TY - JOUR

T1 - Maximum-entropy large-scale structures of Boolean networks optimized for criticality

AU - Möller, Marco

AU - Peixoto, Tiago P.

PY - 2015/4

Y1 - 2015/4

N2 - We construct statistical ensembles of modular Boolean networks that are constrained to lie at the critical line between frozen and chaotic dynamic regimes. The ensembles are maximally random given the imposed constraints, and thus represent null models of critical networks. By varying the network density and the entropic cost associated with biased Boolean functions, the ensembles undergo several phase transitions. The observed structures range from fully random to several ordered ones, including a prominent core–periphery-like structure, and an 'attenuated' two-group structure, where the network is divided in two groups of nodes, and one of them has Boolean functions with very low sensitivity. This shows that such simple large-scale structures are the most likely to occur when optimizing for criticality, in the absence of any other constraint or competing optimization criteria.

AB - We construct statistical ensembles of modular Boolean networks that are constrained to lie at the critical line between frozen and chaotic dynamic regimes. The ensembles are maximally random given the imposed constraints, and thus represent null models of critical networks. By varying the network density and the entropic cost associated with biased Boolean functions, the ensembles undergo several phase transitions. The observed structures range from fully random to several ordered ones, including a prominent core–periphery-like structure, and an 'attenuated' two-group structure, where the network is divided in two groups of nodes, and one of them has Boolean functions with very low sensitivity. This shows that such simple large-scale structures are the most likely to occur when optimizing for criticality, in the absence of any other constraint or competing optimization criteria.

UR - http://dx.doi.org/10.1088/1367-2630/17/4/043021

UR - http://dx.doi.org/10.1088/1367-2630/17/4/043021

U2 - 10.1088/1367-2630/17/4/043021

DO - 10.1088/1367-2630/17/4/043021

M3 - Article

SN - 1367-2630

VL - 17

JO - New Journal of Physics

JF - New Journal of Physics

M1 - 043021

ER -