性,从而抵抗随机的噪声,减少该蛋白含量在不同细胞中的差异。<ref name="bec1">{{cite journal |vauthors=Becskei A, Serrano L |title=Engineering stability in gene networks by autoregulation |journal=Nature |volume=405 |issue=6786 |pages=590–3 |date=June 2000 |pmid=10850721 |doi=10.1038/35014651}}</ref><ref name="dub1">{{cite journal |vauthors=Dublanche Y, Michalodimitrakis K, Kümmerer N, Foglierini M, Serrano L |title=Noise in transcription negative feedback loops: simulation and experimental analysis |journal=Mol. Syst. Biol. |volume=2 |pages=41 |year=2006 |pmid=16883354 |pmc=1681513 |doi=10.1038/msb4100081 |issue=1}}</ref><ref name="shi1">{{cite journal |vauthors=Shimoga V, White J, Li Y, Sontag E, Bleris L |title= Synthetic mammalian transgene negative autoregulation |journal=Mol. Syst. Biol. |volume=9 |pages=670 |year=2013|doi=10.1038/msb.2013.27|pmid= 23736683 |pmc= 3964311 }}</ref><br />
<br />
===正自反馈调控(PAR)===<br />
正自反馈调控是指转录因子增强它自身转录速率的调控。和负自反馈调节相反,NAR模体相比于简单的调控能够延长反应时间。<ref name="mae1">{{cite journal |vauthors=Maeda YT, Sano M |title=Regulatory dynamics of synthetic gene networks with positive feedback |journal=J. Mol. Biol. |volume=359 |issue=4 |pages=1107–24 |date=June 2006 |pmid=16701695 |doi=10.1016/j.jmb.2006.03.064 }}</ref> 在强PAR的情况下,模体可能导致蛋白质水平在细胞群中呈现双峰分布。<ref name="bec2">{{cite journal |vauthors=Becskei A, Séraphin B, Serrano L |title=Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion |journal=EMBO J. |volume=20 |issue=10 |pages=2528–35 |date=May 2001 |pmid=11350942 |pmc=125456 |doi=10.1093/emboj/20.10.2528}}</ref><br />
<br />
===前馈回路 (FFL)===<br />
[[Image:Feed-forward motif.GIF|thumb|Schematic representation of a Feed-forward motif]]<br />
前馈回路普遍存在于许多基因系统和生物体中。这种模体包括三个基因以及三个相互作用。目标基因C被两个转录因子(TFs)A和B调控,并且TF B同时被TF A调控。由于每个调控相互作用可以是正的或者负的,所以总共可能有八种类型的FFL模体。<ref name="man1">{{cite journal |vauthors=Mangan S, Alon U |title=Structure and function of the feed-forward loop network motif |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=100 |issue=21 |pages=11980–5 |date=October 2003 |pmid=14530388 |pmc=218699 |doi=10.1073/pnas.2133841100 |bibcode=2003PNAS..10011980M }}</ref> 其中的两种:一致前馈回路的类型一(C1-FFL)(所有相互作用都是正的)和非一致前馈回路的类型一(I1-FFL)(A激活C和B,B抑制C)在[[大肠杆菌]]和酵母中相比于其他六种更频繁的出现。<ref name="man1"/><ref name="ma1">{{cite journal |vauthors=Ma HW, Kumar B, Ditges U, Gunzer F, Buer J, Zeng AP |title=An extended transcriptional regulatory network of ''Escherichia coli'' and analysis of its hierarchical structure and network motifs |journal=Nucleic Acids Res. |volume=32 |issue=22 |pages=6643–9 |year=2004 |pmid=15604458 |pmc=545451 |doi=10.1093/nar/gkh1009 |url=http://nar.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=15604458}}</ref> 除了网络的结构外,还应该考虑来自A和B的信号被C的启动子集成的方式。在大多数情况下,FFL要么是一个与门(激活C需要A和B),要么是或门(激活C需要A或B),但也可以是其他输入函数。<br />
<br />
===一致前馈回路类型一(C1-FFL)===<br />
具有与门的C1-FFL有“符号-敏感延迟”单元和持久性探测器的功能,这一点在[[大肠杆菌]]阿拉伯糖系系统的理论<ref name="man1"/>和实验上<ref name="man2">{{cite journal |doi=10.1016/j.jmb.2003.09.049 |vauthors=Mangan S, Zaslaver A, Alon U |title=The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks |journal=J. Mol. Biol. |volume=334 |issue=2 |pages=197–204 |date=November 2003 |pmid=14607112 |citeseerx=10.1.1.110.4629 }}</ref> 都有发现。这意味着该模体可以提供脉冲过滤,短脉冲信号不会产生响应,而持久信号在短延迟后会产生响应。当持久脉冲结束时,输出的关闭将很快。与此相反的行为出现在具有快速响应和延迟关闭特性的加和门的情况下,这在[[大肠杆菌]]的鞭毛系统中得到了证明。<ref name="kal1">{{cite journal |vauthors=Kalir S, Mangan S, Alon U |title=A coherent feed-forward loop with a SUM input function prolongs flagella expression in ''Escherichia coli'' |journal=Mol. Syst. Biol. |volume=1 |pages=E1–E6 |year=2005 |pmid=16729041 |pmc=1681456 |doi=10.1038/msb4100010 |issue=1}}</ref>在[[基因调控网络]]的重头进化中,对于滤除理想化的短信号脉冲作为进化压,C1-FFLs已经在计算上被证明可以进化出来。但是对于非理想化的噪声,不同拓扑结构前馈调节的动态系统将被优先考虑。 <ref>{{cite journal |last1=Xiong |first1=Kun |last2=Lancaster |first2=Alex K. |last3=Siegal |first3=Mark L. |last4=Masel |first4=Joanna |title=Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise |journal=Nature Communications |date=3 June 2019 |volume=10 |issue=1 |pages=2418 |doi=10.1038/s41467-019-10388-6|pmid=31160574 |pmc=6546794 }}</ref><br />
<br />
===非一致前馈回路类型一(I1-FFL)===<br />
I1-FFL是一个脉冲生成器和响应加速器。I1-FFL的两种信号通路作用方向相反,一种通路激活Z,而另一种抑制Z。完全的抑制会导致类似脉冲的动力学行为。另外有实验证明,它可以类似于NAR模体起到响应加速器的作用。与NAR模体的不同之处在于,它可以加速任何基因的响应,而不必是转录因子。<ref name="man3">{{cite journal |vauthors=Mangan S, Itzkovitz S, Zaslaver A, Alon U |title=The incoherent feed-forward loop accelerates the response-time of the gal system of ''Escherichia coli'' |journal=J. Mol. Biol. |volume=356 |issue=5 |pages=1073–81 |date=March 2006 |pmid=16406067 |doi=10.1016/j.jmb.2005.12.003 |citeseerx=10.1.1.184.8360 }}</ref>I1-FFL网络还有另外一个功能:在理论和实验上都有证明I1-FFL可以生成非单调的输入函数,无论在人工合成的<ref name="ent1">{{cite journal |vauthors=Entus R, Aufderheide B, Sauro HM |title=Design and implementation of three incoherent feed-forward motif based biological concentration sensors |journal=Syst Synth Biol |volume=1 |issue=3 |pages=119–28 |date=August 2007 |pmid=19003446 |pmc=2398716 |doi=10.1007/s11693-007-9008-6 }}</ref>还是自然的系统中。 <ref name="kap1">{{cite journal |vauthors=Kaplan S, Bren A, Dekel E, Alon U |title=The incoherent feed-forward loop can generate non-monotonic input functions for genes |journal=Mol. Syst. Biol. |volume=4 |pages=203 |year=2008 |pmid=18628744 |pmc=2516365 |doi=10.1038/msb.2008.43 |issue=1}}</ref> 最后,包含非一致前馈调控的基因生成物的表达单元对DNA模板的数量具有适应性,可以优于简单的组合本构启动子。<ref name="ble1">{{cite journal |vauthors=Bleris L, Xie Z, Glass D, Adadey A, Sontag E, Benenson Y |title=Synthetic incoherent feedforward circuits show adaptation to the amount of their genetic template |journal=Mol. Syst. Biol. |volume=7 |pages=519|year=2011 |doi=10.1038/msb.2011.49 |issue=1 |pmid=21811230 |pmc=3202791}}</ref> 前馈调控比负反馈具有更好的适应性,并且基于RNA干扰的网络对DNA模板数具有最高的鲁棒性。<ref name="ble1"/><br />
<br />
===多输出前馈回路===<br />
在某些情况,相同的调控子X和Y可以调控同一系统中的多个Z基因。通过调节相互作用的强度,这些网络可以决定基因激活的时间顺序。这一点在[[大肠杆菌]]的鞭毛系统中有实验证据。<ref name="kal2">{{cite journal |vauthors=Kalir S, McClure J, Pabbaraju K, etal |title=Ordering genes in a flagella pathway by analysis of expression kinetics from living bacteria |journal=Science |volume=292 |issue=5524 |pages=2080–3 |date=June 2001 |pmid=11408658 |doi=10.1126/science.1058758 }}</ref><br />
<br />
===单一输入模块(SIM)===<br />
当单个调控子调控一组基因,并且没有其他的调控因素时,这样的模体叫做单一输入模块(SIM)。当很多基因合作执行某个功能时这是有用的,因为这些基因需要同步地被激活。通过调节相互作用的强度,可以编排它所调控的基因表达的时间顺序。<ref name="zas1">{{cite journal |vauthors=Zaslaver A, Mayo AE, Rosenberg R, etal |title=Just-in-time transcription program in metabolic pathways |journal=Nat. Genet. |volume=36 |issue=5 |pages=486–91 |date=May 2004 |pmid=15107854 |doi=10.1038/ng1348|doi-access=free }}</ref><br />
<br />
在文献中,多输入模块(MIM)来自于SIM的扩展。但是二者的精确定义并不太一致。有一些尝试给出生物网络中规范模体的正交定义,也有一些算法去枚举它们,特别是SIM,MIM和2x2 MIM等。<ref>{{cite journal |vauthors=Konagurthu AS, Lesk AM |title=Single and Multiple Input Modules in regulatory networks |journal=Proteins |volume=73 |issue=2 |pages=320–324 |year=2008 |doi=10.1002/prot.22053|pmid=18433061 }}</ref><br />
<br />
===密集交盖调节网(DOR)===<br />
这种类型的网络存在于多个调节子结合起来控制一组基因的情形,并且有多种调控的组合。这种模体出现在[[大肠杆菌]]的多种系统中,例如碳利用、厌氧生长、应激反应等。<ref name="she1"/><ref name="boy1"/> 为了更好地理解这种网络,我们必须得到关于基因集成多种输入的方式的信息。Kaplan ''et al.''<ref name="kap2">{{cite journal |vauthors=Kaplan S, Bren A, Zaslaver A, Dekel E, Alon U |title=Diverse two-dimensional input functions control bacterial sugar genes |journal=Mol. Cell |volume=29 |issue=6 |pages=786–92 |date=March 2008 |pmid=18374652 |pmc=2366073 |doi=10.1016/j.molcel.2008.01.021 }}</ref>绘制了[[大肠杆菌]]糖利用基因的输入函数,表现出各种各样的形状。<br />
<br />
==活动模体==<br />
<br />
有一个对网络模体的有趣概括:'''活动模体'''是在对节点和边都被量化标注的网络中可发现的【反复】斑图。例如,当新城代谢的边以相应基因的表达量或【时间】来标注时,一些斑图在'''给定的'''底层网络结构里【是反复的】。<ref name="agc">{{cite journal |vauthors=Chechik G, Oh E, Rando O, Weissman J, Regev A, Koller D |title=Activity motifs reveal principles of timing in transcriptional control of the yeast metabolic network |journal=Nat. Biotechnol. |volume=26 |issue=11 |pages=1251–9 |date=November 2008 |pmid=18953355 |pmc=2651818 |doi=10.1038/nbt.1499}}</ref><br />
<br />
==批判==<br />
<br />
对拓扑子结构有一个(某种程度上隐含的)前提性假设是其具有特定的功能重要性。但该假设最近遭到质疑,有人提出在不同的网络环境下模体可能表现出多样性,例如双扇模体,故<ref name="ad">{{cite journal |vauthors=Ingram PJ, Stumpf MP, Stark J |title=Network motifs: structure does not determine function |journal=BMC Genomics |volume=7 |pages=108 |year=2006 |pmid=16677373 |pmc=1488845 |doi=10.1186/1471-2164-7-108 }} </ref>模体的结构不必然决定功能,网络结构也不当然能揭示其功能;这种见解由来已久,可参见【Sin 操纵子】</font>。<ref>{{cite journal |vauthors=Voigt CA, Wolf DM, Arkin AP |title=The ''Bacillus subtilis'' sin operon: an evolvable network motif |journal=Genetics |volume=169 |issue=3 |pages=1187–202 |date=March 2005 |pmid=15466432 |pmc=1449569 |doi=10.1534/genetics.104.031955 |url=http://www.genetics.org/cgi/pmidlookup?view=long&pmid=15466432}}</ref><br />
<br />
<br />
大多数模体功能分析是基于模体孤立运行的情形。最近的研究<ref>{{cite journal |vauthors=Knabe JF, Nehaniv CL, Schilstra MJ |title=Do motifs reflect evolved function?—No convergent evolution of genetic regulatory network subgraph topologies |journal=BioSystems |volume=94 |issue=1–2 |pages=68–74 |year=2008 |pmid=18611431 |doi=10.1016/j.biosystems.2008.05.012 }}</ref>表明网络环境至关重要,不能忽视网络环境而仅从本地结构来对其功能进行推论——引用的论文还回顾了对观测数据的批判及其他可能的解释。人们研究了单个模体模组对网络全局的动力学影响及其分析<ref>{{cite journal |vauthors=Taylor D, Restrepo JG |title=Network connectivity during mergers and growth: Optimizing the addition of a module |journal=Physical Review E |volume=83 |issue=6 |year=2011 |page=66112 |doi=10.1103/PhysRevE.83.066112 |pmid=21797446 |bibcode=2011PhRvE..83f6112T |arxiv=1102.4876 }}</ref>。而另一项近期的研究工作提出生物网络的某些拓扑特征能自然地引起经典模体的常见形态,让人不禁疑问:这样的发生频率是否能证明模体的结构是出于其对所在网络运行的功能性贡献而被选择保留下的结果?<ref>{{cite journal|last1=Konagurthu|first1=Arun S.|last2=Lesk|first2=Arthur M.|title=Single and multiple input modules in regulatory networks|journal=Proteins: Structure, Function, and Bioinformatics|date=23 April 2008|volume=73|issue=2|pages=320–324|doi=10.1002/prot.22053|pmid=18433061}}</ref><ref>{{cite journal |vauthors=Konagurthu AS, Lesk AM |title=On the origin of distribution patterns of motifs in biological networks |journal=BMC Syst Biol |volume=2 |pages=73 |year=2008 |pmid=18700017 |pmc=2538512 |doi=10.1186/1752-0509-2-73 }} </ref><br />
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模体的研究主要应用于静态复杂网络,而时变复杂网络的研究<ref>Braha, D., & Bar‐Yam, Y. (2006). [https://static1.squarespace.com/static/5b68a4e4a2772c2a206180a1/t/5c5de3faf4e1fc43e7b3d21e/1549657083988/Complexity_Braha_Original_w_Cover.pdf From centrality to temporary fame: Dynamic centrality in complex networks]. Complexity, 12(2), 59-63. </ref>就网络模体提出了重大的新解释,并介绍了'''时变网络模体'''的概念。Braha和Bar-Yam<ref> Braha D., Bar-Yam Y. (2009) [https://s3.amazonaws.com/academia.edu.documents/4892116/Adaptive_Networks__Theory__Models_and_Applications__Understanding_Complex_Systems_.pdf?response-content-disposition=inline%3B%20filename%3DRedes_teoria.pdf&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAIWOWYYGZ2Y53UL3A%2F20191111%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20191111T173250Z&X-Amz-Expires=3600&X-Amz-SignedHeaders=host&X-Amz-Signature=89d08c9e92b88ed817e4eb0f87c480757ef79c4b865919a5e0890cbefa164c61#page=55 Time-Dependent Complex Networks: Dynamic Centrality, Dynamic Motifs, and Cycles of Social Interactions]. In: Gross T., Sayama H. (eds) Adaptive Networks. Understanding Complex Systems. Springer, Berlin, Heidelberg </ref>研究了本地模体结构在时间依赖网络/时变网络的动力学,发现的一些反复模式有望成为社会互动周期的经验论据。他们证明了对于时变网络,其本地结构是时间依赖的且可能随时间演变,可作为对复杂网络中稳定模体观及模体表达观的反论,Braha和Bar-Yam还进一步提出,对时变本地结构的分析有可能揭示系统级任务和功能方面的动力学的重要信息。<br />
<br />
==See also==<br />
* [[Clique (graph theory)]]<br />
* [[Graphical model]]<br />
<br />
==References==<br />
{{reflist|2}}<br />
<br />
==External links==<br />
<br />
* [http://www.weizmann.ac.il/mcb/UriAlon/groupNetworkMotifSW.html A software tool that can detect network motifs]<br />
* [http://www.bio-physics.at/wiki/index.php?title=Network_Motifs bio-physics-wiki NETWORK MOTIFS]<br />
* [http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ FANMOD: a tool for fast network motif detection]<br />
* [http://mavisto.ipk-gatersleben.de/ MAVisto: network motif analysis and visualisation tool]<br />
* [https://www.msu.edu/~jinchen/ NeMoFinder]<br />
* [http://people.cs.uchicago.edu/~joshuag/index.html Grochow–Kellis]<br />
* [http://lbb.ut.ac.ir/Download/LBBsoft/MODA/ MODA]<br />
* [http://lbb.ut.ac.ir/Download/LBBsoft/Kavosh/ Kavosh]<br />
* [http://apps.cytoscape.org/apps/cytokavosh CytoKavosh]<br />
* [http://www.dcc.fc.up.pt/gtries/ G-Tries]<br />
* [http://www.ft.unicamp.br/docentes/meira/accmotifs/ acc-MOTIF detection tool]<br />
<br />
[[Category:Gene expression]]<br />
[[Category:Networks]]</div>Imphttps://wiki.swarma.org/index.php?title=%E7%BD%91%E7%BB%9C%E6%A8%A1%E4%BD%93_Network_motifs&diff=7118网络模体 Network motifs2020-05-07T06:15:17Z<p>Imp:/* ESU (FANMOD) */</p>
<hr />
<div>大家好,我们的公众号计划要推送一篇关于网络模体的综述文章,我们希望可以配套建议该重要概念:网络模体。现在希望可以大家一起协作完成这个词条。<br />
翻译任务主要分为以下5个内容:<br />
* 网络定义和历史 ---许菁 <br />
* 网络模体的发现算法 mfinder和FPF算法---李鹏<br />
* 网络模体的发现算法 ESU和对应的软件FANMOD---Imp<br />
* 网络模体的发现算法 G-Trie、算法对比和算法分类——Ricky(中英对照[[用户讨论:Qige96|初稿在这里]])<br />
* 已有网络模体及其函数表示 --周佳欣<br />
* 活动模体+批判 --- 孙宇<br />
* 代码实现<br />
<br />
大家可以在对应感兴趣的部分下面,写上姓名。我们的协作方式是石墨文档上翻译,最后再编辑成文。<br />
对应的词条链接:https://en.wikipedia.org/wiki/Network_motif#Well-established_motifs_and_their_functions<br />
<br />
截止时间:今晚12:00<br />
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<br />
All networks, including [[biological network]]s, social networks, technological networks (e.g., computer networks and electrical circuits) and more, can be represented as [[complex network|graphs]], which include a wide variety of subgraphs. One important local property of networks are so-called '''network motifs''', which are defined as recurrent and [[statistically significant]] sub-graphs or patterns.<br />
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所有网络,包括生物网络(biological networks)、社会网络(social networks)、技术网络(例如计算机网络和电路)等,都可以用图的形式来表示,这些图中会包括各种各样的子图(subgraphs)。网络的一个重要的局部性质是所谓的网络基序,即重复且具有统计意义的子图或模式(patterns)。<br />
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Network motifs are sub-graphs that repeat themselves in a specific network or even among various networks. Each of these sub-graphs, defined by a particular pattern of interactions between vertices, may reflect a framework in which particular functions are achieved efficiently. Indeed, motifs are of notable importance largely because they may reflect functional properties. They have recently gathered much attention as a useful concept to uncover structural design principles of complex networks.<ref name="mas1">{{cite journal |vauthors=Masoudi-Nejad A, Schreiber F, Razaghi MK Z |title=Building Blocks of Biological Networks: A Review on Major Network Motif Discovery Algorithms |journal=IET Systems Biology |volume=6 |issue=5 |pages=164–74 |year=2012|doi=10.1049/iet-syb.2011.0011 |pmid=23101871 }}</ref> Although network motifs may provide a deep insight into the network's functional abilities, their detection is computationally challenging.<br />
网络模体(Network motifs)是指在特定网络或各种网络中重复出现的相同的子图。这些子图由顶点之间特定的交互模式定义,一个子图便可以反映一个框架,这个框架可以有效地实现某个特定的功能。事实上,之所以说模体是一个重要的特性,正是因为它们可能反映出对应网络功能的这一性质。近年来这一概念作为揭示复杂网络结构设计原理的一个有用概念而受到了广泛的关注。<ref name="mas1">{{cite journal |vauthors=Masoudi-Nejad A, Schreiber F, Razaghi MK Z |title=Building Blocks of Biological Networks: A Review on Major Network Motif Discovery Algorithms |journal=IET Systems Biology |volume=6 |issue=5 |pages=164–74 |year=2012|doi=10.1049/iet-syb.2011.0011 |pmid=23101871 }}</ref> 但是,虽然通过研究网络模体可以深入了解网络的功能,但是对于模体的检测在计算上是具有挑战性的。<br />
<br />
==Definition==<br />
Let {{math|G {{=}} (V, E)}} and {{math|G&prime; {{=}} (V&prime;, E&prime;)}} be two graphs. Graph {{math|G&prime;}} is a ''sub-graph'' of graph {{math|G}} (written as {{math|G&prime; ⊆ G}}) if {{math|V&prime; ⊆ V}} and {{math|E&prime; ⊆ E ∩ (V&prime; &times; V&prime;)}}. If {{math|G&prime; ⊆ G}} and {{math|G&prime;}} contains all of the edges {{math|&lang;u, v&rang; ∈ E}} with {{math|u, v ∈ V&prime;}}, then {{math|G&prime;}} is an ''induced sub-graph'' of {{math|G}}. We call {{math|G&prime;}} and {{math|G}} isomorphic (written as {{math|G&prime; ↔ G}}), if there exists a bijection (one-to-one) {{math|f:V&prime; → V}} with {{math|&lang;u, v&rang; ∈ E&prime; ⇔ &lang;f(u), f(v)&rang; ∈ E}} for all {{math|u, v ∈ V&prime;}}. The mapping {{math|f}} is called an isomorphism between {{math|G}} and {{math|G&prime;}}.<ref name="die1">{{cite journal |author=Diestel R |title=Graph Theory (Graduate Texts in Mathematics) |volume=173 |year=2005|publisher=New York: Springer-Verlag Heidelberg}}</ref><br />
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设{{math|G {{=}} (V, E)}} 和 {{math|G&prime; {{=}} (V&prime;, E&prime;)}} 是两个图。若{{math|V&prime; ⊆ V}}且满足{{math|E&prime; ⊆ E ∩ (V&prime; &times; V&prime;)}})(即图{{math|G&prime; ⊆ G}的所有边和点都属于图{{math|G}})则称图{{math|G&prime; ⊆ G}是图{{math|G}}的一个子图<ref name="die1">{{cite journal |author=Diestel R |title=Graph Theory (Graduate Texts in Mathematics) |volume=173 |year=2005|publisher=New York: Springer-Verlag Heidelberg}}</ref><br />
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若{{math|G&prime; ⊆ G}},且对于顶点{{math|u}}、{{math|v}}及其连边,只要{{math|u}}和{{math|v}}存在于{{math|G&prime;}}(即若{{math|U}}, {{math|V&prime; ⊆ V}}),那么{{math|G&prime; ⊆ G}}中就应该包含原图{{math|G}}中的所有{{math|u}}和{{math|V}}的对应连边(即{{math|&lang;u, v&rang; ∈ E}}),则称此时图{{math|G&prime;}}就是图{{math|G}}的导出子图。<br />
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如果存在一个双射(一对一){{math|f:V&prime; → V}},且对所有{{math|u, v ∈ V&prime;}}都有{{math|&lang;u, v&rang; ∈ E&prime; ⇔ &lang;f(u), f(v)&rang; ∈ E}} ,则称{{math|G&prime }}是{{math|G}}的同构图(记作:{{math|G&prime; → G}}),映射f则称为{{math|G}}与{{math|G&prime;}}之间的同构(isomorphism)。[2]<br />
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When {{math|G&Prime; ⊂ G}} and there exists an isomorphism between the sub-graph {{math|G&Prime;}} and a graph {{math|G&prime;}}, this mapping represents an ''appearance'' of {{math|G&prime;}} in {{math|G}}. The number of appearances of graph {{math|G&prime;}} in {{math|G}} is called the frequency {{math|F<sub>G</sub>}} of {{math|G&prime;}} in {{math|G}}. A graph is called ''recurrent'' (or ''frequent'') in {{math|G}}, when its ''frequency'' {{math|F<sub>G</sub>(G&prime;)}} is above a predefined threshold or cut-off value. We use terms ''pattern'' and ''frequent sub-graph'' in this review interchangeably. There is an [[Statistical ensemble (mathematical physics)|ensemble]] {{math|Ω(G)}} of random graphs corresponding to the [[Null model|null-model]] associated to {{math|G}}. We should choose {{math|N}} random graphs uniformly from {{math|Ω(G)}} and calculate the frequency for a particular frequent sub-graph {{math|G&prime;}} in {{math|G}}. If the frequency of {{math|G&prime;}} in {{math|G}} is higher than its arithmetic mean frequency in {{math|N}} random graphs {{math|R<sub>i</sub>}}, where {{math|1 ≤ i ≤ N}}, we call this recurrent pattern ''significant'' and hence treat {{math|G&prime;}} as a ''network motif'' for {{math|G}}. For a small graph {{math|G&prime;}}, the network {{math|G}} and a set of randomized networks {{math|R(G) ⊆ Ω(R)}}, where {{math|1=R(G) {{=}} N}}, the ''Z-Score'' that has been defined by the following formula:<br />
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<math>Z(G^\prime) = \frac{F_G(G^\prime) - \mu_R(G^\prime)}{\sigma_R(G^\prime)}</math><br />
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当{{math|G&Prime; ⊂ G}},且{{math|G&Prime;}}与图{{math|G&prime;}}之间存在同构时,该映射表示{{math|G&prime;}}对于{{math|G}}存在。图{{math|G&prime;}}在{{math|G}}的出现次数称为{{math|G&prime;}}出现在{{math|G}}的频率{{math|F<sub>G</sub>}}。当一个子图的频率{{math|F<sub>G</sub>}}高于预定的阈值或截止值时,则称{{math|G&prime;}}是{{math|G}}中的递归(或频繁)子图。<br />
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在接下来的内容中,我们交替使用术语“模式(motifs)”和“频繁子图(frequent sub-graph)”。<br />
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设从与{{math|G}}相关联的零模型(the null-model)获得的随机图集合为{{math|Ω(G)}},我们从{{math|Ω(G)}}中均匀地选择N个随机图,并计算其特定频繁子图的频率。如果{{math|G&prime;}}出现在{{math|G}}的频率高于N个随机图Ri的算术平均频率,其中{{math|1 ≤ i ≤ N}},我们称此递归模式是有意义的,因此可以将{{math|G&prime;}}视为{{math|G}}的网络模体。<br />
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对于一个小图{{math|G&prime;}},网络{{math|G}}和一组随机网络{{math|R(G) ⊆ Ω(R)}},当{{math|1=R(G) {{=}} N}}时,由其Z分数(Z-score)的定义如下式:<br />
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<math>Z(G^\prime) = \frac{F_G(G^\prime) - \mu_R(G^\prime)}{\sigma_R(G^\prime)}</math><br />
<br />
where {{math|μ<sub>R</sub>(G&prime;)}} and {{math|σ<sub>R</sub>(G&prime;)}} stand for mean and standard deviation frequency in set {{math|R(G)}}, respectively.<ref name="mil1">{{cite journal |vauthors=Milo R, Shen-Orr SS, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |volume=298 |year=2002|journal=Science|issue=5594|pages=824–827 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="alb1">{{cite journal |vauthors=Albert R, Barabási AL |title=Statistical mechanics of complex networks |journal=Reviews of Modern Physics |volume=74 |issue=1 |year=2002 |pages=47–49 |doi=10.1103/RevModPhys.74.47 |bibcode=2002RvMP...74...47A|arxiv=cond-mat/0106096 |citeseerx=10.1.1.242.4753 }}</ref><ref name="mil2">{{cite journal |vauthors=Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheffer M, Alon U |title=Superfamilies of designed and evolved networks |journal=Science |volume=303 |issue=5663 |year=2004 |pages=1538–1542 |pmid=15001784 |doi=10.1126/science.1089167 |bibcode=2004Sci...303.1538M |url=https://semanticscholar.org/paper/87ad24efd5329046d37cd704f970323e878710ca }}</ref><ref name="sch1">{{cite encyclopedia|last=Schwöbbermeyer |first=H |title=Network Motifs |encyclopedia=Analysis of Biological Networks |editor=Junker BH, Schreiber F |publisher=Hoboken, New Jersey: John Wiley & Sons |year=2008 |pages=85–108}}</ref><ref name="bor1">{{cite encyclopedia |last1=Bornholdt |first1=S |last2=Schuster |first2=HG |title=Handbook of graphs and networks : from the genome to the Internet |journal=Handbook of Graphs and Networks: From the Genome to the Internet |pages=417 |year=2003|bibcode=2003hgnf.book.....B }}</ref><ref name="cir1">{{cite journal |vauthors=Ciriello G, Guerra C |title=A review on models and algorithms for motif discovery in protein-protein interaction networks |journal=Briefings in Functional Genomics and Proteomics |year=2008 |volume=7 |issue=2 |pages=147–156 |doi=10.1093/bfgp/eln015|pmid=18443014 |doi-access=free }}</ref> The larger the {{math|Z(G&prime;)}}, the more significant is the sub-graph {{math|G&prime;}} as a motif. Alternatively, another measurement in statistical hypothesis testing that can be considered in motif detection is the P-Value, given as the probability of {{math|F<sub>R</sub>(G&prime;) ≥ F<sub>G</sub>(G&prime;)}} (as its null-hypothesis), where {{math|F<sub>R</sub>(G&prime;)}} indicates the frequency of G' in a randomized network.<ref name="sch1" /> A sub-graph with P-value less than a threshold (commonly 0.01 or 0.05) will be treated as a significant pattern. The P-value is defined as<br />
<br />
<math>P(G^\prime) = \frac{1}{N}\sum_{i=1}^N \delta(c(i)) ; c(i): F_R^i(G^\prime) \ge F_G(G^\prime)</math><br />
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式中,{{math|μ<sub>R</sub>(G&prime;)}} 和 {{math|σ<sub>R</sub>(G&prime;)}}分别代表集合{{math|R(G)}}中的平均和标准偏差频率。.<ref name="mil1">{{cite journal |vauthors=Milo R, Shen-Orr SS, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |volume=298 |year=2002|journal=Science|issue=5594|pages=824–827 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="alb1">{{cite journal |vauthors=Albert R, Barabási AL |title=Statistical mechanics of complex networks |journal=Reviews of Modern Physics |volume=74 |issue=1 |year=2002 |pages=47–49 |doi=10.1103/RevModPhys.74.47 |bibcode=2002RvMP...74...47A|arxiv=cond-mat/0106096 |citeseerx=10.1.1.242.4753 }}</ref><ref name="mil2">{{cite journal |vauthors=Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheffer M, Alon U |title=Superfamilies of designed and evolved networks |journal=Science |volume=303 |issue=5663 |year=2004 |pages=1538–1542 |pmid=15001784 |doi=10.1126/science.1089167 |bibcode=2004Sci...303.1538M |url=https://semanticscholar.org/paper/87ad24efd5329046d37cd704f970323e878710ca }}</ref><ref name="sch1">{{cite encyclopedia|last=Schwöbbermeyer |first=H |title=Network Motifs |encyclopedia=Analysis of Biological Networks |editor=Junker BH, Schreiber F |publisher=Hoboken, New Jersey: John Wiley & Sons |year=2008 |pages=85–108}}</ref><ref name="bor1">{{cite encyclopedia |last1=Bornholdt |first1=S |last2=Schuster |first2=HG |title=Handbook of graphs and networks : from the genome to the Internet |journal=Handbook of Graphs and Networks: From the Genome to the Internet |pages=417 |year=2003|bibcode=2003hgnf.book.....B }}</ref><ref name="cir1">{{cite journal |vauthors=Ciriello G, Guerra C |title=A review on models and algorithms for motif discovery in protein-protein interaction networks |journal=Briefings in Functional Genomics and Proteomics |year=2008 |volume=7 |issue=2 |pages=147–156 |doi=10.1093/bfgp/eln015|pmid=18443014 |doi-access=free }}</ref> {{math|Z(G&prime;)}}越大,子图{{math|G&prime;}}作为模体的意义也就越大。<br />
<br />
此外还可以使用统计假设检验中的另一个测量方法,可以作为模体检测中的一种方法,即P值(P-value),以 {{math|F<sub>R</sub>(G&prime;) ≥ F<sub>G</sub>(G&prime;)}}的概率给出(作为其零假设null-hypothesis),其中{{math|F<sub>R</sub>(G&prime;)}}表示随机网络中{{math|G&prime;}}的频率。<ref name="sch1" /> 当P值小于阈值(通常为0.01或0.05)时,该子图可以被称为显著模式。该P值定义为:<br />
<br />
<math>P(G^\prime) = \frac{1}{N}\sum_{i=1}^N \delta(c(i)) ; c(i): F_R^i(G^\prime) \ge F_G(G^\prime)</math><br />
<br />
[[File:Different occurrences of a sub-graph in a graph.jpg|thumb|''Different occurrences of a sub-graph in a graph''. (M1 – M4) are different occurrences of sub-graph (b) in graph (a). For frequency concept {{math|F<sub>1</sub>}}, the set M1, M2, M3, M4 represent all matches, so {{math|F<sub>1</sub> {{=}} 4}}. For {{math|F<sub>2</sub>}}, one of the two set M1, M4 or M2, M3 are possible matches, {{math|F<sub>2</sub> {{=}} 2}}. Finally, for frequency concept {{math|F<sub>3</sub>}}, merely one of the matches (M1 to M4) is allowed, therefore {{math|F<sub>3</sub> {{=}} 1}}. The frequency of these three frequency concepts decrease as the usage of network elements are restricted.]]<br />
<br />
Where {{math|N}} indicates number of randomized networks, {{math|i}} is defined over an ensemble of randomized networks and the Kronecker delta function {{math|δ(c(i))}} is one if the condition {{math|c(i)}} holds. The concentration <ref name="kas1">{{cite journal |vauthors=Kashtan N, Itzkovitz S, Milo R, Alon U |title=Efficient sampling algorithm for estimating sub-graph concentrations and detecting network motifs |journal=Bioinformatics |year=2004 |volume=20 |issue=11 |pages=1746–1758 |doi=10.1093/bioinformatics/bth163|pmid=15001476 |doi-access=free }}</ref><ref name="wer1">{{cite journal |author=Wernicke S |title=Efficient detection of network motifs |journal=IEEE/ACM Transactions on Computational Biology and Bioinformatics |year=2006 |volume=3 |issue=4 |pages=347–359 |doi=10.1109/tcbb.2006.51|pmid=17085844 |citeseerx=10.1.1.304.2576 }}</ref> of a particular n-size sub-graph {{math|G&prime;}} in network {{math|G}} refers to the ratio of the sub-graph appearance in the network to the total ''n''-size non-isomorphic sub-graphs’ frequencies, which is formulated by<br />
<br />
<math>C_G(G^\prime) = \frac{F_G(G^\prime)}{\sum_i F_G(G_i)}</math><br />
<br />
where index {{math|i}} is defined over the set of all non-isomorphic n-size graphs. Another statistical measurement is defined for evaluating network motifs, but it is rarely used in known algorithms. This measurement is introduced by Picard ''et al.'' in 2008 and used the Poisson distribution, rather than the Gaussian normal distribution that is implicitly being used above.<ref name="pic1">{{cite journal |vauthors=Picard F, Daudin JJ, Schbath S, Robin S |title=Assessing the Exceptionality of Network Motifs |journal=J. Comp. Bio. |year=2005 |volume=15 |issue=1 |pages=1–20|doi=10.1089/cmb.2007.0137 |pmid=18257674 |citeseerx=10.1.1.475.4300 }}</ref><br />
<br />
其中索引 i 定义在所有非同构 n 大小图的集合上。 另一种统计测量是用来评估网络主题的,但在已知的算法中很少使用。 这种测量方法是由 Picard 等人在2008年提出的,使用的是泊松分佈分布,而不是上面隐含使用的高斯正态分布。<ref name="pic1">{{cite journal |vauthors=Picard F, Daudin JJ, Schbath S, Robin S |title=Assessing the Exceptionality of Network Motifs |journal=J. Comp. Bio. |year=2005 |volume=15 |issue=1 |pages=1–20|doi=10.1089/cmb.2007.0137 |pmid=18257674 |citeseerx=10.1.1.475.4300 }}</ref>其中{{math|N}}表示随机网络的数目,{{math|i}}定义在随机网络的集合上,若条件{{math|c(i)}}成立,则Kroneckerδ函数{{math|δ(c(i))}}是1。在网络{{math|G}}中,一个特定的n维子图{{math|N&prime;}}的集中度是指子图在网络中出现频率与n维非同构子图的总频率之比,其计算公式如下:<br />
<br />
<math>C_G(G^\prime) = \frac{F_G(G^\prime)}{\sum_i F_G(G_i)}</math><br />
<br />
<br />
In addition, three specific concepts of sub-graph frequency have been proposed.<ref name="schr1">{{cite book |vauthors=Schreiber F, Schwöbbermeyer H |title=Frequency concepts and pattern detection for the analysis of motifs in networks |journal=Transactions on Computational Systems Biology III |volume=3737 |year=2005 |pages=89–104|doi=10.1007/11599128_7 |citeseerx=10.1.1.73.1130 |series=Lecture Notes in Computer Science |isbn=978-3-540-30883-6 }}</ref> As the figure illustrates, the first frequency concept {{math|F<sub>1</sub>}} considers all matches of a graph in original network. This definition is similar to what we have introduced above. The second concept {{math|F<sub>2</sub>}} is defined as the maximum number of edge-disjoint instances of a given graph in original network. And finally, the frequency concept {{math|F<sub>3</sub>}} entails matches with disjoint edges and nodes. Therefore, the two concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}} restrict the usage of elements of the graph, and as can be inferred, the frequency of a sub-graph declines by imposing restrictions on network element usage. As a result, a network motif detection algorithm would pass over more candidate sub-graphs if we insist on frequency concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}}.<br />
<br />
此外,他们还提出了子图频率的三个具体概念。<ref name="schr1">{{cite book |vauthors=Schreiber F, Schwöbbermeyer H |title=Frequency concepts and pattern detection for the analysis of motifs in networks |journal=Transactions on Computational Systems Biology III |volume=3737 |year=2005 |pages=89–104|doi=10.1007/11599128_7 |citeseerx=10.1.1.73.1130 |series=Lecture Notes in Computer Science |isbn=978-3-540-30883-6 }}</ref> 如图所示,第一频率概念 {{math|F<sub>1</sub>}}考虑原始网络中图的所有匹配,这与我们前面介绍过的类似。第二个概念{{math|F<sub>2</sub>}}定义为原始网络中给定图的最大不相交边的数量。最后,频率概念{{math|F<sub>3</sub>}}包含与不相交边(disjoint edges)和节点的匹配。因此,两个概念F2和F3限制了图元素的使用,并且可以看出,通过对网络元素的使用施加限制,子图的频率下降。因此,如果我们坚持使用频率概念{{math|F<sub>2</sub>}}和{{math|F<sub>3</sub>}},网络模体检测算法将可以筛选出更多的候选子图。<br />
<br />
==History==<br />
The study of network motifs was pioneered by Holland and Leinhardt<ref>Holland, P. W., & Leinhardt, S. (1974). The statistical analysis of local structure in social networks. Working Paper No. 44, National Bureau of Economic Research.</ref><ref>Hollandi, P., & Leinhardt, S. (1975). The Statistical Analysis of Local. Structure in Social Networks. Sociological Methodology, David Heise, ed. San Francisco: Josey-Bass.</ref><ref> Holland, P. W., & Leinhardt, S. (1976). Local structure in social networks. Sociological methodology, 7, 1-45.</ref><ref>Holland, P. W., & Leinhardt, S. (1977). A method for detecting structure in sociometric data. In Social Networks (pp. 411-432). Academic Press.</ref> who introduced the concept of a triad census of networks. They introduced methods to enumerate various types of subgraph configurations, and test whether the subgraph counts are statistically different from those expected in random networks. <br />
霍兰(Holland)和莱因哈特(Leinhardt)率先提出了'''网络三合会普查'''(a triad census of networks)的概念,开创了网络模体研究的先河。<ref>Holland, P. W., & Leinhardt, S. (1974). The statistical analysis of local structure in social networks. Working Paper No. 44, National Bureau of Economic Research.</ref><ref>Hollandi, P., & Leinhardt, S. (1975). The Statistical Analysis of Local. Structure in Social Networks. Sociological Methodology, David Heise, ed. San Francisco: Josey-Bass.</ref><ref> Holland, P. W., & Leinhardt, S. (1976). Local structure in social networks. Sociological methodology, 7, 1-45.</ref><ref>Holland, P. W., & Leinhardt, S. (1977). A method for detecting structure in sociometric data. In Social Networks (pp. 411-432). Academic Press.</ref> 他们介绍了枚举各种子图配置的方法,并测试子图计数是否与随机网络中的期望值存在统计学上的差异。<br />
<br />
这里对于'''网络三合会普查'''(a triad census of networks)这一概念的翻译存疑<br />
<br />
<br />
This idea was further generalized in 2002 by [[Uri Alon]] and his group <ref name="she1">{{cite journal |vauthors=Shen-Orr SS, Milo R, Mangan S, Alon U |title=Network motifs in the transcriptional regulation network of ''Escherichia coli'' |journal=Nat. Genet. |volume=31 |issue=1 |pages=64–8 |date=May 2002 |pmid=11967538 |doi=10.1038/ng881}}</ref> when network motifs were discovered in the gene regulation (transcription) network of the bacteria ''[[Escherichia coli|E. coli]]'' and then in a large set of natural networks. Since then, a considerable number of studies have been conducted on the subject. Some of these studies focus on the biological applications, while others focus on the computational theory of network motifs.<br />
<br />
2002年,Uri Alon和他的团队[17]在大肠杆菌的基因调控(gene regulation network)(转录 transcription)网络中发现了网络模体,随后在大量的自然网络中也发现了网络模体,从而进一步推广了这一观点。自那时起,许多科学家都对这一问题进行了大量的研究。其中一些研究集中在生物学应用上,而另一些则集中在网络模体的计算理论上。<ref name="she1">{{cite journal |vauthors=Shen-Orr SS, Milo R, Mangan S, Alon U |title=Network motifs in the transcriptional regulation network of ''Escherichia coli'' |journal=Nat. Genet. |volume=31 |issue=1 |pages=64–8 |date=May 2002 |pmid=11967538 |doi=10.1038/ng881}}</ref> <br />
<br />
<br />
The biological studies endeavor to interpret the motifs detected for biological networks. For example, in work following,<ref name="she1" /> the network motifs found in ''[[Escherichia coli|E. coli]]'' were discovered in the transcription networks of other bacteria<ref name="eic1">{{cite journal |vauthors=Eichenberger P, Fujita M, Jensen ST, etal |title=The program of gene transcription for a single differentiating cell type during sporulation in ''Bacillus subtilis'' |journal=PLOS Biology |volume=2 |issue=10 |pages=e328 |date=October 2004 |pmid=15383836 |pmc=517825 |doi=10.1371/journal.pbio.0020328 }} </ref> as well as yeast<ref name="mil3">{{cite journal |vauthors=Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |journal=Science |volume=298 |issue=5594 |pages=824–7 |date=October 2002 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="lee1">{{cite journal |vauthors=Lee TI, Rinaldi NJ, Robert F, etal |title=Transcriptional regulatory networks in Saccharomyces cerevisiae |journal=Science |volume=298 |issue=5594 |pages=799–804 |date=October 2002 |pmid=12399584 |doi=10.1126/science.1075090 |bibcode=2002Sci...298..799L }}</ref> and higher organisms.<ref name="odo1">{{cite journal |vauthors=Odom DT, Zizlsperger N, Gordon DB, etal |title=Control of pancreas and liver gene expression by HNF transcription factors |journal=Science |volume=303 |issue=5662 |pages=1378–81 |date=February 2004 |pmid=14988562 |pmc=3012624 |doi=10.1126/science.1089769 |bibcode=2004Sci...303.1378O }}</ref><ref name="boy1">{{cite journal |vauthors=Boyer LA, Lee TI, Cole MF, etal |title=Core transcriptional regulatory circuitry in human embryonic stem cells |journal=Cell |volume=122 |issue=6 |pages=947–56 |date=September 2005 |pmid=16153702 |pmc=3006442 |doi=10.1016/j.cell.2005.08.020 }}</ref><ref name="ira1">{{cite journal |vauthors=Iranfar N, Fuller D, Loomis WF |title=Transcriptional regulation of post-aggregation genes in Dictyostelium by a feed-forward loop involving GBF and LagC |journal=Dev. Biol. |volume=290 |issue=2 |pages=460–9 |date=February 2006 |pmid=16386729 |doi=10.1016/j.ydbio.2005.11.035 |doi-access=free }}</ref> A distinct set of network motifs were identified in other types of biological networks such as neuronal networks and protein interaction networks.<ref name="mil2" /><ref name="maa1">{{cite journal |vauthors=Ma'ayan A, Jenkins SL, Neves S, etal |title=Formation of regulatory patterns during signal propagation in a Mammalian cellular network |journal=Science |volume=309 |issue=5737 |pages=1078–83 |date=August 2005 |pmid=16099987 |pmc=3032439 |doi=10.1126/science.1108876 |bibcode=2005Sci...309.1078M }}</ref><ref name="pta1">{{cite journal |vauthors=Ptacek J, Devgan G, Michaud G, etal |title=Global analysis of protein phosphorylation in yeast |journal=Nature |volume=438 |issue=7068 |pages=679–84 |date=December 2005 |pmid=16319894 |doi=10.1038/nature04187|bibcode=2005Natur.438..679P |url=https://authors.library.caltech.edu/56271/2/Tables.pdf |type=Submitted manuscript }}</ref><br />
<br />
生物学研究试图解释为生物网络检测到的模体。例如,在接下来的工作中,文献[17]在大肠杆菌中发现的网络模体存在于其他细菌<ref name="eic1">{{cite journal |vauthors=Eichenberger P, Fujita M, Jensen ST, etal |title=The program of gene transcription for a single differentiating cell type during sporulation in ''Bacillus subtilis'' |journal=PLOS Biology |volume=2 |issue=10 |pages=e328 |date=October 2004 |pmid=15383836 |pmc=517825 |doi=10.1371/journal.pbio.0020328 }} </ref>以及酵母<ref name="mil3">{{cite journal |vauthors=Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |journal=Science |volume=298 |issue=5594 |pages=824–7 |date=October 2002 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="lee1">{{cite journal |vauthors=Lee TI, Rinaldi NJ, Robert F, etal |title=Transcriptional regulatory networks in Saccharomyces cerevisiae |journal=Science |volume=298 |issue=5594 |pages=799–804 |date=October 2002 |pmid=12399584 |doi=10.1126/science.1075090 |bibcode=2002Sci...298..799L }}</ref>和高等生物的转录网络中。文献<ref name="odo1">{{cite journal |vauthors=Odom DT, Zizlsperger N, Gordon DB, etal |title=Control of pancreas and liver gene expression by HNF transcription factors |journal=Science |volume=303 |issue=5662 |pages=1378–81 |date=February 2004 |pmid=14988562 |pmc=3012624 |doi=10.1126/science.1089769 |bibcode=2004Sci...303.1378O }}</ref><ref name="boy1">{{cite journal |vauthors=Boyer LA, Lee TI, Cole MF, etal |title=Core transcriptional regulatory circuitry in human embryonic stem cells |journal=Cell |volume=122 |issue=6 |pages=947–56 |date=September 2005 |pmid=16153702 |pmc=3006442 |doi=10.1016/j.cell.2005.08.020 }}</ref><ref name="ira1">{{cite journal |vauthors=Iranfar N, Fuller D, Loomis WF |title=Transcriptional regulation of post-aggregation genes in Dictyostelium by a feed-forward loop involving GBF and LagC |journal=Dev. Biol. |volume=290 |issue=2 |pages=460–9 |date=February 2006 |pmid=16386729 |doi=10.1016/j.ydbio.2005.11.035 |doi-access=free }}</ref>在其他类型的生物网络中发现了一组不同的网络模体,如神经元网络和蛋白质相互作用网络。<ref name="mil2" /><ref name="maa1">{{cite journal |vauthors=Ma'ayan A, Jenkins SL, Neves S, etal |title=Formation of regulatory patterns during signal propagation in a Mammalian cellular network |journal=Science |volume=309 |issue=5737 |pages=1078–83 |date=August 2005 |pmid=16099987 |pmc=3032439 |doi=10.1126/science.1108876 |bibcode=2005Sci...309.1078M }}</ref><ref name="pta1">{{cite journal |vauthors=Ptacek J, Devgan G, Michaud G, etal |title=Global analysis of protein phosphorylation in yeast |journal=Nature |volume=438 |issue=7068 |pages=679–84 |date=December 2005 |pmid=16319894 |doi=10.1038/nature04187|bibcode=2005Natur.438..679P |url=https://authors.library.caltech.edu/56271/2/Tables.pdf |type=Submitted manuscript }}</ref><br />
<br />
<br />
The computational research has focused on improving existing motif detection tools to assist the biological investigations and allow larger networks to be analyzed. Several different algorithms have been provided so far, which are elaborated in the next section in chronological order.<br />
<br />
另一方面,对于计算研究的重点则是改进现有的模体检测工具,以协助生物学研究,并允许对更大的网络进行分析。到目前为止,已经提供了几种不同的算法,这些算法将在下一节按时间顺序进行阐述。<br />
<br />
Most recently, the acc-MOTIF tool to detect network motifs was released.<ref>{{Cite web | url=http://www.ft.unicamp.br/docentes/meira/accmotifs/ |title = Acc-Motif: Accelerated Motif Detection}}</ref><br />
<br />
最近,还发布了用于检测网络基序的acc基序工具。<ref>{{Cite web | url=http://www.ft.unicamp.br/docentes/meira/accmotifs/ |title = Acc-Motif: Accelerated Motif Detection}}</ref><br />
<br />
<br />
==模体发现算法 Motif discovery algorithms==<br />
<br />
Various solutions have been proposed for the challenging problem of motif discovery. These algorithms can be classified under various paradigms such as exact counting methods, sampling methods, pattern growth methods and so on. However, motif discovery problem comprises two main steps: first, calculating the number of occurrences of a sub-graph and then, evaluating the sub-graph significance. The recurrence is significant if it is detectably far more than expected. Roughly speaking, the expected number of appearances of a sub-graph can be determined by a Null-model, which is defined by an ensemble of random networks with some of the same properties as the original network.<br />
<br />
针对模体发现这一问题存在多种解决方案。这些算法可以归纳为不同的范式:例如精确计数方法,采样方法,模式增长方法等。但模体发现问题包括两个主要步骤:首先,计算子图的出现次数,然后评估子图的重要性。如果检测到的重现性远超过预期,那么这种重现性是很显著的。粗略地讲,子图的预期出现次数可以由'''零模型 Null-model''' 确定,该模型定义为具有与原始网络某些属性相同的随机网络的集合。<br />
<br />
<br />
Here, a review on computational aspects of major algorithms is given and their related benefits and drawbacks from an algorithmic perspective are discussed.<br />
<br />
接下来,对下列算法的计算原理进行简要回顾,并从算法的角度讨论了它们的优缺点。<br />
<br />
===mfinder 算法===<br />
<br />
''mfinder'', the first motif-mining tool, implements two kinds of motif finding algorithms: a full enumeration and a sampling method. Until 2004, the only exact counting method for NM (network motif) detection was the brute-force one proposed by Milo ''et al.''.<ref name="mil1" /> This algorithm was successful for discovering small motifs, but using this method for finding even size 5 or 6 motifs was not computationally feasible. Hence, a new approach to this problem was needed.<br />
<br />
'''mfinder'''是第一个模体挖掘工具,它主要有两种模体查找算法:完全枚举 full enumeration 和采样方法 sampling method。直到2004年,用于NM('''网络模体 networkmotif''')检测的唯一精确计数方法是'''Milo'''等人提出的暴力穷举方法。<ref name="mil1" />该算法成功地发现了小规模的模体,但是这种方法甚至对于发现规模为5个或6个的模体在计算上都不可行的。因此,需要一种解决该问题的新方法。<br />
<br />
<br />
Kashtan ''et al.'' <ref name="kas1" /> presented the first sampling NM discovery algorithm, which was based on ''edge sampling'' throughout the network. This algorithm estimates concentrations of induced sub-graphs and can be utilized for motif discovery in directed or undirected networks. The sampling procedure of the algorithm starts from an arbitrary edge of the network that leads to a sub-graph of size two, and then expands the sub-graph by choosing a random edge that is incident to the current sub-graph. After that, it continues choosing random neighboring edges until a sub-graph of size n is obtained. Finally, the sampled sub-graph is expanded to include all of the edges that exist in the network between these n nodes. When an algorithm uses a sampling approach, taking unbiased samples is the most important issue that the algorithm might address. The sampling procedure, however, does not take samples uniformly and therefore Kashtan ''et al.'' proposed a weighting scheme that assigns different weights to the different sub-graphs within network.<ref name="kas1" /> The underlying principle of weight allocation is exploiting the information of the [[sampling probability]] for each sub-graph, i.e. the probable sub-graphs will obtain comparatively less weights in comparison to the improbable sub-graphs; hence, the algorithm must calculate the sampling probability of each sub-graph that has been sampled. This weighting technique assists ''mfinder'' to determine sub-graph concentrations impartially.<br />
<br />
'''Kashtan''' 等人<ref name="kas1" />首次提出了一种基于边缘采样的网络模体(NM)采样发现算法。该算法估计了<font color="red">所含子图 induced sub-graphs 的集中度 concentrations </font>,可用于有向或无向网络中的模体发现。该算法的采样过程从网络的任意一条边开始,该边连向大小为2的子图,然后选择一条与当前子图相关的随机边对子图进行扩展。之后,它将继续选择随机的相邻边,直到获得大小为n的子图为止。最后,采样得到的子图扩展为包括这n个节点在内的网络中存在的所有边。当使用采样方法时,获取无偏样本是这类算法可能面临的最重要问题。而且,采样过程并不能保证采到所有的样本(也就是不能保证得到所有的子图,译者注),因此,Kashtan 等人又提出了一种加权方案,为网络中的不同子图分配不同的权重。<ref name="kas1" /> 权重分配的基本原理是利用每个子图的抽样概率信息,即,与不可能的子图相比,可能的子图将获得相对较少的权重;因此,该算法必须计算已采样的每个子图的采样概率。这种加权技术有助于mfinder公正地确定子图的<font color="red">集中度 concentrations </font>。<br />
<br />
<br />
In expanded to include sharp contrast to exhaustive search, the computational time of the algorithm surprisingly is asymptotically independent of the network size. An analysis of the computational time of the algorithm has shown that it takes {{math|O(n<sup>n</sup>)}} for each sample of a sub-graph of size {{math|n}} from the network. On the other hand, there is no analysis in <ref name="kas1" /> on the classification time of sampled sub-graphs that requires solving the ''graph isomorphism'' problem for each sub-graph sample. Additionally, an extra computational effort is imposed on the algorithm by the sub-graph weight calculation. But it is unavoidable to say that the algorithm may sample the same sub-graph multiple times – spending time without gathering any information.<ref name="wer1" /> In conclusion, by taking the advantages of sampling, the algorithm performs more efficiently than an exhaustive search algorithm; however, it only determines sub-graphs concentrations approximately. This algorithm can find motifs up to size 6 because of its main implementation, and as result it gives the most significant motif, not all the others too. Also, it is necessary to mention that this tool has no option of visual presentation. The sampling algorithm is shown briefly:<br />
<br />
与穷举搜索形成鲜明对比的是,该算法的计算时间竟然与网络大小渐近无关。对算法时间复杂度的分析表明,对于网络中大小为n的子图的每个样本,它的时间复杂度为<math>O(n^n)</math>。另一方面,<font color="red">并没有对已采样子图的每一个子图样本判断图同构问题的分类时间进行分析</font><ref name="kas1" />。另外,子图权重计算将额外增加该算法的计算负担。但是不得不指出的是,该算法可能会多次采样相同的子图——花费时间而不收集任何有用信息。<ref name="wer1" />总之,通过利用采样的优势,该算法的性能比穷举搜索算法更有效;但是,它只能大致确定子图的<font color="red">集中度 concentrations </font>。由于该算法的实现方式,使得它可以找到最大为6的模体,并且它会给出的最重要的模体,而不是其他所有模体。另外,有必要提到此工具没有可视化的呈现。采样算法简要显示如下:<br />
<br />
<br />
{| class="wikitable"<br />
|-<br />
! mfinder<br />
|-<br />
| '''Definitions:''' {{math|E<sub>s</sub>}}is the set of picked edges. {{math|V<sub>s</sub>}} is the set of all nodes that are touched by the edges in {{math|E}}.<br />
|-<br />
| Init {{math|V<sub>s</sub>}} and {{math|E<sub>s</sub>}} to be empty sets.<br />
1. Pick a random edge {{math|e<sub>1</sub> {{=}} (v<sub>i</sub>, v<sub>j</sub>)}}. Update {{math|E<sub>s</sub> {{=}} {e<sub>1</sub>}}}, {{math|V<sub>s</sub> {{=}} {v<sub>i</sub>, v<sub>j</sub>}}}<br />
<br />
2. Make a list {{math|L}} of all neighbor edges of {{math|E<sub>s</sub>}}. Omit from {{math|L}} all edges between members of {{math|V<sub>s</sub>}}.<br />
<br />
3. Pick a random edge {{math|e {{=}} {v<sub>k</sub>,v<sub>l</sub>}}} from {{math|L}}. Update {{math|E<sub>s</sub> {{=}} E<sub>s</sub> ⋃ {e}}}, {{math|V<sub>s</sub> {{=}} V<sub>s</sub> ⋃ {v<sub>k</sub>, v<sub>l</sub>}}}.<br />
<br />
4. Repeat steps 2-3 until completing an ''n''-node subgraph (until {{math|{{!}}V<sub>s</sub>{{!}} {{=}} n}}).<br />
<br />
5. Calculate the probability to sample the picked ''n''-node subgraph.<br />
|}<br />
<br />
<br />
{|class="wikitable"<br />
|+ mfinder<br />
|-<br />
!rowspan="1"|定义:<math>E_{s}</math>是采集的边集合。<math>V_{s}</math>是<math>E</math>中所有边的顶点的集合。<br />
|-<br />
|rowspan="5"|初始化<math>V_{s}</math>和<math>E_{s}</math>为空集。<br><br />
1. 随机选择一条边<math> e_{1} = (v_{i}, v_{j}) </math>,更新 <math>E_{s} = \{e_{1}\}, V{s} = \{v_{i}, v_{j}\}</math><br />
<br />
2. 列出<math>E{s}</math>的所有邻边列表<math> L </math>,从<math> L </math>中删除<math>V{s}</math>中所有元素组成的边。<br />
<br />
3. 从<math> L </math>中随机选择一条边<math> e = \{v_{k},v_{l}\} </math>, 更新<math>E_{s} = E_{s} \cup \{e\} , V_{s} = V_{s} \cup \{v_{k}, v_{l}\}</math>。<br />
<br />
4. 重复步骤2-3,直到完成包含n个节点的子图 (<math>\left | V_{s} \right | = n</math>)。<br />
<br />
5. 计算对选取的n节点子图进行采样的概率。<br />
|}<br />
<br />
<br />
===FPF (Mavisto)算法===<br />
<br />
Schreiber and Schwöbbermeyer <ref name="schr1" /> proposed an algorithm named ''flexible pattern finder (FPF)'' for extracting frequent sub-graphs of an input network and implemented it in a system named ''Mavisto''.<ref name="schr2">{{cite journal |vauthors=Schreiber F, Schwobbermeyer H |title=MAVisto: a tool for the exploration of network motifs |journal=Bioinformatics |volume=21 |issue=17|pages=3572–3574 |year=2005 |doi=10.1093/bioinformatics/bti556|pmid=16020473 |doi-access=free }}</ref> Their algorithm exploits the ''downward closure'' property which is applicable for frequency concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}}. The downward closure property asserts that the frequency for sub-graphs decrease monotonically by increasing the size of sub-graphs; however, this property does not hold necessarily for frequency concept {{math|F<sub>1</sub>}}. FPF is based on a ''pattern tree'' (see figure) consisting of nodes that represents different graphs (or patterns), where the parent of each node is a sub-graph of its children nodes; in other words, the corresponding graph of each pattern tree's node is expanded by adding a new edge to the graph of its parent node.<br />
<br />
Schreiber和Schwöbbermeyer <ref name="schr1" />提出了一种称为灵活模式查找器(FPF)的算法,用于提取输入网络的频繁子图,并将其在名为Mavisto的系统中加以实现。<ref name="schr2">{{cite journal |vauthors=Schreiber F, Schwobbermeyer H |title=MAVisto: a tool for the exploration of network motifs |journal=Bioinformatics |volume=21 |issue=17|pages=3572–3574 |year=2005 |doi=10.1093/bioinformatics/bti556|pmid=16020473 |doi-access=free }}</ref> 他们的算法利用了向下闭包特性,该特性适用于频率概念<math>F_{2}</math>和<math>F_{3}</math>。向下闭包性质表明,子图的频率随着子图的大小而单调下降;但这一性质并不一定适用于频率概念<math>F_{1}</math>。FPF算法基于模式树(见右图),由代表不同图形(或模式)的节点组成,其中每个节点的父节点是其子节点的子图;换句话说,每个模式树节点的对应图通过向其父节点图添加新边来扩展。<br />
<br />
<br />
[[Image:The pattern tree in FPF algorithm.jpg|right|thumb|''FPF算法中的模式树展示''.<ref name="schr1" />]]<br />
<br />
<br />
At first, the FPF algorithm enumerates and maintains the information of all matches of a sub-graph located at the root of the pattern tree. Then, one-by-one it builds child nodes of the previous node in the pattern tree by adding one edge supported by a matching edge in the target graph, and tries to expand all of the previous information about matches to the new sub-graph (child node). In next step, it decides whether the frequency of the current pattern is lower than a predefined threshold or not. If it is lower and if downward closure holds, FPF can abandon that path and not traverse further in this part of the tree; as a result, unnecessary computation is avoided. This procedure is continued until there is no remaining path to traverse.<br />
<br />
首先,FPF算法枚举并维护位于模式树根部的子图的所有匹配信息。然后,它通过在目标图中添加匹配边缘支持的一条边缘,在模式树中一一建立前一节点的子节点,然后通过在目标图中添加匹配边支持的一条边,逐个构建模式树中前一个节点的子节点,并尝试将以前关于匹配的所有信息拓展到新的子图(子节点)中。下一步,它判断当前模式的频率是否低于预定义的阈值。如果它低于阈值且保持向下闭包,则FPF算法会放弃该路径,而不会在树的此部分进一步遍历;这样就避免了不必要的计算。重复此过程,直到没有剩余可遍历的路径为止。<br />
<br />
<br />
The advantage of the algorithm is that it does not consider infrequent sub-graphs and tries to finish the enumeration process as soon as possible; therefore, it only spends time for promising nodes in the pattern tree and discards all other nodes. As an added bonus, the pattern tree notion permits FPF to be implemented and executed in a parallel manner since it is possible to traverse each path of the pattern tree independently. However, FPF is most useful for frequency concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}}, because downward closure is not applicable to {{math|F<sub>1</sub>}}. Nevertheless, the pattern tree is still practical for {{math|F<sub>1</sub>}} if the algorithm runs in parallel. Another advantage of the algorithm is that the implementation of this algorithm has no limitation on motif size, which makes it more amenable to improvements. The pseudocode of FPF (Mavisto) is shown below:<br />
<br />
该算法的优点是它不会考虑不频繁的子图,并尝试尽快完成枚举过程;因此,它只花时间在模式树中用于有希望的节点上,而放弃所有其他节点。还有一点额外的好处,模式树概念允许 FPF 以并行方式实现和执行,因为它可以独立地遍历模式树的每个路径。但是,FPF对于频率概念<math>F_{2}</math>和<math>F_{3}</math>最为有用,因为向下闭包不适用于<math>F_{1}</math>。尽管如此,如果算法并行运行,那么模式树对于<math>F_{1}</math>仍然是可行的。该算法的另一个优点是它的实现对模体大小没有限制,这使其更易于改进。FPF(Mavisto)的伪代码如下所示:<br />
<br />
<br />
{| class="wikitable"<br />
|-<br />
! Mavisto<br />
|-<br />
| '''Data:''' Graph {{math|G}}, target pattern size {{math|t}}, frequency concept {{math|F}}<br />
<br />
'''Result:''' Set {{math|R}} of patterns of size {{math|t}} with maximum frequency.<br />
|-<br />
| {{math|R ← φ}}, {{math|f<sub>max</sub> ← 0}}<br />
<br />
{{math|P ←}}start pattern {{math|p1}} of size 1<br />
<br />
{{math|M<sub>p<sub>1</sub></sub> ←}}all matches of {{math|p<sub>1</sub>}} in {{math|G}}<br />
<br />
'''While''' {{math|P &ne; φ}} '''do'''<br />
<br />
{{pad|1em}}{{math|P<sub>max</sub> ←}}select all patterns from {{math|P}} with maximum size.<br />
<br />
{{pad|1em}}{{math|P ←}} select pattern with maximum frequency from {{math|P<sub>max</sub>}}<br />
<br />
{{pad|1em}}{{math|Ε {{=}} ''ExtensionLoop''(G, p, M<sub>p</sub>)}}<br />
<br />
{{pad|1em}}'''Foreach''' pattern {{math|p &isin; E}}<br />
<br />
{{pad|2em}}'''If''' {{math|F {{=}} F<sub>1</sub>}} '''then''' {{math|f ← ''size''(M<sub>p</sub>)}}<br />
<br />
{{pad|2em}}'''Else''' {{math|f ←}} ''Maximum Independent set''{{math|(F, M<sub>p</sub>)}}<br />
<br />
{{pad|2em}}'''End'''<br />
<br />
{{pad|2em}}'''If''' {{math|''size''(p) {{=}} t}} '''then'''<br />
<br />
{{pad|3em}}'''If''' {{math|f {{=}} f<sub>max</sub>}} '''then''' {{math|R ← R ⋃ {p}}}<br />
<br />
{{pad|3em}}'''Else if''' {{math|f > f<sub>max</sub>}} '''then''' {{math|R ← {p}}}; {{math|f<sub>max</sub> ← f}}<br />
<br />
{{pad|3em}}'''End'''<br />
<br />
{{pad|2em}}'''Else'''<br />
<br />
{{pad|3em}}'''If''' {{math|F {{=}} F<sub>1</sub>}} '''or''' {{math|f &ge; f<sub>max</sub>}} '''then''' {{math|P ← P ⋃ {p}}}<br />
<br />
{{pad|3em}}'''End'''<br />
<br />
{{pad|2em}}'''End'''<br />
<br />
{{pad|1em}}'''End'''<br />
<br />
'''End'''<br />
|}<br />
<br />
<br />
{|class="wikitable"<br />
|+ Mavisto<br />
|-<br />
!rowspan="1"|数据: 图 <math>G</math>, 目标模式规模 <math>t</math>, 频率概念 <math>F</math>。<br><br />
结果: 以最大频率设置大小为 <math>t</math>的模式 <math>R</math>.<br><br />
|-<br />
|rowspan="20"| <math>R \leftarrow \Phi , f_{max}\leftarrow 0</math><br><br />
<math>P \leftarrow</math> 开始于大小为1的模式 <math>p_{1}</math><br />
<br />
<math>M_{p_{1}} \leftarrow </math> 图 <math>G</math> 中模式 <math>p_{1}</math> 的所有匹配<br />
<br />
当 <math>P \neq \Phi </math> 时,执行:<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;<math>P_{max} \leftarrow</math> 从 <math>P</math> 中选择最大规模的所有模式<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;<math>P\leftarrow</math> 从 <math>P_{max}</math> 中选择最大频率的模式<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;<math>E = ExtensionLoop(G, p, M_{p})</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;对于 <math>p \in E </math> 的所有模式:<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>F = F_{1}</math> ,那么 <math>f \leftarrow size(M_{p})</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他<math>f \leftarrow</math> 最大独立集 <math>(F, M_{p})</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>size(p) = t</math> ,那么<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>f = f_{max}</math> ,那么 <math>R \leftarrow R \cup \{p\}</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他 如果 <math>f > f_{max}</math> ,那么 <math>R \leftarrow \{p\}</math>; <math>f_{max} \leftarrow f</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>F = F_{1} or f \geq f_{max}</math> ,那么 <math> P \leftarrow P \cup \{p\}</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
结束<br />
|}<br />
<br />
===ESU (FANMOD)算法及对应的软件===<br />
The sampling bias of Kashtan ''et al.'' <ref name="kas1" /> provided great impetus for designing better algorithms for the NM discovery problem. Although Kashtan ''et al.'' tried to settle this drawback by means of a weighting scheme, this method imposed an undesired overhead on the running time as well a more complicated implementation. This tool is one of the most useful ones, as it supports visual options and also is an efficient algorithm with respect to time. But, it has a limitation on motif size as it does not allow searching for motifs of size 9 or higher because of the way the tool is implemented.<br />
由于Kashtan等学者发现的『采样偏差』问题为『the NM discovery problem』设计更好的算法提出了更高要求。虽然Kashtan等人尝试用加权法来解决这个弊端,但这个方法在运行上,消耗了过多的运行时间,且实现起来也变得更加复杂。但这个工具还是最好用的工具之一,因为它支持可视化选项,同时也『是个节约时间的算法』。但是,它在所支持的模体的规模大小还是有局限性。由于该工具在具体实施中,不允许搜索规模大小为9或者更大的模体。<br />
<br />
Wernicke <ref name="wer1" /> introduced an algorithm named ''RAND-ESU'' that provides a significant improvement over ''mfinder''.<ref name="kas1" /> This algorithm, which is based on the exact enumeration algorithm ''ESU'', has been implemented as an application called ''FANMOD''.<ref name="wer1" /> ''RAND-ESU'' is a NM discovery algorithm applicable for both directed and undirected networks, effectively exploits an unbiased node sampling throughout the network, and prevents overcounting sub-graphs more than once. Furthermore, ''RAND-ESU'' uses a novel analytical approach called ''DIRECT'' for determining sub-graph significance instead of using an ensemble of random networks as a Null-model. The ''DIRECT'' method estimates the sub-graph concentration without explicitly generating random networks.<ref name="wer1" /> Empirically, the DIRECT method is more efficient in comparison with the random network ensemble in case of sub-graphs with a very low concentration; however, the classical Null-model is faster than the ''DIRECT'' method for highly concentrated sub-graphs.<ref name="mil1" /><ref name="wer1" /> In the following, we detail the ''ESU'' algorithm and then we show how this exact algorithm can be modified efficiently to ''RAND-ESU'' that estimates sub-graphs concentrations.<br />
<br />
Weinicke引入了一种叫RAND-ESU的算法,这个新引入的算法比Mfinder软件有着更显著的提升。RAND-ESU基于精准的ESU算法,已有对应的软件FANMOD。RAND-ESU是一种[NM算法],可应用于定向的或者不定向的网络中,能够有效的在网络中利用无偏差节点进行采样,以及保证了一个子图仅仅被搜索一次,且不会产生无意义的子图。并且,RAND-ESU采用了一个叫做DIRECT的全新的分析方式,从而来确定子图的重要性,而不是用随机网络的组合来建立『Null模型』。DIRECT方法可以不用大量生成随机网络就能估计子图的浓度。实际上,相较于用随机网络组合分析比较低集中度的子图来说,DIRECT这个方法更加的高效。但是,传统的『Null模型』又比DIRECT这个算法能更加快速地解决高度集中的子图。接下来,我们将详细讲述ESU算法和展示如何把这种精确的算法调整为RAND-ESU算法去估计子图的浓度。<br />
<br />
The algorithms ''ESU'' and ''RAND-ESU'' are fairly simple, and hence easy to implement. ''ESU'' first finds the set of all induced sub-graphs of size {{math|k}}, let {{math|S<sub>k</sub>}} be this set. ''ESU'' can be implemented as a recursive function; the running of this function can be displayed as a tree-like structure of depth {{math|k}}, called the ESU-Tree (see figure). Each of the ESU-Tree nodes indicate the status of the recursive function that entails two consecutive sets SUB and EXT. SUB refers to nodes in the target network that are adjacent and establish a partial sub-graph of size {{math|{{!}}SUB{{!}} ≤ k}}. If {{math|{{!}}SUB{{!}} {{=}} k}}, the algorithm has found an induced complete sub-graph, so {{math|S<sub>k</sub> {{=}} SUB ∪ S<sub>k</sub>}}. However, if {{math|{{!}}SUB{{!}} < k}}, the algorithm must expand SUB to achieve cardinality {{math|k}}. This is done by the EXT set that contains all the nodes that satisfy two conditions: First, each of the nodes in EXT must be adjacent to at least one of the nodes in SUB; second, their numerical labels must be larger than the label of first element in SUB. The first condition makes sure that the expansion of SUB nodes yields a connected graph and the second condition causes ESU-Tree leaves (see figure) to be distinct; as a result, it prevents overcounting. Note that, the EXT set is not a static set, so in each step it may expand by some new nodes that do not breach the two conditions. The next step of ESU involves classification of sub-graphs placed in the ESU-Tree leaves into non-isomorphic size-{{math|k}} graph classes; consequently, ESU determines sub-graphs frequencies and concentrations. This stage has been implemented simply by employing McKay's ''nauty'' algorithm,<ref name="mck1">{{cite journal |author=McKay BD |title=Practical graph isomorphism |journal=Congressus Numerantium |year=1981 |volume=30 |pages=45–87|bibcode=2013arXiv1301.1493M |arxiv=1301.1493 }}</ref><ref name="mck2">{{cite journal |author=McKay BD |title=Isomorph-free exhaustive generation |journal=Journal of Algorithms |year=1998 |volume=26 |issue=2 |pages=306–324 |doi=10.1006/jagm.1997.0898}}</ref> which classifies each sub-graph by performing a graph isomorphism test. Therefore, ESU finds the set of all induced {{math|k}}-size sub-graphs in a target graph by a recursive algorithm and then determines their frequency using an efficient tool.<br />
<br />
ESU和RAND-ESU两种算法都比较简捷,所以实现起来都很容易。『ESU首先找到大小为k的所有诱导子图的集合』,并命名这个集合为Sk。因为EUS以递归函数的形式实现,该函数的运行可以演示为『k级』的树状结构,称为ESU-Tree(见图)。每一个在ESU-Tree上的节点都表示递归函数的状态,这个递归函数需要两个连续集合的SUB和EXT。『SUB指的是在目标网络的相邻节点上,并且是一部分的层级绝对值大小小于等于k的子图集合。』如果SUB集合层级的绝对值等于k,那么这个算法可以找到一个『完整的诱导子图』,所以在此情况下Sk等于SUB与Sk的并集。相反,如果它的绝对值小于k,那么这个算法必须把SUB扩大,才能实现基数为k。『EXT这个集合包含了所有的满足以下两个情况的节点。第一,每个在EXT的节点必须至少与在SUB的一个节点相邻。第二,他们的下标必须比在SUB的第一个元素大。』???第一个条件保证了『SUB节点的展开产生相关的图』,第二个条件能使ESU-Tree树状图上的分支变得离散。所以,这个方法可以避免过度计算。注意,EXT集合不是一个固定的集合。所以每一步都有可能扩展满足于以上两个条件的新节点。下一步包含了在ESU-Tree分支上的子图的分类,『将它们分为非同构的大小为k的图类』。因此,ESU决定了子图的『频率以及浓度』。这一阶段的实施仅通过运用McKay的nauty算法,这一算法可以通过图的同构测试来把每个子图进行分类。所以,ESU能够在目标图中通过递归算法,找到所有规模大小为k的诱导子图集合,且使用高效的工具来确定他们的『频率』。<br />
<br />
The procedure of implementing ''RAND-ESU'' is quite straightforward and is one of the main advantages of ''FANMOD''. One can change the ''ESU'' algorithm to explore just a portion of the ESU-Tree leaves by applying a probability value {{math|0 ≤ p<sub>d</sub> ≤ 1}} for each level of the ESU-Tree and oblige ''ESU'' to traverse each child node of a node in level {{math|d-1}} with probability {{math|p<sub>d</sub>}}. This new algorithm is called ''RAND-ESU''. Evidently, when {{math|p<sub>d</sub> {{=}} 1}} for all levels, ''RAND-ESU'' acts like ''ESU''. For {{math|p<sub>d</sub> {{=}} 0}} the algorithm finds nothing. Note that, this procedure ensures that the chances of visiting each leaf of the ESU-Tree are the same, resulting in ''unbiased'' sampling of sub-graphs through the network. The probability of visiting each leaf is {{math|∏<sub>d</sub>p<sub>d</sub>}} and this is identical for all of the ESU-Tree leaves; therefore, this method guarantees unbiased sampling of sub-graphs from the network. Nonetheless, determining the value of {{math|p<sub>d</sub>}} for {{math|1 ≤ d ≤ k}} is another issue that must be determined manually by an expert to get precise results of sub-graph concentrations.<ref name="cir1" /> While there is no lucid prescript for this matter, the Wernicke provides some general observations that may help in determining p_d values. In summary, ''RAND-ESU'' is a very fast algorithm for NM discovery in the case of induced sub-graphs supporting unbiased sampling method. Although, the main ''ESU'' algorithm and so the ''FANMOD'' tool is known for discovering induced sub-graphs, there is trivial modification to ''ESU'' which makes it possible for finding non-induced sub-graphs, too. The pseudo code of ''ESU (FANMOD)'' is shown below:<br />
运用RAND-ESU的过程十分的简单,这也是FANMOD的一个主要的优点。可以通过对ESU-Tree『树状图』的每个级别应用概率{{math|0 ≤ p<sub>d</sub> ≤ 1}}并强制ESU以概率{{math|p<sub>d</sub>}}遍历{{math|d-1}}级别中节点的每个子节点,来更改ESU算法使其仅搜索ESU-Tree分支的一部分。 这种新的演算方式叫RAND-ESU。显然,当所有阶段{{math|p<sub>d</sub> {{=}} 1}}时,RAND-ESU等同于ESU。当{{math|p<sub>d</sub> {{=}} 0}}时,在这个算法下没有任何意义。注意,这个过程只是确保了可以找到ESU-Tree上的每一分支的机会都是相同的,从而使网络中的子图采样无偏差。访问每个分支的概率为{{math|∏<sub>d</sub>p<sub>d</sub>}},这对于所有ESU-Tree中的分支都是相同的; 因此,该方法可确保从网络中对子图进行无偏采样。但是,设置{{math|1 ≤ d ≤ k}}的{{math|p<sub>d</sub>}}参数是另一个问题,必须由专家人工确定才能获得子图『浓度』的精确结果。尽管对此没有明确的规定,但是Wrenucke提出了一些一般性的观察结论,这些结论有可能可以帮助我们确定p_d值。总的来说,在诱导子图支持无偏采样方法的情况下,RAND-ESU是一个能快速解决『NM discovery problem』的算法。 尽管,ESU算法的主要部分和FANMOD工具是以用来寻找诱导子图而著称的,但只需对ESU进行细小的改动,就可以用来寻找诱导子图。ESU(FANMOD)的伪代码如下:<br />
[[File:ESU-Tree.jpg|thumb|(a) ''A target graph of size 5'', (b) ''the ESU-tree of depth k that is associated to the extraction of sub-graphs of size 3 in the target graph''. Leaves correspond to set S3 or all of the size-3 induced sub-graphs of the target graph (a). Nodes in the ESU-tree include two adjoining sets, the first set contains adjacent nodes called SUB and the second set named EXT holds all nodes that are adjacent to at least one of the SUB nodes and where their numerical labels are larger than the SUB nodes labels. The EXT set is utilized by the algorithm to expand a SUB set until it reaches a desired sub-graph size that are placed at the lowest level of ESU-Tree (or its leaves).]]<br />
<br />
{| class="wikitable"<br />
|-<br />
! Enumeration of ESU (FANMOD)<br />
|-<br />
|'''''EnumerateSubgraphs(G,k)'''''<br />
<br />
'''Input:''' A graph {{math|G {{=}} (V, E)}} and an integer {{math|1 ≤ k ≤ {{!}}V{{!}}}}.<br />
<br />
'''Output:''' All size-{{math|k}} subgraphs in {{math|G}}.<br />
<br />
'''for each''' vertex {{math|v ∈ V}} '''do'''<br />
<br />
{{pad|2em}}{{math|VExtension ← {u ∈ N({v}) {{!}} u > v}}}<br />
<br />
{{pad|2em}}'''call''' {{math|''ExtendSubgraph''({v}, VExtension, v)}}<br />
<br />
'''endfor'''<br />
|-<br />
|'''''ExtendSubgraph(VSubgraph, VExtension, v)'''''<br />
<br />
'''if''' {{math|{{!}}VSubgraph{{!}} {{=}} k}} '''then''' output {{math|G[VSubgraph]}} and '''return'''<br />
<br />
'''while''' {{math|VExtension ≠ ∅}} '''do'''<br />
<br />
{{pad|2em}}Remove an arbitrarily chosen vertex {{math|w}} from {{math|VExtension}}<br />
<br />
{{pad|2em}}{{math|VExtension&prime; ← VExtension ∪ {u ∈ N<sub>excl</sub>(w, VSubgraph) {{!}} u > v}}}<br />
<br />
{{pad|2em}}'''call''' {{math|''ExtendSubgraph''(VSubgraph ∪ {w}, VExtension&prime;, v)}}<br />
<br />
'''return'''<br />
|}<br />
<br />
===NeMoFinder===<br />
Chen ''et al.'' <ref name="che1">{{cite conference |vauthors=Chen J, Hsu W, Li Lee M, etal |title=NeMoFinder: dissecting genome-wide protein-protein interactions with meso-scale network motifs |conference=the 12th ACM SIGKDD international conference on Knowledge discovery and data mining |year=2006 |location=Philadelphia, Pennsylvania, USA |pages=106–115}}</ref> introduced a new NM discovery algorithm called ''NeMoFinder'', which adapts the idea in ''SPIN'' <ref name="hua1">{{cite conference |vauthors=Huan J, Wang W, Prins J, etal |title=SPIN: mining maximal frequent sub-graphs from graph databases |conference=the 10th ACM SIGKDD international conference on Knowledge discovery and data mining |year=2004 |pages=581–586}}</ref> to extract frequent trees and after that expands them into non-isomorphic graphs.<ref name="cir1" /> ''NeMoFinder'' utilizes frequent size-n trees to partition the input network into a collection of size-{{math|n}} graphs, afterward finding frequent size-n sub-graphs by expansion of frequent trees edge-by-edge until getting a complete size-{{math|n}} graph {{math|K<sub>n</sub>}}. The algorithm finds NMs in undirected networks and is not limited to extracting only induced sub-graphs. Furthermore, ''NeMoFinder'' is an exact enumeration algorithm and is not based on a sampling method. As Chen ''et al.'' claim, ''NeMoFinder'' is applicable for detecting relatively large NMs, for instance, finding NMs up to size-12 from the whole ''S. cerevisiae'' (yeast) PPI network as the authors claimed.<ref name="uet1">{{cite journal |vauthors=Uetz P, Giot L, Cagney G, etal |title=A comprehensive analysis of protein-protein interactions in Saccharomyces cerevisiae |journal=Nature |year=2000 |volume=403 |issue=6770 |pages=623–627 |doi=10.1038/35001009 |pmid=10688190|bibcode=2000Natur.403..623U }}</ref><br />
<br />
''NeMoFinder'' consists of three main steps. First, finding frequent size-{{math|n}} trees, then utilizing repeated size-n trees to divide the entire network into a collection of size-{{math|n}} graphs, finally, performing sub-graph join operations to find frequent size-n sub-graphs.<ref name="che1" /> In the first step, the algorithm detects all non-isomorphic size-{{math|n}} trees and mappings from a tree to the network. In the second step, the ranges of these mappings are employed to partition the network into size-n graphs. Up to this step, there is no distinction between ''NeMoFinder'' and an exact enumeration method. However, a large portion of non-isomorphic size-n graphs still remain. ''NeMoFinder'' exploits a heuristic to enumerate non-tree size-n graphs by the obtained information from the preceding steps. The main advantage of the algorithm is in the third step, which generates candidate sub-graphs from previously enumerated sub-graphs. This generation of new size-{{math|n}} sub-graphs is done by joining each previous sub-graph with derivative sub-graphs from itself called ''cousin sub-graphs''. These new sub-graphs contain one additional edge in comparison to the previous sub-graphs. However, there exist some problems in generating new sub-graphs: There is no clear method to derive cousins from a graph, joining a sub-graph with its cousins leads to redundancy in generating particular sub-graph more than once, and cousin determination is done by a canonical representation of the adjacency matrix which is not closed under join operation. ''NeMoFinder'' is an efficient network motif finding algorithm for motifs up to size 12 only for protein-protein interaction networks, which are presented as undirected graphs. And it is not able to work on directed networks which are so important in the field of complex and biological networks. The pseudocode of ''NeMoFinder'' is shown below:<br />
<br />
{| class="wikitable"<br />
|-<br />
! NeMoFinder<br />
|-<br />
|'''Input:'''<br />
<br />
{{math|G}} - PPI network;<br />
<br />
{{math|N}} - Number of randomized networks;<br />
<br />
{{math|K}} - Maximal network motif size;<br />
<br />
{{math|F}} - Frequency threshold;<br />
<br />
{{math|S}} - Uniqueness threshold;<br />
<br />
'''Output:'''<br />
<br />
{{math|U}} - Repeated and unique network motif set;<br />
<br />
{{math|D ← ∅}};<br />
<br />
'''for''' motif-size {{math|k}} '''from''' 3 '''to''' {{math|K}} '''do'''<br />
<br />
{{pad|1em}}{{math|T ← ''FindRepeatedTrees''(k)}};<br />
<br />
{{pad|1em}}{{math|GD<sub>k</sub> ← ''GraphPartition''(G, T)}}<br />
<br />
{{pad|1em}}{{math|D ← D ∪ T}};<br />
<br />
{{pad|1em}}{{math|D&prime; ← T}};<br />
<br />
{{pad|1em}}{{math|i ← k}};<br />
<br />
{{pad|1em}}'''while''' {{math|D&prime; ≠ ∅}} '''and''' {{math|i ≤ k &times; (k - 1) / 2}} '''do'''<br />
<br />
{{pad|2em}}{{math|D&prime; ← ''FindRepeatedGraphs''(k, i, D&prime;)}};<br />
<br />
{{pad|2em}}{{math|D ← D ∪ D&prime;}};<br />
<br />
{{pad|2em}}{{math|i ← i + 1}};<br />
<br />
{{pad|1em}}'''end while'''<br />
<br />
'''end for'''<br />
<br />
'''for''' counter {{math|i}} '''from''' 1 '''to''' {{math|N}} '''do'''<br />
<br />
{{pad|1em}}{{math|G<sub>rand</sub> ← ''RandomizedNetworkGeneration''()}};<br />
<br />
{{pad|1em}}'''for each''' {{math|g ∈ D}} '''do'''<br />
<br />
{{pad|2em}}{{math|''GetRandFrequency''(g, G<sub>rand</sub>)}};<br />
<br />
{{pad|1em}}'''end for'''<br />
<br />
'''end for'''<br />
<br />
{{math|U ← ∅}};<br />
<br />
'''for each''' {{math|g ∈ D}} '''do'''<br />
<br />
{{pad|1em}}{{math|s ← ''GetUniqunessValue''(g)}};<br />
<br />
{{pad|1em}}'''if''' {{math|s ≥ S}} '''then'''<br />
<br />
{{pad|2em}}{{math|U ← U ∪ {g}}};<br />
<br />
{{pad|1em}}'''end if'''<br />
<br />
'''end for'''<br />
<br />
'''return''' {{math|U}};<br />
|}<br />
<br />
===Grochow–Kellis===<br />
Grochow and Kellis <ref name="gro1">{{cite conference|vauthors=Grochow JA, Kellis M |title=Network Motif Discovery Using Sub-graph Enumeration and Symmetry-Breaking |conference=RECOMB |year=2007 |pages=92–106| doi=10.1007/978-3-540-71681-5_7| url=http://www.cs.colorado.edu/~jgrochow/Grochow_Kellis_RECOMB_07_Network_Motifs.pdf}}</ref> proposed an ''exact'' algorithm for enumerating sub-graph appearances. The algorithm is based on a ''motif-centric'' approach, which means that the frequency of a given sub-graph,called the ''query graph'', is exhaustively determined by searching for all possible mappings from the query graph into the larger network. It is claimed <ref name="gro1" /> that a ''motif-centric'' method in comparison to ''network-centric'' methods has some beneficial features. First of all it avoids the increased complexity of sub-graph enumeration. Also, by using mapping instead of enumerating, it enables an improvement in the isomorphism test. To improve the performance of the algorithm, since it is an inefficient exact enumeration algorithm, the authors introduced a fast method which is called ''symmetry-breaking conditions''. During straightforward sub-graph isomorphism tests, a sub-graph may be mapped to the same sub-graph of the query graph multiple times. In the Grochow–Kellis (GK) algorithm symmetry-breaking is used to avoid such multiple mappings. Here we introduce the GK algorithm and the symmetry-breaking condition which eliminates redundant isomorphism tests.<br />
<br />
[[File:Automorphisms of a subgraph.jpg|thumb|(a) ''graph G'', (b) ''illustration of all automorphisms of G that is showed in (a)''. From set AutG we can obtain a set of symmetry-breaking conditions of G given by SymG in (c). Only the first mapping in AutG satisfies the SynG conditions; as a result, by applying SymG in the Isomorphism Extension module the algorithm only enumerate each match-able sub-graph in the network to G once. Note that SynG is not necessarily a unique set for an arbitrary graph G.]]<br />
<br />
The GK algorithm discovers the whole set of mappings of a given query graph to the network in two major steps. It starts with the computation of symmetry-breaking conditions of the query graph. Next, by means of a branch-and-bound method, the algorithm tries to find every possible mapping from the query graph to the network that meets the associated symmetry-breaking conditions. An example of the usage of symmetry-breaking conditions in GK algorithm is demonstrated in figure.<br />
<br />
As it is mentioned above, the symmetry-breaking technique is a simple mechanism that precludes spending time finding a sub-graph more than once due to its symmetries.<ref name="gro1" /><ref name="gro2">{{cite conference|author=Grochow JA |title=On the structure and evolution of protein interaction networks |conference=Thesis M. Eng., Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science|year=2006| url=http://www.cs.toronto.edu/~jgrochow/Grochow_MIT_Masters_06_PPI_Networks.pdf}}</ref> Note that, computing symmetry-breaking conditions requires finding all automorphisms of a given query graph. Even though, there is no efficient (or polynomial time) algorithm for the graph automorphism problem, this problem can be tackled efficiently in practice by McKay's tools.<ref name="mck1" /><ref name="mck2" /> As it is claimed, using symmetry-breaking conditions in NM detection lead to save a great deal of running time. Moreover, it can be inferred from the results in <ref name="gro1" /><ref name="gro2" /> that using the symmetry-breaking conditions results in high efficiency particularly for directed networks in comparison to undirected networks. The symmetry-breaking conditions used in the GK algorithm are similar to the restriction which ''ESU'' algorithm applies to the labels in EXT and SUB sets. In conclusion, the GK algorithm computes the exact number of appearance of a given query graph in a large complex network and exploiting symmetry-breaking conditions improves the algorithm performance. Also, GK algorithm is one of the known algorithms having no limitation for motif size in implementation and potentially it can find motifs of any size.<br />
<br />
===Color-coding approach===<br />
Most algorithms in the field of NM discovery are used to find induced sub-graphs of a network. In 2008, Noga Alon ''et al.'' <ref name="alo1">{{cite journal|author1=Alon N |author2=Dao P |author3=Hajirasouliha I |author4=Hormozdiari F |author5=Sahinalp S.C |title=Biomolecular network motif counting and discovery by color coding |journal=Bioinformatics |year=2008 |volume=24 |issue=13 |pages=i241–i249 |doi=10.1093/bioinformatics/btn163|pmid=18586721 |pmc=2718641 }}</ref> introduced an approach for finding non-induced sub-graphs too. Their technique works on undirected networks such as PPI ones. Also, it counts non-induced trees and bounded treewidth sub-graphs. This method is applied for sub-graphs of size up to 10.<br />
<br />
This algorithm counts the number of non-induced occurrences of a tree {{math|T}} with {{math|k {{=}} O(logn)}} vertices in a network {{math|G}} with {{math|n}} vertices as follows:<br />
<br />
# '''Color coding.''' Color each vertex of input network G independently and uniformly at random with one of the {{math|k}} colors.<br />
# '''Counting.''' Apply a dynamic programming routine to count the number of non-induced occurrences of {{math|T}} in which each vertex has a unique color. For more details on this step, see.<ref name="alo1" /><br />
# Repeat the above two steps {{math|O(e<sup>k</sup>)}} times and add up the number of occurrences of {{math|T}} to get an estimate on the number of its occurrences in {{math|G}}.<br />
<br />
As available PPI networks are far from complete and error free, this approach is suitable for NM discovery for such networks. As Grochow–Kellis Algorithm and this one are the ones popular for non-induced sub-graphs, it is worth to mention that the algorithm introduced by Alon ''et al.'' is less time-consuming than the Grochow–Kellis Algorithm.<ref name="alo1" /><br />
<br />
===MODA===<br />
Omidi ''et al.'' <ref name="omi1">{{cite journal|vauthors=Omidi S, Schreiber F, Masoudi-Nejad A |title=MODA: an efficient algorithm for network motif discovery in biological networks |journal=Genes Genet Syst |year=2009 |volume=84 |issue=5 |pages=385–395 |doi=10.1266/ggs.84.385|pmid=20154426 |doi-access=free }}</ref> introduced a new algorithm for motif detection named ''MODA'' which is applicable for induced and non-induced NM discovery in undirected networks. It is based on the motif-centric approach discussed in the Grochow–Kellis algorithm section. It is very important to distinguish motif-centric algorithms such as MODA and GK algorithm because of their ability to work as query-finding algorithms. This feature allows such algorithms to be able to find a single motif query or a small number of motif queries (not all possible sub-graphs of a given size) with larger sizes. As the number of possible non-isomorphic sub-graphs increases exponentially with sub-graph size, for large size motifs (even larger than 10), the network-centric algorithms, those looking for all possible sub-graphs, face a problem. Although motif-centric algorithms also have problems in discovering all possible large size sub-graphs, but their ability to find small numbers of them is sometimes a significant property.<br />
<br />
Using a hierarchical structure called an ''expansion tree'', the ''MODA'' algorithm is able to extract NMs of a given size systematically and similar to ''FPF'' that avoids enumerating unpromising sub-graphs; ''MODA'' takes into consideration potential queries (or candidate sub-graphs) that would result in frequent sub-graphs. Despite the fact that ''MODA'' resembles ''FPF'' in using a tree like structure, the expansion tree is applicable merely for computing frequency concept {{math|F<sub>1</sub>}}. As we will discuss next, the advantage of this algorithm is that it does not carry out the sub-graph isomorphism test for ''non-tree'' query graphs. Additionally, it utilizes a sampling method in order to speed up the running time of the algorithm.<br />
<br />
Here is the main idea: by a simple criterion one can generalize a mapping of a k-size graph into the network to its same size supergraphs. For example, suppose there is mapping {{math|f(G)}} of graph {{math|G}} with {{math|k}} nodes into the network and we have a same size graph {{math|G&prime;}} with one more edge {{math|&langu, v&rang;}}; {{math|f<sub>G</sub>}} will map {{math|G&prime;}} into the network, if there is an edge {{math|&lang;f<sub>G</sub>(u), f<sub>G</sub>(v)&rang;}} in the network. As a result, we can exploit the mapping set of a graph to determine the frequencies of its same order supergraphs simply in {{math|O(1)}} time without carrying out sub-graph isomorphism testing. The algorithm starts ingeniously with minimally connected query graphs of size k and finds their mappings in the network via sub-graph isomorphism. After that, with conservation of the graph size, it expands previously considered query graphs edge-by-edge and computes the frequency of these expanded graphs as mentioned above. The expansion process continues until reaching a complete graph {{math|K<sub>k</sub>}} (fully connected with {{math|{{frac|k(k-1)|2}}}} edge).<br />
<br />
As discussed above, the algorithm starts by computing sub-tree frequencies in the network and then expands sub-trees edge by edge. One way to implement this idea is called the expansion tree {{math|T<sub>k</sub>}} for each {{math|k}}. Figure shows the expansion tree for size-4 sub-graphs. {{math|T<sub>k</sub>}} organizes the running process and provides query graphs in a hierarchical manner. Strictly speaking, the expansion tree {{math|T<sub>k</sub>}} is simply a [[directed acyclic graph]] or DAG, with its root number {{math|k}} indicating the graph size existing in the expansion tree and each of its other nodes containing the adjacency matrix of a distinct {{math|k}}-size query graph. Nodes in the first level of {{math|T<sub>k</sub>}} are all distinct {{math|k}}-size trees and by traversing {{math|T<sub>k</sub>}} in depth query graphs expand with one edge at each level. A query graph in a node is a sub-graph of the query graph in a node's child with one edge difference. The longest path in {{math|T<sub>k</sub>}} consists of {{math|(k<sup>2</sup>-3k+4)/2}} edges and is the path from the root to the leaf node holding the complete graph. Generating expansion trees can be done by a simple routine which is explained in.<ref name="omi1" /><br />
<br />
''MODA'' traverses {{math|T<sub>k</sub>}} and when it extracts query trees from the first level of {{math|T<sub>k</sub>}} it computes their mapping sets and saves these mappings for the next step. For non-tree queries from {{math|T<sub>k</sub>}}, the algorithm extracts the mappings associated with the parent node in {{math|T<sub>k</sub>}} and determines which of these mappings can support the current query graphs. The process will continue until the algorithm gets the complete query graph. The query tree mappings are extracted using the Grochow–Kellis algorithm. For computing the frequency of non-tree query graphs, the algorithm employs a simple routine that takes {{math|O(1)}} steps. In addition, ''MODA'' exploits a sampling method where the sampling of each node in the network is linearly proportional to the node degree, the probability distribution is exactly similar to the well-known Barabási-Albert preferential attachment model in the field of complex networks.<ref name="bar1">{{cite journal|vauthors=Barabasi AL, Albert R |title=Emergence of scaling in random networks |journal=Science |year=1999 |volume=286 |issue=5439 |pages=509–512 |doi=10.1126/science.286.5439.509 |pmid=10521342|bibcode=1999Sci...286..509B |arxiv=cond-mat/9910332 }}</ref> This approach generates approximations; however, the results are almost stable in different executions since sub-graphs aggregate around highly connected nodes.<ref name="vaz1">{{cite journal |vauthors=Vázquez A, Dobrin R, Sergi D, etal |title=The topological relationship between the large-scale attributes and local interaction patterns of complex networks |journal=PNAS |year=2004 |volume=101 |issue=52 |pages=17940–17945 |doi=10.1073/pnas.0406024101|pmid=15598746 |pmc=539752 |bibcode=2004PNAS..10117940V |arxiv=cond-mat/0408431 }}</ref> The pseudocode of ''MODA'' is shown below:<br />
<br />
[[File:Expansion Tree.jpg|thumb|''Illustration of the expansion tree T4 for 4-node query graphs''. At the first level, there are non-isomorphic k-size trees and at each level, an edge is added to the parent graph to form a child graph. In the second level, there is a graph with two alternative edges that is shown by a dashed red edge. In fact, this node represents two expanded graphs that are isomorphic.<ref name="omi1" />]]<br />
<br />
{| class="wikitable"<br />
|-<br />
! MODA<br />
|-<br />
|'''Input:''' {{math|G}}: Input graph, {{math|k}}: sub-graph size, {{math|Δ}}: threshold value<br />
<br />
'''Output:''' Frequent Subgraph List: List of all frequent {{math|k}}-size sub-graphs<br />
<br />
'''Note:''' {{math|F<sub>G</sub>}}: set of mappings from {{math|G}} in the input graph {{math|G}}<br />
<br />
'''fetch''' {{math|T<sub>k</sub>}}<br />
<br />
'''do'''<br />
<br />
{{pad|1em}}{{math|G&prime; {{=}} ''Get-Next-BFS''(T<sub>k</sub>)}} // {{math|G&prime;}} is a query graph<br />
<br />
{{pad|1em}}if {{math|{{!}}E(G&prime;){{!}} {{=}} (k – 1)}}<br />
<br />
{{pad|1em}}'''call''' {{math|''Mapping-Module''(G&prime;, G)}}<br />
<br />
{{pad|1em}}'''else'''<br />
<br />
{{pad|2em}}'''call''' {{math|''Enumerating-Module''(G&prime;, G, T<sub>k</sub>)}}<br />
<br />
{{pad|1em}}'''end if'''<br />
<br />
{{pad|1em}}'''save''' {{math|F<sub>2</sub>}}<br />
<br />
{{pad|1em}}'''if''' {{math|{{!}}F<sub>G</sub>{{!}} > Δ}} '''then'''<br />
<br />
{{pad|2em}}add {{math|G&prime;}} into Frequent Subgraph List<br />
<br />
{{pad|1em}}'''end if'''<br />
<br />
'''Until''' {{math|{{!}}E(G'){{!}} {{=}} (k – 1)/2}}<br />
<br />
'''return''' Frequent Subgraph List<br />
|}<br />
<br />
===Kavosh===<br />
A recently introduced algorithm named ''Kavosh'' <ref name="kash1">{{cite journal|vauthors=Kashani ZR, Ahrabian H, Elahi E, Nowzari-Dalini A, Ansari ES, Asadi S, Mohammadi S, Schreiber F, Masoudi-Nejad A |title=Kavosh: a new algorithm for finding network motifs |journal=BMC Bioinformatics |year=2009 |volume=10 |issue=318|pages=318 |doi=10.1186/1471-2105-10-318 |pmid=19799800 |pmc=2765973}} </ref> aims at improved main memory usage. ''Kavosh'' is usable to detect NM in both directed and undirected networks. The main idea of the enumeration is similar to the ''GK'' and ''MODA'' algorithms, which first find all {{math|k}}-size sub-graphs that a particular node participated in, then remove the node, and subsequently repeat this process for the remaining nodes.<ref name="kash1" /><br />
<br />
For counting the sub-graphs of size {{math|k}} that include a particular node, trees with maximum depth of k, rooted at this node and based on neighborhood relationship are implicitly built. Children of each node include both incoming and outgoing adjacent nodes. To descend the tree, a child is chosen at each level with the restriction that a particular child can be included only if it has not been included at any upper level. After having descended to the lowest level possible, the tree is again ascended and the process is repeated with the stipulation that nodes visited in earlier paths of a descendant are now considered unvisited nodes. A final restriction in building trees is that all children in a particular tree must have numerical labels larger than the label of the root of the tree. The restrictions on the labels of the children are similar to the conditions which ''GK'' and ''ESU'' algorithm use to avoid overcounting sub-graphs.<br />
<br />
The protocol for extracting sub-graphs makes use of the compositions of an integer. For the extraction of sub-graphs of size {{math|k}}, all possible compositions of the integer {{math|k-1}} must be considered. The compositions of {{math|k-1}} consist of all possible manners of expressing {{math|k-1}} as a sum of positive integers. Summations in which the order of the summands differs are considered distinct. A composition can be expressed as {{math|k<sub>2</sub>,k<sub>3</sub>,…,k<sub>m</sub>}} where {{math|k<sub>2</sub> + k<sub>3</sub> + … + k<sub>m</sub> {{=}} k-1}}. To count sub-graphs based on the composition, {{math|k<sub>i</sub>}} nodes are selected from the {{math|i}}-th level of the tree to be nodes of the sub-graphs ({{math|i {{=}} 2,3,…,m}}). The {{math|k-1}} selected nodes along with the node at the root define a sub-graph within the network. After discovering a sub-graph involved as a match in the target network, in order to be able to evaluate the size of each class according to the target network, ''Kavosh'' employs the ''nauty'' algorithm <ref name="mck1" /><ref name="mck2" /> in the same way as ''FANMOD''. The enumeration part of Kavosh algorithm is shown below:<br />
<br />
{| class="wikitable"<br />
|-<br />
! Enumeration of Kavosh<br />
|-<br />
|'''''Enumerate_Vertex(G, u, S, Remainder, i)'''''<br />
<br />
'''Input:''' {{math|G}}: Input graph<br><br />
{{pad|3em}}{{math|u}}: Root vertex<br><br />
{{pad|3em}}{{math|S}}: selection ({{math|S {{=}} { S<sub>0</sub>,S<sub>1</sub>,...,S<sub>k-1</sub>}}} is an array of the set of all {{math|S<sub>i</sub>}})<br><br />
{{pad|3em}}{{math|Remainder}}: number of remaining vertices to be selected<br><br />
{{pad|3em}}{{math|i}}: Current depth of the tree.<br><br />
'''Output:''' all {{math|k}}-size sub-graphs of graph {{math|G}} rooted in {{math|u}}.<br />
<br />
'''if''' {{math|Remainder {{=}} 0}} '''then'''<br><br />
{{pad|1em}}'''return'''<br><br />
'''else'''<br><br />
{{pad|1em}}{{math|ValList ← ''Validate''(G, S<sub>i-1</sub>, u)}}<br><br />
{{pad|1em}}{{math|n<sub>i</sub> ← ''Min''({{!}}ValList{{!}}, Remainder)}}<br><br />
{{pad|1em}}'''for''' {{math|k<sub>i</sub> {{=}} 1}} '''to''' {{math|n<sub>i</sub>}} '''do'''<br><br />
{{pad|2em}}{{math|C ← ''Initial_Comb''(ValList, k<sub>i</sub>)}}<br><br />
{{pad|2em}}(Make the first vertex combination selection according)<br><br />
{{pad|2em}}'''repeat'''<br><br />
{{pad|3em}}{{math|S<sub>i</sub> ← C}}<br><br />
{{pad|3em}}{{math|''Enumerate_Vertex''(G, u, S, Remainder-k<sub>i</sub>, i+1)}}<br><br />
{{pad|3em}}{{math|''Next_Comb''(ValList, k<sub>i</sub>)}}<br><br />
{{pad|3em}}(Make the next vertex combination selection according)<br><br />
{{pad|2em}}'''until''' {{math|C {{=}} NILL}}<br><br />
{{pad|2em}}'''end for'''<br><br />
{{pad|1em}}'''for each''' {{math|v ∈ ValList}} '''do'''<br><br />
{{pad|2em}}{{math|Visited[v] ← false}}<br><br />
{{pad|1em}}'''end for'''<br><br />
'''end if'''<br />
|-<br />
|'''''Validate(G, Parents, u)'''''<br><br />
'''Input:''' {{math|G}}: input graph, {{math|Parents}}: selected vertices of last layer, {{math|u}}: Root vertex.<br><br />
'''Output:''' Valid vertices of the current level.<br />
<br />
{{math|ValList ← NILL}}<br><br />
'''for each''' {{math|v ∈ Parents}} '''do'''<br><br />
{{pad|1em}}'''for each''' {{math|w ∈ Neighbor[u]}} '''do'''<br><br />
{{pad|2em}}'''if''' {{math|label[u] < label[w]}} '''AND NOT''' {{math|Visited[w]}} '''then'''<br><br />
{{pad|3em}}{{math|Visited[w] ← true}}<br><br />
{{pad|3em}}{{math|ValList {{=}} ValList + w}}<br><br />
{{pad|2em}}'''end if'''<br><br />
{{pad|1em}}'''end for'''<br><br />
'''end for'''<br><br />
'''return''' {{math|ValList}}<br><br />
|}<br />
<br />
Recently a ''Cytoscape'' plugin called ''CytoKavosh'' <ref name="mas2">{{cite journal|author1=Ali Masoudi-Nejad |author2=Mitra Anasariola |author3=Ali Salehzadeh-Yazdi |author4=Sahand Khakabimamaghani |title=CytoKavosh: a Cytoscape Plug-in for Finding Network Motifs in Large Biological Networks |journal=PLoS ONE |volume=7 |issue=8 |pages=e43287 |year=2012 |doi=10.1371/journal.pone.0043287|pmid=22952659 |pmc=3430699 |bibcode=2012PLoSO...743287M }} </ref> is developed for this software. It is available via ''Cytoscape'' web page [http://apps.cytoscape.org/apps/cytokavosh].<br />
<br />
===G-Tries===<br />
2010年, Pedro Ribeiro 和 Fernando Silva 提出了一个叫做''g-trie''的新数据结构,用来存储一组子图。<ref name="rib1">{{cite conference|vauthors=Ribeiro P, Silva F |title=G-Tries: an efficient data structure for discovering network motifs |conference=ACM 25th Symposium On Applied Computing - Bioinformatics Track |location=Sierre, Switzerland |year=2010 |pages=1559–1566 |url=http://www.nrcbioinformatics.ca/acmsac2010/}}</ref>这个在概念上类似前缀树的数据结构,根据子图结构来进行存储,并找出了每个子图在一个更大的图中出现的次数。这个数据结构有一个突出的方面:在应用于模体发现算法时,主网络中的子图需要进行评估。因此,在随机网络中寻找那些在不在主网络中的子图,这个消耗时间的步骤就不再需要执行了。<br />
<br />
''g-trie'' 是一个存储一组图的多叉树。每一个树节点都存储着一个'''图节点'''及其'''对应的到前一个节点的边'''的信息。从根节点到叶节点的一条路径对应一个图。一个 g-trie 节点的子孙节点共享一个子图(即每一次路径的分叉意味着从一个子图结构中扩展出不同的图结构,而这些扩展出来的图结构自然有着相同的子图结构)。如何构造一个 ''g-trie'' 在<ref name="rib1" />中有详细描述。构造好一个 ''g-trie'' 以后,需要进行计数步骤。计数流程的主要思想是回溯所有可能的子图,同时进行同构性测试。这种回溯技术本质上和其他以模体为中心的方法,比如''MODA'' 和 ''GK'' 算法中使用的技术是一样的。这种技术利用了共同的子结构,亦即在一定时间内,几个不同的候选子图中存在部分是同构的。<br />
<br />
在上述算法中,''G-Tries'' 是最快的。然而,它的一个缺点是内存的超量使用,这局限了它在个人电脑运行时所能发现的模体的大小<br />
<br />
===对比===<br />
<br />
下面的表格和数据显示了在各种标准网络中运行上述算法所获得的结果。这些结果皆获取于各自相应的来源<ref name="omi1" /><ref name="kash1" /><ref name="rib1" /> ,因此需要独立地对待它们。<br />
<br />
[[Image:Runtimes of algorithms.jpg|thumb|''Runtimes of Grochow–Kellis, mfinder, FANMOD, FPF and MODA for subgraphs from three nodes up to nine nodes''.<ref name="omi1" />]]<br />
<br />
{|class="wikitable"<br />
|+ Grochow–Kellis, FANMOD, 和 G-Trie 在5个不同网络上生成含3到9个节点子图所用的运行时间 <ref name="rib1" /><br />
|-<br />
!rowspan="2"|网络<br />
!rowspan="2"|子图大小<br />
!colspan="3"|原始网络数据<br />
!colspan="3"|随机网络平均数据<br />
|-<br />
!FANMOD<br />
!GK<br />
!G-Trie<br />
!FANMOD<br />
!GK<br />
!G-Trie<br />
|-<br />
|rowspan="5"|Dolphins<br />
|5 || 0.07 || 0.03 || 0.01 || 0.13 || 0.04 || 0.01<br />
|-<br />
|6||0.48||0.28||0.04||1.14||0.35||0.07<br />
|-<br />
|7||3.02||3.44||0.23||8.34||3.55||0.46<br />
|-<br />
|8||19.44||73.16||1.69||67.94||37.31||4.03<br />
|-<br />
|9||100.86||2984.22||6.98||493.98||366.79||24.84<br />
|-<br />
|rowspan="3"|Circuit<br />
|6||0.49||0.41||0.03||0.55||0.24||0.03<br />
|-<br />
|7||3.28||3.73||0.22||3.53||1.34||0.17<br />
|-<br />
|8||17.78||48.00||1.52||21.42||7.91||1.06<br />
|-<br />
|rowspan="3"|Social<br />
|3||0.31||0.11||0.02||0.35||0.11||0.02<br />
|-<br />
|4||7.78||1.37||0.56||13.27||1.86||0.57<br />
|-<br />
|5||208.30||31.85||14.88||531.65||62.66||22.11<br />
|-<br />
|rowspan="3"|Yeast<br />
|3||0.47||0.33||0.02||0.57||0.35||0.02<br />
|-<br />
|4||10.07||2.04||0.36||12.90||2.25||0.41<br />
|-<br />
|5||268.51||34.10||12.73||400.13||47.16||14.98<br />
|-<br />
|rowspan="5"|Power<br />
|3||0.51||1.46||0.00||0.91||1.37||0.01<br />
|-<br />
|4||1.38||4.34||0.02||3.01||4.40||0.03<br />
|-<br />
|5||4.68||16.95||0.10||12.38||17.54||0.14<br />
|-<br />
|6||20.36||95.58||0.55||67.65||92.74||0.88<br />
|-<br />
|7||101.04||765.91||3.36||408.15||630.65||5.17<br />
|}<br />
<br />
{|class="wikitable"<br />
|+ mfinder, FANMOD, Mavisto 和 Kavosh 在3个不同网络上生成含3到10个节点子图所用的运行时间<ref name="kash1" /><br />
|-<br />
!&nbsp;<br />
!子图大小→<br />
!rowspan="2"|3<br />
!rowspan="2"|4<br />
!rowspan="2"|5<br />
!rowspan="2"|6<br />
!rowspan="2"|7<br />
!rowspan="2"|8<br />
!rowspan="2"|9<br />
!rowspan="2"|10<br />
|-<br />
!网络↓<br />
!算法↓<br />
|-<br />
|rowspan="4"|E. coli<br />
|Kavosh||0.30||1.84||14.91||141.98||1374.0||13173.7||121110.3||1120560.1<br />
|-<br />
|FANMOD||0.81||2.53||15.71||132.24||1205.9||9256.6||-||-<br />
|-<br />
|Mavisto||13532||-||-||-||-||-||-||-<br />
|-<br />
|Mfinder||31.0||297||23671||-||-||-||-||-<br />
|-<br />
|rowspan="4"|Electronic<br />
|Kavosh||0.08||0.36||8.02||11.39||77.22||422.6||2823.7||18037.5<br />
|-<br />
|FANMOD||0.53||1.06||4.34||24.24||160||967.99||-||-<br />
|-<br />
|Mavisto||210.0||1727||-||-||-||-||-||-<br />
|-<br />
|Mfinder||7||14||109.8||2020.2||-||-||-||-<br />
|-<br />
|rowspan="4"|Social<br />
|Kavosh||0.04||0.23||1.63||10.48||69.43||415.66||2594.19||14611.23<br />
|-<br />
|FANMOD||0.46||0.84||3.07||17.63||117.43||845.93||-||-<br />
|-<br />
|Mavisto||393||1492||-||-||-||-||-||-<br />
|-<br />
|Mfinder||12||49||798||181077||-||-||-||-<br />
|}<br />
<br />
===算法的分类===<br />
正如表格所示,模体发现算法可以分为两大类:基于精确计数的算法,以及使用统计采样以及估计的算法。因为后者并不计数所有子图在主网络中出现的次数,所以第二类算法会更快,却也可能产生带有偏向性的,甚至不现实的结果。<br />
<br />
更深一层地,基于精确计数的算法可以分为'''以网络为中心'''的方法以及以'''子图为中心'''的方法。前者在给定网络中搜索给定大小的子图,而后者首先根据给定大小生成各种可能的非同构图,然后在网络中分别搜索这些生成的图。这两种方法都有各自的优缺点,这些在上文有讨论。<br />
<br />
另一方面,基于估计的方法可能会利用如前面描述过的颜色编码手段,其它的手段则通常会在枚举过程中忽略一些子图(比如,像在 FANMOD 中做的那样),然后只在枚举出来的子图上做估计。<br />
<br />
此外,表格还指出了一个算法能否应用于有向网络或无向网络,以及导出子图或非导出子图。更多信息请参考下方提供的网页和实验室地址及联系方式。<br />
{|class="wikitable"<br />
|+ 模体发现算法的分类<br />
|-<br />
!计数方式<br />
!基础<br />
!算法名称<br />
!有向 / 无向<br />
!导出/ 非导出<br />
|-<br />
| rowspan="9" |精确基数<br />
| rowspan="5" |以网络为中心<br />
|[http://www.weizmann.ac.il/mcb/UriAlon/ mfinder]||皆可||导出<br />
|-<br />
|[http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ ESU (FANMOD)]||皆可||导出<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/Kavosh/ Kavosh] (used in [http://apps.cytoscape.org/apps/cytokavosh CytoKavosh])||皆可||导出<br />
|-<br />
|[http://www.dcc.fc.up.pt/gtries/ G-Tries]||皆可||导出<br />
|-<br />
|[http://nesreenahmed.com/graphlets PGD]<br />
|无向<br />
|导出<br />
|-<br />
|rowspan="4"|以子图为中心<br />
|[http://mavisto.ipk-gatersleben.de/ FPF (Mavisto)]||皆可||导出<br />
|-<br />
|[https://www.msu.edu/~jinchen/ NeMoFinder]||无向||导出<br />
|-<br />
|[http://people.cs.uchicago.edu/~joshuag/index.html Grochow–Kellis]||皆可||Both<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/MODA/ MODA]||皆可||皆可<br />
|-<br />
|rowspan="3"|采样估计<br />
|颜色编码<br />
|[http://www.math.tau.ac.il/~nogaa/ N. Alon] ''et al.''’s Algorithm||无向||非导出<br />
|-<br />
|rowspan="2"|其他手段<br />
|[http://www.weizmann.ac.il/mcb/UriAlon/ mfinder]||皆可||导出<br />
|-<br />
|[http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ ESU (FANMOD)]||皆可||导出<br />
|}<br />
<br />
{|class="wikitable"<br />
|+ 算法提出者的地址和联系方式<br />
|-<br />
!算法<br />
!实验室/研究组<br />
!学院<br />
!大学/研究所<br />
!地址<br />
!电子邮件<br />
|-<br />
|[http://www.weizmann.ac.il/mcb/UriAlon/ mfinder]||Uri Alon's Group||Department of Molecular Cell Biology||Weizmann Institute of Science||Rehovot, Israel, Wolfson, Rm. 607||urialon at weizmann.ac.il<br />
|-<br />
|[http://mavisto.ipk-gatersleben.de/ FPF (Mavisto)]||----||----||Leibniz-Institut für Pflanzengenetik und Kulturpflanzenforschung (IPK)||Corrensstraße 3, D-06466 Stadt Seeland, OT Gatersleben, Deutschland||schreibe at ipk-gatersleben.de<br />
|-<br />
|[http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ ESU (FANMOD)]||Lehrstuhl Theoretische Informatik I||Institut für Informatik||Friedrich-Schiller-Universität Jena||Ernst-Abbe-Platz 2,D-07743 Jena, Deutschland||sebastian.wernicke at gmail.com<br />
|-<br />
|[https://www.msu.edu/~jinchen/ NeMoFinder]||----||School of Computing||National University of Singapore||Singapore 119077||chenjin at comp.nus.edu.sg<br />
|-<br />
|[http://www.cs.colorado.edu/~jgrochow/ Grochow–Kellis]||CS Theory Group & Complex Systems Group||Computer Science||University of Colorado, Boulder||1111 Engineering Dr. ECOT 717, 430 UCB Boulder, CO 80309-0430 USA||jgrochow at colorado.edu<br />
|-<br />
|[http://www.math.tau.ac.il/~nogaa/ N. Alon] ''et al.''’s Algorithm||Department of Pure Mathematics||School of Mathematical Sciences||Tel Aviv University||Tel Aviv 69978, Israel||nogaa at post.tau.ac.il<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/MODA/ MODA]||Laboratory of Systems Biology and Bioinformatics (LBB)||Institute of Biochemistry and Biophysics (IBB)||University of Tehran||Enghelab Square, Enghelab Ave, Tehran, Iran||amasoudin at ibb.ut.ac.ir<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/Kavosh/ Kavosh] (used in [http://apps.cytoscape.org/apps/cytokavosh CytoKavosh])||Laboratory of Systems Biology and Bioinformatics (LBB)||Institute of Biochemistry and Biophysics (IBB)||University of Tehran||Enghelab Square, Enghelab Ave, Tehran, Iran||amasoudin at ibb.ut.ac.ir<br />
|-<br />
|[http://www.dcc.fc.up.pt/gtries/ G-Tries]||Center for Research in Advanced Computing Systems||Computer Science||University of Porto||Rua Campo Alegre 1021/1055, Porto, Portugal||pribeiro at dcc.fc.up.pt<br />
|-<br />
|[http://nesreenahmed.com/graphlets PGD]<br />
|Network Learning and Discovery Lab<br />
|Department of Computer Science<br />
|Purdue University<br />
|Purdue University, 305 N University St, West Lafayette, IN 47907<br />
|nkahmed@purdue.edu<br />
|}<br />
<br />
==Well-established motifs and their functions==<br />
Much experimental work has been devoted to understanding network motifs in [[gene regulatory networks]]. These networks control which genes are expressed in the cell in response to biological signals. The network is defined such that genes are nodes, and directed edges represent the control of one gene by a transcription factor (regulatory protein that binds DNA) encoded by another gene. Thus, network motifs are patterns of genes regulating each other's transcription rate. When analyzing transcription networks, it is seen that the same network motifs appear again and again in diverse organisms from bacteria to human. The transcription network of ''[[Escherichia coli|E. coli]]'' and yeast, for example, is made of three main motif families, that make up almost the entire network. The leading hypothesis is that the network motif were independently selected by evolutionary processes in a converging manner,<ref name="bab1">{{cite journal |vauthors=Babu MM, Luscombe NM, Aravind L, Gerstein M, Teichmann SA |title=Structure and evolution of transcriptional regulatory networks |journal=Current Opinion in Structural Biology |volume=14 |issue=3 |pages=283–91 |date=June 2004 |pmid=15193307 |doi=10.1016/j.sbi.2004.05.004 |citeseerx=10.1.1.471.9692 }}</ref><ref name="con1">{{cite journal |vauthors=Conant GC, Wagner A |title=Convergent evolution of gene circuits |journal=Nat. Genet. |volume=34 |issue=3 |pages=264–6 |date=July 2003 |pmid=12819781 |doi=10.1038/ng1181}}</ref> since the creation or elimination of regulatory interactions is fast on evolutionary time scale, relative to the rate at which genes change,<ref name="bab1"/><ref name="con1"/><ref name="dek1">{{cite journal |vauthors=Dekel E, Alon U |title=Optimality and evolutionary tuning of the expression level of a protein |journal=Nature |volume=436 |issue=7050 |pages=588–92 |date=July 2005 |pmid=16049495 |doi=10.1038/nature03842 |bibcode=2005Natur.436..588D }}</ref> Furthermore, experiments on the dynamics generated by network motifs in living cells indicate that they have characteristic dynamical functions. This suggests that the network motif serve as building blocks in gene regulatory networks that are beneficial to the organism.<br />
<br />
The functions associated with common network motifs in transcription networks were explored and demonstrated by several research projects both theoretically and experimentally. Below are some of the most common network motifs and their associated function.<br />
<br />
===Negative auto-regulation (NAR)===<br />
[[Image:Autoregulation motif.png|thumb|Schematic representation of an auto-regulation motif]]<br />
One of simplest and most abundant network motifs in ''[[Escherichia coli|E. coli]]'' is negative auto-regulation in which a transcription factor (TF) represses its own transcription. This motif was shown to perform two important functions. The first function is response acceleration. NAR was shown to speed-up the response to signals both theoretically <ref name="zab1">{{cite journal |doi=10.1016/j.jtbi.2011.06.021 |author=Zabet NR |title=Negative feedback and physical limits of genes |journal=Journal of Theoretical Biology |volume= 284|issue=1 |pages=82–91 |date=September 2011 |pmid=21723295 |arxiv=1408.1869 |citeseerx=10.1.1.759.5418 }}</ref> and experimentally. This was first shown in a synthetic transcription network<ref name="ros1">{{cite journal |doi=10.1016/S0022-2836(02)00994-4 |vauthors=Rosenfeld N, Elowitz MB, Alon U |title=Negative autoregulation speeds the response times of transcription networks |journal=J. Mol. Biol. |volume=323 |issue=5 |pages=785–93 |date=November 2002 |pmid=12417193 |citeseerx=10.1.1.126.2604 }}</ref> and later on in the natural context in the SOS DNA repair system of E .coli.<ref name="cam1">{{cite journal |vauthors=Camas FM, Blázquez J, Poyatos JF |title=Autogenous and nonautogenous control of response in a genetic network |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=103 |issue=34 |pages=12718–23 |date=August 2006 |pmid=16908855 |pmc=1568915 |doi=10.1073/pnas.0602119103 |bibcode=2006PNAS..10312718C }}</ref> The second function is increased stability of the auto-regulated gene product concentration against stochastic noise, thus reducing variations in protein levels between different cells.<ref name="bec1">{{cite journal |vauthors=Becskei A, Serrano L |title=Engineering stability in gene networks by autoregulation |journal=Nature |volume=405 |issue=6786 |pages=590–3 |date=June 2000 |pmid=10850721 |doi=10.1038/35014651}}</ref><ref name="dub1">{{cite journal |vauthors=Dublanche Y, Michalodimitrakis K, Kümmerer N, Foglierini M, Serrano L |title=Noise in transcription negative feedback loops: simulation and experimental analysis |journal=Mol. Syst. Biol. |volume=2 |pages=41 |year=2006 |pmid=16883354 |pmc=1681513 |doi=10.1038/msb4100081 |issue=1}}</ref><ref name="shi1">{{cite journal |vauthors=Shimoga V, White J, Li Y, Sontag E, Bleris L |title= Synthetic mammalian transgene negative autoregulation |journal=Mol. Syst. Biol. |volume=9 |pages=670 |year=2013|doi=10.1038/msb.2013.27|pmid= 23736683 |pmc= 3964311 }}</ref><br />
<br />
<br />
<br />
===Positive auto-regulation (PAR)===<br />
Positive auto-regulation (PAR) occurs when a transcription factor enhances its own rate of production. Opposite to the NAR motif this motif slows the response time compared to simple regulation.<ref name="mae1">{{cite journal |vauthors=Maeda YT, Sano M |title=Regulatory dynamics of synthetic gene networks with positive feedback |journal=J. Mol. Biol. |volume=359 |issue=4 |pages=1107–24 |date=June 2006 |pmid=16701695 |doi=10.1016/j.jmb.2006.03.064 }}</ref> In the case of a strong PAR the motif may lead to a bimodal distribution of protein levels in cell populations.<ref name="bec2">{{cite journal |vauthors=Becskei A, Séraphin B, Serrano L |title=Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion |journal=EMBO J. |volume=20 |issue=10 |pages=2528–35 |date=May 2001 |pmid=11350942 |pmc=125456 |doi=10.1093/emboj/20.10.2528}}</ref><br />
<br />
===Feed-forward loops (FFL)===<br />
[[Image:Feed-forward motif.GIF|thumb|Schematic representation of a Feed-forward motif]]<br />
This motif is commonly found in many gene systems and organisms. The motif consists of three genes and three regulatory interactions. The target gene C is regulated by 2 TFs A and B and in addition TF B is also regulated by TF A . Since each of the regulatory interactions may either be positive or negative there are possibly eight types of FFL motifs.<ref name="man1">{{cite journal |vauthors=Mangan S, Alon U |title=Structure and function of the feed-forward loop network motif |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=100 |issue=21 |pages=11980–5 |date=October 2003 |pmid=14530388 |pmc=218699 |doi=10.1073/pnas.2133841100 |bibcode=2003PNAS..10011980M }}</ref> Two of those eight types: the coherent type 1 FFL (C1-FFL) (where all interactions are positive) and the incoherent type 1 FFL (I1-FFL) (A activates C and also activates B which represses C) are found much more frequently in the transcription network of ''[[Escherichia coli|E. coli]]'' and yeast than the other six types.<ref name="man1"/><ref name="ma1">{{cite journal |vauthors=Ma HW, Kumar B, Ditges U, Gunzer F, Buer J, Zeng AP |title=An extended transcriptional regulatory network of ''Escherichia coli'' and analysis of its hierarchical structure and network motifs |journal=Nucleic Acids Res. |volume=32 |issue=22 |pages=6643–9 |year=2004 |pmid=15604458 |pmc=545451 |doi=10.1093/nar/gkh1009 |url=http://nar.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=15604458}}</ref> In addition to the structure of the circuitry the way in which the signals from A and B are integrated by the C promoter should also be considered. In most of the cases the FFL is either an AND gate (A and B are required for C activation) or OR gate (either A or B are sufficient for C activation) but other input function are also possible.<br />
<br />
===Coherent type 1 FFL (C1-FFL)===<br />
The C1-FFL with an AND gate was shown to have a function of a ‘sign-sensitive delay’ element and a persistence detector both theoretically <ref name="man1"/> and experimentally<ref name="man2">{{cite journal |doi=10.1016/j.jmb.2003.09.049 |vauthors=Mangan S, Zaslaver A, Alon U |title=The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks |journal=J. Mol. Biol. |volume=334 |issue=2 |pages=197–204 |date=November 2003 |pmid=14607112 |citeseerx=10.1.1.110.4629 }}</ref> with the arabinose system of ''[[Escherichia coli|E. coli]]''. This means that this motif can provide pulse filtration in which short pulses of signal will not generate a response but persistent signals will generate a response after short delay. The shut off of the output when a persistent pulse is ended will be fast. The opposite behavior emerges in the case of a sum gate with fast response and delayed shut off as was demonstrated in the flagella system of ''[[Escherichia coli|E. coli]]''.<ref name="kal1">{{cite journal |vauthors=Kalir S, Mangan S, Alon U |title=A coherent feed-forward loop with a SUM input function prolongs flagella expression in ''Escherichia coli'' |journal=Mol. Syst. Biol. |volume=1 |pages=E1–E6 |year=2005 |pmid=16729041 |pmc=1681456 |doi=10.1038/msb4100010 |issue=1}}</ref> De novo evolution of C1-FFLs in [[gene regulatory network]]s has been demonstrated computationally in response to selection to filter out an idealized short signal pulse, but for non-idealized noise, a dynamics-based system of feed-forward regulation with different topology was instead favored.<ref>{{cite journal |last1=Xiong |first1=Kun |last2=Lancaster |first2=Alex K. |last3=Siegal |first3=Mark L. |last4=Masel |first4=Joanna |title=Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise |journal=Nature Communications |date=3 June 2019 |volume=10 |issue=1 |pages=2418 |doi=10.1038/s41467-019-10388-6|pmid=31160574 |pmc=6546794 }}</ref><br />
<br />
===Incoherent type 1 FFL (I1-FFL)===<br />
The I1-FFL is a pulse generator and response accelerator. The two signal pathways of the I1-FFL act in opposite directions where one pathway activates Z and the other represses it. When the repression is complete this leads to a pulse-like dynamics. It was also demonstrated experimentally that the I1-FFL can serve as response accelerator in a way which is similar to the NAR motif. The difference is that the I1-FFL can speed-up the response of any gene and not necessarily a transcription factor gene.<ref name="man3">{{cite journal |vauthors=Mangan S, Itzkovitz S, Zaslaver A, Alon U |title=The incoherent feed-forward loop accelerates the response-time of the gal system of ''Escherichia coli'' |journal=J. Mol. Biol. |volume=356 |issue=5 |pages=1073–81 |date=March 2006 |pmid=16406067 |doi=10.1016/j.jmb.2005.12.003 |citeseerx=10.1.1.184.8360 }}</ref> An additional function was assigned to the I1-FFL network motif: it was shown both theoretically and experimentally that the I1-FFL can generate non-monotonic input function in both a synthetic <ref name="ent1">{{cite journal |vauthors=Entus R, Aufderheide B, Sauro HM |title=Design and implementation of three incoherent feed-forward motif based biological concentration sensors |journal=Syst Synth Biol |volume=1 |issue=3 |pages=119–28 |date=August 2007 |pmid=19003446 |pmc=2398716 |doi=10.1007/s11693-007-9008-6 }}</ref> and native systems.<ref name="kap1">{{cite journal |vauthors=Kaplan S, Bren A, Dekel E, Alon U |title=The incoherent feed-forward loop can generate non-monotonic input functions for genes |journal=Mol. Syst. Biol. |volume=4 |pages=203 |year=2008 |pmid=18628744 |pmc=2516365 |doi=10.1038/msb.2008.43 |issue=1}}</ref> Finally, expression units that incorporate incoherent feedforward control of the gene product provide adaptation to the amount of DNA template and can be superior to simple combinations of constitutive promoters.<ref name="ble1">{{cite journal |vauthors=Bleris L, Xie Z, Glass D, Adadey A, Sontag E, Benenson Y |title=Synthetic incoherent feedforward circuits show adaptation to the amount of their genetic template |journal=Mol. Syst. Biol. |volume=7 |pages=519|year=2011 |doi=10.1038/msb.2011.49 |issue=1 |pmid=21811230 |pmc=3202791}}</ref> Feedforward regulation displayed better adaptation than negative feedback, and circuits based on RNA interference were the most robust to variation in DNA template amounts.<ref name="ble1"/><br />
<br />
===Multi-output FFLs===<br />
In some cases the same regulators X and Y regulate several Z genes of the same system. By adjusting the strength of the interactions this motif was shown to determine the temporal order of gene activation. This was demonstrated experimentally in the flagella system of ''[[Escherichia coli|E. coli]]''.<ref name="kal2">{{cite journal |vauthors=Kalir S, McClure J, Pabbaraju K, etal |title=Ordering genes in a flagella pathway by analysis of expression kinetics from living bacteria |journal=Science |volume=292 |issue=5524 |pages=2080–3 |date=June 2001 |pmid=11408658 |doi=10.1126/science.1058758 }}</ref><br />
<br />
===Single-input modules (SIM)===<br />
This motif occurs when a single regulator regulates a set of genes with no additional regulation. This is useful when the genes are cooperatively carrying out a specific function and therefore always need to be activated in a synchronized manner. By adjusting the strength of the interactions it can create temporal expression program of the genes it regulates.<ref name="zas1">{{cite journal |vauthors=Zaslaver A, Mayo AE, Rosenberg R, etal |title=Just-in-time transcription program in metabolic pathways |journal=Nat. Genet. |volume=36 |issue=5 |pages=486–91 |date=May 2004 |pmid=15107854 |doi=10.1038/ng1348|doi-access=free }}</ref><br />
<br />
In the literature, Multiple-input modules (MIM) arose as a generalization of SIM. However, the precise definitions of SIM and MIM have been a source of inconsistency. There are attempts to provide orthogonal definitions for canonical motifs in biological networks and algorithms to enumerate them, especially SIM, MIM and Bi-Fan (2x2 MIM).<ref>{{cite journal |vauthors=Konagurthu AS, Lesk AM |title=Single and Multiple Input Modules in regulatory networks |journal=Proteins |volume=73 |issue=2 |pages=320–324 |year=2008 |doi=10.1002/prot.22053|pmid=18433061 }}</ref><br />
<br />
===Dense overlapping regulons (DOR)===<br />
This motif occurs in the case that several regulators combinatorially control a set of genes with diverse regulatory combinations. This motif was found in ''[[Escherichia coli|E. coli]]'' in various systems such as carbon utilization, anaerobic growth, stress response and others.<ref name="she1"/><ref name="boy1"/> In order to better understand the function of this motif one has to obtain more information about the way the multiple inputs are integrated by the genes. Kaplan ''et al.''<ref name="kap2">{{cite journal |vauthors=Kaplan S, Bren A, Zaslaver A, Dekel E, Alon U |title=Diverse two-dimensional input functions control bacterial sugar genes |journal=Mol. Cell |volume=29 |issue=6 |pages=786–92 |date=March 2008 |pmid=18374652 |pmc=2366073 |doi=10.1016/j.molcel.2008.01.021 }}</ref> has mapped the input functions of the sugar utilization genes in ''[[Escherichia coli|E. coli]]'', showing diverse shapes.<br />
<br />
==已知的模体及其功能==<br />
许多实验工作致力于理解[[基因调控网络]]中的网络模体。在响应生物信号的过程中,这些网络控制细胞中需要表达的基因。这样的网络以基因作为节点,有向边代表对某个基因的调控,基因调控通过其他基因编码的转录因子[[结合在DNA上的调控蛋白]]来实现。因此,网络模体是基因之间相互调控转录速率的模式。在分析转录调控网络的时候,人们发现某些相同的网络模体在不同的物种中不断地出现,从细菌到人类。例如,''[[大肠杆菌]]''和酵母的转录网络由三种主要的网络模体家族组成,它们可以构建几乎整个网络。主要的假设是在进化的过程中,网络模体是被以收敛的方式独立选择出来的。<ref name="bab1">{{cite journal |vauthors=Babu MM, Luscombe NM, Aravind L, Gerstein M, Teichmann SA |title=Structure and evolution of transcriptional regulatory networks |journal=Current Opinion in Structural Biology |volume=14 |issue=3 |pages=283–91 |date=June 2004 |pmid=15193307 |doi=10.1016/j.sbi.2004.05.004 |citeseerx=10.1.1.471.9692 }}</ref><ref name="con1">{{cite journal |vauthors=Conant GC, Wagner A |title=Convergent evolution of gene circuits |journal=Nat. Genet. |volume=34 |issue=3 |pages=264–6 |date=July 2003 |pmid=12819781 |doi=10.1038/ng1181}}</ref> 因为相对于基因改变的速率,转录相互作用产生和消失的时间尺度在进化上是很快的。<ref name="bab1"/><ref name="con1"/><ref name="dek1">{{cite journal |vauthors=Dekel E, Alon U |title=Optimality and evolutionary tuning of the expression level of a protein |journal=Nature |volume=436 |issue=7050 |pages=588–92 |date=July 2005 |pmid=16049495 |doi=10.1038/nature03842 |bibcode=2005Natur.436..588D }}</ref> 此外,对活细胞中网络模体所产生的动力学行为的实验表明,它们具有典型的动力学功能。这表明,网络模体是基因调控网络中对生物体有益的基本单元。<br />
<br />
一些研究从理论和实验两方面探讨和论证了转录网络中与共同网络模体相关的功能。下面是一些最常见的网络模体及其相关功能。<br />
<br />
===负自反馈调控(NAR)===<br />
[[Image:Autoregulation motif.png|thumb|Schematic representation of an auto-regulation motif]]<br />
负自反馈调控是[[大肠杆菌]]中最简单和最冗余的网络模体之一,其中一个转录因子抑制它自身的转录。这种网络模体有两个重要的功能,其中第一个是加速响应。人们发现在实验和理论上, <ref name="zab1">{{cite journal |doi=10.1016/j.jtbi.2011.06.021 |author=Zabet NR |title=Negative feedback and physical limits of genes |journal=Journal of Theoretical Biology |volume= 284|issue=1 |pages=82–91 |date=September 2011 |pmid=21723295 |arxiv=1408.1869 |citeseerx=10.1.1.759.5418 }}</ref>NAR都可以加快对信号的响应。这个功能首先在一个人工合成的转录网络中被发现,<ref name="ros1">{{cite journal |doi=10.1016/S0022-2836(02)00994-4 |vauthors=Rosenfeld N, Elowitz MB, Alon U |title=Negative autoregulation speeds the response times of transcription networks |journal=J. Mol. Biol. |volume=323 |issue=5 |pages=785–93 |date=November 2002 |pmid=12417193 |citeseerx=10.1.1.126.2604 }}</ref> 然后在大肠杆菌SOS DAN修复系统这个自然体系中也被发现。<ref name="cam1">{{cite journal |vauthors=Camas FM, Blázquez J, Poyatos JF |title=Autogenous and nonautogenous control of response in a genetic network |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=103 |issue=34 |pages=12718–23 |date=August 2006 |pmid=16908855 |pmc=1568915 |doi=10.1073/pnas.0602119103 |bibcode=2006PNAS..10312718C }}</ref> 负自反馈网络的第二个功能是增强自调控基因的产物浓度的稳定性,从而抵抗随机的噪声,减少该蛋白含量在不同细胞中的差异。<ref name="bec1">{{cite journal |vauthors=Becskei A, Serrano L |title=Engineering stability in gene networks by autoregulation |journal=Nature |volume=405 |issue=6786 |pages=590–3 |date=June 2000 |pmid=10850721 |doi=10.1038/35014651}}</ref><ref name="dub1">{{cite journal |vauthors=Dublanche Y, Michalodimitrakis K, Kümmerer N, Foglierini M, Serrano L |title=Noise in transcription negative feedback loops: simulation and experimental analysis |journal=Mol. Syst. Biol. |volume=2 |pages=41 |year=2006 |pmid=16883354 |pmc=1681513 |doi=10.1038/msb4100081 |issue=1}}</ref><ref name="shi1">{{cite journal |vauthors=Shimoga V, White J, Li Y, Sontag E, Bleris L |title= Synthetic mammalian transgene negative autoregulation |journal=Mol. Syst. Biol. |volume=9 |pages=670 |year=2013|doi=10.1038/msb.2013.27|pmid= 23736683 |pmc= 3964311 }}</ref><br />
<br />
===正自反馈调控(PAR)===<br />
正自反馈调控是指转录因子增强它自身转录速率的调控。和负自反馈调节相反,NAR模体相比于简单的调控能够延长反应时间。<ref name="mae1">{{cite journal |vauthors=Maeda YT, Sano M |title=Regulatory dynamics of synthetic gene networks with positive feedback |journal=J. Mol. Biol. |volume=359 |issue=4 |pages=1107–24 |date=June 2006 |pmid=16701695 |doi=10.1016/j.jmb.2006.03.064 }}</ref> 在强PAR的情况下,模体可能导致蛋白质水平在细胞群中呈现双峰分布。<ref name="bec2">{{cite journal |vauthors=Becskei A, Séraphin B, Serrano L |title=Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion |journal=EMBO J. |volume=20 |issue=10 |pages=2528–35 |date=May 2001 |pmid=11350942 |pmc=125456 |doi=10.1093/emboj/20.10.2528}}</ref><br />
<br />
===前馈回路 (FFL)===<br />
[[Image:Feed-forward motif.GIF|thumb|Schematic representation of a Feed-forward motif]]<br />
前馈回路普遍存在于许多基因系统和生物体中。这种模体包括三个基因以及三个相互作用。目标基因C被两个转录因子(TFs)A和B调控,并且TF B同时被TF A调控。由于每个调控相互作用可以是正的或者负的,所以总共可能有八种类型的FFL模体。<ref name="man1">{{cite journal |vauthors=Mangan S, Alon U |title=Structure and function of the feed-forward loop network motif |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=100 |issue=21 |pages=11980–5 |date=October 2003 |pmid=14530388 |pmc=218699 |doi=10.1073/pnas.2133841100 |bibcode=2003PNAS..10011980M }}</ref> 其中的两种:一致前馈回路的类型一(C1-FFL)(所有相互作用都是正的)和非一致前馈回路的类型一(I1-FFL)(A激活C和B,B抑制C)在[[大肠杆菌]]和酵母中相比于其他六种更频繁的出现。<ref name="man1"/><ref name="ma1">{{cite journal |vauthors=Ma HW, Kumar B, Ditges U, Gunzer F, Buer J, Zeng AP |title=An extended transcriptional regulatory network of ''Escherichia coli'' and analysis of its hierarchical structure and network motifs |journal=Nucleic Acids Res. |volume=32 |issue=22 |pages=6643–9 |year=2004 |pmid=15604458 |pmc=545451 |doi=10.1093/nar/gkh1009 |url=http://nar.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=15604458}}</ref> 除了网络的结构外,还应该考虑来自A和B的信号被C的启动子集成的方式。在大多数情况下,FFL要么是一个与门(激活C需要A和B),要么是或门(激活C需要A或B),但也可以是其他输入函数。<br />
<br />
===一致前馈回路类型一(C1-FFL)===<br />
具有与门的C1-FFL有“符号-敏感延迟”单元和持久性探测器的功能,这一点在[[大肠杆菌]]阿拉伯糖系系统的理论<ref name="man1"/>和实验上<ref name="man2">{{cite journal |doi=10.1016/j.jmb.2003.09.049 |vauthors=Mangan S, Zaslaver A, Alon U |title=The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks |journal=J. Mol. Biol. |volume=334 |issue=2 |pages=197–204 |date=November 2003 |pmid=14607112 |citeseerx=10.1.1.110.4629 }}</ref> 都有发现。这意味着该模体可以提供脉冲过滤,短脉冲信号不会产生响应,而持久信号在短延迟后会产生响应。当持久脉冲结束时,输出的关闭将很快。与此相反的行为出现在具有快速响应和延迟关闭特性的加和门的情况下,这在[[大肠杆菌]]的鞭毛系统中得到了证明。<ref name="kal1">{{cite journal |vauthors=Kalir S, Mangan S, Alon U |title=A coherent feed-forward loop with a SUM input function prolongs flagella expression in ''Escherichia coli'' |journal=Mol. Syst. Biol. |volume=1 |pages=E1–E6 |year=2005 |pmid=16729041 |pmc=1681456 |doi=10.1038/msb4100010 |issue=1}}</ref>在[[基因调控网络]]的重头进化中,对于滤除理想化的短信号脉冲作为进化压,C1-FFLs已经在计算上被证明可以进化出来。但是对于非理想化的噪声,不同拓扑结构前馈调节的动态系统将被优先考虑。 <ref>{{cite journal |last1=Xiong |first1=Kun |last2=Lancaster |first2=Alex K. |last3=Siegal |first3=Mark L. |last4=Masel |first4=Joanna |title=Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise |journal=Nature Communications |date=3 June 2019 |volume=10 |issue=1 |pages=2418 |doi=10.1038/s41467-019-10388-6|pmid=31160574 |pmc=6546794 }}</ref><br />
<br />
===非一致前馈回路类型一(I1-FFL)===<br />
I1-FFL是一个脉冲生成器和响应加速器。I1-FFL的两种信号通路作用方向相反,一种通路激活Z,而另一种抑制Z。完全的抑制会导致类似脉冲的动力学行为。另外有实验证明,它可以类似于NAR模体起到响应加速器的作用。与NAR模体的不同之处在于,它可以加速任何基因的响应,而不必是转录因子。<ref name="man3">{{cite journal |vauthors=Mangan S, Itzkovitz S, Zaslaver A, Alon U |title=The incoherent feed-forward loop accelerates the response-time of the gal system of ''Escherichia coli'' |journal=J. Mol. Biol. |volume=356 |issue=5 |pages=1073–81 |date=March 2006 |pmid=16406067 |doi=10.1016/j.jmb.2005.12.003 |citeseerx=10.1.1.184.8360 }}</ref>I1-FFL网络还有另外一个功能:在理论和实验上都有证明I1-FFL可以生成非单调的输入函数,无论在人工合成的<ref name="ent1">{{cite journal |vauthors=Entus R, Aufderheide B, Sauro HM |title=Design and implementation of three incoherent feed-forward motif based biological concentration sensors |journal=Syst Synth Biol |volume=1 |issue=3 |pages=119–28 |date=August 2007 |pmid=19003446 |pmc=2398716 |doi=10.1007/s11693-007-9008-6 }}</ref>还是自然的系统中。 <ref name="kap1">{{cite journal |vauthors=Kaplan S, Bren A, Dekel E, Alon U |title=The incoherent feed-forward loop can generate non-monotonic input functions for genes |journal=Mol. Syst. Biol. |volume=4 |pages=203 |year=2008 |pmid=18628744 |pmc=2516365 |doi=10.1038/msb.2008.43 |issue=1}}</ref> 最后,包含非一致前馈调控的基因生成物的表达单元对DNA模板的数量具有适应性,可以优于简单的组合本构启动子。<ref name="ble1">{{cite journal |vauthors=Bleris L, Xie Z, Glass D, Adadey A, Sontag E, Benenson Y |title=Synthetic incoherent feedforward circuits show adaptation to the amount of their genetic template |journal=Mol. Syst. Biol. |volume=7 |pages=519|year=2011 |doi=10.1038/msb.2011.49 |issue=1 |pmid=21811230 |pmc=3202791}}</ref> 前馈调控比负反馈具有更好的适应性,并且基于RNA干扰的网络对DNA模板数具有最高的鲁棒性。<ref name="ble1"/><br />
<br />
===多输出前馈回路===<br />
在某些情况,相同的调控子X和Y可以调控同一系统中的多个Z基因。通过调节相互作用的强度,这些网络可以决定基因激活的时间顺序。这一点在[[大肠杆菌]]的鞭毛系统中有实验证据。<ref name="kal2">{{cite journal |vauthors=Kalir S, McClure J, Pabbaraju K, etal |title=Ordering genes in a flagella pathway by analysis of expression kinetics from living bacteria |journal=Science |volume=292 |issue=5524 |pages=2080–3 |date=June 2001 |pmid=11408658 |doi=10.1126/science.1058758 }}</ref><br />
<br />
===单一输入模块(SIM)===<br />
当单个调控子调控一组基因,并且没有其他的调控因素时,这样的模体叫做单一输入模块(SIM)。当很多基因合作执行某个功能时这是有用的,因为这些基因需要同步地被激活。通过调节相互作用的强度,可以编排它所调控的基因表达的时间顺序。<ref name="zas1">{{cite journal |vauthors=Zaslaver A, Mayo AE, Rosenberg R, etal |title=Just-in-time transcription program in metabolic pathways |journal=Nat. Genet. |volume=36 |issue=5 |pages=486–91 |date=May 2004 |pmid=15107854 |doi=10.1038/ng1348|doi-access=free }}</ref><br />
<br />
在文献中,多输入模块(MIM)来自于SIM的扩展。但是二者的精确定义并不太一致。有一些尝试给出生物网络中规范模体的正交定义,也有一些算法去枚举它们,特别是SIM,MIM和2x2 MIM等。<ref>{{cite journal |vauthors=Konagurthu AS, Lesk AM |title=Single and Multiple Input Modules in regulatory networks |journal=Proteins |volume=73 |issue=2 |pages=320–324 |year=2008 |doi=10.1002/prot.22053|pmid=18433061 }}</ref><br />
<br />
===密集交盖调节网(DOR)===<br />
这种类型的网络存在于多个调节子结合起来控制一组基因的情形,并且有多种调控的组合。这种模体出现在[[大肠杆菌]]的多种系统中,例如碳利用、厌氧生长、应激反应等。<ref name="she1"/><ref name="boy1"/> 为了更好地理解这种网络,我们必须得到关于基因集成多种输入的方式的信息。Kaplan ''et al.''<ref name="kap2">{{cite journal |vauthors=Kaplan S, Bren A, Zaslaver A, Dekel E, Alon U |title=Diverse two-dimensional input functions control bacterial sugar genes |journal=Mol. Cell |volume=29 |issue=6 |pages=786–92 |date=March 2008 |pmid=18374652 |pmc=2366073 |doi=10.1016/j.molcel.2008.01.021 }}</ref>绘制了[[大肠杆菌]]糖利用基因的输入函数,表现出各种各样的形状。<br />
<br />
==活动模体==<br />
<br />
有一个对网络模体的有趣概括:'''活动模体'''是在对节点和边都被量化标注的网络中可发现的【反复】斑图。例如,当新城代谢的边以相应基因的表达量或【时间】来标注时,一些斑图在'''给定的'''底层网络结构里【是反复的】。<ref name="agc">{{cite journal |vauthors=Chechik G, Oh E, Rando O, Weissman J, Regev A, Koller D |title=Activity motifs reveal principles of timing in transcriptional control of the yeast metabolic network |journal=Nat. Biotechnol. |volume=26 |issue=11 |pages=1251–9 |date=November 2008 |pmid=18953355 |pmc=2651818 |doi=10.1038/nbt.1499}}</ref><br />
<br />
==批判==<br />
<br />
对拓扑子结构有一个(某种程度上隐含的)前提性假设是其具有特定的功能重要性。但该假设最近遭到质疑,有人提出在不同的网络环境下模体可能表现出多样性,例如双扇模体,故<ref name="ad">{{cite journal |vauthors=Ingram PJ, Stumpf MP, Stark J |title=Network motifs: structure does not determine function |journal=BMC Genomics |volume=7 |pages=108 |year=2006 |pmid=16677373 |pmc=1488845 |doi=10.1186/1471-2164-7-108 }} </ref>模体的结构不必然决定功能,网络结构也不当然能揭示其功能;这种见解由来已久,可参见【Sin 操纵子】</font>。<ref>{{cite journal |vauthors=Voigt CA, Wolf DM, Arkin AP |title=The ''Bacillus subtilis'' sin operon: an evolvable network motif |journal=Genetics |volume=169 |issue=3 |pages=1187–202 |date=March 2005 |pmid=15466432 |pmc=1449569 |doi=10.1534/genetics.104.031955 |url=http://www.genetics.org/cgi/pmidlookup?view=long&pmid=15466432}}</ref><br />
<br />
<br />
大多数模体功能分析是基于模体孤立运行的情形。最近的研究<ref>{{cite journal |vauthors=Knabe JF, Nehaniv CL, Schilstra MJ |title=Do motifs reflect evolved function?—No convergent evolution of genetic regulatory network subgraph topologies |journal=BioSystems |volume=94 |issue=1–2 |pages=68–74 |year=2008 |pmid=18611431 |doi=10.1016/j.biosystems.2008.05.012 }}</ref>表明网络环境至关重要,不能忽视网络环境而仅从本地结构来对其功能进行推论——引用的论文还回顾了对观测数据的批判及其他可能的解释。人们研究了单个模体模组对网络全局的动力学影响及其分析<ref>{{cite journal |vauthors=Taylor D, Restrepo JG |title=Network connectivity during mergers and growth: Optimizing the addition of a module |journal=Physical Review E |volume=83 |issue=6 |year=2011 |page=66112 |doi=10.1103/PhysRevE.83.066112 |pmid=21797446 |bibcode=2011PhRvE..83f6112T |arxiv=1102.4876 }}</ref>。而另一项近期的研究工作提出生物网络的某些拓扑特征能自然地引起经典模体的常见形态,让人不禁疑问:这样的发生频率是否能证明模体的结构是出于其对所在网络运行的功能性贡献而被选择保留下的结果?<ref>{{cite journal|last1=Konagurthu|first1=Arun S.|last2=Lesk|first2=Arthur M.|title=Single and multiple input modules in regulatory networks|journal=Proteins: Structure, Function, and Bioinformatics|date=23 April 2008|volume=73|issue=2|pages=320–324|doi=10.1002/prot.22053|pmid=18433061}}</ref><ref>{{cite journal |vauthors=Konagurthu AS, Lesk AM |title=On the origin of distribution patterns of motifs in biological networks |journal=BMC Syst Biol |volume=2 |pages=73 |year=2008 |pmid=18700017 |pmc=2538512 |doi=10.1186/1752-0509-2-73 }} </ref><br />
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<br />
模体的研究主要应用于静态复杂网络,而时变复杂网络的研究<ref>Braha, D., & Bar‐Yam, Y. (2006). [https://static1.squarespace.com/static/5b68a4e4a2772c2a206180a1/t/5c5de3faf4e1fc43e7b3d21e/1549657083988/Complexity_Braha_Original_w_Cover.pdf From centrality to temporary fame: Dynamic centrality in complex networks]. Complexity, 12(2), 59-63. </ref>就网络模体提出了重大的新解释,并介绍了'''时变网络模体'''的概念。Braha和Bar-Yam<ref> Braha D., Bar-Yam Y. (2009) [https://s3.amazonaws.com/academia.edu.documents/4892116/Adaptive_Networks__Theory__Models_and_Applications__Understanding_Complex_Systems_.pdf?response-content-disposition=inline%3B%20filename%3DRedes_teoria.pdf&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAIWOWYYGZ2Y53UL3A%2F20191111%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20191111T173250Z&X-Amz-Expires=3600&X-Amz-SignedHeaders=host&X-Amz-Signature=89d08c9e92b88ed817e4eb0f87c480757ef79c4b865919a5e0890cbefa164c61#page=55 Time-Dependent Complex Networks: Dynamic Centrality, Dynamic Motifs, and Cycles of Social Interactions]. In: Gross T., Sayama H. (eds) Adaptive Networks. Understanding Complex Systems. Springer, Berlin, Heidelberg </ref>研究了本地模体结构在时间依赖网络/时变网络的动力学,发现的一些反复模式有望成为社会互动周期的经验论据。他们证明了对于时变网络,其本地结构是时间依赖的且可能随时间演变,可作为对复杂网络中稳定模体观及模体表达观的反论,Braha和Bar-Yam还进一步提出,对时变本地结构的分析有可能揭示系统级任务和功能方面的动力学的重要信息。<br />
<br />
==See also==<br />
* [[Clique (graph theory)]]<br />
* [[Graphical model]]<br />
<br />
==References==<br />
{{reflist|2}}<br />
<br />
==External links==<br />
<br />
* [http://www.weizmann.ac.il/mcb/UriAlon/groupNetworkMotifSW.html A software tool that can detect network motifs]<br />
* [http://www.bio-physics.at/wiki/index.php?title=Network_Motifs bio-physics-wiki NETWORK MOTIFS]<br />
* [http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ FANMOD: a tool for fast network motif detection]<br />
* [http://mavisto.ipk-gatersleben.de/ MAVisto: network motif analysis and visualisation tool]<br />
* [https://www.msu.edu/~jinchen/ NeMoFinder]<br />
* [http://people.cs.uchicago.edu/~joshuag/index.html Grochow–Kellis]<br />
* [http://lbb.ut.ac.ir/Download/LBBsoft/MODA/ MODA]<br />
* [http://lbb.ut.ac.ir/Download/LBBsoft/Kavosh/ Kavosh]<br />
* [http://apps.cytoscape.org/apps/cytokavosh CytoKavosh]<br />
* [http://www.dcc.fc.up.pt/gtries/ G-Tries]<br />
* [http://www.ft.unicamp.br/docentes/meira/accmotifs/ acc-MOTIF detection tool]<br />
<br />
[[Category:Gene expression]]<br />
[[Category:Networks]]</div>Imphttps://wiki.swarma.org/index.php?title=%E7%BD%91%E7%BB%9C%E6%A8%A1%E4%BD%93_Network_motifs&diff=7109网络模体 Network motifs2020-05-07T05:20:56Z<p>Imp:</p>
<hr />
<div>大家好,我们的公众号计划要推送一篇关于网络模体的综述文章,我们希望可以配套建议该重要概念:网络模体。现在希望可以大家一起协作完成这个词条。<br />
翻译任务主要分为以下5个内容:<br />
* 网络定义和历史 ---许菁 <br />
* 网络模体的发现算法 mfinder和FPF算法---李鹏<br />
* 网络模体的发现算法 ESU和对应的软件FANMOD---Imp<br />
* 网络模体的发现算法 G-Trie、算法对比和算法分类——Ricky(中英对照[[用户讨论:Qige96|初稿在这里]])<br />
* 已有网络模体及其函数表示 --周佳欣<br />
* 活动模体+批判 --- 孙宇<br />
* 代码实现<br />
<br />
大家可以在对应感兴趣的部分下面,写上姓名。我们的协作方式是石墨文档上翻译,最后再编辑成文。<br />
对应的词条链接:https://en.wikipedia.org/wiki/Network_motif#Well-established_motifs_and_their_functions<br />
<br />
截止时间:今晚12:00<br />
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<br />
All networks, including [[biological network]]s, social networks, technological networks (e.g., computer networks and electrical circuits) and more, can be represented as [[complex network|graphs]], which include a wide variety of subgraphs. One important local property of networks are so-called '''network motifs''', which are defined as recurrent and [[statistically significant]] sub-graphs or patterns.<br />
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所有网络,包括生物网络(biological networks)、社会网络(social networks)、技术网络(例如计算机网络和电路)等,都可以用图的形式来表示,这些图中会包括各种各样的子图(subgraphs)。网络的一个重要的局部性质是所谓的网络基序,即重复且具有统计意义的子图或模式(patterns)。<br />
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Network motifs are sub-graphs that repeat themselves in a specific network or even among various networks. Each of these sub-graphs, defined by a particular pattern of interactions between vertices, may reflect a framework in which particular functions are achieved efficiently. Indeed, motifs are of notable importance largely because they may reflect functional properties. They have recently gathered much attention as a useful concept to uncover structural design principles of complex networks.<ref name="mas1">{{cite journal |vauthors=Masoudi-Nejad A, Schreiber F, Razaghi MK Z |title=Building Blocks of Biological Networks: A Review on Major Network Motif Discovery Algorithms |journal=IET Systems Biology |volume=6 |issue=5 |pages=164–74 |year=2012|doi=10.1049/iet-syb.2011.0011 |pmid=23101871 }}</ref> Although network motifs may provide a deep insight into the network's functional abilities, their detection is computationally challenging.<br />
网络模体(Network motifs)是指在特定网络或各种网络中重复出现的相同的子图。这些子图由顶点之间特定的交互模式定义,一个子图便可以反映一个框架,这个框架可以有效地实现某个特定的功能。事实上,之所以说模体是一个重要的特性,正是因为它们可能反映出对应网络功能的这一性质。近年来这一概念作为揭示复杂网络结构设计原理的一个有用概念而受到了广泛的关注。<ref name="mas1">{{cite journal |vauthors=Masoudi-Nejad A, Schreiber F, Razaghi MK Z |title=Building Blocks of Biological Networks: A Review on Major Network Motif Discovery Algorithms |journal=IET Systems Biology |volume=6 |issue=5 |pages=164–74 |year=2012|doi=10.1049/iet-syb.2011.0011 |pmid=23101871 }}</ref> 但是,虽然通过研究网络模体可以深入了解网络的功能,但是对于模体的检测在计算上是具有挑战性的。<br />
<br />
==Definition==<br />
Let {{math|G {{=}} (V, E)}} and {{math|G&prime; {{=}} (V&prime;, E&prime;)}} be two graphs. Graph {{math|G&prime;}} is a ''sub-graph'' of graph {{math|G}} (written as {{math|G&prime; ⊆ G}}) if {{math|V&prime; ⊆ V}} and {{math|E&prime; ⊆ E ∩ (V&prime; &times; V&prime;)}}. If {{math|G&prime; ⊆ G}} and {{math|G&prime;}} contains all of the edges {{math|&lang;u, v&rang; ∈ E}} with {{math|u, v ∈ V&prime;}}, then {{math|G&prime;}} is an ''induced sub-graph'' of {{math|G}}. We call {{math|G&prime;}} and {{math|G}} isomorphic (written as {{math|G&prime; ↔ G}}), if there exists a bijection (one-to-one) {{math|f:V&prime; → V}} with {{math|&lang;u, v&rang; ∈ E&prime; ⇔ &lang;f(u), f(v)&rang; ∈ E}} for all {{math|u, v ∈ V&prime;}}. The mapping {{math|f}} is called an isomorphism between {{math|G}} and {{math|G&prime;}}.<ref name="die1">{{cite journal |author=Diestel R |title=Graph Theory (Graduate Texts in Mathematics) |volume=173 |year=2005|publisher=New York: Springer-Verlag Heidelberg}}</ref><br />
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设{{math|G {{=}} (V, E)}} 和 {{math|G&prime; {{=}} (V&prime;, E&prime;)}} 是两个图。若{{math|V&prime; ⊆ V}}且满足{{math|E&prime; ⊆ E ∩ (V&prime; &times; V&prime;)}})(即图{{math|G&prime; ⊆ G}的所有边和点都属于图{{math|G}})则称图{{math|G&prime; ⊆ G}是图{{math|G}}的一个子图<ref name="die1">{{cite journal |author=Diestel R |title=Graph Theory (Graduate Texts in Mathematics) |volume=173 |year=2005|publisher=New York: Springer-Verlag Heidelberg}}</ref><br />
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若{{math|G&prime; ⊆ G}},且对于顶点{{math|u}}、{{math|v}}及其连边,只要{{math|u}}和{{math|v}}存在于{{math|G&prime;}}(即若{{math|U}}, {{math|V&prime; ⊆ V}}),那么{{math|G&prime; ⊆ G}}中就应该包含原图{{math|G}}中的所有{{math|u}}和{{math|V}}的对应连边(即{{math|&lang;u, v&rang; ∈ E}}),则称此时图{{math|G&prime;}}就是图{{math|G}}的导出子图。<br />
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如果存在一个双射(一对一){{math|f:V&prime; → V}},且对所有{{math|u, v ∈ V&prime;}}都有{{math|&lang;u, v&rang; ∈ E&prime; ⇔ &lang;f(u), f(v)&rang; ∈ E}} ,则称{{math|G&prime }}是{{math|G}}的同构图(记作:{{math|G&prime; → G}}),映射f则称为{{math|G}}与{{math|G&prime;}}之间的同构(isomorphism)。[2]<br />
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When {{math|G&Prime; ⊂ G}} and there exists an isomorphism between the sub-graph {{math|G&Prime;}} and a graph {{math|G&prime;}}, this mapping represents an ''appearance'' of {{math|G&prime;}} in {{math|G}}. The number of appearances of graph {{math|G&prime;}} in {{math|G}} is called the frequency {{math|F<sub>G</sub>}} of {{math|G&prime;}} in {{math|G}}. A graph is called ''recurrent'' (or ''frequent'') in {{math|G}}, when its ''frequency'' {{math|F<sub>G</sub>(G&prime;)}} is above a predefined threshold or cut-off value. We use terms ''pattern'' and ''frequent sub-graph'' in this review interchangeably. There is an [[Statistical ensemble (mathematical physics)|ensemble]] {{math|Ω(G)}} of random graphs corresponding to the [[Null model|null-model]] associated to {{math|G}}. We should choose {{math|N}} random graphs uniformly from {{math|Ω(G)}} and calculate the frequency for a particular frequent sub-graph {{math|G&prime;}} in {{math|G}}. If the frequency of {{math|G&prime;}} in {{math|G}} is higher than its arithmetic mean frequency in {{math|N}} random graphs {{math|R<sub>i</sub>}}, where {{math|1 ≤ i ≤ N}}, we call this recurrent pattern ''significant'' and hence treat {{math|G&prime;}} as a ''network motif'' for {{math|G}}. For a small graph {{math|G&prime;}}, the network {{math|G}} and a set of randomized networks {{math|R(G) ⊆ Ω(R)}}, where {{math|1=R(G) {{=}} N}}, the ''Z-Score'' that has been defined by the following formula:<br />
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<math>Z(G^\prime) = \frac{F_G(G^\prime) - \mu_R(G^\prime)}{\sigma_R(G^\prime)}</math><br />
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当{{math|G&Prime; ⊂ G}},且{{math|G&Prime;}}与图{{math|G&prime;}}之间存在同构时,该映射表示{{math|G&prime;}}对于{{math|G}}存在。图{{math|G&prime;}}在{{math|G}}的出现次数称为{{math|G&prime;}}出现在{{math|G}}的频率{{math|F<sub>G</sub>}}。当一个子图的频率{{math|F<sub>G</sub>}}高于预定的阈值或截止值时,则称{{math|G&prime;}}是{{math|G}}中的递归(或频繁)子图。<br />
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在接下来的内容中,我们交替使用术语“模式(motifs)”和“频繁子图(frequent sub-graph)”。<br />
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设从与{{math|G}}相关联的零模型(the null-model)获得的随机图集合为{{math|Ω(G)}},我们从{{math|Ω(G)}}中均匀地选择N个随机图,并计算其特定频繁子图的频率。如果{{math|G&prime;}}出现在{{math|G}}的频率高于N个随机图Ri的算术平均频率,其中{{math|1 ≤ i ≤ N}},我们称此递归模式是有意义的,因此可以将{{math|G&prime;}}视为{{math|G}}的网络模体。<br />
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对于一个小图{{math|G&prime;}},网络{{math|G}}和一组随机网络{{math|R(G) ⊆ Ω(R)}},当{{math|1=R(G) {{=}} N}}时,由其Z分数(Z-score)的定义如下式:<br />
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<math>Z(G^\prime) = \frac{F_G(G^\prime) - \mu_R(G^\prime)}{\sigma_R(G^\prime)}</math><br />
<br />
where {{math|μ<sub>R</sub>(G&prime;)}} and {{math|σ<sub>R</sub>(G&prime;)}} stand for mean and standard deviation frequency in set {{math|R(G)}}, respectively.<ref name="mil1">{{cite journal |vauthors=Milo R, Shen-Orr SS, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |volume=298 |year=2002|journal=Science|issue=5594|pages=824–827 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="alb1">{{cite journal |vauthors=Albert R, Barabási AL |title=Statistical mechanics of complex networks |journal=Reviews of Modern Physics |volume=74 |issue=1 |year=2002 |pages=47–49 |doi=10.1103/RevModPhys.74.47 |bibcode=2002RvMP...74...47A|arxiv=cond-mat/0106096 |citeseerx=10.1.1.242.4753 }}</ref><ref name="mil2">{{cite journal |vauthors=Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheffer M, Alon U |title=Superfamilies of designed and evolved networks |journal=Science |volume=303 |issue=5663 |year=2004 |pages=1538–1542 |pmid=15001784 |doi=10.1126/science.1089167 |bibcode=2004Sci...303.1538M |url=https://semanticscholar.org/paper/87ad24efd5329046d37cd704f970323e878710ca }}</ref><ref name="sch1">{{cite encyclopedia|last=Schwöbbermeyer |first=H |title=Network Motifs |encyclopedia=Analysis of Biological Networks |editor=Junker BH, Schreiber F |publisher=Hoboken, New Jersey: John Wiley & Sons |year=2008 |pages=85–108}}</ref><ref name="bor1">{{cite encyclopedia |last1=Bornholdt |first1=S |last2=Schuster |first2=HG |title=Handbook of graphs and networks : from the genome to the Internet |journal=Handbook of Graphs and Networks: From the Genome to the Internet |pages=417 |year=2003|bibcode=2003hgnf.book.....B }}</ref><ref name="cir1">{{cite journal |vauthors=Ciriello G, Guerra C |title=A review on models and algorithms for motif discovery in protein-protein interaction networks |journal=Briefings in Functional Genomics and Proteomics |year=2008 |volume=7 |issue=2 |pages=147–156 |doi=10.1093/bfgp/eln015|pmid=18443014 |doi-access=free }}</ref> The larger the {{math|Z(G&prime;)}}, the more significant is the sub-graph {{math|G&prime;}} as a motif. Alternatively, another measurement in statistical hypothesis testing that can be considered in motif detection is the P-Value, given as the probability of {{math|F<sub>R</sub>(G&prime;) ≥ F<sub>G</sub>(G&prime;)}} (as its null-hypothesis), where {{math|F<sub>R</sub>(G&prime;)}} indicates the frequency of G' in a randomized network.<ref name="sch1" /> A sub-graph with P-value less than a threshold (commonly 0.01 or 0.05) will be treated as a significant pattern. The P-value is defined as<br />
<br />
<math>P(G^\prime) = \frac{1}{N}\sum_{i=1}^N \delta(c(i)) ; c(i): F_R^i(G^\prime) \ge F_G(G^\prime)</math><br />
<br />
式中,{{math|μ<sub>R</sub>(G&prime;)}} 和 {{math|σ<sub>R</sub>(G&prime;)}}分别代表集合{{math|R(G)}}中的平均和标准偏差频率。.<ref name="mil1">{{cite journal |vauthors=Milo R, Shen-Orr SS, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |volume=298 |year=2002|journal=Science|issue=5594|pages=824–827 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="alb1">{{cite journal |vauthors=Albert R, Barabási AL |title=Statistical mechanics of complex networks |journal=Reviews of Modern Physics |volume=74 |issue=1 |year=2002 |pages=47–49 |doi=10.1103/RevModPhys.74.47 |bibcode=2002RvMP...74...47A|arxiv=cond-mat/0106096 |citeseerx=10.1.1.242.4753 }}</ref><ref name="mil2">{{cite journal |vauthors=Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheffer M, Alon U |title=Superfamilies of designed and evolved networks |journal=Science |volume=303 |issue=5663 |year=2004 |pages=1538–1542 |pmid=15001784 |doi=10.1126/science.1089167 |bibcode=2004Sci...303.1538M |url=https://semanticscholar.org/paper/87ad24efd5329046d37cd704f970323e878710ca }}</ref><ref name="sch1">{{cite encyclopedia|last=Schwöbbermeyer |first=H |title=Network Motifs |encyclopedia=Analysis of Biological Networks |editor=Junker BH, Schreiber F |publisher=Hoboken, New Jersey: John Wiley & Sons |year=2008 |pages=85–108}}</ref><ref name="bor1">{{cite encyclopedia |last1=Bornholdt |first1=S |last2=Schuster |first2=HG |title=Handbook of graphs and networks : from the genome to the Internet |journal=Handbook of Graphs and Networks: From the Genome to the Internet |pages=417 |year=2003|bibcode=2003hgnf.book.....B }}</ref><ref name="cir1">{{cite journal |vauthors=Ciriello G, Guerra C |title=A review on models and algorithms for motif discovery in protein-protein interaction networks |journal=Briefings in Functional Genomics and Proteomics |year=2008 |volume=7 |issue=2 |pages=147–156 |doi=10.1093/bfgp/eln015|pmid=18443014 |doi-access=free }}</ref> {{math|Z(G&prime;)}}越大,子图{{math|G&prime;}}作为模体的意义也就越大。<br />
<br />
此外还可以使用统计假设检验中的另一个测量方法,可以作为模体检测中的一种方法,即P值(P-value),以 {{math|F<sub>R</sub>(G&prime;) ≥ F<sub>G</sub>(G&prime;)}}的概率给出(作为其零假设null-hypothesis),其中{{math|F<sub>R</sub>(G&prime;)}}表示随机网络中{{math|G&prime;}}的频率。<ref name="sch1" /> 当P值小于阈值(通常为0.01或0.05)时,该子图可以被称为显著模式。该P值定义为:<br />
<br />
<math>P(G^\prime) = \frac{1}{N}\sum_{i=1}^N \delta(c(i)) ; c(i): F_R^i(G^\prime) \ge F_G(G^\prime)</math><br />
<br />
[[File:Different occurrences of a sub-graph in a graph.jpg|thumb|''Different occurrences of a sub-graph in a graph''. (M1 – M4) are different occurrences of sub-graph (b) in graph (a). For frequency concept {{math|F<sub>1</sub>}}, the set M1, M2, M3, M4 represent all matches, so {{math|F<sub>1</sub> {{=}} 4}}. For {{math|F<sub>2</sub>}}, one of the two set M1, M4 or M2, M3 are possible matches, {{math|F<sub>2</sub> {{=}} 2}}. Finally, for frequency concept {{math|F<sub>3</sub>}}, merely one of the matches (M1 to M4) is allowed, therefore {{math|F<sub>3</sub> {{=}} 1}}. The frequency of these three frequency concepts decrease as the usage of network elements are restricted.]]<br />
<br />
Where {{math|N}} indicates number of randomized networks, {{math|i}} is defined over an ensemble of randomized networks and the Kronecker delta function {{math|δ(c(i))}} is one if the condition {{math|c(i)}} holds. The concentration <ref name="kas1">{{cite journal |vauthors=Kashtan N, Itzkovitz S, Milo R, Alon U |title=Efficient sampling algorithm for estimating sub-graph concentrations and detecting network motifs |journal=Bioinformatics |year=2004 |volume=20 |issue=11 |pages=1746–1758 |doi=10.1093/bioinformatics/bth163|pmid=15001476 |doi-access=free }}</ref><ref name="wer1">{{cite journal |author=Wernicke S |title=Efficient detection of network motifs |journal=IEEE/ACM Transactions on Computational Biology and Bioinformatics |year=2006 |volume=3 |issue=4 |pages=347–359 |doi=10.1109/tcbb.2006.51|pmid=17085844 |citeseerx=10.1.1.304.2576 }}</ref> of a particular n-size sub-graph {{math|G&prime;}} in network {{math|G}} refers to the ratio of the sub-graph appearance in the network to the total ''n''-size non-isomorphic sub-graphs’ frequencies, which is formulated by<br />
<br />
<math>C_G(G^\prime) = \frac{F_G(G^\prime)}{\sum_i F_G(G_i)}</math><br />
<br />
where index {{math|i}} is defined over the set of all non-isomorphic n-size graphs. Another statistical measurement is defined for evaluating network motifs, but it is rarely used in known algorithms. This measurement is introduced by Picard ''et al.'' in 2008 and used the Poisson distribution, rather than the Gaussian normal distribution that is implicitly being used above.<ref name="pic1">{{cite journal |vauthors=Picard F, Daudin JJ, Schbath S, Robin S |title=Assessing the Exceptionality of Network Motifs |journal=J. Comp. Bio. |year=2005 |volume=15 |issue=1 |pages=1–20|doi=10.1089/cmb.2007.0137 |pmid=18257674 |citeseerx=10.1.1.475.4300 }}</ref><br />
<br />
其中索引 i 定义在所有非同构 n 大小图的集合上。 另一种统计测量是用来评估网络主题的,但在已知的算法中很少使用。 这种测量方法是由 Picard 等人在2008年提出的,使用的是泊松分佈分布,而不是上面隐含使用的高斯正态分布。<ref name="pic1">{{cite journal |vauthors=Picard F, Daudin JJ, Schbath S, Robin S |title=Assessing the Exceptionality of Network Motifs |journal=J. Comp. Bio. |year=2005 |volume=15 |issue=1 |pages=1–20|doi=10.1089/cmb.2007.0137 |pmid=18257674 |citeseerx=10.1.1.475.4300 }}</ref>其中{{math|N}}表示随机网络的数目,{{math|i}}定义在随机网络的集合上,若条件{{math|c(i)}}成立,则Kroneckerδ函数{{math|δ(c(i))}}是1。在网络{{math|G}}中,一个特定的n维子图{{math|N&prime;}}的集中度是指子图在网络中出现频率与n维非同构子图的总频率之比,其计算公式如下:<br />
<br />
<math>C_G(G^\prime) = \frac{F_G(G^\prime)}{\sum_i F_G(G_i)}</math><br />
<br />
<br />
In addition, three specific concepts of sub-graph frequency have been proposed.<ref name="schr1">{{cite book |vauthors=Schreiber F, Schwöbbermeyer H |title=Frequency concepts and pattern detection for the analysis of motifs in networks |journal=Transactions on Computational Systems Biology III |volume=3737 |year=2005 |pages=89–104|doi=10.1007/11599128_7 |citeseerx=10.1.1.73.1130 |series=Lecture Notes in Computer Science |isbn=978-3-540-30883-6 }}</ref> As the figure illustrates, the first frequency concept {{math|F<sub>1</sub>}} considers all matches of a graph in original network. This definition is similar to what we have introduced above. The second concept {{math|F<sub>2</sub>}} is defined as the maximum number of edge-disjoint instances of a given graph in original network. And finally, the frequency concept {{math|F<sub>3</sub>}} entails matches with disjoint edges and nodes. Therefore, the two concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}} restrict the usage of elements of the graph, and as can be inferred, the frequency of a sub-graph declines by imposing restrictions on network element usage. As a result, a network motif detection algorithm would pass over more candidate sub-graphs if we insist on frequency concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}}.<br />
<br />
此外,他们还提出了子图频率的三个具体概念。<ref name="schr1">{{cite book |vauthors=Schreiber F, Schwöbbermeyer H |title=Frequency concepts and pattern detection for the analysis of motifs in networks |journal=Transactions on Computational Systems Biology III |volume=3737 |year=2005 |pages=89–104|doi=10.1007/11599128_7 |citeseerx=10.1.1.73.1130 |series=Lecture Notes in Computer Science |isbn=978-3-540-30883-6 }}</ref> 如图所示,第一频率概念 {{math|F<sub>1</sub>}}考虑原始网络中图的所有匹配,这与我们前面介绍过的类似。第二个概念{{math|F<sub>2</sub>}}定义为原始网络中给定图的最大不相交边的数量。最后,频率概念{{math|F<sub>3</sub>}}包含与不相交边(disjoint edges)和节点的匹配。因此,两个概念F2和F3限制了图元素的使用,并且可以看出,通过对网络元素的使用施加限制,子图的频率下降。因此,如果我们坚持使用频率概念{{math|F<sub>2</sub>}}和{{math|F<sub>3</sub>}},网络模体检测算法将可以筛选出更多的候选子图。<br />
<br />
==History==<br />
The study of network motifs was pioneered by Holland and Leinhardt<ref>Holland, P. W., & Leinhardt, S. (1974). The statistical analysis of local structure in social networks. Working Paper No. 44, National Bureau of Economic Research.</ref><ref>Hollandi, P., & Leinhardt, S. (1975). The Statistical Analysis of Local. Structure in Social Networks. Sociological Methodology, David Heise, ed. San Francisco: Josey-Bass.</ref><ref> Holland, P. W., & Leinhardt, S. (1976). Local structure in social networks. Sociological methodology, 7, 1-45.</ref><ref>Holland, P. W., & Leinhardt, S. (1977). A method for detecting structure in sociometric data. In Social Networks (pp. 411-432). Academic Press.</ref> who introduced the concept of a triad census of networks. They introduced methods to enumerate various types of subgraph configurations, and test whether the subgraph counts are statistically different from those expected in random networks. <br />
霍兰(Holland)和莱因哈特(Leinhardt)率先提出了'''网络三合会普查'''(a triad census of networks)的概念,开创了网络模体研究的先河。<ref>Holland, P. W., & Leinhardt, S. (1974). The statistical analysis of local structure in social networks. Working Paper No. 44, National Bureau of Economic Research.</ref><ref>Hollandi, P., & Leinhardt, S. (1975). The Statistical Analysis of Local. Structure in Social Networks. Sociological Methodology, David Heise, ed. San Francisco: Josey-Bass.</ref><ref> Holland, P. W., & Leinhardt, S. (1976). Local structure in social networks. Sociological methodology, 7, 1-45.</ref><ref>Holland, P. W., & Leinhardt, S. (1977). A method for detecting structure in sociometric data. In Social Networks (pp. 411-432). Academic Press.</ref> 他们介绍了枚举各种子图配置的方法,并测试子图计数是否与随机网络中的期望值存在统计学上的差异。<br />
<br />
这里对于'''网络三合会普查'''(a triad census of networks)这一概念的翻译存疑<br />
<br />
<br />
This idea was further generalized in 2002 by [[Uri Alon]] and his group <ref name="she1">{{cite journal |vauthors=Shen-Orr SS, Milo R, Mangan S, Alon U |title=Network motifs in the transcriptional regulation network of ''Escherichia coli'' |journal=Nat. Genet. |volume=31 |issue=1 |pages=64–8 |date=May 2002 |pmid=11967538 |doi=10.1038/ng881}}</ref> when network motifs were discovered in the gene regulation (transcription) network of the bacteria ''[[Escherichia coli|E. coli]]'' and then in a large set of natural networks. Since then, a considerable number of studies have been conducted on the subject. Some of these studies focus on the biological applications, while others focus on the computational theory of network motifs.<br />
<br />
2002年,Uri Alon和他的团队[17]在大肠杆菌的基因调控(gene regulation network)(转录 transcription)网络中发现了网络模体,随后在大量的自然网络中也发现了网络模体,从而进一步推广了这一观点。自那时起,许多科学家都对这一问题进行了大量的研究。其中一些研究集中在生物学应用上,而另一些则集中在网络模体的计算理论上。<ref name="she1">{{cite journal |vauthors=Shen-Orr SS, Milo R, Mangan S, Alon U |title=Network motifs in the transcriptional regulation network of ''Escherichia coli'' |journal=Nat. Genet. |volume=31 |issue=1 |pages=64–8 |date=May 2002 |pmid=11967538 |doi=10.1038/ng881}}</ref> <br />
<br />
<br />
The biological studies endeavor to interpret the motifs detected for biological networks. For example, in work following,<ref name="she1" /> the network motifs found in ''[[Escherichia coli|E. coli]]'' were discovered in the transcription networks of other bacteria<ref name="eic1">{{cite journal |vauthors=Eichenberger P, Fujita M, Jensen ST, etal |title=The program of gene transcription for a single differentiating cell type during sporulation in ''Bacillus subtilis'' |journal=PLOS Biology |volume=2 |issue=10 |pages=e328 |date=October 2004 |pmid=15383836 |pmc=517825 |doi=10.1371/journal.pbio.0020328 }} </ref> as well as yeast<ref name="mil3">{{cite journal |vauthors=Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |journal=Science |volume=298 |issue=5594 |pages=824–7 |date=October 2002 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="lee1">{{cite journal |vauthors=Lee TI, Rinaldi NJ, Robert F, etal |title=Transcriptional regulatory networks in Saccharomyces cerevisiae |journal=Science |volume=298 |issue=5594 |pages=799–804 |date=October 2002 |pmid=12399584 |doi=10.1126/science.1075090 |bibcode=2002Sci...298..799L }}</ref> and higher organisms.<ref name="odo1">{{cite journal |vauthors=Odom DT, Zizlsperger N, Gordon DB, etal |title=Control of pancreas and liver gene expression by HNF transcription factors |journal=Science |volume=303 |issue=5662 |pages=1378–81 |date=February 2004 |pmid=14988562 |pmc=3012624 |doi=10.1126/science.1089769 |bibcode=2004Sci...303.1378O }}</ref><ref name="boy1">{{cite journal |vauthors=Boyer LA, Lee TI, Cole MF, etal |title=Core transcriptional regulatory circuitry in human embryonic stem cells |journal=Cell |volume=122 |issue=6 |pages=947–56 |date=September 2005 |pmid=16153702 |pmc=3006442 |doi=10.1016/j.cell.2005.08.020 }}</ref><ref name="ira1">{{cite journal |vauthors=Iranfar N, Fuller D, Loomis WF |title=Transcriptional regulation of post-aggregation genes in Dictyostelium by a feed-forward loop involving GBF and LagC |journal=Dev. Biol. |volume=290 |issue=2 |pages=460–9 |date=February 2006 |pmid=16386729 |doi=10.1016/j.ydbio.2005.11.035 |doi-access=free }}</ref> A distinct set of network motifs were identified in other types of biological networks such as neuronal networks and protein interaction networks.<ref name="mil2" /><ref name="maa1">{{cite journal |vauthors=Ma'ayan A, Jenkins SL, Neves S, etal |title=Formation of regulatory patterns during signal propagation in a Mammalian cellular network |journal=Science |volume=309 |issue=5737 |pages=1078–83 |date=August 2005 |pmid=16099987 |pmc=3032439 |doi=10.1126/science.1108876 |bibcode=2005Sci...309.1078M }}</ref><ref name="pta1">{{cite journal |vauthors=Ptacek J, Devgan G, Michaud G, etal |title=Global analysis of protein phosphorylation in yeast |journal=Nature |volume=438 |issue=7068 |pages=679–84 |date=December 2005 |pmid=16319894 |doi=10.1038/nature04187|bibcode=2005Natur.438..679P |url=https://authors.library.caltech.edu/56271/2/Tables.pdf |type=Submitted manuscript }}</ref><br />
<br />
生物学研究试图解释为生物网络检测到的模体。例如,在接下来的工作中,文献[17]在大肠杆菌中发现的网络模体存在于其他细菌<ref name="eic1">{{cite journal |vauthors=Eichenberger P, Fujita M, Jensen ST, etal |title=The program of gene transcription for a single differentiating cell type during sporulation in ''Bacillus subtilis'' |journal=PLOS Biology |volume=2 |issue=10 |pages=e328 |date=October 2004 |pmid=15383836 |pmc=517825 |doi=10.1371/journal.pbio.0020328 }} </ref>以及酵母<ref name="mil3">{{cite journal |vauthors=Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U |title=Network motifs: simple building blocks of complex networks |journal=Science |volume=298 |issue=5594 |pages=824–7 |date=October 2002 |doi=10.1126/science.298.5594.824 |pmid=12399590|bibcode=2002Sci...298..824M |citeseerx=10.1.1.225.8750 }}</ref><ref name="lee1">{{cite journal |vauthors=Lee TI, Rinaldi NJ, Robert F, etal |title=Transcriptional regulatory networks in Saccharomyces cerevisiae |journal=Science |volume=298 |issue=5594 |pages=799–804 |date=October 2002 |pmid=12399584 |doi=10.1126/science.1075090 |bibcode=2002Sci...298..799L }}</ref>和高等生物的转录网络中。文献<ref name="odo1">{{cite journal |vauthors=Odom DT, Zizlsperger N, Gordon DB, etal |title=Control of pancreas and liver gene expression by HNF transcription factors |journal=Science |volume=303 |issue=5662 |pages=1378–81 |date=February 2004 |pmid=14988562 |pmc=3012624 |doi=10.1126/science.1089769 |bibcode=2004Sci...303.1378O }}</ref><ref name="boy1">{{cite journal |vauthors=Boyer LA, Lee TI, Cole MF, etal |title=Core transcriptional regulatory circuitry in human embryonic stem cells |journal=Cell |volume=122 |issue=6 |pages=947–56 |date=September 2005 |pmid=16153702 |pmc=3006442 |doi=10.1016/j.cell.2005.08.020 }}</ref><ref name="ira1">{{cite journal |vauthors=Iranfar N, Fuller D, Loomis WF |title=Transcriptional regulation of post-aggregation genes in Dictyostelium by a feed-forward loop involving GBF and LagC |journal=Dev. Biol. |volume=290 |issue=2 |pages=460–9 |date=February 2006 |pmid=16386729 |doi=10.1016/j.ydbio.2005.11.035 |doi-access=free }}</ref>在其他类型的生物网络中发现了一组不同的网络模体,如神经元网络和蛋白质相互作用网络。<ref name="mil2" /><ref name="maa1">{{cite journal |vauthors=Ma'ayan A, Jenkins SL, Neves S, etal |title=Formation of regulatory patterns during signal propagation in a Mammalian cellular network |journal=Science |volume=309 |issue=5737 |pages=1078–83 |date=August 2005 |pmid=16099987 |pmc=3032439 |doi=10.1126/science.1108876 |bibcode=2005Sci...309.1078M }}</ref><ref name="pta1">{{cite journal |vauthors=Ptacek J, Devgan G, Michaud G, etal |title=Global analysis of protein phosphorylation in yeast |journal=Nature |volume=438 |issue=7068 |pages=679–84 |date=December 2005 |pmid=16319894 |doi=10.1038/nature04187|bibcode=2005Natur.438..679P |url=https://authors.library.caltech.edu/56271/2/Tables.pdf |type=Submitted manuscript }}</ref><br />
<br />
<br />
The computational research has focused on improving existing motif detection tools to assist the biological investigations and allow larger networks to be analyzed. Several different algorithms have been provided so far, which are elaborated in the next section in chronological order.<br />
<br />
另一方面,对于计算研究的重点则是改进现有的模体检测工具,以协助生物学研究,并允许对更大的网络进行分析。到目前为止,已经提供了几种不同的算法,这些算法将在下一节按时间顺序进行阐述。<br />
<br />
Most recently, the acc-MOTIF tool to detect network motifs was released.<ref>{{Cite web | url=http://www.ft.unicamp.br/docentes/meira/accmotifs/ |title = Acc-Motif: Accelerated Motif Detection}}</ref><br />
<br />
最近,还发布了用于检测网络基序的acc基序工具。<ref>{{Cite web | url=http://www.ft.unicamp.br/docentes/meira/accmotifs/ |title = Acc-Motif: Accelerated Motif Detection}}</ref><br />
<br />
<br />
==模体发现算法 Motif discovery algorithms==<br />
<br />
Various solutions have been proposed for the challenging problem of motif discovery. These algorithms can be classified under various paradigms such as exact counting methods, sampling methods, pattern growth methods and so on. However, motif discovery problem comprises two main steps: first, calculating the number of occurrences of a sub-graph and then, evaluating the sub-graph significance. The recurrence is significant if it is detectably far more than expected. Roughly speaking, the expected number of appearances of a sub-graph can be determined by a Null-model, which is defined by an ensemble of random networks with some of the same properties as the original network.<br />
<br />
针对模体发现这一问题存在多种解决方案。这些算法可以归纳为不同的范式:例如精确计数方法,采样方法,模式增长方法等。但模体发现问题包括两个主要步骤:首先,计算子图的出现次数,然后评估子图的重要性。如果检测到的重现性远超过预期,那么这种重现性是很显著的。粗略地讲,子图的预期出现次数可以由'''零模型 Null-model''' 确定,该模型定义为具有与原始网络某些属性相同的随机网络的集合。<br />
<br />
<br />
Here, a review on computational aspects of major algorithms is given and their related benefits and drawbacks from an algorithmic perspective are discussed.<br />
<br />
接下来,对下列算法的计算原理进行简要回顾,并从算法的角度讨论了它们的优缺点。<br />
<br />
===mfinder 算法===<br />
<br />
''mfinder'', the first motif-mining tool, implements two kinds of motif finding algorithms: a full enumeration and a sampling method. Until 2004, the only exact counting method for NM (network motif) detection was the brute-force one proposed by Milo ''et al.''.<ref name="mil1" /> This algorithm was successful for discovering small motifs, but using this method for finding even size 5 or 6 motifs was not computationally feasible. Hence, a new approach to this problem was needed.<br />
<br />
'''mfinder'''是第一个模体挖掘工具,它主要有两种模体查找算法:完全枚举 full enumeration 和采样方法 sampling method。直到2004年,用于NM('''网络模体 networkmotif''')检测的唯一精确计数方法是'''Milo'''等人提出的暴力穷举方法。<ref name="mil1" />该算法成功地发现了小规模的模体,但是这种方法甚至对于发现规模为5个或6个的模体在计算上都不可行的。因此,需要一种解决该问题的新方法。<br />
<br />
<br />
Kashtan ''et al.'' <ref name="kas1" /> presented the first sampling NM discovery algorithm, which was based on ''edge sampling'' throughout the network. This algorithm estimates concentrations of induced sub-graphs and can be utilized for motif discovery in directed or undirected networks. The sampling procedure of the algorithm starts from an arbitrary edge of the network that leads to a sub-graph of size two, and then expands the sub-graph by choosing a random edge that is incident to the current sub-graph. After that, it continues choosing random neighboring edges until a sub-graph of size n is obtained. Finally, the sampled sub-graph is expanded to include all of the edges that exist in the network between these n nodes. When an algorithm uses a sampling approach, taking unbiased samples is the most important issue that the algorithm might address. The sampling procedure, however, does not take samples uniformly and therefore Kashtan ''et al.'' proposed a weighting scheme that assigns different weights to the different sub-graphs within network.<ref name="kas1" /> The underlying principle of weight allocation is exploiting the information of the [[sampling probability]] for each sub-graph, i.e. the probable sub-graphs will obtain comparatively less weights in comparison to the improbable sub-graphs; hence, the algorithm must calculate the sampling probability of each sub-graph that has been sampled. This weighting technique assists ''mfinder'' to determine sub-graph concentrations impartially.<br />
<br />
'''Kashtan''' 等人<ref name="kas1" />首次提出了一种基于边缘采样的网络模体(NM)采样发现算法。该算法估计了<font color="red">所含子图 induced sub-graphs 的集中度 concentrations </font>,可用于有向或无向网络中的模体发现。该算法的采样过程从网络的任意一条边开始,该边连向大小为2的子图,然后选择一条与当前子图相关的随机边对子图进行扩展。之后,它将继续选择随机的相邻边,直到获得大小为n的子图为止。最后,采样得到的子图扩展为包括这n个节点在内的网络中存在的所有边。当使用采样方法时,获取无偏样本是这类算法可能面临的最重要问题。而且,采样过程并不能保证采到所有的样本(也就是不能保证得到所有的子图,译者注),因此,Kashtan 等人又提出了一种加权方案,为网络中的不同子图分配不同的权重。<ref name="kas1" /> 权重分配的基本原理是利用每个子图的抽样概率信息,即,与不可能的子图相比,可能的子图将获得相对较少的权重;因此,该算法必须计算已采样的每个子图的采样概率。这种加权技术有助于mfinder公正地确定子图的<font color="red">集中度 concentrations </font>。<br />
<br />
<br />
In expanded to include sharp contrast to exhaustive search, the computational time of the algorithm surprisingly is asymptotically independent of the network size. An analysis of the computational time of the algorithm has shown that it takes {{math|O(n<sup>n</sup>)}} for each sample of a sub-graph of size {{math|n}} from the network. On the other hand, there is no analysis in <ref name="kas1" /> on the classification time of sampled sub-graphs that requires solving the ''graph isomorphism'' problem for each sub-graph sample. Additionally, an extra computational effort is imposed on the algorithm by the sub-graph weight calculation. But it is unavoidable to say that the algorithm may sample the same sub-graph multiple times – spending time without gathering any information.<ref name="wer1" /> In conclusion, by taking the advantages of sampling, the algorithm performs more efficiently than an exhaustive search algorithm; however, it only determines sub-graphs concentrations approximately. This algorithm can find motifs up to size 6 because of its main implementation, and as result it gives the most significant motif, not all the others too. Also, it is necessary to mention that this tool has no option of visual presentation. The sampling algorithm is shown briefly:<br />
<br />
与穷举搜索形成鲜明对比的是,该算法的计算时间竟然与网络大小渐近无关。对算法时间复杂度的分析表明,对于网络中大小为n的子图的每个样本,它的时间复杂度为<math>O(n^n)</math>。另一方面,<font color="red">并没有对已采样子图的每一个子图样本判断图同构问题的分类时间进行分析</font><ref name="kas1" />。另外,子图权重计算将额外增加该算法的计算负担。但是不得不指出的是,该算法可能会多次采样相同的子图——花费时间而不收集任何有用信息。<ref name="wer1" />总之,通过利用采样的优势,该算法的性能比穷举搜索算法更有效;但是,它只能大致确定子图的<font color="red">集中度 concentrations </font>。由于该算法的实现方式,使得它可以找到最大为6的模体,并且它会给出的最重要的模体,而不是其他所有模体。另外,有必要提到此工具没有可视化的呈现。采样算法简要显示如下:<br />
<br />
<br />
{| class="wikitable"<br />
|-<br />
! mfinder<br />
|-<br />
| '''Definitions:''' {{math|E<sub>s</sub>}}is the set of picked edges. {{math|V<sub>s</sub>}} is the set of all nodes that are touched by the edges in {{math|E}}.<br />
|-<br />
| Init {{math|V<sub>s</sub>}} and {{math|E<sub>s</sub>}} to be empty sets.<br />
1. Pick a random edge {{math|e<sub>1</sub> {{=}} (v<sub>i</sub>, v<sub>j</sub>)}}. Update {{math|E<sub>s</sub> {{=}} {e<sub>1</sub>}}}, {{math|V<sub>s</sub> {{=}} {v<sub>i</sub>, v<sub>j</sub>}}}<br />
<br />
2. Make a list {{math|L}} of all neighbor edges of {{math|E<sub>s</sub>}}. Omit from {{math|L}} all edges between members of {{math|V<sub>s</sub>}}.<br />
<br />
3. Pick a random edge {{math|e {{=}} {v<sub>k</sub>,v<sub>l</sub>}}} from {{math|L}}. Update {{math|E<sub>s</sub> {{=}} E<sub>s</sub> ⋃ {e}}}, {{math|V<sub>s</sub> {{=}} V<sub>s</sub> ⋃ {v<sub>k</sub>, v<sub>l</sub>}}}.<br />
<br />
4. Repeat steps 2-3 until completing an ''n''-node subgraph (until {{math|{{!}}V<sub>s</sub>{{!}} {{=}} n}}).<br />
<br />
5. Calculate the probability to sample the picked ''n''-node subgraph.<br />
|}<br />
<br />
<br />
{|class="wikitable"<br />
|+ mfinder<br />
|-<br />
!rowspan="1"|定义:<math>E_{s}</math>是采集的边集合。<math>V_{s}</math>是<math>E</math>中所有边的顶点的集合。<br />
|-<br />
|rowspan="5"|初始化<math>V_{s}</math>和<math>E_{s}</math>为空集。<br><br />
1. 随机选择一条边<math> e_{1} = (v_{i}, v_{j}) </math>,更新 <math>E_{s} = \{e_{1}\}, V{s} = \{v_{i}, v_{j}\}</math><br />
<br />
2. 列出<math>E{s}</math>的所有邻边列表<math> L </math>,从<math> L </math>中删除<math>V{s}</math>中所有元素组成的边。<br />
<br />
3. 从<math> L </math>中随机选择一条边<math> e = \{v_{k},v_{l}\} </math>, 更新<math>E_{s} = E_{s} \cup \{e\} , V_{s} = V_{s} \cup \{v_{k}, v_{l}\}</math>。<br />
<br />
4. 重复步骤2-3,直到完成包含n个节点的子图 (<math>\left | V_{s} \right | = n</math>)。<br />
<br />
5. 计算对选取的n节点子图进行采样的概率。<br />
|}<br />
<br />
<br />
===FPF (Mavisto)算法===<br />
<br />
Schreiber and Schwöbbermeyer <ref name="schr1" /> proposed an algorithm named ''flexible pattern finder (FPF)'' for extracting frequent sub-graphs of an input network and implemented it in a system named ''Mavisto''.<ref name="schr2">{{cite journal |vauthors=Schreiber F, Schwobbermeyer H |title=MAVisto: a tool for the exploration of network motifs |journal=Bioinformatics |volume=21 |issue=17|pages=3572–3574 |year=2005 |doi=10.1093/bioinformatics/bti556|pmid=16020473 |doi-access=free }}</ref> Their algorithm exploits the ''downward closure'' property which is applicable for frequency concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}}. The downward closure property asserts that the frequency for sub-graphs decrease monotonically by increasing the size of sub-graphs; however, this property does not hold necessarily for frequency concept {{math|F<sub>1</sub>}}. FPF is based on a ''pattern tree'' (see figure) consisting of nodes that represents different graphs (or patterns), where the parent of each node is a sub-graph of its children nodes; in other words, the corresponding graph of each pattern tree's node is expanded by adding a new edge to the graph of its parent node.<br />
<br />
Schreiber和Schwöbbermeyer <ref name="schr1" />提出了一种称为灵活模式查找器(FPF)的算法,用于提取输入网络的频繁子图,并将其在名为Mavisto的系统中加以实现。<ref name="schr2">{{cite journal |vauthors=Schreiber F, Schwobbermeyer H |title=MAVisto: a tool for the exploration of network motifs |journal=Bioinformatics |volume=21 |issue=17|pages=3572–3574 |year=2005 |doi=10.1093/bioinformatics/bti556|pmid=16020473 |doi-access=free }}</ref> 他们的算法利用了向下闭包特性,该特性适用于频率概念<math>F_{2}</math>和<math>F_{3}</math>。向下闭包性质表明,子图的频率随着子图的大小而单调下降;但这一性质并不一定适用于频率概念<math>F_{1}</math>。FPF算法基于模式树(见右图),由代表不同图形(或模式)的节点组成,其中每个节点的父节点是其子节点的子图;换句话说,每个模式树节点的对应图通过向其父节点图添加新边来扩展。<br />
<br />
<br />
[[Image:The pattern tree in FPF algorithm.jpg|right|thumb|''FPF算法中的模式树展示''.<ref name="schr1" />]]<br />
<br />
<br />
At first, the FPF algorithm enumerates and maintains the information of all matches of a sub-graph located at the root of the pattern tree. Then, one-by-one it builds child nodes of the previous node in the pattern tree by adding one edge supported by a matching edge in the target graph, and tries to expand all of the previous information about matches to the new sub-graph (child node). In next step, it decides whether the frequency of the current pattern is lower than a predefined threshold or not. If it is lower and if downward closure holds, FPF can abandon that path and not traverse further in this part of the tree; as a result, unnecessary computation is avoided. This procedure is continued until there is no remaining path to traverse.<br />
<br />
首先,FPF算法枚举并维护位于模式树根部的子图的所有匹配信息。然后,它通过在目标图中添加匹配边缘支持的一条边缘,在模式树中一一建立前一节点的子节点,然后通过在目标图中添加匹配边支持的一条边,逐个构建模式树中前一个节点的子节点,并尝试将以前关于匹配的所有信息拓展到新的子图(子节点)中。下一步,它判断当前模式的频率是否低于预定义的阈值。如果它低于阈值且保持向下闭包,则FPF算法会放弃该路径,而不会在树的此部分进一步遍历;这样就避免了不必要的计算。重复此过程,直到没有剩余可遍历的路径为止。<br />
<br />
<br />
The advantage of the algorithm is that it does not consider infrequent sub-graphs and tries to finish the enumeration process as soon as possible; therefore, it only spends time for promising nodes in the pattern tree and discards all other nodes. As an added bonus, the pattern tree notion permits FPF to be implemented and executed in a parallel manner since it is possible to traverse each path of the pattern tree independently. However, FPF is most useful for frequency concepts {{math|F<sub>2</sub>}} and {{math|F<sub>3</sub>}}, because downward closure is not applicable to {{math|F<sub>1</sub>}}. Nevertheless, the pattern tree is still practical for {{math|F<sub>1</sub>}} if the algorithm runs in parallel. Another advantage of the algorithm is that the implementation of this algorithm has no limitation on motif size, which makes it more amenable to improvements. The pseudocode of FPF (Mavisto) is shown below:<br />
<br />
该算法的优点是它不会考虑不频繁的子图,并尝试尽快完成枚举过程;因此,它只花时间在模式树中用于有希望的节点上,而放弃所有其他节点。还有一点额外的好处,模式树概念允许 FPF 以并行方式实现和执行,因为它可以独立地遍历模式树的每个路径。但是,FPF对于频率概念<math>F_{2}</math>和<math>F_{3}</math>最为有用,因为向下闭包不适用于<math>F_{1}</math>。尽管如此,如果算法并行运行,那么模式树对于<math>F_{1}</math>仍然是可行的。该算法的另一个优点是它的实现对模体大小没有限制,这使其更易于改进。FPF(Mavisto)的伪代码如下所示:<br />
<br />
<br />
{| class="wikitable"<br />
|-<br />
! Mavisto<br />
|-<br />
| '''Data:''' Graph {{math|G}}, target pattern size {{math|t}}, frequency concept {{math|F}}<br />
<br />
'''Result:''' Set {{math|R}} of patterns of size {{math|t}} with maximum frequency.<br />
|-<br />
| {{math|R ← φ}}, {{math|f<sub>max</sub> ← 0}}<br />
<br />
{{math|P ←}}start pattern {{math|p1}} of size 1<br />
<br />
{{math|M<sub>p<sub>1</sub></sub> ←}}all matches of {{math|p<sub>1</sub>}} in {{math|G}}<br />
<br />
'''While''' {{math|P &ne; φ}} '''do'''<br />
<br />
{{pad|1em}}{{math|P<sub>max</sub> ←}}select all patterns from {{math|P}} with maximum size.<br />
<br />
{{pad|1em}}{{math|P ←}} select pattern with maximum frequency from {{math|P<sub>max</sub>}}<br />
<br />
{{pad|1em}}{{math|Ε {{=}} ''ExtensionLoop''(G, p, M<sub>p</sub>)}}<br />
<br />
{{pad|1em}}'''Foreach''' pattern {{math|p &isin; E}}<br />
<br />
{{pad|2em}}'''If''' {{math|F {{=}} F<sub>1</sub>}} '''then''' {{math|f ← ''size''(M<sub>p</sub>)}}<br />
<br />
{{pad|2em}}'''Else''' {{math|f ←}} ''Maximum Independent set''{{math|(F, M<sub>p</sub>)}}<br />
<br />
{{pad|2em}}'''End'''<br />
<br />
{{pad|2em}}'''If''' {{math|''size''(p) {{=}} t}} '''then'''<br />
<br />
{{pad|3em}}'''If''' {{math|f {{=}} f<sub>max</sub>}} '''then''' {{math|R ← R ⋃ {p}}}<br />
<br />
{{pad|3em}}'''Else if''' {{math|f > f<sub>max</sub>}} '''then''' {{math|R ← {p}}}; {{math|f<sub>max</sub> ← f}}<br />
<br />
{{pad|3em}}'''End'''<br />
<br />
{{pad|2em}}'''Else'''<br />
<br />
{{pad|3em}}'''If''' {{math|F {{=}} F<sub>1</sub>}} '''or''' {{math|f &ge; f<sub>max</sub>}} '''then''' {{math|P ← P ⋃ {p}}}<br />
<br />
{{pad|3em}}'''End'''<br />
<br />
{{pad|2em}}'''End'''<br />
<br />
{{pad|1em}}'''End'''<br />
<br />
'''End'''<br />
|}<br />
<br />
<br />
{|class="wikitable"<br />
|+ Mavisto<br />
|-<br />
!rowspan="1"|数据: 图 <math>G</math>, 目标模式规模 <math>t</math>, 频率概念 <math>F</math>。<br><br />
结果: 以最大频率设置大小为 <math>t</math>的模式 <math>R</math>.<br><br />
|-<br />
|rowspan="20"| <math>R \leftarrow \Phi , f_{max}\leftarrow 0</math><br><br />
<math>P \leftarrow</math> 开始于大小为1的模式 <math>p_{1}</math><br />
<br />
<math>M_{p_{1}} \leftarrow </math> 图 <math>G</math> 中模式 <math>p_{1}</math> 的所有匹配<br />
<br />
当 <math>P \neq \Phi </math> 时,执行:<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;<math>P_{max} \leftarrow</math> 从 <math>P</math> 中选择最大规模的所有模式<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;<math>P\leftarrow</math> 从 <math>P_{max}</math> 中选择最大频率的模式<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;<math>E = ExtensionLoop(G, p, M_{p})</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;对于 <math>p \in E </math> 的所有模式:<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>F = F_{1}</math> ,那么 <math>f \leftarrow size(M_{p})</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他<math>f \leftarrow</math> 最大独立集 <math>(F, M_{p})</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>size(p) = t</math> ,那么<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>f = f_{max}</math> ,那么 <math>R \leftarrow R \cup \{p\}</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他 如果 <math>f > f_{max}</math> ,那么 <math>R \leftarrow \{p\}</math>; <math>f_{max} \leftarrow f</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;其他<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;如果 <math>F = F_{1} or f \geq f_{max}</math> ,那么 <math> P \leftarrow P \cup \{p\}</math><br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
&nbsp;&nbsp;&nbsp;&nbsp;结束<br />
<br />
结束<br />
|}<br />
<br />
===ESU (FANMOD)===<br />
The sampling bias of Kashtan ''et al.'' <ref name="kas1" /> provided great impetus for designing better algorithms for the NM discovery problem. Although Kashtan ''et al.'' tried to settle this drawback by means of a weighting scheme, this method imposed an undesired overhead on the running time as well a more complicated implementation. This tool is one of the most useful ones, as it supports visual options and also is an efficient algorithm with respect to time. But, it has a limitation on motif size as it does not allow searching for motifs of size 9 or higher because of the way the tool is implemented.<br />
<br />
Wernicke <ref name="wer1" /> introduced an algorithm named ''RAND-ESU'' that provides a significant improvement over ''mfinder''.<ref name="kas1" /> This algorithm, which is based on the exact enumeration algorithm ''ESU'', has been implemented as an application called ''FANMOD''.<ref name="wer1" /> ''RAND-ESU'' is a NM discovery algorithm applicable for both directed and undirected networks, effectively exploits an unbiased node sampling throughout the network, and prevents overcounting sub-graphs more than once. Furthermore, ''RAND-ESU'' uses a novel analytical approach called ''DIRECT'' for determining sub-graph significance instead of using an ensemble of random networks as a Null-model. The ''DIRECT'' method estimates the sub-graph concentration without explicitly generating random networks.<ref name="wer1" /> Empirically, the DIRECT method is more efficient in comparison with the random network ensemble in case of sub-graphs with a very low concentration; however, the classical Null-model is faster than the ''DIRECT'' method for highly concentrated sub-graphs.<ref name="mil1" /><ref name="wer1" /> In the following, we detail the ''ESU'' algorithm and then we show how this exact algorithm can be modified efficiently to ''RAND-ESU'' that estimates sub-graphs concentrations.<br />
<br />
The algorithms ''ESU'' and ''RAND-ESU'' are fairly simple, and hence easy to implement. ''ESU'' first finds the set of all induced sub-graphs of size {{math|k}}, let {{math|S<sub>k</sub>}} be this set. ''ESU'' can be implemented as a recursive function; the running of this function can be displayed as a tree-like structure of depth {{math|k}}, called the ESU-Tree (see figure). Each of the ESU-Tree nodes indicate the status of the recursive function that entails two consecutive sets SUB and EXT. SUB refers to nodes in the target network that are adjacent and establish a partial sub-graph of size {{math|{{!}}SUB{{!}} ≤ k}}. If {{math|{{!}}SUB{{!}} {{=}} k}}, the algorithm has found an induced complete sub-graph, so {{math|S<sub>k</sub> {{=}} SUB ∪ S<sub>k</sub>}}. However, if {{math|{{!}}SUB{{!}} < k}}, the algorithm must expand SUB to achieve cardinality {{math|k}}. This is done by the EXT set that contains all the nodes that satisfy two conditions: First, each of the nodes in EXT must be adjacent to at least one of the nodes in SUB; second, their numerical labels must be larger than the label of first element in SUB. The first condition makes sure that the expansion of SUB nodes yields a connected graph and the second condition causes ESU-Tree leaves (see figure) to be distinct; as a result, it prevents overcounting. Note that, the EXT set is not a static set, so in each step it may expand by some new nodes that do not breach the two conditions. The next step of ESU involves classification of sub-graphs placed in the ESU-Tree leaves into non-isomorphic size-{{math|k}} graph classes; consequently, ESU determines sub-graphs frequencies and concentrations. This stage has been implemented simply by employing McKay's ''nauty'' algorithm,<ref name="mck1">{{cite journal |author=McKay BD |title=Practical graph isomorphism |journal=Congressus Numerantium |year=1981 |volume=30 |pages=45–87|bibcode=2013arXiv1301.1493M |arxiv=1301.1493 }}</ref><ref name="mck2">{{cite journal |author=McKay BD |title=Isomorph-free exhaustive generation |journal=Journal of Algorithms |year=1998 |volume=26 |issue=2 |pages=306–324 |doi=10.1006/jagm.1997.0898}}</ref> which classifies each sub-graph by performing a graph isomorphism test. Therefore, ESU finds the set of all induced {{math|k}}-size sub-graphs in a target graph by a recursive algorithm and then determines their frequency using an efficient tool.<br />
<br />
The procedure of implementing ''RAND-ESU'' is quite straightforward and is one of the main advantages of ''FANMOD''. One can change the ''ESU'' algorithm to explore just a portion of the ESU-Tree leaves by applying a probability value {{math|0 ≤ p<sub>d</sub> ≤ 1}} for each level of the ESU-Tree and oblige ''ESU'' to traverse each child node of a node in level {{math|d-1}} with probability {{math|p<sub>d</sub>}}. This new algorithm is called ''RAND-ESU''. Evidently, when {{math|p<sub>d</sub> {{=}} 1}} for all levels, ''RAND-ESU'' acts like ''ESU''. For {{math|p<sub>d</sub> {{=}} 0}} the algorithm finds nothing. Note that, this procedure ensures that the chances of visiting each leaf of the ESU-Tree are the same, resulting in ''unbiased'' sampling of sub-graphs through the network. The probability of visiting each leaf is {{math|∏<sub>d</sub>p<sub>d</sub>}} and this is identical for all of the ESU-Tree leaves; therefore, this method guarantees unbiased sampling of sub-graphs from the network. Nonetheless, determining the value of {{math|p<sub>d</sub>}} for {{math|1 ≤ d ≤ k}} is another issue that must be determined manually by an expert to get precise results of sub-graph concentrations.<ref name="cir1" /> While there is no lucid prescript for this matter, the Wernicke provides some general observations that may help in determining p_d values. In summary, ''RAND-ESU'' is a very fast algorithm for NM discovery in the case of induced sub-graphs supporting unbiased sampling method. Although, the main ''ESU'' algorithm and so the ''FANMOD'' tool is known for discovering induced sub-graphs, there is trivial modification to ''ESU'' which makes it possible for finding non-induced sub-graphs, too. The pseudo code of ''ESU (FANMOD)'' is shown below:<br />
<br />
[[File:ESU-Tree.jpg|thumb|(a) ''A target graph of size 5'', (b) ''the ESU-tree of depth k that is associated to the extraction of sub-graphs of size 3 in the target graph''. Leaves correspond to set S3 or all of the size-3 induced sub-graphs of the target graph (a). Nodes in the ESU-tree include two adjoining sets, the first set contains adjacent nodes called SUB and the second set named EXT holds all nodes that are adjacent to at least one of the SUB nodes and where their numerical labels are larger than the SUB nodes labels. The EXT set is utilized by the algorithm to expand a SUB set until it reaches a desired sub-graph size that are placed at the lowest level of ESU-Tree (or its leaves).]]<br />
<br />
{| class="wikitable"<br />
|-<br />
! Enumeration of ESU (FANMOD)<br />
|-<br />
|'''''EnumerateSubgraphs(G,k)'''''<br />
<br />
'''Input:''' A graph {{math|G {{=}} (V, E)}} and an integer {{math|1 ≤ k ≤ {{!}}V{{!}}}}.<br />
<br />
'''Output:''' All size-{{math|k}} subgraphs in {{math|G}}.<br />
<br />
'''for each''' vertex {{math|v ∈ V}} '''do'''<br />
<br />
{{pad|2em}}{{math|VExtension ← {u ∈ N({v}) {{!}} u > v}}}<br />
<br />
{{pad|2em}}'''call''' {{math|''ExtendSubgraph''({v}, VExtension, v)}}<br />
<br />
'''endfor'''<br />
|-<br />
|'''''ExtendSubgraph(VSubgraph, VExtension, v)'''''<br />
<br />
'''if''' {{math|{{!}}VSubgraph{{!}} {{=}} k}} '''then''' output {{math|G[VSubgraph]}} and '''return'''<br />
<br />
'''while''' {{math|VExtension ≠ ∅}} '''do'''<br />
<br />
{{pad|2em}}Remove an arbitrarily chosen vertex {{math|w}} from {{math|VExtension}}<br />
<br />
{{pad|2em}}{{math|VExtension&prime; ← VExtension ∪ {u ∈ N<sub>excl</sub>(w, VSubgraph) {{!}} u > v}}}<br />
<br />
{{pad|2em}}'''call''' {{math|''ExtendSubgraph''(VSubgraph ∪ {w}, VExtension&prime;, v)}}<br />
<br />
'''return'''<br />
|}<br />
<br />
===NeMoFinder===<br />
Chen ''et al.'' <ref name="che1">{{cite conference |vauthors=Chen J, Hsu W, Li Lee M, etal |title=NeMoFinder: dissecting genome-wide protein-protein interactions with meso-scale network motifs |conference=the 12th ACM SIGKDD international conference on Knowledge discovery and data mining |year=2006 |location=Philadelphia, Pennsylvania, USA |pages=106–115}}</ref> introduced a new NM discovery algorithm called ''NeMoFinder'', which adapts the idea in ''SPIN'' <ref name="hua1">{{cite conference |vauthors=Huan J, Wang W, Prins J, etal |title=SPIN: mining maximal frequent sub-graphs from graph databases |conference=the 10th ACM SIGKDD international conference on Knowledge discovery and data mining |year=2004 |pages=581–586}}</ref> to extract frequent trees and after that expands them into non-isomorphic graphs.<ref name="cir1" /> ''NeMoFinder'' utilizes frequent size-n trees to partition the input network into a collection of size-{{math|n}} graphs, afterward finding frequent size-n sub-graphs by expansion of frequent trees edge-by-edge until getting a complete size-{{math|n}} graph {{math|K<sub>n</sub>}}. The algorithm finds NMs in undirected networks and is not limited to extracting only induced sub-graphs. Furthermore, ''NeMoFinder'' is an exact enumeration algorithm and is not based on a sampling method. As Chen ''et al.'' claim, ''NeMoFinder'' is applicable for detecting relatively large NMs, for instance, finding NMs up to size-12 from the whole ''S. cerevisiae'' (yeast) PPI network as the authors claimed.<ref name="uet1">{{cite journal |vauthors=Uetz P, Giot L, Cagney G, etal |title=A comprehensive analysis of protein-protein interactions in Saccharomyces cerevisiae |journal=Nature |year=2000 |volume=403 |issue=6770 |pages=623–627 |doi=10.1038/35001009 |pmid=10688190|bibcode=2000Natur.403..623U }}</ref><br />
<br />
''NeMoFinder'' consists of three main steps. First, finding frequent size-{{math|n}} trees, then utilizing repeated size-n trees to divide the entire network into a collection of size-{{math|n}} graphs, finally, performing sub-graph join operations to find frequent size-n sub-graphs.<ref name="che1" /> In the first step, the algorithm detects all non-isomorphic size-{{math|n}} trees and mappings from a tree to the network. In the second step, the ranges of these mappings are employed to partition the network into size-n graphs. Up to this step, there is no distinction between ''NeMoFinder'' and an exact enumeration method. However, a large portion of non-isomorphic size-n graphs still remain. ''NeMoFinder'' exploits a heuristic to enumerate non-tree size-n graphs by the obtained information from the preceding steps. The main advantage of the algorithm is in the third step, which generates candidate sub-graphs from previously enumerated sub-graphs. This generation of new size-{{math|n}} sub-graphs is done by joining each previous sub-graph with derivative sub-graphs from itself called ''cousin sub-graphs''. These new sub-graphs contain one additional edge in comparison to the previous sub-graphs. However, there exist some problems in generating new sub-graphs: There is no clear method to derive cousins from a graph, joining a sub-graph with its cousins leads to redundancy in generating particular sub-graph more than once, and cousin determination is done by a canonical representation of the adjacency matrix which is not closed under join operation. ''NeMoFinder'' is an efficient network motif finding algorithm for motifs up to size 12 only for protein-protein interaction networks, which are presented as undirected graphs. And it is not able to work on directed networks which are so important in the field of complex and biological networks. The pseudocode of ''NeMoFinder'' is shown below:<br />
<br />
{| class="wikitable"<br />
|-<br />
! NeMoFinder<br />
|-<br />
|'''Input:'''<br />
<br />
{{math|G}} - PPI network;<br />
<br />
{{math|N}} - Number of randomized networks;<br />
<br />
{{math|K}} - Maximal network motif size;<br />
<br />
{{math|F}} - Frequency threshold;<br />
<br />
{{math|S}} - Uniqueness threshold;<br />
<br />
'''Output:'''<br />
<br />
{{math|U}} - Repeated and unique network motif set;<br />
<br />
{{math|D ← ∅}};<br />
<br />
'''for''' motif-size {{math|k}} '''from''' 3 '''to''' {{math|K}} '''do'''<br />
<br />
{{pad|1em}}{{math|T ← ''FindRepeatedTrees''(k)}};<br />
<br />
{{pad|1em}}{{math|GD<sub>k</sub> ← ''GraphPartition''(G, T)}}<br />
<br />
{{pad|1em}}{{math|D ← D ∪ T}};<br />
<br />
{{pad|1em}}{{math|D&prime; ← T}};<br />
<br />
{{pad|1em}}{{math|i ← k}};<br />
<br />
{{pad|1em}}'''while''' {{math|D&prime; ≠ ∅}} '''and''' {{math|i ≤ k &times; (k - 1) / 2}} '''do'''<br />
<br />
{{pad|2em}}{{math|D&prime; ← ''FindRepeatedGraphs''(k, i, D&prime;)}};<br />
<br />
{{pad|2em}}{{math|D ← D ∪ D&prime;}};<br />
<br />
{{pad|2em}}{{math|i ← i + 1}};<br />
<br />
{{pad|1em}}'''end while'''<br />
<br />
'''end for'''<br />
<br />
'''for''' counter {{math|i}} '''from''' 1 '''to''' {{math|N}} '''do'''<br />
<br />
{{pad|1em}}{{math|G<sub>rand</sub> ← ''RandomizedNetworkGeneration''()}};<br />
<br />
{{pad|1em}}'''for each''' {{math|g ∈ D}} '''do'''<br />
<br />
{{pad|2em}}{{math|''GetRandFrequency''(g, G<sub>rand</sub>)}};<br />
<br />
{{pad|1em}}'''end for'''<br />
<br />
'''end for'''<br />
<br />
{{math|U ← ∅}};<br />
<br />
'''for each''' {{math|g ∈ D}} '''do'''<br />
<br />
{{pad|1em}}{{math|s ← ''GetUniqunessValue''(g)}};<br />
<br />
{{pad|1em}}'''if''' {{math|s ≥ S}} '''then'''<br />
<br />
{{pad|2em}}{{math|U ← U ∪ {g}}};<br />
<br />
{{pad|1em}}'''end if'''<br />
<br />
'''end for'''<br />
<br />
'''return''' {{math|U}};<br />
|}<br />
<br />
===Grochow–Kellis===<br />
Grochow and Kellis <ref name="gro1">{{cite conference|vauthors=Grochow JA, Kellis M |title=Network Motif Discovery Using Sub-graph Enumeration and Symmetry-Breaking |conference=RECOMB |year=2007 |pages=92–106| doi=10.1007/978-3-540-71681-5_7| url=http://www.cs.colorado.edu/~jgrochow/Grochow_Kellis_RECOMB_07_Network_Motifs.pdf}}</ref> proposed an ''exact'' algorithm for enumerating sub-graph appearances. The algorithm is based on a ''motif-centric'' approach, which means that the frequency of a given sub-graph,called the ''query graph'', is exhaustively determined by searching for all possible mappings from the query graph into the larger network. It is claimed <ref name="gro1" /> that a ''motif-centric'' method in comparison to ''network-centric'' methods has some beneficial features. First of all it avoids the increased complexity of sub-graph enumeration. Also, by using mapping instead of enumerating, it enables an improvement in the isomorphism test. To improve the performance of the algorithm, since it is an inefficient exact enumeration algorithm, the authors introduced a fast method which is called ''symmetry-breaking conditions''. During straightforward sub-graph isomorphism tests, a sub-graph may be mapped to the same sub-graph of the query graph multiple times. In the Grochow–Kellis (GK) algorithm symmetry-breaking is used to avoid such multiple mappings. Here we introduce the GK algorithm and the symmetry-breaking condition which eliminates redundant isomorphism tests.<br />
<br />
[[File:Automorphisms of a subgraph.jpg|thumb|(a) ''graph G'', (b) ''illustration of all automorphisms of G that is showed in (a)''. From set AutG we can obtain a set of symmetry-breaking conditions of G given by SymG in (c). Only the first mapping in AutG satisfies the SynG conditions; as a result, by applying SymG in the Isomorphism Extension module the algorithm only enumerate each match-able sub-graph in the network to G once. Note that SynG is not necessarily a unique set for an arbitrary graph G.]]<br />
<br />
The GK algorithm discovers the whole set of mappings of a given query graph to the network in two major steps. It starts with the computation of symmetry-breaking conditions of the query graph. Next, by means of a branch-and-bound method, the algorithm tries to find every possible mapping from the query graph to the network that meets the associated symmetry-breaking conditions. An example of the usage of symmetry-breaking conditions in GK algorithm is demonstrated in figure.<br />
<br />
As it is mentioned above, the symmetry-breaking technique is a simple mechanism that precludes spending time finding a sub-graph more than once due to its symmetries.<ref name="gro1" /><ref name="gro2">{{cite conference|author=Grochow JA |title=On the structure and evolution of protein interaction networks |conference=Thesis M. Eng., Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science|year=2006| url=http://www.cs.toronto.edu/~jgrochow/Grochow_MIT_Masters_06_PPI_Networks.pdf}}</ref> Note that, computing symmetry-breaking conditions requires finding all automorphisms of a given query graph. Even though, there is no efficient (or polynomial time) algorithm for the graph automorphism problem, this problem can be tackled efficiently in practice by McKay's tools.<ref name="mck1" /><ref name="mck2" /> As it is claimed, using symmetry-breaking conditions in NM detection lead to save a great deal of running time. Moreover, it can be inferred from the results in <ref name="gro1" /><ref name="gro2" /> that using the symmetry-breaking conditions results in high efficiency particularly for directed networks in comparison to undirected networks. The symmetry-breaking conditions used in the GK algorithm are similar to the restriction which ''ESU'' algorithm applies to the labels in EXT and SUB sets. In conclusion, the GK algorithm computes the exact number of appearance of a given query graph in a large complex network and exploiting symmetry-breaking conditions improves the algorithm performance. Also, GK algorithm is one of the known algorithms having no limitation for motif size in implementation and potentially it can find motifs of any size.<br />
<br />
===Color-coding approach===<br />
Most algorithms in the field of NM discovery are used to find induced sub-graphs of a network. In 2008, Noga Alon ''et al.'' <ref name="alo1">{{cite journal|author1=Alon N |author2=Dao P |author3=Hajirasouliha I |author4=Hormozdiari F |author5=Sahinalp S.C |title=Biomolecular network motif counting and discovery by color coding |journal=Bioinformatics |year=2008 |volume=24 |issue=13 |pages=i241–i249 |doi=10.1093/bioinformatics/btn163|pmid=18586721 |pmc=2718641 }}</ref> introduced an approach for finding non-induced sub-graphs too. Their technique works on undirected networks such as PPI ones. Also, it counts non-induced trees and bounded treewidth sub-graphs. This method is applied for sub-graphs of size up to 10.<br />
<br />
This algorithm counts the number of non-induced occurrences of a tree {{math|T}} with {{math|k {{=}} O(logn)}} vertices in a network {{math|G}} with {{math|n}} vertices as follows:<br />
<br />
# '''Color coding.''' Color each vertex of input network G independently and uniformly at random with one of the {{math|k}} colors.<br />
# '''Counting.''' Apply a dynamic programming routine to count the number of non-induced occurrences of {{math|T}} in which each vertex has a unique color. For more details on this step, see.<ref name="alo1" /><br />
# Repeat the above two steps {{math|O(e<sup>k</sup>)}} times and add up the number of occurrences of {{math|T}} to get an estimate on the number of its occurrences in {{math|G}}.<br />
<br />
As available PPI networks are far from complete and error free, this approach is suitable for NM discovery for such networks. As Grochow–Kellis Algorithm and this one are the ones popular for non-induced sub-graphs, it is worth to mention that the algorithm introduced by Alon ''et al.'' is less time-consuming than the Grochow–Kellis Algorithm.<ref name="alo1" /><br />
<br />
===MODA===<br />
Omidi ''et al.'' <ref name="omi1">{{cite journal|vauthors=Omidi S, Schreiber F, Masoudi-Nejad A |title=MODA: an efficient algorithm for network motif discovery in biological networks |journal=Genes Genet Syst |year=2009 |volume=84 |issue=5 |pages=385–395 |doi=10.1266/ggs.84.385|pmid=20154426 |doi-access=free }}</ref> introduced a new algorithm for motif detection named ''MODA'' which is applicable for induced and non-induced NM discovery in undirected networks. It is based on the motif-centric approach discussed in the Grochow–Kellis algorithm section. It is very important to distinguish motif-centric algorithms such as MODA and GK algorithm because of their ability to work as query-finding algorithms. This feature allows such algorithms to be able to find a single motif query or a small number of motif queries (not all possible sub-graphs of a given size) with larger sizes. As the number of possible non-isomorphic sub-graphs increases exponentially with sub-graph size, for large size motifs (even larger than 10), the network-centric algorithms, those looking for all possible sub-graphs, face a problem. Although motif-centric algorithms also have problems in discovering all possible large size sub-graphs, but their ability to find small numbers of them is sometimes a significant property.<br />
<br />
Using a hierarchical structure called an ''expansion tree'', the ''MODA'' algorithm is able to extract NMs of a given size systematically and similar to ''FPF'' that avoids enumerating unpromising sub-graphs; ''MODA'' takes into consideration potential queries (or candidate sub-graphs) that would result in frequent sub-graphs. Despite the fact that ''MODA'' resembles ''FPF'' in using a tree like structure, the expansion tree is applicable merely for computing frequency concept {{math|F<sub>1</sub>}}. As we will discuss next, the advantage of this algorithm is that it does not carry out the sub-graph isomorphism test for ''non-tree'' query graphs. Additionally, it utilizes a sampling method in order to speed up the running time of the algorithm.<br />
<br />
Here is the main idea: by a simple criterion one can generalize a mapping of a k-size graph into the network to its same size supergraphs. For example, suppose there is mapping {{math|f(G)}} of graph {{math|G}} with {{math|k}} nodes into the network and we have a same size graph {{math|G&prime;}} with one more edge {{math|&langu, v&rang;}}; {{math|f<sub>G</sub>}} will map {{math|G&prime;}} into the network, if there is an edge {{math|&lang;f<sub>G</sub>(u), f<sub>G</sub>(v)&rang;}} in the network. As a result, we can exploit the mapping set of a graph to determine the frequencies of its same order supergraphs simply in {{math|O(1)}} time without carrying out sub-graph isomorphism testing. The algorithm starts ingeniously with minimally connected query graphs of size k and finds their mappings in the network via sub-graph isomorphism. After that, with conservation of the graph size, it expands previously considered query graphs edge-by-edge and computes the frequency of these expanded graphs as mentioned above. The expansion process continues until reaching a complete graph {{math|K<sub>k</sub>}} (fully connected with {{math|{{frac|k(k-1)|2}}}} edge).<br />
<br />
As discussed above, the algorithm starts by computing sub-tree frequencies in the network and then expands sub-trees edge by edge. One way to implement this idea is called the expansion tree {{math|T<sub>k</sub>}} for each {{math|k}}. Figure shows the expansion tree for size-4 sub-graphs. {{math|T<sub>k</sub>}} organizes the running process and provides query graphs in a hierarchical manner. Strictly speaking, the expansion tree {{math|T<sub>k</sub>}} is simply a [[directed acyclic graph]] or DAG, with its root number {{math|k}} indicating the graph size existing in the expansion tree and each of its other nodes containing the adjacency matrix of a distinct {{math|k}}-size query graph. Nodes in the first level of {{math|T<sub>k</sub>}} are all distinct {{math|k}}-size trees and by traversing {{math|T<sub>k</sub>}} in depth query graphs expand with one edge at each level. A query graph in a node is a sub-graph of the query graph in a node's child with one edge difference. The longest path in {{math|T<sub>k</sub>}} consists of {{math|(k<sup>2</sup>-3k+4)/2}} edges and is the path from the root to the leaf node holding the complete graph. Generating expansion trees can be done by a simple routine which is explained in.<ref name="omi1" /><br />
<br />
''MODA'' traverses {{math|T<sub>k</sub>}} and when it extracts query trees from the first level of {{math|T<sub>k</sub>}} it computes their mapping sets and saves these mappings for the next step. For non-tree queries from {{math|T<sub>k</sub>}}, the algorithm extracts the mappings associated with the parent node in {{math|T<sub>k</sub>}} and determines which of these mappings can support the current query graphs. The process will continue until the algorithm gets the complete query graph. The query tree mappings are extracted using the Grochow–Kellis algorithm. For computing the frequency of non-tree query graphs, the algorithm employs a simple routine that takes {{math|O(1)}} steps. In addition, ''MODA'' exploits a sampling method where the sampling of each node in the network is linearly proportional to the node degree, the probability distribution is exactly similar to the well-known Barabási-Albert preferential attachment model in the field of complex networks.<ref name="bar1">{{cite journal|vauthors=Barabasi AL, Albert R |title=Emergence of scaling in random networks |journal=Science |year=1999 |volume=286 |issue=5439 |pages=509–512 |doi=10.1126/science.286.5439.509 |pmid=10521342|bibcode=1999Sci...286..509B |arxiv=cond-mat/9910332 }}</ref> This approach generates approximations; however, the results are almost stable in different executions since sub-graphs aggregate around highly connected nodes.<ref name="vaz1">{{cite journal |vauthors=Vázquez A, Dobrin R, Sergi D, etal |title=The topological relationship between the large-scale attributes and local interaction patterns of complex networks |journal=PNAS |year=2004 |volume=101 |issue=52 |pages=17940–17945 |doi=10.1073/pnas.0406024101|pmid=15598746 |pmc=539752 |bibcode=2004PNAS..10117940V |arxiv=cond-mat/0408431 }}</ref> The pseudocode of ''MODA'' is shown below:<br />
<br />
[[File:Expansion Tree.jpg|thumb|''Illustration of the expansion tree T4 for 4-node query graphs''. At the first level, there are non-isomorphic k-size trees and at each level, an edge is added to the parent graph to form a child graph. In the second level, there is a graph with two alternative edges that is shown by a dashed red edge. In fact, this node represents two expanded graphs that are isomorphic.<ref name="omi1" />]]<br />
<br />
{| class="wikitable"<br />
|-<br />
! MODA<br />
|-<br />
|'''Input:''' {{math|G}}: Input graph, {{math|k}}: sub-graph size, {{math|Δ}}: threshold value<br />
<br />
'''Output:''' Frequent Subgraph List: List of all frequent {{math|k}}-size sub-graphs<br />
<br />
'''Note:''' {{math|F<sub>G</sub>}}: set of mappings from {{math|G}} in the input graph {{math|G}}<br />
<br />
'''fetch''' {{math|T<sub>k</sub>}}<br />
<br />
'''do'''<br />
<br />
{{pad|1em}}{{math|G&prime; {{=}} ''Get-Next-BFS''(T<sub>k</sub>)}} // {{math|G&prime;}} is a query graph<br />
<br />
{{pad|1em}}if {{math|{{!}}E(G&prime;){{!}} {{=}} (k – 1)}}<br />
<br />
{{pad|1em}}'''call''' {{math|''Mapping-Module''(G&prime;, G)}}<br />
<br />
{{pad|1em}}'''else'''<br />
<br />
{{pad|2em}}'''call''' {{math|''Enumerating-Module''(G&prime;, G, T<sub>k</sub>)}}<br />
<br />
{{pad|1em}}'''end if'''<br />
<br />
{{pad|1em}}'''save''' {{math|F<sub>2</sub>}}<br />
<br />
{{pad|1em}}'''if''' {{math|{{!}}F<sub>G</sub>{{!}} > Δ}} '''then'''<br />
<br />
{{pad|2em}}add {{math|G&prime;}} into Frequent Subgraph List<br />
<br />
{{pad|1em}}'''end if'''<br />
<br />
'''Until''' {{math|{{!}}E(G'){{!}} {{=}} (k – 1)/2}}<br />
<br />
'''return''' Frequent Subgraph List<br />
|}<br />
<br />
===Kavosh===<br />
A recently introduced algorithm named ''Kavosh'' <ref name="kash1">{{cite journal|vauthors=Kashani ZR, Ahrabian H, Elahi E, Nowzari-Dalini A, Ansari ES, Asadi S, Mohammadi S, Schreiber F, Masoudi-Nejad A |title=Kavosh: a new algorithm for finding network motifs |journal=BMC Bioinformatics |year=2009 |volume=10 |issue=318|pages=318 |doi=10.1186/1471-2105-10-318 |pmid=19799800 |pmc=2765973}} </ref> aims at improved main memory usage. ''Kavosh'' is usable to detect NM in both directed and undirected networks. The main idea of the enumeration is similar to the ''GK'' and ''MODA'' algorithms, which first find all {{math|k}}-size sub-graphs that a particular node participated in, then remove the node, and subsequently repeat this process for the remaining nodes.<ref name="kash1" /><br />
<br />
For counting the sub-graphs of size {{math|k}} that include a particular node, trees with maximum depth of k, rooted at this node and based on neighborhood relationship are implicitly built. Children of each node include both incoming and outgoing adjacent nodes. To descend the tree, a child is chosen at each level with the restriction that a particular child can be included only if it has not been included at any upper level. After having descended to the lowest level possible, the tree is again ascended and the process is repeated with the stipulation that nodes visited in earlier paths of a descendant are now considered unvisited nodes. A final restriction in building trees is that all children in a particular tree must have numerical labels larger than the label of the root of the tree. The restrictions on the labels of the children are similar to the conditions which ''GK'' and ''ESU'' algorithm use to avoid overcounting sub-graphs.<br />
<br />
The protocol for extracting sub-graphs makes use of the compositions of an integer. For the extraction of sub-graphs of size {{math|k}}, all possible compositions of the integer {{math|k-1}} must be considered. The compositions of {{math|k-1}} consist of all possible manners of expressing {{math|k-1}} as a sum of positive integers. Summations in which the order of the summands differs are considered distinct. A composition can be expressed as {{math|k<sub>2</sub>,k<sub>3</sub>,…,k<sub>m</sub>}} where {{math|k<sub>2</sub> + k<sub>3</sub> + … + k<sub>m</sub> {{=}} k-1}}. To count sub-graphs based on the composition, {{math|k<sub>i</sub>}} nodes are selected from the {{math|i}}-th level of the tree to be nodes of the sub-graphs ({{math|i {{=}} 2,3,…,m}}). The {{math|k-1}} selected nodes along with the node at the root define a sub-graph within the network. After discovering a sub-graph involved as a match in the target network, in order to be able to evaluate the size of each class according to the target network, ''Kavosh'' employs the ''nauty'' algorithm <ref name="mck1" /><ref name="mck2" /> in the same way as ''FANMOD''. The enumeration part of Kavosh algorithm is shown below:<br />
<br />
{| class="wikitable"<br />
|-<br />
! Enumeration of Kavosh<br />
|-<br />
|'''''Enumerate_Vertex(G, u, S, Remainder, i)'''''<br />
<br />
'''Input:''' {{math|G}}: Input graph<br><br />
{{pad|3em}}{{math|u}}: Root vertex<br><br />
{{pad|3em}}{{math|S}}: selection ({{math|S {{=}} { S<sub>0</sub>,S<sub>1</sub>,...,S<sub>k-1</sub>}}} is an array of the set of all {{math|S<sub>i</sub>}})<br><br />
{{pad|3em}}{{math|Remainder}}: number of remaining vertices to be selected<br><br />
{{pad|3em}}{{math|i}}: Current depth of the tree.<br><br />
'''Output:''' all {{math|k}}-size sub-graphs of graph {{math|G}} rooted in {{math|u}}.<br />
<br />
'''if''' {{math|Remainder {{=}} 0}} '''then'''<br><br />
{{pad|1em}}'''return'''<br><br />
'''else'''<br><br />
{{pad|1em}}{{math|ValList ← ''Validate''(G, S<sub>i-1</sub>, u)}}<br><br />
{{pad|1em}}{{math|n<sub>i</sub> ← ''Min''({{!}}ValList{{!}}, Remainder)}}<br><br />
{{pad|1em}}'''for''' {{math|k<sub>i</sub> {{=}} 1}} '''to''' {{math|n<sub>i</sub>}} '''do'''<br><br />
{{pad|2em}}{{math|C ← ''Initial_Comb''(ValList, k<sub>i</sub>)}}<br><br />
{{pad|2em}}(Make the first vertex combination selection according)<br><br />
{{pad|2em}}'''repeat'''<br><br />
{{pad|3em}}{{math|S<sub>i</sub> ← C}}<br><br />
{{pad|3em}}{{math|''Enumerate_Vertex''(G, u, S, Remainder-k<sub>i</sub>, i+1)}}<br><br />
{{pad|3em}}{{math|''Next_Comb''(ValList, k<sub>i</sub>)}}<br><br />
{{pad|3em}}(Make the next vertex combination selection according)<br><br />
{{pad|2em}}'''until''' {{math|C {{=}} NILL}}<br><br />
{{pad|2em}}'''end for'''<br><br />
{{pad|1em}}'''for each''' {{math|v ∈ ValList}} '''do'''<br><br />
{{pad|2em}}{{math|Visited[v] ← false}}<br><br />
{{pad|1em}}'''end for'''<br><br />
'''end if'''<br />
|-<br />
|'''''Validate(G, Parents, u)'''''<br><br />
'''Input:''' {{math|G}}: input graph, {{math|Parents}}: selected vertices of last layer, {{math|u}}: Root vertex.<br><br />
'''Output:''' Valid vertices of the current level.<br />
<br />
{{math|ValList ← NILL}}<br><br />
'''for each''' {{math|v ∈ Parents}} '''do'''<br><br />
{{pad|1em}}'''for each''' {{math|w ∈ Neighbor[u]}} '''do'''<br><br />
{{pad|2em}}'''if''' {{math|label[u] < label[w]}} '''AND NOT''' {{math|Visited[w]}} '''then'''<br><br />
{{pad|3em}}{{math|Visited[w] ← true}}<br><br />
{{pad|3em}}{{math|ValList {{=}} ValList + w}}<br><br />
{{pad|2em}}'''end if'''<br><br />
{{pad|1em}}'''end for'''<br><br />
'''end for'''<br><br />
'''return''' {{math|ValList}}<br><br />
|}<br />
<br />
Recently a ''Cytoscape'' plugin called ''CytoKavosh'' <ref name="mas2">{{cite journal|author1=Ali Masoudi-Nejad |author2=Mitra Anasariola |author3=Ali Salehzadeh-Yazdi |author4=Sahand Khakabimamaghani |title=CytoKavosh: a Cytoscape Plug-in for Finding Network Motifs in Large Biological Networks |journal=PLoS ONE |volume=7 |issue=8 |pages=e43287 |year=2012 |doi=10.1371/journal.pone.0043287|pmid=22952659 |pmc=3430699 |bibcode=2012PLoSO...743287M }} </ref> is developed for this software. It is available via ''Cytoscape'' web page [http://apps.cytoscape.org/apps/cytokavosh].<br />
<br />
===G-Tries===<br />
2010年, Pedro Ribeiro 和 Fernando Silva 提出了一个叫做''g-trie''的新数据结构,用来存储一组子图。<ref name="rib1">{{cite conference|vauthors=Ribeiro P, Silva F |title=G-Tries: an efficient data structure for discovering network motifs |conference=ACM 25th Symposium On Applied Computing - Bioinformatics Track |location=Sierre, Switzerland |year=2010 |pages=1559–1566 |url=http://www.nrcbioinformatics.ca/acmsac2010/}}</ref>这个在概念上类似前缀树的数据结构,根据子图结构来进行存储,并找出了每个子图在一个更大的图中出现的次数。这个数据结构有一个突出的方面:在应用于模体发现算法时,主网络中的子图需要进行评估。因此,在随机网络中寻找那些在不在主网络中的子图,这个消耗时间的步骤就不再需要执行了。<br />
<br />
''g-trie'' 是一个存储一组图的多叉树。每一个树节点都存储着一个'''图节点'''及其'''对应的到前一个节点的边'''的信息。从根节点到叶节点的一条路径对应一个图。一个 g-trie 节点的子孙节点共享一个子图(即每一次路径的分叉意味着从一个子图结构中扩展出不同的图结构,而这些扩展出来的图结构自然有着相同的子图结构)。如何构造一个 ''g-trie'' 在<ref name="rib1" />中有详细描述。构造好一个 ''g-trie'' 以后,需要进行计数步骤。计数流程的主要思想是回溯所有可能的子图,同时进行同构性测试。这种回溯技术本质上和其他以模体为中心的方法,比如''MODA'' 和 ''GK'' 算法中使用的技术是一样的。这种技术利用了共同的子结构,亦即在一定时间内,几个不同的候选子图中存在部分是同构的。<br />
<br />
在上述算法中,''G-Tries'' 是最快的。然而,它的一个缺点是内存的超量使用,这局限了它在个人电脑运行时所能发现的模体的大小<br />
<br />
===对比===<br />
<br />
下面的表格和数据显示了在各种标准网络中运行上述算法所获得的结果。这些结果皆获取于各自相应的来源<ref name="omi1" /><ref name="kash1" /><ref name="rib1" /> ,因此需要独立地对待它们。<br />
<br />
[[Image:Runtimes of algorithms.jpg|thumb|''Runtimes of Grochow–Kellis, mfinder, FANMOD, FPF and MODA for subgraphs from three nodes up to nine nodes''.<ref name="omi1" />]]<br />
<br />
{|class="wikitable"<br />
|+ Grochow–Kellis, FANMOD, 和 G-Trie 在5个不同网络上生成含3到9个节点子图所用的运行时间 <ref name="rib1" /><br />
|-<br />
!rowspan="2"|网络<br />
!rowspan="2"|子图大小<br />
!colspan="3"|原始网络数据<br />
!colspan="3"|随机网络平均数据<br />
|-<br />
!FANMOD<br />
!GK<br />
!G-Trie<br />
!FANMOD<br />
!GK<br />
!G-Trie<br />
|-<br />
|rowspan="5"|Dolphins<br />
|5 || 0.07 || 0.03 || 0.01 || 0.13 || 0.04 || 0.01<br />
|-<br />
|6||0.48||0.28||0.04||1.14||0.35||0.07<br />
|-<br />
|7||3.02||3.44||0.23||8.34||3.55||0.46<br />
|-<br />
|8||19.44||73.16||1.69||67.94||37.31||4.03<br />
|-<br />
|9||100.86||2984.22||6.98||493.98||366.79||24.84<br />
|-<br />
|rowspan="3"|Circuit<br />
|6||0.49||0.41||0.03||0.55||0.24||0.03<br />
|-<br />
|7||3.28||3.73||0.22||3.53||1.34||0.17<br />
|-<br />
|8||17.78||48.00||1.52||21.42||7.91||1.06<br />
|-<br />
|rowspan="3"|Social<br />
|3||0.31||0.11||0.02||0.35||0.11||0.02<br />
|-<br />
|4||7.78||1.37||0.56||13.27||1.86||0.57<br />
|-<br />
|5||208.30||31.85||14.88||531.65||62.66||22.11<br />
|-<br />
|rowspan="3"|Yeast<br />
|3||0.47||0.33||0.02||0.57||0.35||0.02<br />
|-<br />
|4||10.07||2.04||0.36||12.90||2.25||0.41<br />
|-<br />
|5||268.51||34.10||12.73||400.13||47.16||14.98<br />
|-<br />
|rowspan="5"|Power<br />
|3||0.51||1.46||0.00||0.91||1.37||0.01<br />
|-<br />
|4||1.38||4.34||0.02||3.01||4.40||0.03<br />
|-<br />
|5||4.68||16.95||0.10||12.38||17.54||0.14<br />
|-<br />
|6||20.36||95.58||0.55||67.65||92.74||0.88<br />
|-<br />
|7||101.04||765.91||3.36||408.15||630.65||5.17<br />
|}<br />
<br />
{|class="wikitable"<br />
|+ mfinder, FANMOD, Mavisto 和 Kavosh 在3个不同网络上生成含3到10个节点子图所用的运行时间<ref name="kash1" /><br />
|-<br />
!&nbsp;<br />
!子图大小→<br />
!rowspan="2"|3<br />
!rowspan="2"|4<br />
!rowspan="2"|5<br />
!rowspan="2"|6<br />
!rowspan="2"|7<br />
!rowspan="2"|8<br />
!rowspan="2"|9<br />
!rowspan="2"|10<br />
|-<br />
!网络↓<br />
!算法↓<br />
|-<br />
|rowspan="4"|E. coli<br />
|Kavosh||0.30||1.84||14.91||141.98||1374.0||13173.7||121110.3||1120560.1<br />
|-<br />
|FANMOD||0.81||2.53||15.71||132.24||1205.9||9256.6||-||-<br />
|-<br />
|Mavisto||13532||-||-||-||-||-||-||-<br />
|-<br />
|Mfinder||31.0||297||23671||-||-||-||-||-<br />
|-<br />
|rowspan="4"|Electronic<br />
|Kavosh||0.08||0.36||8.02||11.39||77.22||422.6||2823.7||18037.5<br />
|-<br />
|FANMOD||0.53||1.06||4.34||24.24||160||967.99||-||-<br />
|-<br />
|Mavisto||210.0||1727||-||-||-||-||-||-<br />
|-<br />
|Mfinder||7||14||109.8||2020.2||-||-||-||-<br />
|-<br />
|rowspan="4"|Social<br />
|Kavosh||0.04||0.23||1.63||10.48||69.43||415.66||2594.19||14611.23<br />
|-<br />
|FANMOD||0.46||0.84||3.07||17.63||117.43||845.93||-||-<br />
|-<br />
|Mavisto||393||1492||-||-||-||-||-||-<br />
|-<br />
|Mfinder||12||49||798||181077||-||-||-||-<br />
|}<br />
<br />
===算法的分类===<br />
正如表格所示,模体发现算法可以分为两大类:基于精确计数的算法,以及使用统计采样以及估计的算法。因为后者并不计数所有子图在主网络中出现的次数,所以第二类算法会更快,却也可能产生带有偏向性的,甚至不现实的结果。<br />
<br />
更深一层地,基于精确计数的算法可以分为'''以网络为中心'''的方法以及以'''子图为中心'''的方法。前者在给定网络中搜索给定大小的子图,而后者首先根据给定大小生成各种可能的非同构图,然后在网络中分别搜索这些生成的图。这两种方法都有各自的优缺点,这些在上文有讨论。<br />
<br />
另一方面,基于估计的方法可能会利用如前面描述过的颜色编码手段,其它的手段则通常会在枚举过程中忽略一些子图(比如,像在 FANMOD 中做的那样),然后只在枚举出来的子图上做估计。<br />
<br />
此外,表格还指出了一个算法能否应用于有向网络或无向网络,以及导出子图或非导出子图。更多信息请参考下方提供的网页和实验室地址及联系方式。<br />
{|class="wikitable"<br />
|+ 模体发现算法的分类<br />
|-<br />
!计数方式<br />
!基础<br />
!算法名称<br />
!有向 / 无向<br />
!导出/ 非导出<br />
|-<br />
| rowspan="9" |精确基数<br />
| rowspan="5" |以网络为中心<br />
|[http://www.weizmann.ac.il/mcb/UriAlon/ mfinder]||皆可||导出<br />
|-<br />
|[http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ ESU (FANMOD)]||皆可||导出<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/Kavosh/ Kavosh] (used in [http://apps.cytoscape.org/apps/cytokavosh CytoKavosh])||皆可||导出<br />
|-<br />
|[http://www.dcc.fc.up.pt/gtries/ G-Tries]||皆可||导出<br />
|-<br />
|[http://nesreenahmed.com/graphlets PGD]<br />
|无向<br />
|导出<br />
|-<br />
|rowspan="4"|以子图为中心<br />
|[http://mavisto.ipk-gatersleben.de/ FPF (Mavisto)]||皆可||导出<br />
|-<br />
|[https://www.msu.edu/~jinchen/ NeMoFinder]||无向||导出<br />
|-<br />
|[http://people.cs.uchicago.edu/~joshuag/index.html Grochow–Kellis]||皆可||Both<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/MODA/ MODA]||皆可||皆可<br />
|-<br />
|rowspan="3"|采样估计<br />
|颜色编码<br />
|[http://www.math.tau.ac.il/~nogaa/ N. Alon] ''et al.''’s Algorithm||无向||非导出<br />
|-<br />
|rowspan="2"|其他手段<br />
|[http://www.weizmann.ac.il/mcb/UriAlon/ mfinder]||皆可||导出<br />
|-<br />
|[http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ ESU (FANMOD)]||皆可||导出<br />
|}<br />
<br />
{|class="wikitable"<br />
|+ 算法提出者的地址和联系方式<br />
|-<br />
!算法<br />
!实验室/研究组<br />
!学院<br />
!大学/研究所<br />
!地址<br />
!电子邮件<br />
|-<br />
|[http://www.weizmann.ac.il/mcb/UriAlon/ mfinder]||Uri Alon's Group||Department of Molecular Cell Biology||Weizmann Institute of Science||Rehovot, Israel, Wolfson, Rm. 607||urialon at weizmann.ac.il<br />
|-<br />
|[http://mavisto.ipk-gatersleben.de/ FPF (Mavisto)]||----||----||Leibniz-Institut für Pflanzengenetik und Kulturpflanzenforschung (IPK)||Corrensstraße 3, D-06466 Stadt Seeland, OT Gatersleben, Deutschland||schreibe at ipk-gatersleben.de<br />
|-<br />
|[http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ ESU (FANMOD)]||Lehrstuhl Theoretische Informatik I||Institut für Informatik||Friedrich-Schiller-Universität Jena||Ernst-Abbe-Platz 2,D-07743 Jena, Deutschland||sebastian.wernicke at gmail.com<br />
|-<br />
|[https://www.msu.edu/~jinchen/ NeMoFinder]||----||School of Computing||National University of Singapore||Singapore 119077||chenjin at comp.nus.edu.sg<br />
|-<br />
|[http://www.cs.colorado.edu/~jgrochow/ Grochow–Kellis]||CS Theory Group & Complex Systems Group||Computer Science||University of Colorado, Boulder||1111 Engineering Dr. ECOT 717, 430 UCB Boulder, CO 80309-0430 USA||jgrochow at colorado.edu<br />
|-<br />
|[http://www.math.tau.ac.il/~nogaa/ N. Alon] ''et al.''’s Algorithm||Department of Pure Mathematics||School of Mathematical Sciences||Tel Aviv University||Tel Aviv 69978, Israel||nogaa at post.tau.ac.il<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/MODA/ MODA]||Laboratory of Systems Biology and Bioinformatics (LBB)||Institute of Biochemistry and Biophysics (IBB)||University of Tehran||Enghelab Square, Enghelab Ave, Tehran, Iran||amasoudin at ibb.ut.ac.ir<br />
|-<br />
|[http://lbb.ut.ac.ir/Download/LBBsoft/Kavosh/ Kavosh] (used in [http://apps.cytoscape.org/apps/cytokavosh CytoKavosh])||Laboratory of Systems Biology and Bioinformatics (LBB)||Institute of Biochemistry and Biophysics (IBB)||University of Tehran||Enghelab Square, Enghelab Ave, Tehran, Iran||amasoudin at ibb.ut.ac.ir<br />
|-<br />
|[http://www.dcc.fc.up.pt/gtries/ G-Tries]||Center for Research in Advanced Computing Systems||Computer Science||University of Porto||Rua Campo Alegre 1021/1055, Porto, Portugal||pribeiro at dcc.fc.up.pt<br />
|-<br />
|[http://nesreenahmed.com/graphlets PGD]<br />
|Network Learning and Discovery Lab<br />
|Department of Computer Science<br />
|Purdue University<br />
|Purdue University, 305 N University St, West Lafayette, IN 47907<br />
|nkahmed@purdue.edu<br />
|}<br />
<br />
==Well-established motifs and their functions==<br />
Much experimental work has been devoted to understanding network motifs in [[gene regulatory networks]]. These networks control which genes are expressed in the cell in response to biological signals. The network is defined such that genes are nodes, and directed edges represent the control of one gene by a transcription factor (regulatory protein that binds DNA) encoded by another gene. Thus, network motifs are patterns of genes regulating each other's transcription rate. When analyzing transcription networks, it is seen that the same network motifs appear again and again in diverse organisms from bacteria to human. The transcription network of ''[[Escherichia coli|E. coli]]'' and yeast, for example, is made of three main motif families, that make up almost the entire network. The leading hypothesis is that the network motif were independently selected by evolutionary processes in a converging manner,<ref name="bab1">{{cite journal |vauthors=Babu MM, Luscombe NM, Aravind L, Gerstein M, Teichmann SA |title=Structure and evolution of transcriptional regulatory networks |journal=Current Opinion in Structural Biology |volume=14 |issue=3 |pages=283–91 |date=June 2004 |pmid=15193307 |doi=10.1016/j.sbi.2004.05.004 |citeseerx=10.1.1.471.9692 }}</ref><ref name="con1">{{cite journal |vauthors=Conant GC, Wagner A |title=Convergent evolution of gene circuits |journal=Nat. Genet. |volume=34 |issue=3 |pages=264–6 |date=July 2003 |pmid=12819781 |doi=10.1038/ng1181}}</ref> since the creation or elimination of regulatory interactions is fast on evolutionary time scale, relative to the rate at which genes change,<ref name="bab1"/><ref name="con1"/><ref name="dek1">{{cite journal |vauthors=Dekel E, Alon U |title=Optimality and evolutionary tuning of the expression level of a protein |journal=Nature |volume=436 |issue=7050 |pages=588–92 |date=July 2005 |pmid=16049495 |doi=10.1038/nature03842 |bibcode=2005Natur.436..588D }}</ref> Furthermore, experiments on the dynamics generated by network motifs in living cells indicate that they have characteristic dynamical functions. This suggests that the network motif serve as building blocks in gene regulatory networks that are beneficial to the organism.<br />
<br />
The functions associated with common network motifs in transcription networks were explored and demonstrated by several research projects both theoretically and experimentally. Below are some of the most common network motifs and their associated function.<br />
<br />
===Negative auto-regulation (NAR)===<br />
[[Image:Autoregulation motif.png|thumb|Schematic representation of an auto-regulation motif]]<br />
One of simplest and most abundant network motifs in ''[[Escherichia coli|E. coli]]'' is negative auto-regulation in which a transcription factor (TF) represses its own transcription. This motif was shown to perform two important functions. The first function is response acceleration. NAR was shown to speed-up the response to signals both theoretically <ref name="zab1">{{cite journal |doi=10.1016/j.jtbi.2011.06.021 |author=Zabet NR |title=Negative feedback and physical limits of genes |journal=Journal of Theoretical Biology |volume= 284|issue=1 |pages=82–91 |date=September 2011 |pmid=21723295 |arxiv=1408.1869 |citeseerx=10.1.1.759.5418 }}</ref> and experimentally. This was first shown in a synthetic transcription network<ref name="ros1">{{cite journal |doi=10.1016/S0022-2836(02)00994-4 |vauthors=Rosenfeld N, Elowitz MB, Alon U |title=Negative autoregulation speeds the response times of transcription networks |journal=J. Mol. Biol. |volume=323 |issue=5 |pages=785–93 |date=November 2002 |pmid=12417193 |citeseerx=10.1.1.126.2604 }}</ref> and later on in the natural context in the SOS DNA repair system of E .coli.<ref name="cam1">{{cite journal |vauthors=Camas FM, Blázquez J, Poyatos JF |title=Autogenous and nonautogenous control of response in a genetic network |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=103 |issue=34 |pages=12718–23 |date=August 2006 |pmid=16908855 |pmc=1568915 |doi=10.1073/pnas.0602119103 |bibcode=2006PNAS..10312718C }}</ref> The second function is increased stability of the auto-regulated gene product concentration against stochastic noise, thus reducing variations in protein levels between different cells.<ref name="bec1">{{cite journal |vauthors=Becskei A, Serrano L |title=Engineering stability in gene networks by autoregulation |journal=Nature |volume=405 |issue=6786 |pages=590–3 |date=June 2000 |pmid=10850721 |doi=10.1038/35014651}}</ref><ref name="dub1">{{cite journal |vauthors=Dublanche Y, Michalodimitrakis K, Kümmerer N, Foglierini M, Serrano L |title=Noise in transcription negative feedback loops: simulation and experimental analysis |journal=Mol. Syst. Biol. |volume=2 |pages=41 |year=2006 |pmid=16883354 |pmc=1681513 |doi=10.1038/msb4100081 |issue=1}}</ref><ref name="shi1">{{cite journal |vauthors=Shimoga V, White J, Li Y, Sontag E, Bleris L |title= Synthetic mammalian transgene negative autoregulation |journal=Mol. Syst. Biol. |volume=9 |pages=670 |year=2013|doi=10.1038/msb.2013.27|pmid= 23736683 |pmc= 3964311 }}</ref><br />
<br />
<br />
<br />
===Positive auto-regulation (PAR)===<br />
Positive auto-regulation (PAR) occurs when a transcription factor enhances its own rate of production. Opposite to the NAR motif this motif slows the response time compared to simple regulation.<ref name="mae1">{{cite journal |vauthors=Maeda YT, Sano M |title=Regulatory dynamics of synthetic gene networks with positive feedback |journal=J. Mol. Biol. |volume=359 |issue=4 |pages=1107–24 |date=June 2006 |pmid=16701695 |doi=10.1016/j.jmb.2006.03.064 }}</ref> In the case of a strong PAR the motif may lead to a bimodal distribution of protein levels in cell populations.<ref name="bec2">{{cite journal |vauthors=Becskei A, Séraphin B, Serrano L |title=Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion |journal=EMBO J. |volume=20 |issue=10 |pages=2528–35 |date=May 2001 |pmid=11350942 |pmc=125456 |doi=10.1093/emboj/20.10.2528}}</ref><br />
<br />
===Feed-forward loops (FFL)===<br />
[[Image:Feed-forward motif.GIF|thumb|Schematic representation of a Feed-forward motif]]<br />
This motif is commonly found in many gene systems and organisms. The motif consists of three genes and three regulatory interactions. The target gene C is regulated by 2 TFs A and B and in addition TF B is also regulated by TF A . Since each of the regulatory interactions may either be positive or negative there are possibly eight types of FFL motifs.<ref name="man1">{{cite journal |vauthors=Mangan S, Alon U |title=Structure and function of the feed-forward loop network motif |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=100 |issue=21 |pages=11980–5 |date=October 2003 |pmid=14530388 |pmc=218699 |doi=10.1073/pnas.2133841100 |bibcode=2003PNAS..10011980M }}</ref> Two of those eight types: the coherent type 1 FFL (C1-FFL) (where all interactions are positive) and the incoherent type 1 FFL (I1-FFL) (A activates C and also activates B which represses C) are found much more frequently in the transcription network of ''[[Escherichia coli|E. coli]]'' and yeast than the other six types.<ref name="man1"/><ref name="ma1">{{cite journal |vauthors=Ma HW, Kumar B, Ditges U, Gunzer F, Buer J, Zeng AP |title=An extended transcriptional regulatory network of ''Escherichia coli'' and analysis of its hierarchical structure and network motifs |journal=Nucleic Acids Res. |volume=32 |issue=22 |pages=6643–9 |year=2004 |pmid=15604458 |pmc=545451 |doi=10.1093/nar/gkh1009 |url=http://nar.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=15604458}}</ref> In addition to the structure of the circuitry the way in which the signals from A and B are integrated by the C promoter should also be considered. In most of the cases the FFL is either an AND gate (A and B are required for C activation) or OR gate (either A or B are sufficient for C activation) but other input function are also possible.<br />
<br />
===Coherent type 1 FFL (C1-FFL)===<br />
The C1-FFL with an AND gate was shown to have a function of a ‘sign-sensitive delay’ element and a persistence detector both theoretically <ref name="man1"/> and experimentally<ref name="man2">{{cite journal |doi=10.1016/j.jmb.2003.09.049 |vauthors=Mangan S, Zaslaver A, Alon U |title=The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks |journal=J. Mol. Biol. |volume=334 |issue=2 |pages=197–204 |date=November 2003 |pmid=14607112 |citeseerx=10.1.1.110.4629 }}</ref> with the arabinose system of ''[[Escherichia coli|E. coli]]''. This means that this motif can provide pulse filtration in which short pulses of signal will not generate a response but persistent signals will generate a response after short delay. The shut off of the output when a persistent pulse is ended will be fast. The opposite behavior emerges in the case of a sum gate with fast response and delayed shut off as was demonstrated in the flagella system of ''[[Escherichia coli|E. coli]]''.<ref name="kal1">{{cite journal |vauthors=Kalir S, Mangan S, Alon U |title=A coherent feed-forward loop with a SUM input function prolongs flagella expression in ''Escherichia coli'' |journal=Mol. Syst. Biol. |volume=1 |pages=E1–E6 |year=2005 |pmid=16729041 |pmc=1681456 |doi=10.1038/msb4100010 |issue=1}}</ref> De novo evolution of C1-FFLs in [[gene regulatory network]]s has been demonstrated computationally in response to selection to filter out an idealized short signal pulse, but for non-idealized noise, a dynamics-based system of feed-forward regulation with different topology was instead favored.<ref>{{cite journal |last1=Xiong |first1=Kun |last2=Lancaster |first2=Alex K. |last3=Siegal |first3=Mark L. |last4=Masel |first4=Joanna |title=Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise |journal=Nature Communications |date=3 June 2019 |volume=10 |issue=1 |pages=2418 |doi=10.1038/s41467-019-10388-6|pmid=31160574 |pmc=6546794 }}</ref><br />
<br />
===Incoherent type 1 FFL (I1-FFL)===<br />
The I1-FFL is a pulse generator and response accelerator. The two signal pathways of the I1-FFL act in opposite directions where one pathway activates Z and the other represses it. When the repression is complete this leads to a pulse-like dynamics. It was also demonstrated experimentally that the I1-FFL can serve as response accelerator in a way which is similar to the NAR motif. The difference is that the I1-FFL can speed-up the response of any gene and not necessarily a transcription factor gene.<ref name="man3">{{cite journal |vauthors=Mangan S, Itzkovitz S, Zaslaver A, Alon U |title=The incoherent feed-forward loop accelerates the response-time of the gal system of ''Escherichia coli'' |journal=J. Mol. Biol. |volume=356 |issue=5 |pages=1073–81 |date=March 2006 |pmid=16406067 |doi=10.1016/j.jmb.2005.12.003 |citeseerx=10.1.1.184.8360 }}</ref> An additional function was assigned to the I1-FFL network motif: it was shown both theoretically and experimentally that the I1-FFL can generate non-monotonic input function in both a synthetic <ref name="ent1">{{cite journal |vauthors=Entus R, Aufderheide B, Sauro HM |title=Design and implementation of three incoherent feed-forward motif based biological concentration sensors |journal=Syst Synth Biol |volume=1 |issue=3 |pages=119–28 |date=August 2007 |pmid=19003446 |pmc=2398716 |doi=10.1007/s11693-007-9008-6 }}</ref> and native systems.<ref name="kap1">{{cite journal |vauthors=Kaplan S, Bren A, Dekel E, Alon U |title=The incoherent feed-forward loop can generate non-monotonic input functions for genes |journal=Mol. Syst. Biol. |volume=4 |pages=203 |year=2008 |pmid=18628744 |pmc=2516365 |doi=10.1038/msb.2008.43 |issue=1}}</ref> Finally, expression units that incorporate incoherent feedforward control of the gene product provide adaptation to the amount of DNA template and can be superior to simple combinations of constitutive promoters.<ref name="ble1">{{cite journal |vauthors=Bleris L, Xie Z, Glass D, Adadey A, Sontag E, Benenson Y |title=Synthetic incoherent feedforward circuits show adaptation to the amount of their genetic template |journal=Mol. Syst. Biol. |volume=7 |pages=519|year=2011 |doi=10.1038/msb.2011.49 |issue=1 |pmid=21811230 |pmc=3202791}}</ref> Feedforward regulation displayed better adaptation than negative feedback, and circuits based on RNA interference were the most robust to variation in DNA template amounts.<ref name="ble1"/><br />
<br />
===Multi-output FFLs===<br />
In some cases the same regulators X and Y regulate several Z genes of the same system. By adjusting the strength of the interactions this motif was shown to determine the temporal order of gene activation. This was demonstrated experimentally in the flagella system of ''[[Escherichia coli|E. coli]]''.<ref name="kal2">{{cite journal |vauthors=Kalir S, McClure J, Pabbaraju K, etal |title=Ordering genes in a flagella pathway by analysis of expression kinetics from living bacteria |journal=Science |volume=292 |issue=5524 |pages=2080–3 |date=June 2001 |pmid=11408658 |doi=10.1126/science.1058758 }}</ref><br />
<br />
===Single-input modules (SIM)===<br />
This motif occurs when a single regulator regulates a set of genes with no additional regulation. This is useful when the genes are cooperatively carrying out a specific function and therefore always need to be activated in a synchronized manner. By adjusting the strength of the interactions it can create temporal expression program of the genes it regulates.<ref name="zas1">{{cite journal |vauthors=Zaslaver A, Mayo AE, Rosenberg R, etal |title=Just-in-time transcription program in metabolic pathways |journal=Nat. Genet. |volume=36 |issue=5 |pages=486–91 |date=May 2004 |pmid=15107854 |doi=10.1038/ng1348|doi-access=free }}</ref><br />
<br />
In the literature, Multiple-input modules (MIM) arose as a generalization of SIM. However, the precise definitions of SIM and MIM have been a source of inconsistency. There are attempts to provide orthogonal definitions for canonical motifs in biological networks and algorithms to enumerate them, especially SIM, MIM and Bi-Fan (2x2 MIM).<ref>{{cite journal |vauthors=Konagurthu AS, Lesk AM |title=Single and Multiple Input Modules in regulatory networks |journal=Proteins |volume=73 |issue=2 |pages=320–324 |year=2008 |doi=10.1002/prot.22053|pmid=18433061 }}</ref><br />
<br />
===Dense overlapping regulons (DOR)===<br />
This motif occurs in the case that several regulators combinatorially control a set of genes with diverse regulatory combinations. This motif was found in ''[[Escherichia coli|E. coli]]'' in various systems such as carbon utilization, anaerobic growth, stress response and others.<ref name="she1"/><ref name="boy1"/> In order to better understand the function of this motif one has to obtain more information about the way the multiple inputs are integrated by the genes. Kaplan ''et al.''<ref name="kap2">{{cite journal |vauthors=Kaplan S, Bren A, Zaslaver A, Dekel E, Alon U |title=Diverse two-dimensional input functions control bacterial sugar genes |journal=Mol. Cell |volume=29 |issue=6 |pages=786–92 |date=March 2008 |pmid=18374652 |pmc=2366073 |doi=10.1016/j.molcel.2008.01.021 }}</ref> has mapped the input functions of the sugar utilization genes in ''[[Escherichia coli|E. coli]]'', showing diverse shapes.<br />
<br />
==已知的模体及其功能==<br />
许多实验工作致力于理解[[基因调控网络]]中的网络模体。在响应生物信号的过程中,这些网络控制细胞中需要表达的基因。这样的网络以基因作为节点,有向边代表对某个基因的调控,基因调控通过其他基因编码的转录因子[[结合在DNA上的调控蛋白]]来实现。因此,网络模体是基因之间相互调控转录速率的模式。在分析转录调控网络的时候,人们发现某些相同的网络模体在不同的物种中不断地出现,从细菌到人类。例如,''[[大肠杆菌]]''和酵母的转录网络由三种主要的网络模体家族组成,它们可以构建几乎整个网络。主要的假设是在进化的过程中,网络模体是被以收敛的方式独立选择出来的。<ref name="bab1">{{cite journal |vauthors=Babu MM, Luscombe NM, Aravind L, Gerstein M, Teichmann SA |title=Structure and evolution of transcriptional regulatory networks |journal=Current Opinion in Structural Biology |volume=14 |issue=3 |pages=283–91 |date=June 2004 |pmid=15193307 |doi=10.1016/j.sbi.2004.05.004 |citeseerx=10.1.1.471.9692 }}</ref><ref name="con1">{{cite journal |vauthors=Conant GC, Wagner A |title=Convergent evolution of gene circuits |journal=Nat. Genet. |volume=34 |issue=3 |pages=264–6 |date=July 2003 |pmid=12819781 |doi=10.1038/ng1181}}</ref> 因为相对于基因改变的速率,转录相互作用产生和消失的时间尺度在进化上是很快的。<ref name="bab1"/><ref name="con1"/><ref name="dek1">{{cite journal |vauthors=Dekel E, Alon U |title=Optimality and evolutionary tuning of the expression level of a protein |journal=Nature |volume=436 |issue=7050 |pages=588–92 |date=July 2005 |pmid=16049495 |doi=10.1038/nature03842 |bibcode=2005Natur.436..588D }}</ref> 此外,对活细胞中网络模体所产生的动力学行为的实验表明,它们具有典型的动力学功能。这表明,网络模体是基因调控网络中对生物体有益的基本单元。<br />
<br />
一些研究从理论和实验两方面探讨和论证了转录网络中与共同网络模体相关的功能。下面是一些最常见的网络模体及其相关功能。<br />
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===负自反馈调控(NAR)===<br />
[[Image:Autoregulation motif.png|thumb|Schematic representation of an auto-regulation motif]]<br />
负自反馈调控是[[大肠杆菌]]中最简单和最冗余的网络模体之一,其中一个转录因子抑制它自身的转录。这种网络模体有两个重要的功能,其中第一个是加速响应。人们发现在实验和理论上, <ref name="zab1">{{cite journal |doi=10.1016/j.jtbi.2011.06.021 |author=Zabet NR |title=Negative feedback and physical limits of genes |journal=Journal of Theoretical Biology |volume= 284|issue=1 |pages=82–91 |date=September 2011 |pmid=21723295 |arxiv=1408.1869 |citeseerx=10.1.1.759.5418 }}</ref>NAR都可以加快对信号的响应。这个功能首先在一个人工合成的转录网络中被发现,<ref name="ros1">{{cite journal |doi=10.1016/S0022-2836(02)00994-4 |vauthors=Rosenfeld N, Elowitz MB, Alon U |title=Negative autoregulation speeds the response times of transcription networks |journal=J. Mol. Biol. |volume=323 |issue=5 |pages=785–93 |date=November 2002 |pmid=12417193 |citeseerx=10.1.1.126.2604 }}</ref> 然后在大肠杆菌SOS DAN修复系统这个自然体系中也被发现。<ref name="cam1">{{cite journal |vauthors=Camas FM, Blázquez J, Poyatos JF |title=Autogenous and nonautogenous control of response in a genetic network |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=103 |issue=34 |pages=12718–23 |date=August 2006 |pmid=16908855 |pmc=1568915 |doi=10.1073/pnas.0602119103 |bibcode=2006PNAS..10312718C }}</ref> 负自反馈网络的第二个功能是增强自调控基因的产物浓度的稳定性,从而抵抗随机的噪声,减少该蛋白含量在不同细胞中的差异。<ref name="bec1">{{cite journal |vauthors=Becskei A, Serrano L |title=Engineering stability in gene networks by autoregulation |journal=Nature |volume=405 |issue=6786 |pages=590–3 |date=June 2000 |pmid=10850721 |doi=10.1038/35014651}}</ref><ref name="dub1">{{cite journal |vauthors=Dublanche Y, Michalodimitrakis K, Kümmerer N, Foglierini M, Serrano L |title=Noise in transcription negative feedback loops: simulation and experimental analysis |journal=Mol. Syst. Biol. |volume=2 |pages=41 |year=2006 |pmid=16883354 |pmc=1681513 |doi=10.1038/msb4100081 |issue=1}}</ref><ref name="shi1">{{cite journal |vauthors=Shimoga V, White J, Li Y, Sontag E, Bleris L |title= Synthetic mammalian transgene negative autoregulation |journal=Mol. Syst. Biol. |volume=9 |pages=670 |year=2013|doi=10.1038/msb.2013.27|pmid= 23736683 |pmc= 3964311 }}</ref><br />
<br />
===正自反馈调控(PAR)===<br />
正自反馈调控是指转录因子增强它自身转录速率的调控。和负自反馈调节相反,NAR模体相比于简单的调控能够延长反应时间。<ref name="mae1">{{cite journal |vauthors=Maeda YT, Sano M |title=Regulatory dynamics of synthetic gene networks with positive feedback |journal=J. Mol. Biol. |volume=359 |issue=4 |pages=1107–24 |date=June 2006 |pmid=16701695 |doi=10.1016/j.jmb.2006.03.064 }}</ref> 在强PAR的情况下,模体可能导致蛋白质水平在细胞群中呈现双峰分布。<ref name="bec2">{{cite journal |vauthors=Becskei A, Séraphin B, Serrano L |title=Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion |journal=EMBO J. |volume=20 |issue=10 |pages=2528–35 |date=May 2001 |pmid=11350942 |pmc=125456 |doi=10.1093/emboj/20.10.2528}}</ref><br />
<br />
===前馈回路 (FFL)===<br />
[[Image:Feed-forward motif.GIF|thumb|Schematic representation of a Feed-forward motif]]<br />
前馈回路普遍存在于许多基因系统和生物体中。这种模体包括三个基因以及三个相互作用。目标基因C被两个转录因子(TFs)A和B调控,并且TF B同时被TF A调控。由于每个调控相互作用可以是正的或者负的,所以总共可能有八种类型的FFL模体。<ref name="man1">{{cite journal |vauthors=Mangan S, Alon U |title=Structure and function of the feed-forward loop network motif |journal=Proc. Natl. Acad. Sci. U.S.A. |volume=100 |issue=21 |pages=11980–5 |date=October 2003 |pmid=14530388 |pmc=218699 |doi=10.1073/pnas.2133841100 |bibcode=2003PNAS..10011980M }}</ref> 其中的两种:一致前馈回路的类型一(C1-FFL)(所有相互作用都是正的)和非一致前馈回路的类型一(I1-FFL)(A激活C和B,B抑制C)在[[大肠杆菌]]和酵母中相比于其他六种更频繁的出现。<ref name="man1"/><ref name="ma1">{{cite journal |vauthors=Ma HW, Kumar B, Ditges U, Gunzer F, Buer J, Zeng AP |title=An extended transcriptional regulatory network of ''Escherichia coli'' and analysis of its hierarchical structure and network motifs |journal=Nucleic Acids Res. |volume=32 |issue=22 |pages=6643–9 |year=2004 |pmid=15604458 |pmc=545451 |doi=10.1093/nar/gkh1009 |url=http://nar.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=15604458}}</ref> 除了网络的结构外,还应该考虑来自A和B的信号被C的启动子集成的方式。在大多数情况下,FFL要么是一个与门(激活C需要A和B),要么是或门(激活C需要A或B),但也可以是其他输入函数。<br />
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===一致前馈回路类型一(C1-FFL)===<br />
具有与门的C1-FFL有“符号-敏感延迟”单元和持久性探测器的功能,这一点在[[大肠杆菌]]阿拉伯糖系系统的理论<ref name="man1"/>和实验上<ref name="man2">{{cite journal |doi=10.1016/j.jmb.2003.09.049 |vauthors=Mangan S, Zaslaver A, Alon U |title=The coherent feedforward loop serves as a sign-sensitive delay element in transcription networks |journal=J. Mol. Biol. |volume=334 |issue=2 |pages=197–204 |date=November 2003 |pmid=14607112 |citeseerx=10.1.1.110.4629 }}</ref> 都有发现。这意味着该模体可以提供脉冲过滤,短脉冲信号不会产生响应,而持久信号在短延迟后会产生响应。当持久脉冲结束时,输出的关闭将很快。与此相反的行为出现在具有快速响应和延迟关闭特性的加和门的情况下,这在[[大肠杆菌]]的鞭毛系统中得到了证明。<ref name="kal1">{{cite journal |vauthors=Kalir S, Mangan S, Alon U |title=A coherent feed-forward loop with a SUM input function prolongs flagella expression in ''Escherichia coli'' |journal=Mol. Syst. Biol. |volume=1 |pages=E1–E6 |year=2005 |pmid=16729041 |pmc=1681456 |doi=10.1038/msb4100010 |issue=1}}</ref>在[[基因调控网络]]的重头进化中,对于滤除理想化的短信号脉冲作为进化压,C1-FFLs已经在计算上被证明可以进化出来。但是对于非理想化的噪声,不同拓扑结构前馈调节的动态系统将被优先考虑。 <ref>{{cite journal |last1=Xiong |first1=Kun |last2=Lancaster |first2=Alex K. |last3=Siegal |first3=Mark L. |last4=Masel |first4=Joanna |title=Feed-forward regulation adaptively evolves via dynamics rather than topology when there is intrinsic noise |journal=Nature Communications |date=3 June 2019 |volume=10 |issue=1 |pages=2418 |doi=10.1038/s41467-019-10388-6|pmid=31160574 |pmc=6546794 }}</ref><br />
<br />
===非一致前馈回路类型一(I1-FFL)===<br />
I1-FFL是一个脉冲生成器和响应加速器。I1-FFL的两种信号通路作用方向相反,一种通路激活Z,而另一种抑制Z。完全的抑制会导致类似脉冲的动力学行为。另外有实验证明,它可以类似于NAR模体起到响应加速器的作用。与NAR模体的不同之处在于,它可以加速任何基因的响应,而不必是转录因子。<ref name="man3">{{cite journal |vauthors=Mangan S, Itzkovitz S, Zaslaver A, Alon U |title=The incoherent feed-forward loop accelerates the response-time of the gal system of ''Escherichia coli'' |journal=J. Mol. Biol. |volume=356 |issue=5 |pages=1073–81 |date=March 2006 |pmid=16406067 |doi=10.1016/j.jmb.2005.12.003 |citeseerx=10.1.1.184.8360 }}</ref>I1-FFL网络还有另外一个功能:在理论和实验上都有证明I1-FFL可以生成非单调的输入函数,无论在人工合成的<ref name="ent1">{{cite journal |vauthors=Entus R, Aufderheide B, Sauro HM |title=Design and implementation of three incoherent feed-forward motif based biological concentration sensors |journal=Syst Synth Biol |volume=1 |issue=3 |pages=119–28 |date=August 2007 |pmid=19003446 |pmc=2398716 |doi=10.1007/s11693-007-9008-6 }}</ref>还是自然的系统中。 <ref name="kap1">{{cite journal |vauthors=Kaplan S, Bren A, Dekel E, Alon U |title=The incoherent feed-forward loop can generate non-monotonic input functions for genes |journal=Mol. Syst. Biol. |volume=4 |pages=203 |year=2008 |pmid=18628744 |pmc=2516365 |doi=10.1038/msb.2008.43 |issue=1}}</ref> 最后,包含非一致前馈调控的基因生成物的表达单元对DNA模板的数量具有适应性,可以优于简单的组合本构启动子。<ref name="ble1">{{cite journal |vauthors=Bleris L, Xie Z, Glass D, Adadey A, Sontag E, Benenson Y |title=Synthetic incoherent feedforward circuits show adaptation to the amount of their genetic template |journal=Mol. Syst. Biol. |volume=7 |pages=519|year=2011 |doi=10.1038/msb.2011.49 |issue=1 |pmid=21811230 |pmc=3202791}}</ref> 前馈调控比负反馈具有更好的适应性,并且基于RNA干扰的网络对DNA模板数具有最高的鲁棒性。<ref name="ble1"/><br />
<br />
===多输出前馈回路===<br />
在某些情况,相同的调控子X和Y可以调控同一系统中的多个Z基因。通过调节相互作用的强度,这些网络可以决定基因激活的时间顺序。这一点在[[大肠杆菌]]的鞭毛系统中有实验证据。<ref name="kal2">{{cite journal |vauthors=Kalir S, McClure J, Pabbaraju K, etal |title=Ordering genes in a flagella pathway by analysis of expression kinetics from living bacteria |journal=Science |volume=292 |issue=5524 |pages=2080–3 |date=June 2001 |pmid=11408658 |doi=10.1126/science.1058758 }}</ref><br />
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===单一输入模块(SIM)===<br />
当单个调控子调控一组基因,并且没有其他的调控因素时,这样的模体叫做单一输入模块(SIM)。当很多基因合作执行某个功能时这是有用的,因为这些基因需要同步地被激活。通过调节相互作用的强度,可以编排它所调控的基因表达的时间顺序。<ref name="zas1">{{cite journal |vauthors=Zaslaver A, Mayo AE, Rosenberg R, etal |title=Just-in-time transcription program in metabolic pathways |journal=Nat. Genet. |volume=36 |issue=5 |pages=486–91 |date=May 2004 |pmid=15107854 |doi=10.1038/ng1348|doi-access=free }}</ref><br />
<br />
在文献中,多输入模块(MIM)来自于SIM的扩展。但是二者的精确定义并不太一致。有一些尝试给出生物网络中规范模体的正交定义,也有一些算法去枚举它们,特别是SIM,MIM和2x2 MIM等。<ref>{{cite journal |vauthors=Konagurthu AS, Lesk AM |title=Single and Multiple Input Modules in regulatory networks |journal=Proteins |volume=73 |issue=2 |pages=320–324 |year=2008 |doi=10.1002/prot.22053|pmid=18433061 }}</ref><br />
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===密集交盖调节网(DOR)===<br />
这种类型的网络存在于多个调节子结合起来控制一组基因的情形,并且有多种调控的组合。这种模体出现在[[大肠杆菌]]的多种系统中,例如碳利用、厌氧生长、应激反应等。<ref name="she1"/><ref name="boy1"/> 为了更好地理解这种网络,我们必须得到关于基因集成多种输入的方式的信息。Kaplan ''et al.''<ref name="kap2">{{cite journal |vauthors=Kaplan S, Bren A, Zaslaver A, Dekel E, Alon U |title=Diverse two-dimensional input functions control bacterial sugar genes |journal=Mol. Cell |volume=29 |issue=6 |pages=786–92 |date=March 2008 |pmid=18374652 |pmc=2366073 |doi=10.1016/j.molcel.2008.01.021 }}</ref>绘制了[[大肠杆菌]]糖利用基因的输入函数,表现出各种各样的形状。<br />
<br />
==活动模体==<br />
<br />
有一个对网络模体的有趣概括:'''活动模体'''是在对节点和边都被量化标注的网络中可发现的【反复】斑图。例如,当新城代谢的边以相应基因的表达量或【时间】来标注时,一些斑图在'''给定的'''底层网络结构里【是反复的】。<ref name="agc">{{cite journal |vauthors=Chechik G, Oh E, Rando O, Weissman J, Regev A, Koller D |title=Activity motifs reveal principles of timing in transcriptional control of the yeast metabolic network |journal=Nat. Biotechnol. |volume=26 |issue=11 |pages=1251–9 |date=November 2008 |pmid=18953355 |pmc=2651818 |doi=10.1038/nbt.1499}}</ref><br />
<br />
==批判==<br />
<br />
对拓扑子结构有一个(某种程度上隐含的)前提性假设是其具有特定的功能重要性。但该假设最近遭到质疑,有人提出在不同的网络环境下模体可能表现出多样性,例如双扇模体,故<ref name="ad">{{cite journal |vauthors=Ingram PJ, Stumpf MP, Stark J |title=Network motifs: structure does not determine function |journal=BMC Genomics |volume=7 |pages=108 |year=2006 |pmid=16677373 |pmc=1488845 |doi=10.1186/1471-2164-7-108 }} </ref>模体的结构不必然决定功能,网络结构也不当然能揭示其功能;这种见解由来已久,可参见【Sin 操纵子】</font>。<ref>{{cite journal |vauthors=Voigt CA, Wolf DM, Arkin AP |title=The ''Bacillus subtilis'' sin operon: an evolvable network motif |journal=Genetics |volume=169 |issue=3 |pages=1187–202 |date=March 2005 |pmid=15466432 |pmc=1449569 |doi=10.1534/genetics.104.031955 |url=http://www.genetics.org/cgi/pmidlookup?view=long&pmid=15466432}}</ref><br />
<br />
<br />
大多数模体功能分析是基于模体孤立运行的情形。最近的研究<ref>{{cite journal |vauthors=Knabe JF, Nehaniv CL, Schilstra MJ |title=Do motifs reflect evolved function?—No convergent evolution of genetic regulatory network subgraph topologies |journal=BioSystems |volume=94 |issue=1–2 |pages=68–74 |year=2008 |pmid=18611431 |doi=10.1016/j.biosystems.2008.05.012 }}</ref>表明网络环境至关重要,不能忽视网络环境而仅从本地结构来对其功能进行推论——引用的论文还回顾了对观测数据的批判及其他可能的解释。人们研究了单个模体模组对网络全局的动力学影响及其分析<ref>{{cite journal |vauthors=Taylor D, Restrepo JG |title=Network connectivity during mergers and growth: Optimizing the addition of a module |journal=Physical Review E |volume=83 |issue=6 |year=2011 |page=66112 |doi=10.1103/PhysRevE.83.066112 |pmid=21797446 |bibcode=2011PhRvE..83f6112T |arxiv=1102.4876 }}</ref>。而另一项近期的研究工作提出生物网络的某些拓扑特征能自然地引起经典模体的常见形态,让人不禁疑问:这样的发生频率是否能证明模体的结构是出于其对所在网络运行的功能性贡献而被选择保留下的结果?<ref>{{cite journal|last1=Konagurthu|first1=Arun S.|last2=Lesk|first2=Arthur M.|title=Single and multiple input modules in regulatory networks|journal=Proteins: Structure, Function, and Bioinformatics|date=23 April 2008|volume=73|issue=2|pages=320–324|doi=10.1002/prot.22053|pmid=18433061}}</ref><ref>{{cite journal |vauthors=Konagurthu AS, Lesk AM |title=On the origin of distribution patterns of motifs in biological networks |journal=BMC Syst Biol |volume=2 |pages=73 |year=2008 |pmid=18700017 |pmc=2538512 |doi=10.1186/1752-0509-2-73 }} </ref><br />
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<br />
模体的研究主要应用于静态复杂网络,而时变复杂网络的研究<ref>Braha, D., & Bar‐Yam, Y. (2006). [https://static1.squarespace.com/static/5b68a4e4a2772c2a206180a1/t/5c5de3faf4e1fc43e7b3d21e/1549657083988/Complexity_Braha_Original_w_Cover.pdf From centrality to temporary fame: Dynamic centrality in complex networks]. Complexity, 12(2), 59-63. </ref>就网络模体提出了重大的新解释,并介绍了'''时变网络模体'''的概念。Braha和Bar-Yam<ref> Braha D., Bar-Yam Y. (2009) [https://s3.amazonaws.com/academia.edu.documents/4892116/Adaptive_Networks__Theory__Models_and_Applications__Understanding_Complex_Systems_.pdf?response-content-disposition=inline%3B%20filename%3DRedes_teoria.pdf&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAIWOWYYGZ2Y53UL3A%2F20191111%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20191111T173250Z&X-Amz-Expires=3600&X-Amz-SignedHeaders=host&X-Amz-Signature=89d08c9e92b88ed817e4eb0f87c480757ef79c4b865919a5e0890cbefa164c61#page=55 Time-Dependent Complex Networks: Dynamic Centrality, Dynamic Motifs, and Cycles of Social Interactions]. In: Gross T., Sayama H. (eds) Adaptive Networks. Understanding Complex Systems. Springer, Berlin, Heidelberg </ref>研究了本地模体结构在时间依赖网络/时变网络的动力学,发现的一些反复模式有望成为社会互动周期的经验论据。他们证明了对于时变网络,其本地结构是时间依赖的且可能随时间演变,可作为对复杂网络中稳定模体观及模体表达观的反论,Braha和Bar-Yam还进一步提出,对时变本地结构的分析有可能揭示系统级任务和功能方面的动力学的重要信息。<br />
<br />
==See also==<br />
* [[Clique (graph theory)]]<br />
* [[Graphical model]]<br />
<br />
==References==<br />
{{reflist|2}}<br />
<br />
==External links==<br />
<br />
* [http://www.weizmann.ac.il/mcb/UriAlon/groupNetworkMotifSW.html A software tool that can detect network motifs]<br />
* [http://www.bio-physics.at/wiki/index.php?title=Network_Motifs bio-physics-wiki NETWORK MOTIFS]<br />
* [http://theinf1.informatik.uni-jena.de/~wernicke/motifs/ FANMOD: a tool for fast network motif detection]<br />
* [http://mavisto.ipk-gatersleben.de/ MAVisto: network motif analysis and visualisation tool]<br />
* [https://www.msu.edu/~jinchen/ NeMoFinder]<br />
* [http://people.cs.uchicago.edu/~joshuag/index.html Grochow–Kellis]<br />
* [http://lbb.ut.ac.ir/Download/LBBsoft/MODA/ MODA]<br />
* [http://lbb.ut.ac.ir/Download/LBBsoft/Kavosh/ Kavosh]<br />
* [http://apps.cytoscape.org/apps/cytokavosh CytoKavosh]<br />
* [http://www.dcc.fc.up.pt/gtries/ G-Tries]<br />
* [http://www.ft.unicamp.br/docentes/meira/accmotifs/ acc-MOTIF detection tool]<br />
<br />
[[Category:Gene expression]]<br />
[[Category:Networks]]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6835哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-05T14:10:40Z<p>Imp:</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔([https://en.wikipedia.org/wiki/Kurt_G%C3%B6del KurtGödel]),艺术家埃舍尔([https://en.wikipedia.org/wiki/M._C._Escher M. C. Escher])和作曲家巴赫([https://en.wikipedia.org/wiki/Johann_Sebastian_Bach Johann Sebastian Bach])的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
[[File:ddd.jpg|200px]]<br />
<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向[https://en.wikipedia.org/wiki/Willard_Van_Orman_Quine Willard Van Orman Quine]致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿基里斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳([https://en.wikipedia.org/wiki/Martin_Gardner Martin Gardner])1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯([https://en.wikipedia.org/wiki/Bruce_Edwards_Ivins Bruce Edwards Ivins])受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
[[File:s1789059.jpg|200px]]<br />
<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
<br />
===作者简介===<br />
[[File:OIP.jpg|400px]]<br />
<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名[[侯世达]],美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
<br />
侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
<br />
* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
<br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
<br />
以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
<br />
*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
<br />
*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]<br />
<br />
本词条内容部分翻译自 wikipedia.org,遵守 CC3.0协议。</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6834哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-05T14:09:53Z<p>Imp:/* 基本信息 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔([https://en.wikipedia.org/wiki/Kurt_G%C3%B6del KurtGödel]),艺术家埃舍尔([https://en.wikipedia.org/wiki/M._C._Escher M. C. Escher])和作曲家巴赫([https://en.wikipedia.org/wiki/Johann_Sebastian_Bach Johann Sebastian Bach])的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
[[File:ddd.jpg|200px]]<br />
<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向[https://en.wikipedia.org/wiki/Willard_Van_Orman_Quine Willard Van Orman Quine]致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿基里斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳([https://en.wikipedia.org/wiki/Martin_Gardner Martin Gardner])1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯([https://en.wikipedia.org/wiki/Bruce_Edwards_Ivins Bruce Edwards Ivins])受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
[[File:s1789059.jpg|200px]]<br />
<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
<br />
===作者简介===<br />
[[File:OIP.jpg|400px]]<br />
<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名[[侯世达]],美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
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侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
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===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
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* 第二部分 EGB<br />
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* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
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薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
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以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
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*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
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*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
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*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
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*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
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===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6795哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-05T11:11:35Z<p>Imp:/* 主题 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔([https://en.wikipedia.org/wiki/Kurt_G%C3%B6del KurtGödel]),艺术家埃舍尔([https://en.wikipedia.org/wiki/M._C._Escher M. C. Escher])和作曲家巴赫([https://en.wikipedia.org/wiki/Johann_Sebastian_Bach Johann Sebastian Bach])的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
[[File:ddd.jpg|200px]]<br />
<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向[https://en.wikipedia.org/wiki/Willard_Van_Orman_Quine Willard Van Orman Quine]致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿基里斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳([https://en.wikipedia.org/wiki/Martin_Gardner Martin Gardner])1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯([https://en.wikipedia.org/wiki/Bruce_Edwards_Ivins Bruce Edwards Ivins])受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
[[File:s1789059.jpg|100px]]<br />
<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
<br />
===作者简介===<br />
[[File:OIP.jpg|400px]]<br />
<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名[[侯世达]],美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
<br />
侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
<br />
* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
<br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
<br />
以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
<br />
*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
<br />
*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6794哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-05T11:11:23Z<p>Imp:/* 主题 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔([https://en.wikipedia.org/wiki/Kurt_G%C3%B6del KurtGödel]),艺术家埃舍尔([https://en.wikipedia.org/wiki/M._C._Escher M. C. Escher])和作曲家巴赫([https://en.wikipedia.org/wiki/Johann_Sebastian_Bach Johann Sebastian Bach])的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
[[File:ddd.jpg|100px]]<br />
<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向[https://en.wikipedia.org/wiki/Willard_Van_Orman_Quine Willard Van Orman Quine]致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿基里斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳([https://en.wikipedia.org/wiki/Martin_Gardner Martin Gardner])1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯([https://en.wikipedia.org/wiki/Bruce_Edwards_Ivins Bruce Edwards Ivins])受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
[[File:s1789059.jpg|100px]]<br />
<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
<br />
===作者简介===<br />
[[File:OIP.jpg|400px]]<br />
<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名[[侯世达]],美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
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侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
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侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
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===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
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* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
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* 第二部分 EGB<br />
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* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
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薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
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===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
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以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
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*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
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*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
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*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
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*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
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===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6793哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-05T11:11:08Z<p>Imp:/* 主题 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔([https://en.wikipedia.org/wiki/Kurt_G%C3%B6del KurtGödel]),艺术家埃舍尔([https://en.wikipedia.org/wiki/M._C._Escher M. C. Escher])和作曲家巴赫([https://en.wikipedia.org/wiki/Johann_Sebastian_Bach Johann Sebastian Bach])的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
[[File:ddd.jpg|400px]]<br />
<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向[https://en.wikipedia.org/wiki/Willard_Van_Orman_Quine Willard Van Orman Quine]致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿基里斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳([https://en.wikipedia.org/wiki/Martin_Gardner Martin Gardner])1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯([https://en.wikipedia.org/wiki/Bruce_Edwards_Ivins Bruce Edwards Ivins])受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
[[File:s1789059.jpg|100px]]<br />
<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
<br />
===作者简介===<br />
[[File:OIP.jpg|400px]]<br />
<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名[[侯世达]],美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
<br />
侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
<br />
* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
<br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
<br />
以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
<br />
*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
<br />
*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E6%96%87%E4%BB%B6:Ddd.jpg&diff=6792文件:Ddd.jpg2020-05-05T11:10:53Z<p>Imp:基于MsUpload的文件上传</p>
<hr />
<div>基于MsUpload的文件上传</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6789哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-05T11:05:28Z<p>Imp:/* 概述 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔([https://en.wikipedia.org/wiki/Kurt_G%C3%B6del KurtGödel]),艺术家埃舍尔([https://en.wikipedia.org/wiki/M._C._Escher M. C. Escher])和作曲家巴赫([https://en.wikipedia.org/wiki/Johann_Sebastian_Bach Johann Sebastian Bach])的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向[https://en.wikipedia.org/wiki/Willard_Van_Orman_Quine Willard Van Orman Quine]致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿基里斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳([https://en.wikipedia.org/wiki/Martin_Gardner Martin Gardner])1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯([https://en.wikipedia.org/wiki/Bruce_Edwards_Ivins Bruce Edwards Ivins])受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
[[File:s1789059.jpg|100px]]<br />
<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
<br />
===作者简介===<br />
[[File:OIP.jpg|400px]]<br />
<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名[[侯世达]],美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
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侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
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侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
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===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
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* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
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* 第二部分 EGB<br />
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* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
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薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
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===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
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以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
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*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
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*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
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*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
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*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
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===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6788哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-05T11:03:13Z<p>Imp:/* 主题 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向[https://en.wikipedia.org/wiki/Willard_Van_Orman_Quine Willard Van Orman Quine]致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿基里斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳([https://en.wikipedia.org/wiki/Martin_Gardner Martin Gardner])1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯([https://en.wikipedia.org/wiki/Bruce_Edwards_Ivins Bruce Edwards Ivins])受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
[[File:s1789059.jpg|100px]]<br />
<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
<br />
===作者简介===<br />
[[File:OIP.jpg|400px]]<br />
<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名[[侯世达]],美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
<br />
侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
<br />
* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
<br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
<br />
以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
<br />
*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
<br />
*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6786哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-05T11:02:07Z<p>Imp:/* 影响 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳([https://en.wikipedia.org/wiki/Martin_Gardner Martin Gardner])1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯([https://en.wikipedia.org/wiki/Bruce_Edwards_Ivins Bruce Edwards Ivins])受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
[[File:s1789059.jpg|100px]]<br />
<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
<br />
===作者简介===<br />
[[File:OIP.jpg|400px]]<br />
<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名[[侯世达]],美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
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侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
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侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
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===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
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* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
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* 第二部分 EGB<br />
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* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
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薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
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===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
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以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
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*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
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*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
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*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
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*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
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===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6784哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-05T10:59:19Z<p>Imp:/* 作者简介 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
[[File:s1789059.jpg|100px]]<br />
<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
<br />
===作者简介===<br />
[[File:OIP.jpg|400px]]<br />
<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名[[侯世达]],美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
<br />
侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
<br />
* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
<br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
<br />
以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
<br />
*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
<br />
*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6694哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-05T03:04:41Z<p>Imp:/* 基本信息 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
[[File:s1789059.jpg|100px]]<br />
<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
<br />
===作者简介===<br />
[[File:OIP.jpg|400px]]<br />
<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
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侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
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===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
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* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
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* 第二部分 EGB<br />
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* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
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薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
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===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
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以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
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*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
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*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
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*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
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*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
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===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
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'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6692哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-05T03:04:30Z<p>Imp:/* 基本信息 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
[[File:s1789059.jpg|40px]]<br />
<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
<br />
===作者简介===<br />
[[File:OIP.jpg|400px]]<br />
<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
<br />
侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
<br />
* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
<br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
<br />
以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
<br />
*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
<br />
*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6691哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-05T03:04:01Z<p>Imp:/* 基本信息 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
[[File:s1789059.jpg|400px]]<br />
<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
<br />
===作者简介===<br />
[[File:OIP.jpg|400px]]<br />
<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
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侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
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===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
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* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
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* 第二部分 EGB<br />
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* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
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薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
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===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
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以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
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*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
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*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
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*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
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*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
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===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
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'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E6%96%87%E4%BB%B6:S1789059.jpg&diff=6690文件:S1789059.jpg2020-05-05T03:03:45Z<p>Imp:基于MsUpload的文件上传</p>
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<div>基于MsUpload的文件上传</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6687哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-05T03:02:32Z<p>Imp:/* 作者简介 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
===作者简介===<br />
[[File:OIP.jpg|400px]]<br />
<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
<br />
侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
<br />
* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
<br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
<br />
以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
<br />
*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
<br />
*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6686哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-05T03:02:15Z<p>Imp:/* 作者简介 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
===作者简介===<br />
[[File:OIP.jpg|400px]]<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
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侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
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===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
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* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
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* 第二部分 EGB<br />
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* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
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薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
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===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
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以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
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*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
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*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
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*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
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*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
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===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
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'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E6%96%87%E4%BB%B6:OIP.jpg&diff=6681文件:OIP.jpg2020-05-05T02:53:30Z<p>Imp:基于MsUpload的文件上传</p>
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<div>基于MsUpload的文件上传</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6424哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-02T02:02:11Z<p>Imp:/* 重点摘要 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
===作者简介===<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
<br />
侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
<br />
* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
<br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
<br />
以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
<br />
*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
<br />
*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6423哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-02T02:01:43Z<p>Imp:/* 重点摘要 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
===作者简介===<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
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侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
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* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
<br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
<br />
以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
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*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
<br />
*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。<br />
分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。<br />
正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6422哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-02T02:01:04Z<p>Imp:/* 重点摘要 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
===作者简介===<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
<br />
侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
<br />
* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
<br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
<br />
以下为本书讨论的部分理论<br />
*邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
<br />
*考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
<br />
*分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。<br />
分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
*同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。<br />
正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
*元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).<br />
<br />
Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6390哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-01T12:41:33Z<p>Imp:/* 参考文献 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
===作者简介===<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
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侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
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* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
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薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
以下为本书讨论的部分理论<br />
邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
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考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
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分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。<br />
分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。<br />
正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).<br />
<br />
Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6389哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-01T12:40:14Z<p>Imp:/* 参考文献 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
===作者简介===<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
<br />
侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
<br />
* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
<br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
以下为本书讨论的部分理论<br />
邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
<br />
考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
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分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。<br />
分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
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同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。<br />
正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
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元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).<br />
<br />
Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* <ref>[https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* <ref>[https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6388哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-01T12:39:35Z<p>Imp:/* 原版目录 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
===作者简介===<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
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侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering 巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground 图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
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* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
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薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
以下为本书讨论的部分理论<br />
邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
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考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
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分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。<br />
分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。<br />
正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).<br />
<br />
Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6387哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-01T12:37:42Z<p>Imp:/* 原版目录 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
===作者简介===<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
<br />
侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering **巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle **MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground *图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry * 符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure * 递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning 信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus 命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) * TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel ** 禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
<br />
* CH 10. Levels of Description & Optimal Systems 在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts 大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts 意念和认知<br />
* CH 13. Bloop, Floop, Gloop * 3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems ** 哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system 哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep 自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others * 邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects * 图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects * 知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops 总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
<br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
以下为本书讨论的部分理论<br />
邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
<br />
考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
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分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。<br />
分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
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同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。<br />
正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
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元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).<br />
<br />
Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
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'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6386哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-01T12:36:20Z<p>Imp:/* 原文摘录 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
===作者简介===<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
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侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering **<br />
巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle **<br />
MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math<br />
PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground *<br />
图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry *<br />
符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure *<br />
递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning<br />
信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus<br />
命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) *<br />
TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel **<br />
禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
<br />
* CH 10. Levels of Description & Optimal Systems<br />
在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts<br />
大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts<br />
意念和认知<br />
* CH 13. Bloop, Floop, Gloop *<br />
3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems **<br />
哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system<br />
哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep<br />
自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others *<br />
邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects *<br />
图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects *<br />
知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops<br />
总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
<br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
以下为本书讨论的部分理论<br />
邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
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考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
<br />
分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。<br />
分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。<br />
正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).<br />
<br />
Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6385哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-01T12:35:55Z<p>Imp:/* 参考文献 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
===作者简介===<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
<br />
侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering **<br />
巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle **<br />
MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math<br />
PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground *<br />
图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry *<br />
符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure *<br />
递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning<br />
信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus<br />
命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) *<br />
TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel **<br />
禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
<br />
* CH 10. Levels of Description & Optimal Systems<br />
在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts<br />
大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts<br />
意念和认知<br />
* CH 13. Bloop, Floop, Gloop *<br />
3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems **<br />
哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system<br />
哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep<br />
自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others *<br />
邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects *<br />
图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects *<br />
知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops<br />
总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
以下为本书讨论的部分理论<br />
邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
<br />
考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
<br />
分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。<br />
分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。<br />
正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).<br />
<br />
Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
* [https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
* [https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
*<br />
<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6384哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-01T12:35:25Z<p>Imp:/* 部分书评 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
===作者简介===<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
<br />
侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering **<br />
巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle **<br />
MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math<br />
PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground *<br />
图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry *<br />
符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure *<br />
递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning<br />
信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus<br />
命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) *<br />
TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel **<br />
禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
<br />
* CH 10. Levels of Description & Optimal Systems<br />
在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts<br />
大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts<br />
意念和认知<br />
* CH 13. Bloop, Floop, Gloop *<br />
3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems **<br />
哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system<br />
哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep<br />
自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others *<br />
邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects *<br />
图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects *<br />
知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops<br />
总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
以下为本书讨论的部分理论<br />
邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
<br />
考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
<br />
分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。<br />
分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。<br />
正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).<br />
<br />
Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
[https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
[https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6383哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-01T12:34:33Z<p>Imp:</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
这本书包含许多递归和自指的实例,其中的对象和观点都在谈论或回指自己。其中之一就是奎因(Quining),这是侯世达创造旨在向Willard Van Orman Quine致敬,指的是产生自己源代码的程序。另一个是索引中有一个虚构的作家Egbert B. Gebstadter,他的名字的首字母为E,G和B,并且姓与Hofstadter后半部分相同。一个被称为“电唱机X”的电唱机机通过播放名为“我不能在电唱机X上播放”(类似于哥德尔的不完全性定理)的唱片,一个关于卡农的检验,还有一个讨论埃舍尔的版画—两只手相互绘出彼此。为了描述这种自指对象,侯世达创造了“怪圈”一词,这是他在后续书《我是个怪圈》中更深入地研究的概念。为了避免这些自指对象带来的许多逻辑矛盾,侯世达讨论了禅宗公案。他试图向读者展示如何通过跳出经验来感知现实,并通过拒绝假设来接受此类悖论性的问题,这种策略也称为“无门”。GEB中讨论了调用栈之类的计算机科学内容,因为一个对话描述了阿喀琉斯和乌龟的冒险,因为他们利用“推入药水”和“弹出药水”来进入和离开不同层次的现实。随后的部分讨论逻辑的基本原理,自指语句,(“无类型”)系统,甚至编程。 侯世达进一步创建了两种简单的编程语言BlooP和FlooP,以说明他的观点。<br />
====谜题====<br />
这本书充满了迷题,包括侯世达著名的MU难题。 另一个例子可以在Contracrostipunctus(对位藏头诗)一章中找到,该名称结合了acrostic(藏头诗)和contrapunctus (counterpoint)。 在阿基里斯与乌龟之间的对话中,作者暗示在提到自己(侯世达)和巴赫的这一章中有一个藏头诗。 可以通过用每个段落的第一个单词来组成以下内容:侯世达的对位藏头诗反向拼写是J.S. 巴赫(中译本:赫赫有名的德国作曲家给了侯世达灵感)。 通过反向阅读单词的第一个字母(粗体),得到“ J S Bach”,这是第二个藏头诗—和第一个藏头诗的描述一致。<br />
====影响====<br />
GEB获得了普利策非科幻类奖[4]和美国国图书奖科学类。[5] [a]马丁·加德纳(Martin Gardner)1979年7月在《科学美国人》上发表的专栏表示:“每隔几十年,会有一位作家带来一本如此有深度,清晰,广博,智慧,美感和创意的书并且它会立刻被公认为重要的作品。” [6]在2007年夏季,麻省理工学院围绕这本书为高中生开设了在线课程。[7]在2010年2月19日关于2001年炭疽热袭击的调查摘要中,联邦调查局表示布鲁斯·爱德华兹·伊文斯(Bruce Edwards Ivins)受这本书的启发,按第404页所建议,使用粗体隐藏了他于2001年9月和10月[8] 寄给炭疽病的信件中基于核苷酸序列的编码。[9] [10] FBI同时也指出他试图将该书扔进垃圾箱来对躲避调查。<br />
====翻译====<br />
侯世达说,当他写这本书时,他从来没有考虑过翻译,但是当他的出版商提出时,他非常想看到GEB如何在其他语言中呈现,特别是法语。可是,他知道翻译时“要考虑一百万个问题”,[11]因为这本书不仅依赖文字游戏,而且还依赖于“结构性双关”,即作品的形式和内容相互镜像(例如“螃蟹卡农”的对话,向前和向后读取的内容几乎完全相同)。<br />
侯世达在“Mr. Tortoise, Meet Madame Tortue”一段中举例说明了翻译方面的麻烦,他说译者“一头扎进了法语中乌龟(Tortue)特指雌性与我书中角色 (Tortoise)的阳刚之气之间的麻烦之中。” [ [11]所以侯世达同意了翻译者的建议,将法语人物命名为Madame Tortue(乌龟女士),将意大利语命名为Signorina Tartaruga。[12]由于其他译者可能还留存于表层意义上的麻烦,侯世达“仔细地浏览了GEB中的每一句话,为翻译人员加了注释,以翻译成任何可能的语言。” [11]<br />
翻译还为侯世达提供了一种创造新含义和双关的途径。例如,中文书名不是永恒金带的翻译,而是一个似乎无关的词组“集异璧”,与GEB的中文谐音对应;为此侯世达特地出版了新书《 Le Ton beau de Marot》,来讨论这类翻译情况。<br />
===基本信息===<br />
* 书名:哥德尔、艾舍尔、巴赫<br />
* 副标题:集异璧之大成<br />
* 作者:侯世达<br />
* 出版地:美国<br />
* 语言:英文/中译本<br />
* 题材:人工智能<br />
* 出版商:Basic Books(英文)<br />
* 商务印书馆(中译本)<br />
* 出版日期:1979年<br />
* 页数:777<br />
* ISBN:978-0465026562<br />
* 所属领域:数理逻辑 哲学 计算机<br />
===作者简介===<br />
道格拉斯·理查·郝夫斯台特(Douglas Richard Hofstadter,1945年2月15日-),中文名侯世达,美国学者、作家。他的主要研究领域包括意识、类比、艺术创造、文学翻译以及数学和物理学探索。 因其著作《哥德尔、埃舍尔、巴赫》获得普立兹奖(非小说 类别) 和美国国家图书奖(科学类别)。<br />
<br />
侯世达是美国印第安纳大学文理学院认知科学杰出教授,主管概念和认知研究中心。他本人和他辅导的研究生组成“流体类推研究小组”。1977年,侯世达原本属于印第安纳大学的计算机科学系,然后他开始了自己的研究项目,研究心理活动的计算机建模(他原本称之为“人工智能研究”,不久就改称为“认知科学研究”)。1984年,侯世达受聘于密歇根大学,任心理学教授,同时负责人类认识研究。1988年,他回到印第安纳大学,任“文理学院教授”,参与认知科学和计算机科学两个学科,同时还是科学史和科学哲学、哲学、比较文学、心理学的兼职教授,当然侯世达本人表示他只是在名义上参与这些系科的工作。2009年4月,侯世达被选为美国文理科学院院士,并成为美国哲学会会员。<br />
<br />
侯世达曾说过他对“以计算机为中心的宅文化感到不适”。他承认“(他的受众中)很大一部分人是被技术吸引”,但提到他的成果“激励了很多学生开始计算机和人工智能方面的研究”时,他回应说尽管他对此感到高兴,但他本人“对计算机没有兴趣”。那次访谈中他谈到一门他在印第安纳大学教授过两次的课程,在那门课程中,他以“怀疑的眼光审视了众多广受赞誉的人工智能项目和整体的发展”。例如,就国际象棋选手卡斯帕罗夫被超级计算机深蓝击败一事,他评论说“这是历史性的转折,但和电脑变聪明了没有关系”。<br />
===内容目录===<br />
====目录大纲====<br />
===== 中文目录 =====<br />
* 目录: 作者为中文版所写的前言<br />
* 译校者的话<br />
* 概览<br />
* 插图目示<br />
* 鸣谢<br />
* 上篇:集异璧geb<br />
* 导言 一首音乐--逻辑的奉献:三部创意曲<br />
* 第一章 wu谜题:二部创意曲<br />
* 第二章 数学中的意义与形式:无伴奏阿基里斯奏鸣曲<br />
* 第三章 图形与衬底:对位藏头诗<br />
* 第四章 一致性、完全性与几何学:和声小迷宫<br />
* 第五章 递归结构和递归过程:音程增值的卡农<br />
* 第六章 意义位于何处:半音阶幻想曲,及互格<br />
* 第七章 命题演算:螃蟹卡农<br />
* 第八章 印符数论:一首无的奉献<br />
* 第九章 无门与歌德尔<br />
* 下篇:异集璧egb<br />
* 前奏曲<br />
* 第十章 描述的层次和计算机系统:蚂蚁赋格<br />
* 第十一章 大脑和思维:英、法、德、中组曲<br />
* 第十二章 心智和思维:咏叹调及其种种变奏<br />
* 第十三章 bloop和floop和gloop:g弦上的咏叹调<br />
* 第十四章 论tnt及有关系统中形式上不可判定的命题:生日大合唱哇哇哇乌阿乌阿乌阿<br />
* 第十五章 跳出系统:一位烟民富于启发性的思想<br />
* 第十六章 自指和自复制:的确该赞美螃蟹<br />
* 第十七章 丘奇、图灵、塔斯基及别的人:施德鲁,人设计的玩具<br />
* 第十八章 人工智能:回顾:对实<br />
* 第十九章 人工智能:展望:树懒卡农<br />
* 第二十章 怪圈,或缠结的层次结构:六部无插入赋格<br />
* 注释<br />
* 文献目录<br />
* 索引<br />
===== 原版目录 =====<br />
第一部分 GEB<br />
<br />
* Introduction: A Musico-Logical Offering **<br />
巴赫觐见国王, 加农和赋格, 艾舍尔, 哥德尔, 计算机, 人工智能, 图灵<br />
* CH 1. The MU puzzle **<br />
MIU-系统, 形式系统,公理,定理,规则<br />
* CH 2. Meaning and Form in math<br />
PQ-系统及其含义,同构性,真,证明,符号操作,形式<br />
* CH 3. Figure and ground *<br />
图像/背景, 理论/非理论, 递归可数集合/递归集合<br />
* CH 4. Consistency, Completeness and Geometry *<br />
符号获得其含义, 欧氏几何/非欧几何, 隐式/显式含义, 知觉<br />
* CH 5. Recursion and Structure *<br />
递归, 栈, 出现在: 音乐/语言学/几何/数学/物理/程序设计<br />
* CH 6. Location of meaning<br />
信息/解码/接收器, DNA/古代文字石刻/宇航中的留声机, 智能/绝对含义<br />
* CH 7. The propositional calculus<br />
命题代数,形式规则,同构性,含义的自动获取<br />
* CH 8. Typographical Number Theory (TNT) *<br />
TNT: 命题代数的扩展, 数字理论推理转化为符号操作<br />
* CH 9. Mumon and Gödel **<br />
禅,偈, 和数学的类似之处, 哥德尔编码, 哥德尔定理简介<br />
<br />
* 第二部分 EGB<br />
<br />
* CH 10. Levels of Description & Optimal Systems<br />
在不同的层次观察绘画,象棋,计算机系统。中间层的存在性<br />
* CH 11. Brains and Thoughts<br />
大脑的结构, 意念和思想, 概念和神经元活动<br />
* CH 12. Minds and Thoughts<br />
意念和认知<br />
* CH 13. Bloop, Floop, Gloop *<br />
3种计算机语言. Bloop: 可预测有限搜索, Floop: 不可预测/无限搜索. 元递归函数/一般递归函数<br />
* CH 14. formally undecidable proposition of TNT & related systems **<br />
哥德尔定理的证明. TNT的自洽导致其不完备<br />
* CH 15. Jumping out of the system<br />
哥德尔定理的普适性,TNT不仅是不完备,而且是本质上不完备<br />
* CH 16. Self-Ref and Self-Rep<br />
自指和自我复制的关系,信息在层次间的流动,分子生物学<br />
* CH 17. Church, Turing, Tarski and others *<br />
邱奇-图灵猜想,图灵停机问题,塔斯基不可定义定理. 人工智能和人脑过程<br />
* CH 18. AI: retrospects *<br />
图灵,图灵测试,游戏,定理证明,问题解答,谱曲,数学,自然语言<br />
* CH 19. AI: prospects *<br />
知识表示 (knowledge representation),frames,概念的相互作用,创造性. 关于AI的十个问题和猜想<br />
* CH 20. Strange loops<br />
总结 等级 (hierarchy) 和自指. 哥德尔,艾舍尔,巴赫再聚首<br />
<br />
====原文摘录====<br />
一个人永远也不能给出一个最终的、绝对的证明,去阐明在某个系统中的一个证明是正确的。当然,一个人可以给出一个关于证明的证明,或者关于一个证明的证明的证明——但是,最外层的系统有效性总还是一个未经证明的假设,是凭我们的信仰来接收的。<br />
——— 引自章节:第七章 命题演算 <br />
薛定谔的非周期性晶体结构:是什么东西使我们在某些对象中看到框架信息,而在另一些对象中看不到呢?当外星人截获了一张在太空中漂游的唱片时,他们凭什么假定其中隐含着消息?一张唱片和一块陨石有什么不同?显然,其几何形状提供了最初的线索,说明“这是些有趣的东西”。唱片螺线…DNA碱基对双螺旋排列…薛定谔…纯理论预言好认为遗传信息一定是存储于“非周期性晶体结构”之中。事实上,书籍本身就是规整的几何形状中的非周期性晶体结构。这些例子说明,一旦我们在某处发现一个非常规则的几何结构中“包裹着”非周期性晶体结构,那里就可能隐藏着一些内在消息。<br />
———引自章节 第六章 意义位于何处<br />
===重点摘要===<br />
《哥德尔、艾舍尔、巴赫:集异璧之大成》的内容是如此宽泛,讲了音乐(巴赫),讲了艺术(艾舍尔 Maurits Cornelius Escher,1898-1972),讲了分子生物学、计算机语言、人工智能以至禅。多年来,许多读者读毕全书,竟然归纳不出这《哥德尔、艾舍尔、巴赫:集异璧之大成》究竟是要说什么。答案正如作者所说:“我认识到,哥德尔、埃舍尔和巴赫只是用不同的方式来表达一样相同的本质。我尝试重现这种本质而写出这本书。<br />
因此此书在深层次上并非研究这三个人。那只不过是通往该书中心主题的其中一条路——侯世达在序言指出:“到底文字和思想是否依从俱形式的规则?这正是此书的中心问题。”(Do words and thoughts follow formal rules, or do they not? That problem is the problem of this book.)<br />
以下为本书讨论的部分理论<br />
邱奇-图灵论题(英语:Church–Turing thesis,又称邱奇-图灵猜想,邱奇论题,邱奇猜想,图灵论题)是一个关于可计算性理论的假设。该假设论述了关于函数特性的,可有效计算的函数值(用更现代的表述来说--在算法上可计算的)。简单来说,邱奇-图灵论题认为“任何在算法上可计算的问题同样可由图灵机计算”。<br />
<br />
考拉兹猜想(英语:Collatz conjecture),又称为奇偶归一猜想、3n+1猜想、冰雹猜想、角谷猜想、哈塞猜想、乌拉姆猜想或叙拉古猜想,是指对于每一个正整数,如果它是奇数,则对它乘3再加1,如果它是偶数,则对它除以2,如此循环,最终都能够得到1。<br />
<br />
分形(英语:fractal,源自拉丁语:frāctus,有“零碎”、“破裂”之意),又称碎形、残形,通常被定义为“一个粗糙或零碎的几何形状,可以分成数个部分,且每一部分都(至少近似地)是整体缩小后的形状”,即具有自相似的性质。 分形在数学中是一种抽象的物体,用于描述自然界中存在的事物。人工分形通常在放大后能展现出相似的形状。 分形也被称为扩展对称或展开对称。如果在每次放大后,形状的重复是完全相同的,这被称为自相似。<br />
分形与其他几何图形相似但又有所不同。当你缩放一个图形时,你就能看出分形和其他几何图形的区别。将一个多边形的边长加倍,它的面积变为原来的四倍。新的边长与旧边长相比增加了 2 倍,而面积增加了 4 倍。平面内的多边形在二维空间中,指数 2 刚好是多边形所在的二维空间的维数。类似的,对于三维空间中的球,如果它的半径加倍,则它的体积变为原来的 8 倍,指数 3 依旧是球所在空间的维数。如果将分形的一维长度加倍,此时不一定是以整数的幂进行缩放。<br />
<br />
同构(英语:isomorphism)指的是一个保持结构的双射。在更一般的范畴论语言中,同构指的是一个态射,且存在另一个态射,使得两者的复合是一个恒等态射。<br />
正式的表述是:同构是在数学对象之间定义的一类映射,它能揭示出在这些对象的属性或者操作之间存在的关系。若两个数学结构之间存在同构映射,那么这两个结构叫做是同构的。一般来说,如果忽略掉同构的对象的属性或操作的具体定义,单从结构上讲,同构的对象是完全等价的。<br />
<br />
元定理(metatheorem)A notable early citation is Quine's 1937 use of the word "metatheorem",[6] where meta- has the modern meaning of "an X about X". (Note earlier uses of "meta-economics" and even "metaphysics" do not have this doubled conceptual structure – they are about or beyond X but they do not themselves constitute an X).<br />
<br />
Douglas Hofstadter, in his 1979 book Gödel, Escher, Bach (and in the sequel, Metamagical Themas), popularized this meaning of the term. The book, which deals with self-reference and strange loops, and touches on Quine and his work, was influential in many computer-related subcultures and may be responsible for the popularity of the prefix, for its use as a solo term, and for the many recent coinages which use it.[7] Hofstadter uses meta as a stand-alone word, as an adjective and as a directional preposition ("going meta," a term he coins for the old rhetorical trick of taking a debate or analysis to another level of abstraction, as when somebody says "This debate isn't going anywhere"). This book may also be responsible for the association of "meta" with strange loops, as opposed to just abstraction.[citation needed] The sentence "This sentence contains thirty-six letters," and the sentence which embeds it, are examples of "metasentences" referencing themselves in this way.<br />
===部分书评===<br />
"Every few decades an unknown author brings out a book of such depth, clarity, range, wit, beauty and originality that it is recognized at once as a major literary event. This is such a work."<br />
'''--- Martin Gardner, Scientific American'''<br />
<br />
'''摘自豆瓣网友:邱小石'''<br />
80年代之后,计算机的能力爆炸性增长,紧接着互联网时代的到来,基于大数据下的计算使电脑不断的解决人们实际的问题。最恰当的例子如GOOGLE翻译,人们认为,自然语言理论的确立,在大数据下的支持下,只要不断累积数据,积累足够多的例子,最终会使电脑接近人脑的处理。<br />
侯世达不是这么看的,他认为这根本不是人工智能。这只是人给予电脑的命令而不是电脑自己的思考。比如计算机国际象棋战胜世界冠军,它只是能够大量的快速运算各种可能,最后选择一种得分最高的下法,这种大数据和编程为基础的方向,完全忘记了人工智能的真正含义。<br />
计算机至今无法识别一个手写的A,这就是“验证码”的由来,需要知道所有A有什么共同特点,“需要理解思维范畴的流动本质”,大脑有办法透过不相关的表面信息直击要害,提取核心,从你的想法和经历中找到一个故事或一句话来回应,“运用创造性类比”,这才是人类智慧的核心。<br />
侯世达在1980年之后的30多年以来,一直很落寞的自我心理建设的做着自己认为正确的方向研究,大部分时间都消磨在自己的书房,按照侯世达的说法,现在的人工智能都在研究产品,而他一直在探索“什么是思考”。这很像一个输家对功利世界的抱怨以及自我安慰。<br />
前后的阅读最令我震动的是下面发生的事,它和我的直接体验有关。<br />
GOOGLE翻译刚出来的时候,我欣喜若狂,我在想,虽然它现在翻译不准确,但五六年后,大数据的运算,一定会最终解决翻译的问题,我们再也没有学习语言的烦恼。情况真的如此吗?GOOGLE的工程师发现,系统依然在变好,但进步的幅度明显变小了。我自己使用GOOGLE翻译的体验,这个感觉很强烈,最近几年,我感受不到它的改变。<br />
举个简单的例子,说明语言的复杂性。我跟朋友散步,路遇车位管理人员指挥一个司机停车,大声的叫:“打死了,打死了!”GOOGLE翻译如何理解?需要多大的数据才能理解?自然语言生成理论的数据收集,和语言的随机性、跳跃性以及发展变化,节奏能够同步么?这让我想到宇宙,它还在不断膨胀,人类需要探索的空间,是增大了,还是变小了?<br />
思考的歧途?思考一下侯世达的“思考”,也是有趣的。<br />
'''摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ'''<br />
GEB is a singularity of very cool ideas.<br />
Some of the topics explored: artificial intelligence, cognitive science, mathematics, programming, consciousness, zen, philosophy, linguistics, neuroscience, genetics, physics, music, art, logic, infinity, paradox, self-similarity. Metamathematics. Metathinking. Meta-everything.<br />
The author said he was trying to make the point that consciousness was recursive, a kind of mental fractal. Your mind will certainly feel that way when you are done.<br />
This is not a dry discussion of these topics. The author recognizes that he's exploring things that are intrinsically fascinating and fun, and has fun with them the whole way through. He doesn't just discuss the ideas, he demonstrates them, sometimes while he's discussing them, in clever and subtle ways.<br />
Inbetween chapters, he switches to a dialogue format between fantasy characters; here he plays with the ideas being discussed, and performs postmodern literary experiments. For example, one of his dialogues makes sense read both forwards and backwards. In another, the characters jump into a book, and then jump deeper into a book that was in the book. In yet another, a programmer calmly explains the function and output of a chatbot while the chatbot calmly explains the function and output of the programmer. I find the author's sense of humor in these delightful.<br />
In a word, it's brilliant. GEB combines the playful spirit of Lewis Carroll, the labyrinthine madness of Borges, the structural perfectionism of Joyce, the elegant beauty of mathematics, and the quintessential fascination of mind, all under one roof. It's become something of a cult phenomenon, and it has its own subreddit, r/GEB, and even its own MIT course.<br />
<br />
Does the book succeed in its goal? One of the common criticisms is that the author never gets to the point and proves his thesis, and instead spends time on endlessly swirling diversions. But I don't blame him; the task of connecting mind to math is insanely speculative territory. All he can do is spiral the topic and view it from every conceivable direction. He decided to take a loopy approach to a loopy idea, and I think that's very fitting. If you want a more linear approach to the same idea, you could read I Am A Strange Loop. However, the way GEB weaves a tapestry of interrelated ideas, rather than focusing on just one, is a major part of its charm.<br />
In the grand line of reductionism, where we in theory reduce consciousness to cognitive science to neuroscience to biology to chemistry to physics to math to metamath, GEB positions itself at the wraparound point at unsigned infinity, where the opposite ends of the spectrum meet.<br />
It is an utter gem, a classic, and a pleasure to read. I cannot recommend it enough.<br />
=== 相关书籍===<br />
* Metamagical Themas (ISBN 0-465-04566-9) (collection of Scientific American columns and other essays, all with postscripts)<br />
* Ambigrammi: un microcosmo ideale per lo studio della creatività (ISBN 88-7757-006-7) (in Italian only)<br />
* 《表象与本质》 Fluid Concepts and Creative Analogies (co-authored with several of Hofstadter's graduate students) (ISBN 0-465-02475-0)<br />
* Rhapsody on a Theme by Clement Marot (ISBN 0-910153-11-6) (1995, published 1996; volume 16 of series The Grace A. Tanner Lecture in Human Values)<br />
* Le Ton beau de Marot: In Praise of the Music of Language (ISBN 0-465-08645-4)<br />
* 《我是个怪圈》 I Am a Strange Loop (ISBN 0-465-03078-5) (2007)<br />
* Surfaces and Essences: Analogy as the Fuel and Fire of Thinking, co-authored with Emmanuel Sander (ISBN 0-465-01847-5) (first published in French as L'Analogie. Cœur de la pensée; published in English in the US in April 2013)<br />
=== 参考文献 ===<br />
[https://book.douban.com/review/6645917/ 摘自豆瓣网友:邱小石]<br />
[https://www.amazon.com/-/zh/gp/customer-reviews/R1APIOHTQMP6TS/ref=cm_cr_dp_d_rvw_ttl?ie=UTF8&ASIN=0465026567 摘自亚马逊Customer Review:Ƹ̵̡Ӝ̵̨Ʒ]<br />
=== 英文书籍资料 ===<br />
[https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden/dp/0465026567 1、亚马逊的购买链接]<br />
<br />
[https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach 2、维基百科的介绍]<br />
===编辑推荐 ===<br />
* [https://swarma.org/?p=18525 分形几何:寻找隐藏的维度 | 集智百科]<br />
* [https://swarma.org/?p=13678 埃舍尔画作中的数学秘密]<br />
* [https://swarma.org/?p=3034 自指——连接图形与衬底的金带]</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6347哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-01T07:05:34Z<p>Imp:/* 结构 */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(鸡尾酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
<br />
====主题====<br />
<br />
====谜题====<br />
<br />
====影响====<br />
<br />
====个性翻译====<br />
<br />
===基本信息===<br />
<br />
===作者简介===<br />
<br />
===内容目录===<br />
====目录大纲====<br />
====原文摘录====<br />
<br />
===重点摘要===<br />
<br />
===部分书评===<br />
<br />
=== 相关书籍===<br />
<br />
=== 参考文献 ===<br />
<br />
=== 英文书籍资料 ===<br />
<br />
===编辑推荐 ===</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6346哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-05-01T07:04:51Z<p>Imp:</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统本身是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法与局限性,甚至是“意义”本身的意义。<br />
为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。本书中一个观点表达了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
“以刘易斯·卡罗尔的精神对心智和机器进行隐喻的赋格”出版者如此描述这本书。[3]<br />
====结构====<br />
GEB采取了交织的叙事形式。主要章节交替出现在虚构人物之间,通常是阿基里斯与乌龟之间的对话,最初由芝诺(Zeno of Elea)使用,后来由刘易斯·卡洛尔(Lewis Carroll)在《乌龟对阿基里斯说了啥》中使用。这些初始角色与前两次对话有关,后来的对话引入了新角色,比如“螃蟹”。这些叙述经常浸入自指和元小说中。文字游戏在书中也很突出。双关语有时被用来连接概念,例如“ Magnificrab,indeed”与巴赫’‘magnificat in D’‘谐音相同。 "SHRDLU, Toy of Man's Designing" 与"Bach's Jesu, Joy of Man's Desiring";以及“印符数论”—“ TNT”(Typographical Number Theory)——当试图对自身进行陈述时,不可避免地会发生“爆炸”。一个对话包含一个有关精灵(来自阿拉伯语“ Djinn”)和各种“ tonics(调酒)”(液体和音乐混合)的故事,标题为“ Djinn and Tonic”。书中的一个对话以螃蟹卡农的形式写成,其中点之前的每一行对应于中点之后的同一行。由于使用了可以用作见面问候或告别(good day)的常用短语,并且将所在行数翻倍用作原下一行问题的答案,因此对话仍然有意义。另一个是树懒卡农,其中一个字符重复另一个字符,但速度较慢且取反。<br />
====主题====<br />
<br />
====谜题====<br />
<br />
====影响====<br />
<br />
====个性翻译====<br />
<br />
===基本信息===<br />
<br />
===作者简介===<br />
<br />
===内容目录===<br />
====目录大纲====<br />
====原文摘录====<br />
<br />
===重点摘要===<br />
<br />
===部分书评===<br />
<br />
=== 相关书籍===<br />
<br />
=== 参考文献 ===<br />
<br />
=== 英文书籍资料 ===<br />
<br />
===编辑推荐 ===</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6269哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-04-30T14:05:31Z<p>Imp:</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
=== 内容简介 ===<br />
<br />
====概述====<br />
哥德尔(Gödel),埃舍尔(Escher),巴赫(Bach):永恒的金色纽带,简称为GEB,是道格拉斯·霍夫施塔特(Douglas Hofstadter)于1979年所著。通过探讨逻辑学家哥德尔(KurtGödel),艺术家埃舍尔(M. C. Escher)和作曲家巴赫(Johann Sebastian Bach)的生活和作品中的共同主题,该书阐述了数学,对称性和智能的基本概念。通过说明和分析,这本书讨论了系统如何通过自指和形式规则来获得意义,尽管系统是由“无意义的”元素构成的。它还讨论了交流的含义,如何表示和存储知识,符号表示的方法和限制,甚至是“意义”本身的意义。<br />
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为了回应对本书主题的困惑,侯世达(霍夫施塔特)强调说,《G.E.B.》与数学,艺术和音乐之间的关系无关,而是与隐藏的神经机制如何产生认知有关。这本书中有一点提出了一个类比,即通过将大脑中的单个神经元与蚁群中表现出的社会组织进行比较,从而阐明大脑如何协调而产生统一的思想。[1] [2]<br />
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出版商使用标语“以刘易斯·卡罗尔的精神对机器进行隐喻的赋格”来描述这本书。[3]<br />
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=== 英文书籍资料 ===<br />
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===编辑推荐 ===</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6150哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-04-30T04:12:18Z<p>Imp:</p>
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<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Linked:Gödel, Escher, Bach: An Eternal Golden Braid ==<br />
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====原文摘录====<br />
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===重点摘要===<br />
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===部分书评===<br />
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=== 相关书籍===<br />
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=== 参考文献 ===<br />
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=== 英文书籍资料 ===<br />
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===编辑推荐 ===</div>Imphttps://wiki.swarma.org/index.php?title=%E5%85%A5%E9%97%A8%E4%BB%BB%E5%8A%A1%E6%B8%85%E5%8D%95&diff=6138入门任务清单2020-04-30T03:54:28Z<p>Imp:/* 书籍列表 */</p>
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<div>请大家在以下的书籍或者人物列表中任选一个,参考相应的模板为其建立主页。选定词条后请在后面写上自己的名字以标注,避免重复操作~<br />
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== 书籍列表 ==<br />
[[书籍模板]]、优秀的书籍案例:[[链接:网络新科学 Linked: The New Science of Networks]]<br />
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[[规模 Scale]](施工中: Ricky)<br />
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生命体、城市、公司,乃至一切复杂万物,是否都存在相通的内在生长逻辑?《规模》将帮助你重新思考生命、认识自身、了解你的生活与工作,并告诉你复杂世界其实充满简单的逻辑,只要跳脱思维框架,打破学科限制,你就会重新看清你周遭的一切。<br />
本书作者[[杰弗里·韦斯特 Geoffery West]]是全球复杂性科学研究中心、“没有围墙的”学术圣地——[[圣塔菲研究所 Santa Fe Institute]]前所长,数十年致力于“规模”的研究工作,其研究成果被应用在理解生命体、城市可持续发展、企业运营等众多领域,被业内奉为“跨学科诺贝奖”的不二人选。北京师范大学教授、集智俱乐部创始人张江,是这本书的校译者。<br />
集智俱乐部特别邀请[[杰弗里·韦斯特 Geoffery West]]在 AI&Society 学术沙龙做专场报告,深入解读了《规模》一书背后系统性的规模法则(Scaling Law)。在[[杰弗里·韦斯特 Geoffery West]]眼中,人类创新与发展呈现出超指数增长态势,奇点(singularity)正在快速临近。<br />
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标签:复杂系统,城市科学<br />
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作者:[[杰弗里·韦斯特 Geoffery West]]<br />
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[[Networks: An Introduction]](未建立词条)<br />
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著名网络科学学者、密歇根大学物理学杰出教授、[[圣塔菲研究所 Santa Fe Institute]]外聘教授 Mark Newman凭借在计算机、信息论、物理等相关学科的深入研究和丰富经验,系统地分析和论述了网络理论在现实生活各方面的应用,在2010年出版了网络科学领域的权威书籍 Networks:An Introduction ,有中译版《网络科学引论》。<br />
在2018年9月初,由牛津大学出版社出版了 Networks: An Introduction 的第二版,更新了网络科学的最新研究突破和进展,包括社区检测(community detection)、复杂网络传播(complex contagion)、网络统计(network statistics)和多层网络(multilayer networks)等网络科学的最新研究进展。<br />
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标签:网络科学,圣塔菲研究所<br />
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作者:Mark Newman<br />
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[[复杂 complexity]](未建立词条)<br />
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2018年2月,备受推崇的复杂性科学科普读物、经典译作《复杂》再版了。为什么蚂蚁在组成群体时表现得如此精密而有目的?数以亿计的神经元是如何产生出像意识这样极度复杂的事物?是什么在引导免疫系统、互联网、全球经济和人类基因组等自组织结构?这些迷人而令人费解的问题都是复杂系统科学尝试回答的一部分。<br />
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在《复杂》一书中,波特兰州立大学计算机科学专业教授、[[圣塔菲研究所 Santa Fe Institute]]客座教授[[梅拉妮·米歇尔Melanie Mitchell]]以清晰的思路介绍了复杂系统的研究,横跨生物、技术和社会学等领域,并探寻复杂系统的普遍规律,与此同时,她还探讨了复杂性与进化、人工智能、计算、遗传、信息处理等领域的关系。<br />
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标签:复杂性科学理论,科普 <br />
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作者:[[梅拉妮·米歇尔Melanie Mitchell]]<br />
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[[重塑:信息经济的结构]](未建立词条)<br />
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《重塑:信息经济的结构》是一本复杂性科学学者完成的经济学作品。作者包括信息经济先行者、深具国际影响力的理论物理学家之一、金融市场少数者博弈模型提出者[[张翼成]],国家优秀青年基金获得者、电子科技大学教授[[吕琳媛]],和电子科技大学教授、成都市新经济发展研究院执行院长[[周涛]]。<br />
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《重塑》一书,系统分析了传统经济学的缺陷,首次将“信息”这一重要的无形产品真正纳入经济解释的分析框架,引入了分配、创造的新范式,为新经济提供了与之配套的新理论、新方法和新政策,为中国经济的转型升级提供了核心动力。<br />
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标签:复杂系统 金融系统<br />
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作者:[[吕琳媛]] [[张翼成]] [[周涛]]<br />
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[[宇宙从何而来]](未建立词条)<br />
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从混沌到宇宙诞生,从气态到固态;从原子分子到生命形成,从原始生产到人工智能。霍金向人类发问:我们为何在此?我们从何而来?物理学家不断探索宇宙意义,是在寻找万物来路。<br />
东京大学博士后研研究员、知乎物理学领域优秀答主、集智科学家傅渥成,在《宇宙从何而来》中,尝试采用系统科学和复杂性的视角,重新看待整个物理学。这是一本有深度又好读的科普好书。<br />
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标签:混沌 物理<br />
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作者:[[傅渥成]]<br />
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[[计算传播学导论]](施工中:FlyingdoubleG)<br />
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在大数据和人工智能时代,未来的计算社会科学家更需要训练问题意识、培养计算思维、增强数据挖掘和分析的能力。作为计算传播学的首部系统性的中文专著,本书详细总结了“计算传播学”的传播学研究范式,和数据收集、分析、结果呈现的实践经验。<br />
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《计算传播学导论》作者包括北京师范大学数字媒体系副教授、香港城市大学博士、中文信息学会社会化媒体专业委员会委员张伦,南京大学新闻传播学院副教授、计算传播学学会秘书长、集智科学家[[王成军]],大连民族大学计算机科学学院教授许小可。<br />
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标签:社会学 计算科学<br />
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作者:张伦 [[王成军]] 许小可<br />
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[[三生有幸:幸福心理学的三种时间尺度]](未建立词条)<br />
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意识从何而来?心流从何而来?任教于复旦大学的“集友”李晓煦,从时间尺度扩展了 Daniel Dennett 的多重草稿意识模型,对 Mihalyi Csikszentmihalyi 心流(flow)学说的“大我” 体验和存在主义心理学的“使命”体验给出统一的操作化解释。 <br />
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标签:意识科学 心理学<br />
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作者:李晓煦<br />
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[[深度思考 Deep Thinking: Where Machine Intelligence Ends and Human Creativity Begins]](未建立词条)<br />
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20年前,国际象棋世界冠军加里·卡斯帕罗夫(Garry Kasparov)被IBM公司的超级计算机“深蓝”击败。20年后,卡斯帕罗夫在《深度思考——人工智能的终点与人类创造力的起点》一书中强有力地论证了:人类不应害怕我们最为非凡的创造物,而应与之协作,达到新的高度。《深度思考》是集智俱乐部多位译友,以众包翻译的形式完成的作品。<br />
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标签:人工智能 众包译作<br />
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作者:[[集智俱乐部]]<br />
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[[我是个怪圈 I am not a Loop]](未建立词条)<br />
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著名学者、神书《GEB》作者[[侯世达]],在《GEB》出版30余年后,侯世达完成了I am not a Loop,把自我和意识的本质当做一种“怪圈”(loop),讨论了在哥德尔不完备性定理中得到充分说明的自我指涉(self-reference)如何刻画了我们的心智。其中文版《我是个怪圈》于2018年出版。<br />
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标签:意识科学 认知神经<br />
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作者:[[侯世达]]<br />
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[[同步 Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life]](未建立词条)<br />
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本书讲述了宇宙中的同步现象,秩序会从混沌中自发产生。<br />
本书作者[[斯蒂芬·斯托加茨(Steven Strogatz)]],曾担任哈佛大学和麻省理工学院讲师,1994年成为康奈尔大学应用数学教授,在混沌理论和复杂性理论方面的开创性研究工作获得了广泛认可。<br />
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标签:混沌 涌现<br />
作者:[[斯蒂芬·斯托加茨(Steven Strogatz)]]<br />
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[[复杂经济学 Complexity and the Economy]](未建立词条)<br />
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[[圣塔菲研究所 Santa Fe Institute]]元老、斯坦福大学经济学教授、“复杂经济学”创始人、“拉格朗日奖”“熊彼特奖”得主[[布莱恩·阿瑟 W.Brian Arthur]]重磅新书。作为“复杂经济学”的创始人,布莱恩·阿瑟在本书中汇集了多年对复杂经济学的研究。其核心思想可以归结为:经济不一定处于均衡状态,演绎推理将被归纳推理所取代。<br />
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标签:经济学 金融系统<br />
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作者:[[布莱恩·阿瑟 W.Brian Arthur]]<br />
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[[多样性红利 The Difference]](未建立词条)<br />
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多样性和能力哪个更重要?人和计算机相比谁拥有更多样性的视角?[[圣塔菲研究所 Santa Fe Institute]]外聘教授、密歇根大学复杂性研究中心掌门人[[斯科特·佩奇 Scott Page]] 在《多样性红利》中,给出多样性视角、启发式、预测和解释模型四个认知工具箱,并得出惊人结论——一个人是否聪明不是由智商决定的,而取决于认知工具的多样性!本书将告诉你如何应用工具箱中的工具,用多样性创造更多的红利。<br />
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标签:圣塔菲 复杂性研究<br />
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作者:[[斯科特·佩奇 Scott Page]]<br />
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[[复杂的引擎 The Engine of Complexity]](未建立词条)<br />
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本书结合信息、进化和计算对生物进化进行了阐释,证明了计算在进化中的核心作用,并将这套计算和进化相结合的核心机制扩展到其他领域,用来解释复杂生命、结构、组织和社会秩序的形成。这是一次正在进行的重大的科学认知范式的转换,它不仅会改变科学,也会改变人类对自身境况的认知。<br />
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该书作者约翰•E.梅菲尔德,是美国爱荷华州立大学遗传、发育、和细胞生物学名誉教授,同时也是加州理工学院、卡耐基梅隆大学和哈佛大学的兼职教授。他致力于利用数学和物理学原理研究广义进化理论,并应用于认知和社会文化领域。<br />
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标签:物理学 计算科学<br />
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作者:约翰•E.梅菲尔德<br />
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[[巴拉巴西成功定律 The Formula: The Universal Laws of Success]](厚朴已建立词条)<br />
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[[艾伯特-拉斯洛·巴拉巴西 Albert-László Barabási]] 作为网络科学的领军人物,是东北大学的杰出大学教授。曾出版过[[《链接:网络新科学 Linked: The New Science of Networks》]]、《爆发》等多部畅销科普作品。在他最新的科普著作中,开创性地揭示了促进成功的科学原理,为人们在当今社会中如何取得成功提供了新的启迪。<br />
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在这本“成功公式”中,[[艾伯特-拉斯洛·巴拉巴西 Albert-László Barabási]]借助于大数据分析和历史案例探究,解释了谁能成为拔得头筹及其原因的潜在规则,并梳理出决定这一现象的十二条法则,以及我们如何利用这些法则来发挥自己的专长。<br />
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标签:网络科学<br />
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作者:[[艾伯特-拉斯洛·巴拉巴西 Albert-László Barabási]]<br />
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[[复杂科学的哲学 Philosophy of Complex Systems]](未建立词条)<br />
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本书由澳大利亚纽卡斯尔大学的哲学教授、复杂适应性系统研究小组的主任Clifford A.Hooker所著,内容全面覆盖了复杂系统的哲学理论,描述了非线性系统及其复杂性在哲学方面的独特影响。<br />
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标签:哲学 复杂理论<br />
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作者:[[Clifford A.Hooker]]<br />
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[[社会和生态科学的复杂性和韧性 Untangling Complex Systems: A Grand Challenge for Science]](未建立词条)<br />
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通过对多学科的处理,尤其是化学、生物、物理、经济和哲学,化学博士Pier Luigi Gentili 在本书中,给出了解开复杂系统的一个教学路线和研究路径,论述了自然复杂性和计算复杂性的相关联性,为如何理解复杂系统的新理论形式铺平了道路。<br />
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标签:应用 自然科学<br />
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作者:Pier Luigi Gentili<br />
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[[数字时代的社会生态学 Social Ecology in the Digital Age—Solving Complex Problems in a Globalized World]](未建立词条)<br />
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本书是由著名学者丹尼尔·斯托克斯(Daniel Stokols)所著,他全面概述了社会生态理论、研究和实践应用,提炼总结了生态科学各个方面的关键原则,为跨学科的研究和社会问题的解决提供了一个强有力的框架。本书强调了多规模跨科学研究在解决现代生活的复杂问题方面的重要价值,将生态思维扩展到了我们今天所处的数字世界和虚拟世界。<br />
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标签:社会理论 跨学科<br />
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作者:丹尼尔·斯托克斯(Daniel Stokols)<br />
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[[命名博弈:研究语言的形成与演化 Naming Game: Models, Simulations and Analysis]](未建立词条)<br />
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本书由香港城市大学电子工程学系[[陈关荣]]老师和香港城市大学混沌与复杂网络中心楼洋博士合著。这本书详细地、完整地介绍了命名博弈。本书已于2019年1月正式出版。这本书详细地、完整地介绍了命名博弈。本书总共有八个章节,从最小命名博弈开始,到命名博弈和复杂网络结合,命名博弈在复杂网络上的应用,最后介绍了命名博弈与多种语言的关系,最重要的是,还提出作者自己的研究发现和发展,为未来的研究发展打下了坚实的基础。<br />
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标签:理论基础<br />
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作者:[[陈关荣]] 楼洋<br />
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[[迈向数字化的启蒙:数字革命双刃剑 Towards Digital Enlightenment: Essays on the Dark and Light Sides of the Digital Revolution]](未建立词条)<br />
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如斯诺登等人爆料出存在大规模监视行为那样,这个社会似乎在走向技术极权道路。紧接着苏黎世联邦理工学院计算社会学教授、苏黎世联邦理工学院风险中心创始人之一Dirk Helbing 出版了这本书。现在越来越清楚的是,我们正在迅速走向一个机器控制的社会,在这个社会中,算法和社交机器的隐含目标,就是控制社会变化和个人行为。<br />
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标签:社交媒体 社会生态<br />
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作者:Dirk Helbing <br />
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[[为什么:因果关系的新科学 The Book of Why: The New Science of Cause and Effect]](未建立词条)<br />
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本书作者Judea Pearl 是贝叶斯网络之父、人工智能领域的先驱。在本书中,Pearl认为,人工智能已经在近十几年的快速发展中陷入了僵局。人工智能如何进一步发展?Pearl 的想法是,教会机器理解问题背后的根源,这才是“真正的智能”。<br />
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标签:哲学 人工智能<br />
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作者:[[Judea Pearl] <br />
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[[表象与本质 ]](未建立词条)<br />
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在[[侯世达]]和法国心理学家埃马纽埃尔·桑德(Emmanuel Sander )合著的书Surfaces and Essences:Analogy as the Fuel and Fire of Thinking 中,两位作者就阐明表象、本质和类比这三个核心概念之间的关联。<br />
人类大脑中的每个概念都源于多年来不知不觉中形成的一长串类比,这些类比赋予每个概念生命,我们在一生中不断充实这些概念。大脑无时无刻都在作类比。类比,就是思考之源和思维之火。<br />
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我们的大脑是如何工作的?所谓的类比到底是什么?我们是怎么在截然不同的情景间建立起联系的?类比在学习的过程中发挥着怎样的作用?在爱因斯坦发现相对论的过程中,类比又扮演着怎样的角色?<br />
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标签:思维 心理学<br />
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作者:[[侯世达]]<br />
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[[复杂:一门诞生于秩序与混沌边缘的学科 An Introduction to Models in the Social Sciences]](未建立词条)<br />
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说明:[[集智俱乐部]]曾多次推荐本书,其中译版于 1997 年由三联出版社出版,印数不到一万册,后无再版。有需求请自寻中英文资源,并期待再版吧~<br />
这部书叙述一群美国科学家如何开创“21世纪的科学”的故事,对正在形成的科学的复杂体系做了深入浅出的描述。介绍了“一场新的启蒙运动”。它为我们讲述了美国的一些不同领域的科学家们越来越无法忍受自牛顿以来一直主导科学的线性和还原的思想束缚。他们在各自领域发现,这个世界是一个相互关联和相互进化的世界,并非线性发展的,并非现有科学可以解释清楚的。他们认为这个世界上不仅存在着混沌,也存在着结构和秩序,他们逐渐将自己的新发现和新观点聚集起来,共同努力形成对整个自然界,对人类社会的一个全新的认识。<br />
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标签:入门,经典,故事,历史<br />
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作者:[[米歇尔·沃尔德罗普]]<br />
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[[隐秩序:适应性造就复杂性 ]](未建立词条)<br />
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推荐语:遗传算法之父[[约翰·霍兰德 John Holland]]在本书中首次强调了适应性在复杂性中的作用,并将复杂适应系统看作是积木块的拼接组合,同时积木又可以行成层级结构。<br />
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作为遗传算法之父和复杂性科学的先驱者之一,[[约翰·霍兰德 John Holland]]从一开始就处于复杂适应系统(CAS)这一新兴研究领域的中心。<br />
这部里程碑式著作为这一崭新领域首次提供了一种协调一致的综合,展示了[[约翰·霍兰德 John Holland]]的独特洞见。《隐秩序:适应性造就复杂性》强调寻找支配CAS行为的一般原理,注重扩展众多科学家的直觉。书中提供了一个适用于全部CAS的计算机模型。[[约翰·霍兰德 John Holland]]通过描述我们能够做什么,总结了如何增强对CAS的理论认识。他提出的若干理论方法,可以指导人们对付耗尽资源、置我们世界于危险境地的棘手的CAS问题。<br />
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标签:遗传算法 <br />
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作者:[[约翰·霍兰德 John Holland]]<br />
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[[链接:网络新科学 Linked: The New Science of Networks]](厚朴已建立词条)<br />
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推荐语:复杂网络研究权威巴拉巴西的经典著作,回顾了网络科学的研究历史,解释了“富者愈富”的无标度网络背后的机制,为理解生命和社会提供了崭新视角。<br />
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[[艾伯特-拉斯洛·巴拉巴西 Albert-László Barabási]]在书中追溯了网络的数学起源,分析了社会学家在此基础上得出的研究成果,最后提出自己的观点:我们周围的复杂网络,从鸡尾酒会、恐怖组织、细胞网络、跨国公司到万维网,等等,所有这些网络都不是随机的,都可以用同一个稳健而普适的架构来刻画。这一发现为我们的网络研究提供了一个全新的视角。<br />
本书叙事生动,充满真知灼见,它使我们认识了许多现代社会的“制图师”,这些人正在多个科学领域研究绘制网络地图,在超级计算机的帮助下,他们正一步步揭示出社会关系网络、企业和细胞等拥有的相似性其实超出了它们之间的差异。他们的发现为我们提供了了解自己周围相互连接的世界的重要的新视角。<br />
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标签:网络科学 社会学<br />
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作者:[[艾伯特-拉斯洛·巴拉巴西 Albert-László Barabási]]<br />
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[[从存在到演化 From being to becoming ]](未建立词条)<br />
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推荐语:普利高津可谓是从动力系统和热力学研究复杂性科学的先驱。热力学,时间之箭,混沌在这本书中完美融合。<br />
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本书试图回答自然界是怎样演化发展的。作者根据耗散结构理论等非平衡自组织理论的成果,结合当代科学的其他新成果,并放到科学史和文化史中进行考察,指出自然系统从混沌到有序、从已有的有序演化到新的有序的过程,是“活”物质的自组织过程。<br />
作者志在把热力学嵌入到动力学之中,重新发现时间的意义,进而消除物理学和生物学的对立,把自然科学和人文科学、西方文化和东方文化结合起来,在更高的起点上建立起人与自然的新联盟。<br />
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标签:热力学 经典<br />
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作者:普里高津<br />
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[[失控 : 全人类的最终命运和结局 Out of Control: The New Biology of Machines, Social Systems, and the Economic World]](施工中:Jie)<br />
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推荐语:失控是站在旁观者的视角介绍复杂性科学最全面和精彩的一本书。<br />
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这是一部思考人类社会(或更一般意义上的复杂系统)进化的“大部头”著作,对于那些不惧于“头脑体操”的读者来说,必然会开卷有益。<br />
《失控》成书于1994年,作者是《连线》杂志的创始主编[[凯文·凯利]]。这本书所记述的,是他对当时科技、社会和经济最前沿的一次漫游,以及借此所窥得的未来图景。<br />
书中提到并且今天正在兴起或大热的概念包括:大众智慧、云计算、物联网、虚拟现实、敏捷开发、协作、双赢、共生、共同进化、网络社区、网络经济,等等。说它是一本“预言式”的书并不为过。其中必定还隐藏着我们尚未印证或窥破的对未来的“预言”。<br />
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标签:社会生态 前沿<br />
作者:[[凯文·凯利]]<br />
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[[哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid]](施工中:Imp)<br />
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推荐语:GEB是一本奇书,它完美地用高超的文学技巧向我们的心智展现了复杂性中的本质困惑——[[涌现]],[[整体论]],[[还原论]],自我的本质究竟是什么?如果你没有对这些问题产生困惑,那你就没有真正理解它们。<br />
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集异璧-GEB,是数学家哥德尔、版画家艾舍尔、音乐家巴赫三个名字的前缀。《哥德尔、艾舍尔、巴赫书:集异璧之大成》是在英语世界中有极高评价的科普著作,曾获得普利策文学奖。<br />
它通过对哥德尔的数理逻辑,艾舍尔的版画和巴赫的音乐三者的综合阐述,引人入胜地介绍了数理逻辑学、可计算理论、人工智能学、语言学、遗传学、音乐、绘画的理论等方面,构思精巧、含义深刻、视野广阔、富于哲学韵味。<br />
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标签:经典 理论<br />
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作者:[[侯世达]]<br />
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[[系统科学]](未建立词条)<br />
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荐书语:该书较为全面系统地介绍了系统科学的各个分枝,是入门必读读物。<br />
《系统科学》全面介绍了系统科学的基础理论、应用理论和工程应用,重点是基础理论的内容。《系统科学》系统阐述了对各类系统的结构、功能和演化有普适意义的动力学系统理论(包括分岔、混沌等)、自组织理论、随机性理论,以及简单巨系统、复杂适应系统、开放的复杂巨系统的理论,对信息论、控制论、运筹学、系统工程方法论等系统工程技术作了简要介绍。<br />
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标签:教材 经典<br />
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作者:[[许国志]]<br />
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[[网络、群体与市场 ]](未建立词条)<br />
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荐书语:该书利用系统科学工具包括复杂网络、博弈论等研究社会经济系统问题。<br />
本书是本科生的入门教材,同时也适合希望进入相关领域的高层次读者。它从交叉学科的角度出发,综合运用经济学、社会学、计算与信息科学以及应用数学的有关概念与方法,考察网络行为原理及其效应机制。以深入浅出的方式描述了在网络的作用下正在浮现与发展起来的一些交叉学科领域,讨论了社会、经济和技术领域相互联系的若干基本问题。本书是一本带你跨入信息科学和社会科学交叉领域研究之门的优秀参考书。<br />
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标签:教材 入门<br />
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作者:大卫·伊斯利 / 乔恩·克莱因伯格<br />
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[[网络科学引论 ]](未建立词条)<br />
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荐书语:该书为复杂网络的进阶教材,全面而系统。<br />
网络科学大牛 Mark Newman 作品,刚刚更新至第二版,第一版有中译本。<br />
作者凭借在计算机、信息论、物理等相关学科的深入研究和丰富经验,系统地分析和论述了网络作为一门科学理论如何应用在现实生活中的方方面面。全书分为5部分,讨论了目前科学研究中的网络类型和用以确定其结构的各种技术,介绍了研究网络的基本数学理论及用以量化网络结构的各类测度与参数,描述了有效分析网络数据的计算机算法,以及有助于预测网络系统行为并理解其生成和演化过程的网络结构数学模型,最后给出了网络上的一些动力学过程,如社会网络中的疾病传染或计算机网络上的搜索过程。<br />
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标签:教材,经典<br />
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作者:[[马克·纽曼]]<br />
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[[从抛物线谈起:混沌动力学引论]](未建立词条)<br />
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著名理论物理、计算物理学家[[郝柏林]]教授的作品。本书借助于抛物线映射这一很初等的工具,介绍混沌动力学的一些最基本的概念和方法。全书计分七章,即:最简单的非线性模型,抛物线映射,倍周期分岔序列,切分岔,混沌映射,吸引子的刻划,过渡过程。本书深入浅出,图文并茂,文献丰富。可供理工科大学教师、高年级学生、研究生、博士后阅读,也可供自然科学和工程技术领域中的研究人员参考。<br />
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标签:进阶,经典<br />
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作者:[[郝柏林]]<br />
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[[热力学与统计物理学 ]](未建立词条)<br />
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荐书语:热力学和统计物理是步入复杂性科学大门的必备知识。<br />
热力学及其引申的统计物理是另外一个研究系统和复杂性的分支,思想来源于10世纪的热力学以及后来的玻尔兹曼、吉布斯统计物理再到后来的普利高津的耗散结构论,这一分支可归结为对一类热、熵、流等现象的研究。<br />
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标签:统计物理 热力学<br />
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作者:[[林宗涵]]<br />
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[[复杂性和临界状态 ]](未建立词条)<br />
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荐书语:详细讲述了临界、相变、标度律等入门复杂性科学的基本概念。<br />
《复杂性和临界状态》是作者在从2000年开始给伦敦帝国理工学院研究生讲授统计力学的讲稿基础上形成的。<br />
复杂性是21世纪的重点研究课题之一,而临界状态则是统计物理中已有相当深入研究的一个分支,《复杂性和临界状态》旨在采用统计力学的方法,以渗滤和伊辛模型为范例,讨论突破复杂性研究的途径。<br />
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标签:理论 统计力学<br />
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作者:[[Kim Christen]]<br />
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[[信息论基础 ]](未建立词条)<br />
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荐书语:掌握信息论中的相关概念是横跨统计物理与计算科学的必备知识。<br />
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《信息论基础》(原书第2版)是信息论领域中一本简明易懂的教材。主要内容包括:熵、信源、信道容量、率失真、数据压缩与编码理论和复杂度理论等方面的介绍。《信息论基础》(原书第2版)还对网络信息论和假设检验等进行了介绍,并且以赛马模型为出发点,将对证券市场的研究纳入了信息论的框架,从新的视角给投资组合的研究带来了全新的投资理念和研究技巧。<br />
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标签:信息论 理论<br />
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作者:[[Thomas M. Cove]]<br />
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[[非线性动力学与混沌]](未建立词条)<br />
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荐书语:该书较为系统全面地介绍了系统动力学与混沌的相关知识。<br />
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Steven Strogatz 教授是美国艺术与科学院院士,康奈尔大学应用数学系 Schurman 讲席教授,国际非线性动力学专家。本书是他的经典入门教材,试图建立一个非线性系统动力学的学科框架,已经更新至第三版,第二版有中译本。<br />
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标签:非线性 动力学<br />
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作者:[[Steven H. Strogatz]]<br />
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[[随机方法手册 Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences ]](未建立词条)<br />
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荐书语:随机过程是连接系统动力学与统计物理的中间纽带,是分析复杂系统的必备工具。<br />
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如何理解复杂系统中的随机过程?这本书系统地以简单的语言介绍了马尔科夫系统基础、随机微分方程、Fokker-Planck 方程、逼近方法和 quatum-mechanical 马尔科夫过程等。这本也包含了关于各种系统形式的民间传说,适合作为参考。<br />
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标签:系统动力学<br />
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作者:[[Crispin Gardiner]]<br />
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[[城市与复杂性: 运用元胞自动机、主体建模和分形理解城市]](未建立词条)<br />
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随着城市规划从集中的、自上而下的模式转向分散的、自下而上的模式,我们对城市系统概念的认知正在发生变化。 在书中,迈克尔 · 巴蒂在复杂性理论的背景下提供了城市动态的全面观点,展示了复杂性理论如何包含无数的过程和元素,并将其组合成有机整体的模型。 他认为,自下而上的过程——其结果总是不确定的——可以与与分形模式和混沌动力学相关的新几何形式相结合,提供适用于城市等高度复杂系统的理论。 Batty 从基于元胞自动机(CA)的模型开始,通过自动机的局部作用模拟城市动态。 然后,他介绍了[[主体建模 Agent-based Models]](ABM) ,其中代理主体是可移动的,并在位置之间移动。 这些模型涉及到许多尺度,从街道的规模到城市地区规模的模式和结构。 最后,Batty 开发了所有这些模型在特定城市情况下的应用,在空间发展的背景下讨论了临界性、阈值、突然性、新颖性和相变等概念。 书中提出的每一个理论和模型都是通过从简化和假设到实际的例子发展起来的。利用大量的视觉、数学和文本材料,《城市与复杂性》将被城市研究人员和对新型计算模型感兴趣的复杂性理论学者阅读。<br />
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标签:Cellular Automata, Scaling, Agent-Based Modeling, Cities<br />
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作者:M. Batty<br />
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[[一种新科学 A New Kind of Science]](厚朴已建立词条)<br />
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荐书语:该书可作为计算理论、元胞自动机、多主体模拟的参考读物。<br />
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一本上千页,至今未成功翻译成中文的神书。什么是计算?简单如何定义复杂,如何产生随机,如何理解计算等价性?元胞自动机如何应用于计算机、人工智能等领域?这本书都给了解答。作者是 Mathematica 软件之父,Wolfram 语言发明人,元胞自动机资深研究者。<br />
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标签:元胞自动机 系统理论<br />
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作者:[[史蒂芬·沃尔夫勒姆 Stephen Wolfram]]<br />
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[[为什么:因果关系的新科学 The Book of Why: The New Science of Cause and Effect]]<br />
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在本书中,人工智能领域的权威专家朱迪亚·珀尔及其同事领导的因果关系革命突破多年的迷雾,厘清了知识的本质,确立了因果关系研究在科学探索中的核心地位。<br />
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而因果关系科学真正重要的应用则体现在人工智能领域。作者在本书中回答的核心问题是:如何让智能机器像人一样思考?换言之,“强人工智能”可以实现吗?借助因果关系之梯的三个层级逐步深入地揭示因果推理的本质,并据此构建出相应的自动化处理工具和数学分析范式,作者给出了一个肯定的答案。作者认为,今天为我们所熟知的大部分机器学习技术,都建基于相关关系,而非因果关系。要实现强人工智能,乃至将智能机器转变为具有道德意识的有机体,我们就必须让机器学会问“为什么”,也就是要让机器学会因果推理,理解因果关系。或许,这正是我们能对准备接管我们未来生活的智能机器所做的最有意义的工作。<br />
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标签:哲学 理论 人工智能<br />
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作者:[[朱迪亚·珀尔 Judea Pearl]]<br />
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[[因果关系: 模型、推理和推断 Causality:Moedels,Reasoning,and Inference]]<br />
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这本书展现了因果关系是如何从一个模糊的概念发展成为一个在统计学、人工智能、经济学、哲学、认知科学以及健康和社会科学领域有着重要应用的数学理论的过程。朱迪亚·珀尔提出和统一的概率,操纵,反事实,因果关系,使用结构化的推断方法和简单数学工具进行因果关系和统计之间联系的研究。这本书将开辟道路,包括因果分析在统计学,人工智能,商业,流行病学,社会科学和经济学的标准课程。任何人想要从数据中阐明具有意义的关系,预测行动和政策的影响,评估报告事件的解释,或形成理论的因果理解和因果讲演,将发现会这本书是有价值的。<br />
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标签:哲学 理论 人工智能<br />
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作者:[[朱迪亚·珀尔 Judea Pearl]]<br />
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== 人物列表 ==<br />
[[人物模板]]、优秀的人物案例<br />
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* 默里·盖尔曼 Murray Gell-Mann<br />
* 皮尔 · 巴克 Per Bak<br />
* 霍华德 · 托马斯 · 奥德姆 Howard T. Odum<br />
* 马贾斯·佩尔奇 Matjaž Perc<br />
* 马文·明斯基 Marvin Minsky<br />
* 朱尔斯·亨利·庞加莱 Jules HenriPoincaré<br />
* 斯图尔特·考夫曼 Stuart Kauffman<br />
* 赫尔曼·哈肯 Hermann Haken<br />
* 托马斯·谢林 Thomas C. Schelling<br />
* 德克·赫尔宾 Dirk Helbing<br />
* 弗里德里希·哈耶克 F. A. Hayek<br />
* Ludwig Boltzmann<br />
* 詹姆士·約克 James A. Yorke<br />
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== 希望新增的词条信息 ==</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6134哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-04-30T03:48:35Z<p>Imp:/* 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid */</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid(施工中) ==</div>Imphttps://wiki.swarma.org/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E3%80%81%E8%89%BE%E8%88%8D%E5%B0%94%E3%80%81%E5%B7%B4%E8%B5%AB%EF%BC%9A%E9%9B%86%E5%BC%82%E7%92%A7%E4%B9%8B%E5%A4%A7%E6%88%90_G%C3%B6del,_Escher,_Bach:_An_Eternal_Golden_Braid&diff=6133哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid2020-04-30T03:46:10Z<p>Imp:创建页面,内容为“== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==”</p>
<hr />
<div>== 哥德尔、艾舍尔、巴赫:集异璧之大成 Gödel, Escher, Bach: An Eternal Golden Braid ==</div>Imphttps://wiki.swarma.org/index.php?title=%E7%94%A8%E6%88%B7:Imp&diff=6112用户:Imp2020-04-30T02:56:31Z<p>Imp:/* 自我介绍 */</p>
<hr />
<div>==基本信息==<br />
===自我介绍===<br />
* 昵称 :Imp<br />
* 性别 :男<br />
* 学校 :西南大学(中国)<br />
* 兴趣方向 :生物信息学、机器学习、区块链<br />
* 兴趣爱好 :篮球、徒步、健身、阅读、语言、经济<br />
(作为生物狗希望能和其他领域的大佬多多学习)<br />
===联系方式===<br />
邮箱 :impwang@outlook.com<br />
<br />
==我与集智==<br />
我依稀记得似乎是相对论带给了我这个与集智相遇的机会,从爱因斯坦了解到哥德尔,从哥德尔不完备定理到侯世达的《GEB》,似乎是在对这本书一筹莫展时搜索资料偶然了解到了复杂科学,也自然发现了集智,也从此开始领悟到复杂系统的美妙.我的爱好比较宽泛,因为我相信学科交叉能产生奇妙的反应,但同时自己也很难从中做出取舍,反而一无所长,希望通过这个机会能让自己专注于这一件事从中学到更多,也希望能与集智一起成长,看到不同的风景,认识更多有趣的人.</div>Imphttps://wiki.swarma.org/index.php?title=%E7%94%A8%E6%88%B7:Imp&diff=6107用户:Imp2020-04-30T02:52:57Z<p>Imp:/* 我与集智 */</p>
<hr />
<div>==基本信息==<br />
===自我介绍===<br />
* 昵称 :Imp<br />
* 性别 :男<br />
* 学校 :西南大学(中国)<br />
* 兴趣方向 :机器学习、复杂系统、区块链、生物信息学、心理学<br />
* 兴趣爱好 :篮球、轻装徒步、棋类、阅读、语言、经济<br />
* 邮箱 :impwang@outlook.com<br />
==我与集智==<br />
我依稀记得似乎是相对论带给了我这个与集智相遇的机会,从爱因斯坦了解到哥德尔,从哥德尔不完备定理到侯世达的《GEB》,似乎是在对这本书一筹莫展时搜索资料偶然了解到了复杂科学,也自然发现了集智,也从此开始领悟到复杂系统的美妙.我的爱好比较宽泛,因为我相信学科交叉能产生奇妙的反应,但同时自己也很难从中做出取舍,反而一无所长,希望通过这个机会能让自己专注于这一件事从中学到更多,也希望能与集智一起成长,看到不同的风景,认识更多有趣的人.</div>Imphttps://wiki.swarma.org/index.php?title=%E7%94%A8%E6%88%B7:Imp&diff=6085用户:Imp2020-04-30T02:15:22Z<p>Imp:/* 我与集智 */</p>
<hr />
<div>==基本信息==<br />
===自我介绍===<br />
* 昵称 :Imp<br />
* 性别 :男<br />
* 学校 :西南大学(中国)<br />
* 兴趣方向 :机器学习、复杂系统、区块链、生物信息学、心理学<br />
* 兴趣爱好 :篮球、轻装徒步、棋类、阅读、语言、经济<br />
* 邮箱 :impwang@outlook.com<br />
==我与集智==<br />
我依稀记得似乎是相对论带给了我这个与集智相遇的机会,从爱因斯坦了解到哥德尔,从哥德尔不完备定理到侯世达的《GEB》,似乎是在啃不动这本书时搜索资料偶然了解到了复杂科学,也自然发现了集智,也从此开始领悟到复杂系统的美妙.我的爱好比较宽泛,因为我相信学科交叉能产生奇妙的反应,但同时自己也很难从中做出取舍,反而一无所长,希望复杂是一个解决方案;同时也希望能通过与集智一起成长,看到不同的风景,认识更多有趣的人.</div>Imphttps://wiki.swarma.org/index.php?title=%E7%94%A8%E6%88%B7:Imp&diff=6081用户:Imp2020-04-30T02:09:11Z<p>Imp:/* 我与集智 */</p>
<hr />
<div>==基本信息==<br />
===自我介绍===<br />
* 昵称 :Imp<br />
* 性别 :男<br />
* 学校 :西南大学(中国)<br />
* 兴趣方向 :机器学习、复杂系统、区块链、生物信息学、心理学<br />
* 兴趣爱好 :篮球、轻装徒步、棋类、阅读、语言、经济<br />
* 邮箱 :impwang@outlook.com<br />
==我与集智==<br />
我依稀记得似乎是相对论带给了我这个与集智相遇的机会,从爱因斯坦了解到哥德尔,从哥德尔不完备定理到侯世达的《GEB》,似乎是在啃不动这本书时搜索资料偶然了解到了复杂科学,也自然发现了集智,也从此开始领悟到复杂系统的美妙.学科交叉能产生奇妙的反应,希望能通过集智提升自我,看到不同的风景,认识更多有趣的人.</div>Imphttps://wiki.swarma.org/index.php?title=%E7%94%A8%E6%88%B7:Imp&diff=6071用户:Imp2020-04-30T02:02:55Z<p>Imp:</p>
<hr />
<div>==基本信息==<br />
===自我介绍===<br />
* 昵称 :Imp<br />
* 性别 :男<br />
* 学校 :西南大学(中国)<br />
* 兴趣方向 :机器学习、复杂系统、区块链、生物信息学、心理学<br />
* 兴趣爱好 :篮球、轻装徒步、棋类、阅读、语言、经济<br />
* 邮箱 :impwang@outlook.com<br />
==我与集智==<br />
我依稀记得似乎是相对论带给了我这个与集智相遇的机会,从爱因斯坦了解到哥德尔,从哥德尔不完备定理到侯世达的《GEB》,似乎是在啃不动这本书时搜索资料偶然了解到了复杂科学,也自然发现了集智,也从此开始领悟到复杂系统的美妙.</div>Imphttps://wiki.swarma.org/index.php?title=%E7%94%A8%E6%88%B7:Imp&diff=6061用户:Imp2020-04-30T01:57:51Z<p>Imp:创建页面,内容为“#基本信息 ##自我介绍 -***昵称***:Imp -***性别***:男 -***学校***:西南大学(中国) -***兴趣方向***:机器学习、复杂系统、区…”</p>
<hr />
<div>#基本信息<br />
##自我介绍<br />
-***昵称***:Imp<br />
-***性别***:男<br />
-***学校***:西南大学(中国)<br />
-***兴趣方向***:机器学习、复杂系统、区块链、生物信息学、心理学<br />
-***兴趣爱好***:篮球、轻装徒步、棋类、阅读、语言、经济<br />
**邮箱**:impwang@outlook.com<br />
#我与集智<br />
我依稀记得似乎是相对论带给了我这个与集智相遇的机会,从爱因斯坦了解到哥德尔,从哥德尔不完备定理到侯世达的《GEB》,似乎是在啃不动这本书时搜索资料偶然了解到了复杂科学,也自然发现了集智,也从此开始领悟到复杂系统的美妙.</div>Imp