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自组织临界性 (查看源代码)

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在物理学中，'''自组织临界性 Self-organized criticality (SOC)'''是动力系统的一种特性，动力系统有一个临界点作为吸引子 Attractor。它们在相变临界点的宏观行为因此显示了空间或时间尺度不变特性，但不需要把控制参数调整到一个精确的值，因为系统有效地自我调整趋向于临界状态。
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在物理学中，'''自组织临界性 Self-organized criticality (SOC)</font>'''是动力系统的一种特性，动力系统有一个临界点作为吸引子 Attractor。它们在相变临界点的宏观行为因此显示了空间或时间尺度不变特性，但不需要把控制参数调整到一个精确的值，因为系统有效地自我调整趋向于临界状态。
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{{cite journal |author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi.  |name-list-style=amp | year = 2001 | title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations | journal = J. Neurosci. | volume = 21 | pages = 1370&ndash;1377 | pmid = 11160408 | issue = 4|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003>{{cite journal |author1=J. M. Beggs  |author2=D. Plenz  |name-list-style=amp | year = 2006 | title = Neuronal Avalanches in Neocortical Circuits | journal = J. Neurosci. | volume = 23|issue=35 |pages=11167–77 |doi=10.1523/JNEUROSCI.23-35-11167.2003 |pmid=14657176 |pmc=6741045
 
{{cite journal |author1=K. Linkenkaer-Hansen |author2=V. V. Nikouline |author3=J. M. Palva |author4=R. J. Ilmoniemi.  |name-list-style=amp | year = 2001 | title = Long-Range Temporal Correlations and Scaling Behavior in Human Brain Oscillations | journal = J. Neurosci. | volume = 21 | pages = 1370&ndash;1377 | pmid = 11160408 | issue = 4|doi=10.1523/JNEUROSCI.21-04-01370.2001 |pmc=6762238 }}</ref><ref name=Beggs2003>{{cite journal |author1=J. M. Beggs  |author2=D. Plenz  |name-list-style=amp | year = 2006 | title = Neuronal Avalanches in Neocortical Circuits | journal = J. Neurosci. | volume = 23|issue=35 |pages=11167–77 |doi=10.1523/JNEUROSCI.23-35-11167.2003 |pmid=14657176 |pmc=6741045
 
  }}</ref><ref name=Chialvo2004>{{cite journal | author =Chialvo, D. R. | year = 2004 | title = Critical brain networks | journal = Physica A | volume = 340 | issue =4 | pages = 756&ndash;765 | doi = 10.1016/j.physa.2004.05.064
 
  }}</ref><ref name=Chialvo2004>{{cite journal | author =Chialvo, D. R. | year = 2004 | title = Critical brain networks | journal = Physica A | volume = 340 | issue =4 | pages = 756&ndash;765 | doi = 10.1016/j.physa.2004.05.064
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|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo }}</ref>'''SOC'''通常在多自由度、强非线性动力学的缓慢驱动非平衡系统中被观察到。自从 BTW 的原始论文以来，已经确定了许多单独的例子，但是到目前为止还没有一组已知的一般特征来保证一个系统将显示 '''<font color="#ff8000"> SOC</font>'''。
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|arxiv = cond-mat/0402538 |bibcode = 2004PhyA..340..756R | author-link = Dante R. Chialvo }}</ref>'''SOC'''通常在多自由度、强非线性动力学的缓慢驱动非平衡系统中被观察到。自从 BTW 的原始论文以来，已经确定了许多单独的例子，但是到目前为止还没有一组已知的一般特征来保证一个系统将显示 SOC。
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此外，SOC 已经应用于计算算法。最近，人们发现来自 SOC 过程的雪崩，如 BTW 模型，在图的最优解的随机搜索中形成有效的模式。 <ref name=Hoffmann2018>{{cite journal| author = H. Hoffmann and D. W. Payton| year = 2018| title = Optimization by Self-Organized Criticality| journal = Scientific Reports| volume = 8| issue = 1| pages = 2358| doi=10.1038/s41598-018-20275-7
 
此外，SOC 已经应用于计算算法。最近，人们发现来自 SOC 过程的雪崩，如 BTW 模型，在图的最优解的随机搜索中形成有效的模式。 <ref name=Hoffmann2018>{{cite journal| author = H. Hoffmann and D. W. Payton| year = 2018| title = Optimization by Self-Organized Criticality| journal = Scientific Reports| volume = 8| issue = 1| pages = 2358| doi=10.1038/s41598-018-20275-7
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| pmid = 29402956| pmc = 5799203| bibcode = 2018NatSR...8.2358H}}</ref> 图着色就是这种最佳化问题的一个例子。'''<font color="#ff8000"> SOC</font>''' 过程显然有助于避免优化陷入局部最优，而无需使用任何以前的极值优化工作所建议的退火方案。
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| pmid = 29402956| pmc = 5799203| bibcode = 2018NatSR...8.2358H}}</ref> 图着色就是这种最佳化问题的一个例子。SOC过程显然有助于避免优化陷入局部最优，而无需使用任何以前的极值优化工作所建议的退火方案。
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The recent excitement generated by [[scale-free networks]] has raised some interesting new questions for SOC-related research: a number of different SOC models have been shown to generate such networks as an emergent phenomenon, as opposed to the simpler models proposed by network researchers where the network tends to be assumed to exist independently of any physical space or dynamics. While many single phenomena have been shown to exhibit scale-free properties over narrow ranges, a phenomenon offering by far a larger amount of data is solvent-accessible surface areas in globular proteins.<ref name=Moret2007>
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{{cite journal
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| author = [[M. A. Moret|Moret, M. A.]] and [[G. Zebende|Zebende, G.]]
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| year = 2007
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| title = Amino acid hydrophobicity and accessible surface area
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| journal = [[Phys. Rev. E]]
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| volume = 75
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| issue = 1
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| pages = 011920
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| doi=10.1103/PhysRevE.75.011920
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| pmid = 17358197
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| bibcode = 2007PhRvE..75a1920M
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}}</ref>
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These studies quantify the differential geometry of proteins, and resolve many evolutionary puzzles regarding the biological emergence of complexity.<ref name=Phillips2014>
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{{cite journal
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| author = Phillips, J. C.
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| year = 2014
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| title = Fractals and self-organized criticality in proteins
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| journal = Physica A
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| volume = 415
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| pages = 440–448 
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| doi=10.1016/j.physa.2014.08.034
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| bibcode = 2014PhyA..415..440P
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| author-link = J. C. Phillips
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}}</ref>
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'''<font color="#ff8000"> 无标度网络Scale-free networks</font>'''最近的热潮为 '''<font color="#ff8000">SOC</font>'''相关研究提出了一些有趣的新问题: 许多不同的 '''<font color="#ff8000"> SOC</font>'''模型已经被证明是作为一种涌现现象产生这样的网络，而不是网络研究人员提出的更简单的模型，其中网络往往被假定独立于任何物理空间或动力学存在。虽然许多单一现象已被证明在狭窄的范围内表现出无标度特性，但是到目前为止提供了大量数据的现象是球状蛋白质中溶剂可及的表面区域。这些研究量化了蛋白质的微分几何，并解决了许多关于生物复杂性出现的进化之谜
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Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form. Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model.[1] However, it has been argued that this model would actually generate 1/f2 noise rather than 1/f noise.[15] This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models generally produce 1/fa spectra, with a<2.[16] Other simulation models were proposed later that could produce true 1/f noise,[17] and experimental sandpile models were observed to yield 1/f noise.[18] In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon information theory,[19] mean field theory,[20] the convergence of random variables,[21] and cluster formation.[22] A continuous model of self-organised criticality is proposed by using tropical geometry.[23]
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Despite the considerable interest and research output generated from the SOC hypothesis, there remains no general agreement with regards to its mechanisms in abstract mathematical form.  Bak Tang and Wiesenfeld based their hypothesis on the behavior of their sandpile model.<ref name=Bak1987/>  However,
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it has been argued that this model would actually generate 1/f<sup>2</sup> noise rather than 1/f noise.<ref name=Jensen1989>
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{{cite journal
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| author = [[H. J. Jensen|Jensen, H. J.]], [[K. Christensen|Christensen, K.]] and [[H. C. Fogedby|Fogedby, H. C.]]
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| year = 1989
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| title = 1/f noise, distribution of lifetimes, and a pile of sand
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| journal = [[Phys. Rev. B]]
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| volume = 40
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| issue = 10
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| pages = 7425–7427
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| doi=10.1103/physrevb.40.7425
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| pmid = 9991162
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|bibcode = 1989PhRvB..40.7425J }}
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</ref>
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This claim was based on untested scaling assumptions, and a more rigorous analysis showed that sandpile models
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generally produce 1/f<sup>a</sup> spectra, with a<2.<ref name=Laurson2005>
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{{cite journal |author1=Laurson, Lasse |author2=Alava, Mikko J. |author3=Zapperi, Stefano |title=Letter: Power spectra of self-organized critical sand piles |journal=Journal of Statistical Mechanics: Theory and Experiment |volume=0511 |id=L001 |date=15 September 2005 }}</ref>
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Other simulation models were proposed later that could produce true 1/f noise,<ref name=Maslov1999>
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{{cite journal
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| author = [[S. Maslov|Maslov, S.]], [[C. Tang|Tang, C.]] and [[Y. –C. Zhang|Zhang, Y. - C.]]
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| year = 1999
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| title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes
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| journal = [[Phys. Rev. Lett.]]
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| volume = 83
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| issue = 12
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| pages = 2449–2452
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| doi=10.1103/physrevlett.83.2449
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|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}
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</ref> and experimental sandpile models were observed to yield 1/f noise.<ref name=Frette1996>
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{{cite journal
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| author = [[V.Frette|Frette, V.]], [[K. Christiansen|Christinasen, K.]], [[A. Malthe-Sørenssen|Malthe-Sørenssen, A.]], [[J. Feder|Feder, J]], [[T. Jøssang|Jøssang, T]] and [[P. Meakin|Meaken, P]]
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| year = 1996
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| title = Avalanche dynamics in a pile of rice
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| journal = [[Nature (journal)|Nature]]
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| volume = 379
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| issue = 6560
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| pages = 49–52
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| doi =10.1038/379049a0
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| bibcode= 1996Natur.379...49F}}
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</ref> In addition to the nonconservative theoretical model mentioned above, other theoretical models for SOC have been based upon [[information theory]],<ref name=Dewar2003>
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{{cite journal
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| author = Dewar, R.
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| year = 2003
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| title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states
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| journal =J. Phys. A: Math. Gen.
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| volume = 36
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| pages =631&ndash;641
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| doi = 10.1088/0305-4470/36/3/303
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| issue = 3
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|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 | author-link = R Dewar
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}}</ref>
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[[mean field theory]],<ref name=Vespignani1998>
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{{cite journal
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| author = [[Alessandro Vespignani|Vespignani, A.]], and [[Stefano Zapperi|Zapperi, S.]]
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| year = 1998
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| title = How self-organized criticality works: a unified mean-field picture
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| journal =Phys. Rev. E
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| volume = 57
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| pages =6345–6362
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| doi = 10.1103/physreve.57.6345
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| issue = 6
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| bibcode = 1998PhRvE..57.6345V
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| arxiv = cond-mat/9709192
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| hdl = 2047/d20002173
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}}</ref>
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the [[convergence of random variables]],<ref name=Kendal2015>
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{{cite journal
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| author = Kendal, WS
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| year = 2015
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| title = Self-organized criticality attributed to a central limit-like convergence effect
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| journal =Physica A
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| volume = 421
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| pages =141&ndash;150
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| doi = 10.1016/j.physa.2014.11.035
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|bibcode =2015PhyA..421..141K | author-link = Wayne Kendal
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}}</ref>
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and cluster formation.<ref name=Hoffmann2018b>
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{{cite journal
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| author = Hoffmann, H.
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| year = 2018
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| title = Impact of Network Topology on Self-Organized Criticality
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| journal = Phys. Rev. E
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| volume = 97
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| pages =022313
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| pmid =  29548239
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| doi = 10.1103/PhysRevE.97.022313
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| issue = 2
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| bibcode =2018PhRvE..97b2313H
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| author-link = Heiko Hoffmann
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| doi-access = free
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}}</ref> A continuous model of self-organised criticality is proposed by using [[tropical geometry]].<ref>{{Cite journal|last=Kalinin|first=N.|last2=Guzmán-Sáenz|first2=A.|last3=Prieto|first3=Y.|last4=Shkolnikov|first4=M.|last5=Kalinina|first5=V.|last6=Lupercio|first6=E.|date=2018-08-15|title=Self-organized criticality and pattern emergence through the lens of tropical geometry|journal=Proceedings of the National Academy of Sciences|volume=115|issue=35|language=en|pages=E8135–E8142|doi=10.1073/pnas.1805847115|issn=0027-8424|pmid=30111541|pmc=6126730|arxiv=1806.09153}}</ref>
     −
尽管 SOC 假说引起了相当大的兴趣和研究成果，但是关于其抽象数学形式的机制仍然没有普遍的一致性。Bak Tang 和 Wiesenfeld 基于他们的沙堆模型的行为建立了他们的假设。然而,有人认为，这种模型实际上会产生1 / f sup 2 / sup 噪声而不是1 / f 噪声。这种说法是基于未经测试的比例假设，更严格的分析表明在a>2沙堆模型一般产生1 / f sup a / sup 光谱。
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[[无标度网络]] Scale-free networks最近的热潮为SOC相关研究提出了一些有趣的新问题：许多不同的SOC模型已经被证明是作为一种涌现现象产生这样的网络，而不是网络研究人员提出的更简单的模型，其中网络往往被假定独立于任何物理空间或动力学存在。虽然许多单一现象已被证明在狭窄的范围内表现出无标度特性，但是到目前为止提供了大量数据的现象是球状蛋白质中溶剂可及的表面区域。<ref name=Moret2007>{{cite journal| author = M. A. Moret and G. Zebende| year = 2007| title = Amino acid hydrophobicity and accessible surface area| journal = Phys. Rev. E| volume = 75| issue = 1| pages = 011920| doi=10.1103/PhysRevE.75.011920| pmid = 17358197| bibcode = 2007PhRvE..75a1920M}}</ref>这些研究量化了蛋白质的微分几何，并解决了许多关于生物复杂性出现的进化之谜。<ref name=Phillips2014>{{cite journal| author = Phillips, J. C.| year = 2014| title = Fractals and self-organized criticality in proteins| journal = Physica A| volume = 415| pages = 440–448  | doi=10.1016/j.physa.2014.08.034| bibcode = 2014PhyA..415..440P}}</ref>
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其他的仿真模型能产生真正的1/f的噪声也被提出，并且实验上的实验模型能被观测到产生1/f噪音。除了上面提到的非保守理论模型之外，其他关于 SOC 的理论模型都是基于信息论, 平均场论，随机变量的收敛和剧集信息一个'''<font color="#ff8000"> 自组织临界Self-organised criticality</font>'''的连续模型是通过使用热带几何来提出的。
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== Examples of self-organized critical dynamics自组织临界动力学的例子 ==
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尽管 SOC 假说引起了相当大的兴趣和研究成果，但是关于其抽象数学形式的机制仍然没有普遍的一致性。Bak Tang 和 Wiesenfeld 基于他们的沙堆模型的行为建立了他们的假设。然而,有人认为，这种模型实际上会产生1/f<sup>a</sup> 噪声而不是1 / f 噪声。<ref name=Jensen1989>{{cite journal | author = H. J. Jensen, K. Christensen and H. C. Fogedby | year = 1989 | title = 1/f noise, distribution of lifetimes, and a pile of sand | journal = Phys. Rev. B | volume = 40 | issue = 10 | pages = 7425–7427 | doi=10.1103/physrevb.40.7425| pmid = 9991162 |bibcode = 1989PhRvB..40.7425J }}</ref>这种说法是基于未经测试的比例假设，更严格的分析表明在a>2沙堆模型一般产生1/f<sup>a</sup> 光谱。<ref name=Laurson2005>
 +
{{cite journal |author1=Laurson, Lasse |author2=Alava, Mikko J. |author3=Zapperi, Stefano |title=Letter: Power spectra of self-organized critical sand piles |journal=Journal of Statistical Mechanics: Theory and Experiment |volume=0511 |id=L001 |date=15 September 2005 }}</ref>其他的仿真模型能产生真正的1/f的噪声也被提出，<ref name=Maslov1999>{{cite journal | author = S. Maslov, C. Tang and Y. –C. Zhang | year = 1999 | title = 1/f noise in Bak-Tang-Wiesenfeld models on narrow stripes | journal = Phys. Rev. Lett. | volume = 83 | issue = 12 | pages = 2449–2452 | doi=10.1103/physrevlett.83.2449|arxiv = cond-mat/9902074 |bibcode = 1999PhRvL..83.2449M }}</ref>并且实验上的实验模型能被观测到产生1/f噪音。<ref name=Frette1996>{{cite journal | author = V.Frette, K. Christiansen, A. Malthe-Sørenssen, J. Feder, T. Jøssang and P. Meakin | year = 1996 | title = Avalanche dynamics in a pile of rice | journal = Nature | volume = 379 | issue = 6560 | pages = 49–52 | doi =10.1038/379049a0 | bibcode= 1996Natur.379...49F}}</ref>除了上面提到的非保守理论模型之外，其他关于 SOC 的理论模型都是基于信息论, <ref name=Dewar2003>{{cite journal | author = Dewar, R. | year = 2003 | title = Information theory explanation of the fluctuation theorem, maximum entropy production and self-organized criticality in non-equilibrium stationary states | journal =J. Phys. A: Math. Gen.  | volume = 36 | pages =631&ndash;641 | doi = 10.1088/0305-4470/36/3/303 | issue = 3|bibcode = 2003JPhA...36..631D|arxiv = cond-mat/0005382 }}</ref> 平均场论，<ref name=Vespignani1998>{{cite journal | author = Alessandro Vespignani, and Stefano Zapperi | year = 1998 | title = How self-organized criticality works: a unified mean-field picture | journal =Phys. Rev. E  | volume = 57 | pages =6345–6362 | doi = 10.1103/physreve.57.6345 | issue = 6 | bibcode = 1998PhRvE..57.6345V | arxiv = cond-mat/9709192| hdl = 2047/d20002173 }}</ref>随机变量的收敛<ref name=Kendal2015>
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{{cite journal | author = Kendal, WS | year = 2015 | title = Self-organized criticality attributed to a central limit-like convergence effect | journal =Physica A  | volume = 421 | pages =141&ndash;150 | doi = 10.1016/j.physa.2014.11.035|bibcode =2015PhyA..421..141K  }}</ref>和聚集信息。<ref name=Hoffmann2018b>
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{{cite journal | author = Hoffmann, H. | year = 2018 | title = Impact of Network Topology on Self-Organized Criticality | journal = Phys. Rev. E  | volume = 97 | pages =022313 | pmid =  29548239 | doi = 10.1103/PhysRevE.97.022313
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| issue = 2 | bibcode =2018PhRvE..97b2313H  | doi-access = free }}</ref>一个自组织临界的连续模型是通过使用热带几何来提出的。<ref>{{Cite journal|last=Kalinin|first=N.|last2=Guzmán-Sáenz|first2=A.|last3=Prieto|first3=Y.|last4=Shkolnikov|first4=M.|last5=Kalinina|first5=V.|last6=Lupercio|first6=E.|date=2018-08-15|title=Self-organized criticality and pattern emergence through the lens of tropical geometry|journal=Proceedings of the National Academy of Sciences|volume=115|issue=35|language=en|pages=E8135–E8142|doi=10.1073/pnas.1805847115|issn=0027-8424|pmid=30111541|pmc=6126730|arxiv=1806.09153}}</ref>
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In chronological order of development:
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In chronological order of development:
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== 自组织临界动力学的例子 ==
    
按发展时间顺序排列:
 
按发展时间顺序排列:
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* Stick-slip model of fault failure<ref name="TurcotteSmalleySolla85" /><ref name="SmalleyTurcotteSolla85" />
      
*断层破坏的粘滑模型<ref name="TurcotteSmalleySolla85" /><ref name="SmalleyTurcotteSolla85" />
 
*断层破坏的粘滑模型<ref name="TurcotteSmalleySolla85" /><ref name="SmalleyTurcotteSolla85" />
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*[[Abelian sandpile model|Bak–Tang–Wiesenfeld sandpile]]
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*[[阿贝尔沙堆模型 | Bak–Tang–Wiesenfeld沙堆]] Abelian sandpile model
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*[[阿贝尔沙堆模型| Bak–Tang–Wiesenfeld沙堆]]
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* [[Forest-fire model]]
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*[[森林火灾模型]]
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* [[Olami–Feder–Christensen model]]
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* [[奥拉米·费德·克里斯滕森模型]]
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* [[Bak–Sneppen model]]
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*[[背景模型]]
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== See also 参见==
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* [[Pink noise|1/f noise]]
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*[[粉红噪音| 1/f噪音]]
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* [[Complex system]]s
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*[[森林火灾模型]] Forest-fire model
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* [[复杂系统]]s
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* [[奥拉米·费德·克里斯滕森模型]] Olami–Feder–Christensen model
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* [[Critical brain hypothesis]]
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*[[背景模型]] Bak–Sneppen model
   −
*[[【关键大脑假说】]]
     −
* [[Critical exponents]]
+
== 参见==
   −
*[[临界指数]]
+
* [[粉红噪音| 1/f噪音]] Pink noise
   −
* [[Detrended fluctuation analysis]], a method to detect power-law scaling in time series.
+
* [[复杂系统]] Complex system
   −
*[[Detrended涨落分析]]，一种检测中幂律标度的方法
+
*[[关键大脑假说]] Critical brain hypothesis
   −
* [[Dual-phase evolution]], another process that contributes to self-organization in complex systems.
+
*[[临界指数]] Critical exponents
   −
* [[双相演化]],另一个有助于自我组织的过程
+
* [[Detrended涨落分析]]，一种检测中幂律标度的方法
   −
* [[Fractal]]s
+
* [[双相演化]] Dual-phase evolution,另一个有助于自我组织的过程
   −
* [[分形]]s;
+
* [[分形]] Fractal;
   −
* [[Ilya Prigogine]], a systems scientist who helped formalize dissipative system behavior in general terms.
+
*[[伊利亚·普里高津]] Ilya Prigogine，一位帮助将耗散系统形式化的系统科学家
   −
*[[伊利亚·普里高津]]，一位帮助将耗散系统形式化的系统科学家
+
*[[幂律]] Power law
   −
* [[Power law]]s
+
*[[红皇后假说]] Red Queen hypothesis
   −
*[[幂律]]s
+
* [[标度不变性]] Scale invariance
   −
* [[Red Queen hypothesis]]
+
* [[自组织]] Self-organization
   −
*[[红皇后假说]]
  −
  −
* [[Scale invariance]]
  −
  −
* [[标度不变性]]
  −
  −
* [[Self-organization]]
  −
  −
* [[自组织]]
  −
  −
* [[Self-organized criticality control]]
  −
  −
*[[自组织临界控制]]
  −
  −
==References参考资料==
      +
*[[自组织临界控制]] Self-organized criticality control
    +
==参考文献==
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