Emergent Criticality Through Adaptive Information Processing in Boolean Networks
Alireza Goudarzi, Natali Gulbahce, Thimo Rohlf, and Christof Teuscher
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Submission date: 26. Apr. 2011
published in: Physical review letters, 108 (2011) 12, art-no. 128702
DOI number (of the published article): 10.1103/PhysRevLett.108.128702
PACS-Numbers: 89.75.Hc, 05.45.-a, 05.65.+b, 89.75.-k
Keywords and phrases: criticality, learning, Boolean network, adaptation
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We study information processing in populations of Boolean networks with evolving connectivity and systematically explore the interplay between the learning capability, robustness, the network topology, and the task complexity. We solve a long-standing open question and find computationally that, for large system sizes N, adaptive information processing drives the networks to a critical connectivity Kc = 2. For finite size networks, the connectivity approaches the critical value with a power-law of the system size N. We show that network learning and generalization are optimized near criticality, given task complexity and the amount of information provided surpass threshold values. Both random and evolved networks exhibit maximal topological diversity near Kc. We hypothesize that this diversity supports efficient exploration and robustness of solutions, also reflected in our observation that the variance of the fitness values is maximal in critical network populations. Finally, we discuss implications of our results for determining the optimal topology of adaptive dynamical networks that solve computational tasks.