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Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Mar;89(3):032802. Epub 2014 Mar 10.

Local paths to global coherence: cutting networks down to size.

Author information

  • 1Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA.
  • 2Department of Mathematics, University of Houston, Houston, Texas 77204-5001, USA.
  • 3Department of Mathematics, University of Houston, Houston, Texas 77204-5001, USA and Department of Biology and Biochemistry, University of Houston, Houston, Texas 77204-5001, USA.
  • 4Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA and Program in Neurobiology and Behavior, University of Washington, Seattle, Washington 98195, USA and Department of Physiology and Biophysics, University of Washington, Seattle, Washington 98195, USA.

Abstract

How does connectivity impact network dynamics? We address this question by linking network characteristics on two scales. On the global scale, we consider the coherence of overall network dynamics. We show that such global coherence in activity can often be predicted from the local structure of the network. To characterize local network structure, we use "motif cumulants," a measure of the deviation of pathway counts from those expected in a minimal probabilistic network model. We extend previous results in three ways. First, we give acombinatorial formulation of motif cumulants that relates to the allied concept in probability theory. Second, we show that the link between global network dynamics and local network architecture is strongly affected by heterogeneity in network connectivity. However, we introduce a network-partitioning method that recovers a tight relationship between architecture and dynamics. Third, for a particular set of models, we generalize the underlying theory to treat dynamical coherence at arbitrary orders (i.e., triplet correlations and beyond). We show that at any order, only a highly restricted set of motifs impacts dynamical correlations.

PMID:
24730894
DOI:
10.1103/PhysRevE.89.032802
[PubMed - indexed for MEDLINE]
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