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Supercriticality of an annealed approximation of Boolean networks

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	Supercriticality of an annealed approximation of Boolean networks
2.	Creator	Author's name, affiliation, country	Daniel Valesin; University of British Columbia; Canada
2.	Creator	Author's name, affiliation, country	Thomas Mountford; École Polytechnique Fédérale de Lausanne; Switzerland
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	threshold contact process; random graphs; boolean networks
3.	Subject	Subject classification	Interacting Particle Systems
4.	Description	Abstract	We consider a model recently proposed by Chatterjee and Durrett as an "annealed approximation'' of boolean networks, which are a class of cellular automata on a random graph, as defined by S. Kauffman. The starting point is a random directed graph on $n$ vertices; each vertex has $r$ input vertices pointing to it. For the model of Chatterjee and Durrett, a discrete time threshold contact process is then considered on this graph: at each instant, each vertex has probability $q$ of choosing to receive input; if it does, and if at least one of its input vertices were in state 1 at the previous instant, then it is labelled with a 1; in all other cases, it is labelled with a 0. $r$ and $q$ are kept fixed and $n$ is taken to infinity. Improving a result of Chatterjee and Durrett, we show that if $qr > 1$, then the time of persistence of activity of the dynamics is exponential in $n$.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2013-05-04
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/2479
10.	Identifier	Digital Object Identifier	10.1214/ECP.v18-2479
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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