Spike trains statistics in integrate and fire models: exact results.

Bruno Cessac 1, * Hassan Nasser 1 Juan Carlos Vasquez 1
* Corresponding author
1 NEUROMATHCOMP
CRISAM - Inria Sophia Antipolis - Méditerranée , INRIA Rocquencourt, ENS Paris - École normale supérieure - Paris, UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : We briefly review and highlight the consequence of rigorous and exact results obtained in \cite{cessac:10}, characterizing the statistics of spike trains in a network of leaky integrate-and-fire neurons,where time is discrete and where neurons are subject to noise,without restriction on the synaptic weights connectivity. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. To our knowledge this is the first example where the Gibbs distribution of a neural network is rigorously and explicitly computed in computational neuroscience. Its form is not conventional since the potential has infinite range. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics. This gives us a parametric statistical model where the probability has the form of a Gibbs distribution with finite range potential. This paradigm does not only allow us to estimate the spike statistics, given a design choice, but also to compare different models, thus answering comparative questions about the neural code.
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  • HAL Id : hal-00553403, version 1
  • ARXIV : 1008.5074

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Bruno Cessac, Hassan Nasser, Juan Carlos Vasquez. Spike trains statistics in integrate and fire models: exact results.. Cinquième conférence plénière française de Neurosciences Computationnelles, "Neurocomp'10", Aug 2010, Lyon, France. ⟨hal-00553403⟩

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