How Gibbs Distributions May Naturally Arise from Synaptic Adaptation Mechanisms. A Model-Based Argumentation

Bruno Cessac; Horacio Rostro; Juan Carlos Vasquez; Thierry Viéville

inria-00407905, version 1

How Gibbs Distributions May Naturally Arise from Synaptic Adaptation Mechanisms. A Model-Based Argumentation

Bruno Cessac () ^1, 2, Horacio Rostro () ¹, Juan Carlos Vasquez () ¹, Thierry Viéville () ³

Journal of Statistical Physics 136, 3 (2009) 565-602

Abstract: This paper addresses two questions in the context of neuronal networks dynamics, using methods from dynamical systems theory and statistical physics: (i) How to characterize the statistical properties of sequences of action potentials ("spike trains") produced by neuronal networks? and; (ii) what are the effects of synaptic plasticity on these statistics? We introduce a framework in which spike trains are associated to a coding of membrane potential trajectories, and actually, constitute a symbolic coding in important explicit examples (the so-called gIF models). On this basis, we use the thermodynamic formalism from ergodic theory to show how Gibbs distributions are natural probability measures to describe the statistics of spike trains, given the empirical averages of prescribed quantities. As a second result, we show that Gibbs distributions naturally arise when considering "slow" synaptic plasticity rules where the characteristic time for synapse adaptation is quite longer than the characteristic time for neurons dynamics.

1: NEUROMATHCOMP (INRIA Sophia Antipolis / Inria Rocquencourt)
INRIA – Université Nice Sophia Antipolis [UNS] – CNRS : UMR6621 – Ecole normale supérieure de Paris - ENS Paris
2: Laboratoire Jean Alexandre Dieudonné (JAD)
CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS]
3: CORTEX (INRIA Lorraine - LORIA)
INRIA – CNRS : UMR7503 – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL)

inria-00407905, version 1
http://hal.inria.fr/inria-00407905
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From: Thierry Viéville <>
Submitted on: Monday, 27 July 2009 19:21:15
Updated on: Wednesday, 22 June 2011 11:03:43

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DOI: 10.1007/s10955-009-9786-1

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%% inria-00407905, version 1
%% http://hal.inria.fr/inria-00407905
@article{cessac:inria-00407905,
    hal_id = {inria-00407905},
    url = {http://hal.inria.fr/inria-00407905},
    title = {{How Gibbs Distributions May Naturally Arise from Synaptic Adaptation Mechanisms. A Model-Based Argumentation}},
    author = {Cessac, Bruno and Rostro, Horacio and Vasquez, Juan Carlos and Vi{\'e}ville, Thierry},
    abstract = {{This paper addresses two questions in the context of neuronal networks dynamics, using methods from dynamical systems theory and statistical physics: (i) How to characterize the statistical properties of sequences of action potentials ("spike trains") produced by neuronal networks? and; (ii) what are the effects of synaptic plasticity on these statistics? We introduce a framework in which spike trains are associated to a coding of membrane potential trajectories, and actually, constitute a symbolic coding in important explicit examples (the so-called gIF models). On this basis, we use the thermodynamic formalism from ergodic theory to show how Gibbs distributions are natural probability measures to describe the statistics of spike trains, given the empirical averages of prescribed quantities. As a second result, we show that Gibbs distributions naturally arise when considering "slow" synaptic plasticity rules where the characteristic time for synapse adaptation is quite longer than the characteristic time for neurons dynamics.}},
    keywords = {Neurons dynamics - Spike coding - Statistical physics - Gibbs distributions - Thermodynamic formalism},
    language = {English},
    affiliation = {NEUROMATHCOMP - INRIA Sophia Antipolis / Inria Rocquencourt , Laboratoire Jean Alexandre Dieudonn{\'e} - JAD , CORTEX - INRIA Lorraine - LORIA},
    booktitle = {{Journal of Statistical Physics}},
    publisher = {Springer},
    pages = {565-602},
    journal = {Journal of Statistical Physics},
    volume = {136},
    number = {3 },
    note = {ANR MACCAC },
    audience = {international },
    doi = {10.1007/s10955-009-9786-1 },
    year = {2009},
}

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