Patterns in randomly evolving networks: Idiotypic networks
Brede, Markus and Behn, Ulrich (2003) Patterns in randomly evolving networks: Idiotypic networks. Physical Review E, 67, (3) (doi:10.1103/PhysRevE.67.031920).
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We present a model for the evolution of networks of occupied sites on undirected regular graphs. At every iteration step in a parallel update, I randomly chosen empty sites are occupied and occupied sites having occupied neighbor degree outside of a given interval (t(l),t(u)) are set empty. Depending on the influx I and the values of both lower threshold and upper threshold of the occupied neighbor degree, different kinds of behavior can be observed. In certain regimes stable long-living patterns appear. We distinguish two types of patterns: static patterns arising on graphs with low connectivity and dynamic patterns found on high connectivity graphs. Increasing I patterns become unstable and transitions between almost stable patterns, interrupted by disordered phases, occur. For still larger I the lifetime of occupied sites becomes very small and network structures are dominated by randomness. We develop methods to analyze the nature and dynamics of these network patterns, give a statistical description of defects and fluctuations around them, and elucidate the transitions between different patterns. Results and methods presented can be applied to a variety of problems in different fields and a broad class of graphs. Aiming chiefly at the modeling of functional networks of interacting antibodies and B cells of the immune system (idiotypic networks), we focus on a class of graphs constructed by bit chains. The biological relevance of the patterns and possible operational modes of idiotypic networks are discussed.
|Divisions:||Faculty of Physical and Applied Science > Electronics and Computer Science > Agents, Interactions & Complexity
|Date Deposited:||29 Sep 2011 16:31|
|Last Modified:||02 Mar 2012 11:41|
|Contributors:||Brede, Markus (Author)
Behn, Ulrich (Author)
|Publisher:||The American Physical Society|
|Further Information:||Google Scholar|
|ISI Citation Count:||10|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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