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| − | 此词条暂由Bnustv整理和审校,带来阅读不便,请见谅。<br>
| + | 此词条由Bnustv整理和审校。<br> |
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| | '''<font color="#FF8000">布尔函数Boolean function</font>'''是一种可用于通过逻辑类型的计算来评估与其布尔输入有关的任何布尔输出的函数。这些功能在复杂性理论中起着基本作用。当布尔函数应用于复杂网络中时,我们定义了'''<font color="#FF8000">布尔网络 Boolean Network </font>'''的概念:布尔网络是由一组离散的布尔变量组成,每个变量都被分配了一个布尔函数(可能每个变量都不同),它从这些变量的子集中获取输入,并输出决定其被分配的变量的状态。 | | '''<font color="#FF8000">布尔函数Boolean function</font>'''是一种可用于通过逻辑类型的计算来评估与其布尔输入有关的任何布尔输出的函数。这些功能在复杂性理论中起着基本作用。当布尔函数应用于复杂网络中时,我们定义了'''<font color="#FF8000">布尔网络 Boolean Network </font>'''的概念:布尔网络是由一组离散的布尔变量组成,每个变量都被分配了一个布尔函数(可能每个变量都不同),它从这些变量的子集中获取输入,并输出决定其被分配的变量的状态。 |
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| − | ==经典模型== | + | ==经典模型 == |
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| | !平均吸引子长度 | | !平均吸引子长度 |
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| | !平均吸引子数量 | | !平均吸引子数量 |
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| − | !平均吸引子数
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| − | !评论
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| | |Kauffmann <ref name="KauffmanOriginal" /> | | |Kauffmann <ref name="KauffmanOriginal" /> |
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| − | | Kauffmann
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| | |1969 | | |1969 |
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| | |<math>\langle A\rangle\sim \sqrt{N}</math> | | |<math>\langle A\rangle\sim \sqrt{N}</math> |
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| − | |<math>\langle A\rangle\sim \sqrt{N}</math>
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| − | |< math > langle a rangle sim sqrt { n } <nowiki></math ></nowiki>
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| − | |<math>\langle\nu\rangle\sim \sqrt{N}</math>
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| | |<math>\langle\nu\rangle\sim \sqrt{N}</math> | | |<math>\langle\nu\rangle\sim \sqrt{N}</math> |
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| − | | < math > langle nu rangle sim sqrt { n } <nowiki></math ></nowiki>
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| | |Bastolla/ Parisi<ref name="BastollaParisi1998">{{cite journal|last1=Bastolla|first1=U.|last2=Parisi|first2=G.|title=The modular structure of Kauffman networks|journal=Physica D: Nonlinear Phenomena|date=May 1998|volume=115|issue=3–4|pages=219–233|doi=10.1016/S0167-2789(97)00242-X|arxiv = cond-mat/9708214 |bibcode = 1998PhyD..115..219B }}<!--|accessdate=26 November 2014--></ref> | | |Bastolla/ Parisi<ref name="BastollaParisi1998">{{cite journal|last1=Bastolla|first1=U.|last2=Parisi|first2=G.|title=The modular structure of Kauffman networks|journal=Physica D: Nonlinear Phenomena|date=May 1998|volume=115|issue=3–4|pages=219–233|doi=10.1016/S0167-2789(97)00242-X|arxiv = cond-mat/9708214 |bibcode = 1998PhyD..115..219B }}<!--|accessdate=26 November 2014--></ref> |
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| − | |Bastolla/ Parisi
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| | |收敛速度比幂律快 <math>\langle A\rangle > N^x \forall x</math> | | |收敛速度比幂律快 <math>\langle A\rangle > N^x \forall x</math> |
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| − | |收敛速度比幂律快, <math>\langle A\rangle > N^x \forall x</math>
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| − | | 收敛速度比幂定律快,< math > langle a rangle > n ^ x for all x <nowiki></math ></nowiki>
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| − | |收敛速度比幂律快, <math>\langle\nu\rangle > N^x \forall x</math>
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| | |收敛速度比幂律快, <math>\langle\nu\rangle > N^x \forall x</math> | | |收敛速度比幂律快, <math>\langle\nu\rangle > N^x \forall x</math> |
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| − | |收敛速度比幂定律快,< math > langle nu rangle > n ^ x for all x <nowiki></math ></nowiki>
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| − | |第一个数学证据
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| | |首个数学上的证据 | | |首个数学上的证据 |
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| | |Bilke/ Sjunnesson<ref>{{cite journal|last1=Bilke|first1=Sven|last2=Sjunnesson|first2=Fredrik|title=Stability of the Kauffman model|journal=Physical Review E|date=December 2001|volume=65|issue=1|pages=016129|doi=10.1103/PhysRevE.65.016129|pmid=11800758|arxiv = cond-mat/0107035 |bibcode = 2002PhRvE..65a6129B }}<!--|accessdate=26 November 2014--></ref> | | |Bilke/ Sjunnesson<ref>{{cite journal|last1=Bilke|first1=Sven|last2=Sjunnesson|first2=Fredrik|title=Stability of the Kauffman model|journal=Physical Review E|date=December 2001|volume=65|issue=1|pages=016129|doi=10.1103/PhysRevE.65.016129|pmid=11800758|arxiv = cond-mat/0107035 |bibcode = 2002PhRvE..65a6129B }}<!--|accessdate=26 November 2014--></ref> |
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| − | |与系统大小成线性关系, | + | | 与系统大小成线性关系, |
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| − | |与系统大小成线性关系, <math>\langle\nu\rangle \sim N</math>
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| | |与系统大小成线性关系, <math>\langle\nu\rangle \sim N</math> | | |与系统大小成线性关系, <math>\langle\nu\rangle \sim N</math> |
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| − | |与系统大小成线性关系
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| | |Socolar/Kauffman<ref>{{cite journal|last1=Socolar|first1=J.|last2=Kauffman|first2=S.|title=Scaling in Ordered and Critical Random Boolean Networks|journal=Physical Review Letters|date=February 2003|volume=90|issue=6|pages=068702|doi=10.1103/PhysRevLett.90.068702|pmid=12633339|bibcode=2003PhRvL..90f8702S|arxiv = cond-mat/0212306 }}</ref> | | |Socolar/Kauffman<ref>{{cite journal|last1=Socolar|first1=J.|last2=Kauffman|first2=S.|title=Scaling in Ordered and Critical Random Boolean Networks|journal=Physical Review Letters|date=February 2003|volume=90|issue=6|pages=068702|doi=10.1103/PhysRevLett.90.068702|pmid=12633339|bibcode=2003PhRvL..90f8702S|arxiv = cond-mat/0212306 }}</ref> |
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| | |快于线性关系, | | |快于线性关系, |
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| − | |快于线性关系, <math>\langle\nu\rangle > N^x</math> <math>x > 1</math>
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| | |快于线性关系, <math>\langle\nu\rangle > N^x</math> <math>x > 1</math> | | |快于线性关系, <math>\langle\nu\rangle > N^x</math> <math>x > 1</math> |
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| | |Samuelsson/Troein<ref>{{cite journal|last1=Samuelsson|first1=Björn|last2=Troein|first2=Carl|title=Superpolynomial Growth in the Number of Attractors in Kauffman Networks|journal=Physical Review Letters|date=March 2003|volume=90|issue=9|doi=10.1103/PhysRevLett.90.098701|bibcode=2003PhRvL..90i8701S|pmid=12689263|page=098701}}<!--|accessdate=26 November 2014--></ref> | | |Samuelsson/Troein<ref>{{cite journal|last1=Samuelsson|first1=Björn|last2=Troein|first2=Carl|title=Superpolynomial Growth in the Number of Attractors in Kauffman Networks|journal=Physical Review Letters|date=March 2003|volume=90|issue=9|doi=10.1103/PhysRevLett.90.098701|bibcode=2003PhRvL..90i8701S|pmid=12689263|page=098701}}<!--|accessdate=26 November 2014--></ref> |
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| | |超多项式增长, | | |超多项式增长, |
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| | |超多项式增长, <math>\langle\nu\rangle > N^x \forall x</math> | | |超多项式增长, <math>\langle\nu\rangle > N^x \forall x</math> |
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| − | | 超多项式增长,< math > langle nu rangle > n ^ x for all x <nowiki></math ></nowiki>
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| | |提供数学证明 | | |提供数学证明 |
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| | |Mihaljev/Drossel<ref>{{cite journal|last1=Mihaljev|first1=Tamara|last2=Drossel|first2=Barbara|title=Scaling in a general class of critical random Boolean networks|journal=Physical Review E|date=October 2006|volume=74|issue=4|pages=046101|doi=10.1103/PhysRevE.74.046101|pmid=17155127|arxiv = cond-mat/0606612 |bibcode = 2006PhRvE..74d6101M }}<!--|accessdate=26 November 2014--></ref> | | |Mihaljev/Drossel<ref>{{cite journal|last1=Mihaljev|first1=Tamara|last2=Drossel|first2=Barbara|title=Scaling in a general class of critical random Boolean networks|journal=Physical Review E|date=October 2006|volume=74|issue=4|pages=046101|doi=10.1103/PhysRevE.74.046101|pmid=17155127|arxiv = cond-mat/0606612 |bibcode = 2006PhRvE..74d6101M }}<!--|accessdate=26 November 2014--></ref> |
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| | |2005 | | |2005 |
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| | |收敛速度比幂律快, <math>\langle\nu\rangle > N^x \forall x</math> | | |收敛速度比幂律快, <math>\langle\nu\rangle > N^x \forall x</math> |
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| | 模型的变化<br> | | 模型的变化<br> |
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| − | == Other topologies== | + | ==Other topologies== |
| | 其他拓扑性质<br> | | 其他拓扑性质<br> |
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| − | == Classification== | + | ==Classification== |
| | 分类<br> | | 分类<br> |
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| | '''<font color="#FF8000">NK模型 NK Model </font>''' | | '''<font color="#FF8000">NK模型 NK Model </font>''' |
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| − | ==References == | + | ==References== |
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| | {{Reflist|30em}} | | {{Reflist|30em}} |
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| − | *Dubrova, E., Teslenko, M., Martinelli, A., (2005). *[http://dl.acm.org/citation.cfm?id=1129670 Kauffman Networks: Analysis and Applications], in "Proceedings of International Conference on Computer-Aided Design", pages 479-484.<!-- to be cited or not --> | + | * Dubrova, E., Teslenko, M., Martinelli, A., (2005). *[http://dl.acm.org/citation.cfm?id=1129670 Kauffman Networks: Analysis and Applications], in "Proceedings of International Conference on Computer-Aided Design", pages 479-484.<!-- to be cited or not --> |
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