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      Influence and Dynamic Behavior in Random Boolean Networks

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          Abstract

          We present a rigorous mathematical framework for analyzing dynamics of a broad class of Boolean network models. We use this framework to provide the first formal proof of many of the standard critical transition results in Boolean network analysis, and offer analogous characterizations for novel classes of random Boolean networks. We precisely connect the short-run dynamic behavior of a Boolean network to the average influence of the transfer functions. We show that some of the assumptions traditionally made in the more common mean-field analysis of Boolean networks do not hold in general. For example, we offer some evidence that imbalance, or expected internal inhomogeneity, of transfer functions is a crucial feature that tends to drive quiescent behavior far more strongly than previously observed.

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          Journal
          2011-07-19
          Article
          10.1103/PhysRevLett.107.108701
          1107.3792
          bed147f3-d54e-476e-8da5-48ff41d4a004

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Phys. Rev. Lett. 107, 108701 (2011)
          To appear as a Letter in Physical Review Letters 8 pages, 4 figures
          cond-mat.dis-nn cs.AI cs.DM nlin.AO

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