A kinetic theory approach to capturing interneuronal correlation: The feed-forward case

Chin Yueh Liu, Duane Q. Nykamp

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Abstract

We present an approach for using kinetic theory to capture first and second order statistics of neuronal activity. We coarse grain neuronal networks into populations of neurons and calculate the population average firing rate and output cross-correlation in response to time varying correlated input. We derive coupling equations for the populations based on first and second order statistics of the network connectivity. This coupling scheme is based on the hypothesis that second order statistics of the network connectivity are sufficient to determine second order statistics of neuronal activity. We implement a kinetic theory representation of a simple feed-forward network and demonstrate that the kinetic theory model captures key aspects of the emergence and propagation of correlations in the network, as long as the correlations do not become too strong. By analyzing the correlated activity of feed-forward networks with a variety of connectivity patterns, we provide evidence supporting our hypothesis of the sufficiency of second order connectivity statistics.

Original languageEnglish (US)
Pages (from-to)339-368
Number of pages30
JournalJournal of Computational Neuroscience
Volume26
Issue number3
DOIs
StatePublished - Jan 1 2009

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Keywords

  • Connectivity patterns
  • Maximum entropy
  • Neuronal network
  • Population density
  • Syn-fire chain
  • Synchrony

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