The behavior of noise-resilient Boolean networks with diverse topologies

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Abstract

The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the dynamics always undergoes a phase transition from a non-ergodic regime, where a memory of its past states is preserved, to an ergodic regime, where no such memory exists and every microstate is equally probable. Both the average error on the network and the critical value of noise where the transition occurs are investigated analytically, and compared to numerical simulations. The results for 'partially dense' networks, comprising relatively few, but dynamically important nodes, which have a number of inputs that greatly exceeds the average for the entire network, give very general upper bounds on the maximum resilience against noise attainable on globally sparse systems.
Original languageEnglish
Article numberP01006
JournalJournal of Statistical Mechanics-Theory and Experiment
Volume2012
DOIs
Publication statusPublished - 10 Jan 2012

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Boolean Networks
topology
Topology
Resilience
resilience
Probable
Critical value
Exceed
Phase Transition
Entire
Upper bound
Numerical Simulation
Configuration
Vertex of a graph
configurations
simulation
Class

Cite this

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abstract = "The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the dynamics always undergoes a phase transition from a non-ergodic regime, where a memory of its past states is preserved, to an ergodic regime, where no such memory exists and every microstate is equally probable. Both the average error on the network and the critical value of noise where the transition occurs are investigated analytically, and compared to numerical simulations. The results for 'partially dense' networks, comprising relatively few, but dynamically important nodes, which have a number of inputs that greatly exceeds the average for the entire network, give very general upper bounds on the maximum resilience against noise attainable on globally sparse systems.",
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AB - The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the dynamics always undergoes a phase transition from a non-ergodic regime, where a memory of its past states is preserved, to an ergodic regime, where no such memory exists and every microstate is equally probable. Both the average error on the network and the critical value of noise where the transition occurs are investigated analytically, and compared to numerical simulations. The results for 'partially dense' networks, comprising relatively few, but dynamically important nodes, which have a number of inputs that greatly exceeds the average for the entire network, give very general upper bounds on the maximum resilience against noise attainable on globally sparse systems.

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