Dynamics of Boolean networks: an exact solution

Alexander Mozeika, David Saad

Research output: Contribution to journalArticle

Abstract

The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides exact solutions and insight into the evolution of order parameters and properties of the stationary states, which are inaccessible via existing methodology. We identify cases where the commonly used annealed approximation is valid and others where it breaks down. Broader links between BN and general Boolean formulas are highlighted.
Original languageEnglish
Article number214101
Pages (from-to)214101
Number of pages1
JournalPhysical Review Letters
Volume106
Issue number21
DOIs
Publication statusPublished - 24 May 2011

Fingerprint

Boolean functions
thermal noise
breakdown
disorders
methodology
formulations
approximation

Bibliographical note

© 2011 The American Physical Society

Keywords

  • Boolean networks
  • quenched disorder and thermal noise
  • general formulation
  • Boolean formulas
  • cond-mat.dis-nn

Cite this

Mozeika, Alexander ; Saad, David. / Dynamics of Boolean networks: an exact solution. In: Physical Review Letters. 2011 ; Vol. 106, No. 21. pp. 214101.
@article{02b38c3afbc04fc2a8866390512dc2f4,
title = "Dynamics of Boolean networks: an exact solution",
abstract = "The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides exact solutions and insight into the evolution of order parameters and properties of the stationary states, which are inaccessible via existing methodology. We identify cases where the commonly used annealed approximation is valid and others where it breaks down. Broader links between BN and general Boolean formulas are highlighted.",
keywords = "Boolean networks, quenched disorder and thermal noise, general formulation, Boolean formulas, cond-mat.dis-nn",
author = "Alexander Mozeika and David Saad",
note = "{\circledC} 2011 The American Physical Society",
year = "2011",
month = "5",
day = "24",
doi = "10.1103/PhysRevLett.106.214101",
language = "English",
volume = "106",
pages = "214101",
journal = "Physical Review Letters",
issn = "0031-9007",
publisher = "American Physical Society",
number = "21",

}

Dynamics of Boolean networks: an exact solution. / Mozeika, Alexander; Saad, David.

In: Physical Review Letters, Vol. 106, No. 21, 214101, 24.05.2011, p. 214101.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Dynamics of Boolean networks: an exact solution

AU - Mozeika, Alexander

AU - Saad, David

N1 - © 2011 The American Physical Society

PY - 2011/5/24

Y1 - 2011/5/24

N2 - The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides exact solutions and insight into the evolution of order parameters and properties of the stationary states, which are inaccessible via existing methodology. We identify cases where the commonly used annealed approximation is valid and others where it breaks down. Broader links between BN and general Boolean formulas are highlighted.

AB - The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides exact solutions and insight into the evolution of order parameters and properties of the stationary states, which are inaccessible via existing methodology. We identify cases where the commonly used annealed approximation is valid and others where it breaks down. Broader links between BN and general Boolean formulas are highlighted.

KW - Boolean networks

KW - quenched disorder and thermal noise

KW - general formulation

KW - Boolean formulas

KW - cond-mat.dis-nn

UR - http://www.scopus.com/inward/record.url?scp=79960620010&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.106.214101

DO - 10.1103/PhysRevLett.106.214101

M3 - Article

VL - 106

SP - 214101

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 21

M1 - 214101

ER -