Persistence of activity in threshold contact processes, an “Annealed approximation” of random Boolean networks
Year: 2011
Type: article
Abstract: We consider a model for gene regulatory networks that is a modification of Kauffmann's J Theor Biol 22 (1969), 437–467 random Boolean networks. There are three parameters:$n = {\rm the}$ number of nodes,$r = {\rm the}$ number of inputs to each node, and$p = {\rm the}$ expected fraction of 1'sin the Boolean functions at each node. Following a standard practice in thephysics literature, we use a threshold contact process on a random graph onnnodes, in which each node has in degreer, to approximate its dynamics. We show that if$r\ge 3$ and$r \cdot 2p(1-p)>1$ , then the threshold contact process persists for a long time, which correspond to chaotic behavior of the Boolean network. Unfortunately, we are only able to prove the persistence time is$\ge \exp(cn^{b(p)})$ with$b(p)>0$ when$r\cdot 2p(1-p)> 1$ , and$b(p)=1$ when$(r-1)\cdot 2p(1-p)>1$ . © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2011
Source: Random Structures and Algorithms
DOI: 10.1002/rsa.20357
Authors: Shirshendu Chatterjee, Rick Durrett
Institutions: Duke University, Cornell University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W1997575864