Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2007-04-25
Chaos 17, 026109 (2007)
Physics
Condensed Matter
Statistical Mechanics
19 pages, 14 figures, to appear in Chaos
Scientific paper
10.1063/1.2742931
Boolean Networks and their dynamics are of great interest as abstract modeling schemes in various disciplines, ranging from biology to computer science. Whereas parallel update schemes have been studied extensively in past years, the level of understanding of asynchronous updates schemes is still very poor. In this paper we study the propagation of external information given by regulatory input variables into a random Boolean network. We compute both analytically and numerically the time evolution and the asymptotic behavior of this propagation of external regulation (PER). In particular, this allows us to identify variables which are completely determined by this external information. All those variables in the network which are not directly fixed by PER form a core which contains in particular all non-trivial feedback loops. We design a message-passing approach allowing to characterize the statistical properties of these cores in dependence of the Boolean network and the external condition. At the end we establish a link between PER dynamics and the full random asynchronous dynamics of a Boolean network.
Mahmoudi Hamed
Pagnani Andrea
Weigt Martin
Zecchina Riccardo
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