Paper Info
Title
A Stochastic Model for Layered Self-organizing Complex Systems
Abstract
In this paper we study a problem common to complex systems that dynamically self-organize to an optimal configuration. Assuming the network nodes are of two types, and that one type is subjected to a an upward pressure according to a preferential stochastic model, we wish to determine the distribution of the active nodes over the levels of the network. We generalize the problem to the case of layered graphs as follows. Let G be a connected graph with M vertices which are divided into d levels where the vertices of each edge of G belong to consecutive levels. Initially each vertex has a value of 0 or 1 assigned at random. At each step of the stochastic process an edge is chosen at random. Then, the labels of the vertices of this edge are exchanged with probability 1 if the vertex on the higher level has the label 0 and the lower vertex has the label 1. The labels are switched with probability lambda, if the lower vertex has value of 0 and the higher vertex has the value of 1. This stochastic process has the Markov chain property and is related to random walks on graphs. We derive formulas for the steady state distribution of the number of vertices with label 1 on the levels of the graph.
Year
DOI
Venue
2009
10.1007/978-3-642-02469-6_29
Lecture Notes of the Institute for Computer Sciences Social Informatics and Telecommunications Engineering
Keywords
Field
DocType
connected graph,stochastic process,markov chain,complex system,stochastic model,self organization,steady state
Discrete mathematics,Combinatorics,Random graph,Vertex (geometry),Markov property,Discrete-time stochastic process,Random walk,Stochastic process,Continuous-time stochastic process,Connectivity,Mathematics
Conference
Volume
ISSN
Citations 
5
1867-8211
0
PageRank 
References 
Authors
0.34
7
2
Name
Order
Citations
PageRank
Yuri Dimitrov120.75
Mario Lauria262895.12