Wednesday, December 19, 2012

1212.4239 (Yu Hu et al.)

Local paths to global coherence: cutting networks down to size    [PDF]

Yu Hu, James Trousdale, Eric Shea-Brown, Krešimir Josić
How does connectivity impact network dynamics? We address this question by providing a widely-applicable link between network characteristics on two scales. On the global scale we consider the coherence of overall network activity. We show that such global coherence can often be predicted from the local structure of the network. To characterize this local structure we introduce motif cumulants, which measure the deviation of pathway counts from those expected in a minimal probabilistic network model. Importantly, this link between global dynamics and local architecture is strongly affected by heterogeneity in the network connectivity. The relationship can be strengthened if the network is divided into connectivity-based subpopulations. Extensions of the theory relate higher-order (i.e., beyond pairwise) statistics of network-wide dynamics and more complex patterns of local connectivity.
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