Core percolation and onset of complexity in Boolean networks

TL;DR

This paper introduces a method to identify the core variables in large Boolean networks, revealing the transition point from simple to complex regulatory behavior through a combination of theoretical and algorithmic analysis.

Contribution

It presents a novel simplification scheme to extract the computational core of Boolean networks and characterizes the phase transition to complexity.

Findings

Identification of the computational core in Boolean networks

Theoretical and algorithmic characterization of the phase transition

Criteria for the onset of complex regulatory behavior

Abstract

The determination and classification of fixed points of large Boolean networks is addressed in terms of constraint satisfaction problem. We develop a general simplification scheme that, removing all those variables and functions belonging to trivial logical cascades, returns the computational core of the network. The onset of an easy-to-complex regulatory phase is introduced as a function of the parameters of the model, identifying both theoretically and algorithmically the relevant regulatory variables.