State Concentration Exponent as a Measure of Quickness in Kauffman-type Networks

Details State Concentration Exponent as a Measure of Quickness in Kauffman-type Networks State Concentration Exponent as a Measure of Quickness in Kauffman-type Networks

2012-02-29

arxiv.org/abs/1202.6526v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 figures

Scientific paper

The quickness of large network dynamics is quantified by the length of transient paths, an analytically intractable measure. For discrete-time dynamics of networks of binary elements, we address this dilemma with a unified framework termed state concentration, defined as the exponent of the average number of t-step ancestors in state transition graphs. The state transition graph is defined by nodes corresponding to network states and directed links corresponding to transitions. Using this exponent, we interrogate random Boolean and majority vote networks. We find that extremely sparse Boolean networks and majority vote networks with arbitrary density achieve quickness, owing in part to long-tailed indegree distributions. As a corollary, only dense majority vote networks can achieve both quickness and robustness.

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