MERCREDI 25 FEVRIER 2009
14 heures
Salle Séminaire 5
Centre de Physique Théorique
Marseille-Luminy

Bruno Cessac
LJAD, UniversitŽ de Nice et Neuromath-INRIA

Title: How Gibbs distributions may naturally arise from synaptic adaptation
mechanisms

Abstract: This talk 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.