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Patterns in randomly evolving networks: Idiotypic networks

Patterns in randomly evolving networks: Idiotypic networks
Patterns in randomly evolving networks: Idiotypic networks
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.
1539-3755
Brede, Markus
bbd03865-8e0b-4372-b9d7-cd549631f3f7
Behn, Ulrich
878cca24-03dd-4682-be65-86e075bfc839
Brede, Markus
bbd03865-8e0b-4372-b9d7-cd549631f3f7
Behn, Ulrich
878cca24-03dd-4682-be65-86e075bfc839

Brede, Markus and Behn, Ulrich (2003) Patterns in randomly evolving networks: Idiotypic networks. Physical Review E, 67 (3). (doi:10.1103/PhysRevE.67.031920).

Record type: Article

Abstract

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.

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More information

Published date: 2003
Organisations: Agents, Interactions & Complexity

Identifiers

Local EPrints ID: 272891
URI: http://eprints.soton.ac.uk/id/eprint/272891
ISSN: 1539-3755
PURE UUID: 6486c152-4c7d-4041-aad1-76fdcde2c137

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Date deposited: 29 Sep 2011 16:31
Last modified: 16 Jul 2019 22:12

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