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Axe Interdisciplinaire de Recherche de l’Université de Nice – Sophia Antipolis

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Mini-Symposium à l’INRIA

mercredi 29 octobre 2014

From Statistical Physics to Neuronal Network Dynamic

Jeudi 6 Novembre - 9h à 12h

Amphithéatre Morgenstern, INRIA

  • 9h00-9h30. To be announced, Alain Destexhe, Laboratory for Computational Neuroscience, UNIC-CNRS, Gif-sur-Yvette, France.
  • 9h30-10h00. A bound on the efficiency of some frictional Brownian motors, Pierre Collet, Centre de Physique Th ́eorique, Ecole Polytechnique, Palaiseau, France.
  • 10h-10h30. Coffee break.
  • 10h30-11h00. Regular non-Markovian processes may not be Gibbsian measures, Roberto Fernandez, Utrecht University, Netherlands.
  • 11h00-11h30. To be announced, Fred Wolf, Max-Planck-Institut fuer Dynamik und Selbstorganisation Theoretische, Göttingen, Germany.
  • 11h30-12h00. Dynamical criticality in the collective activity of a population of retinal neurons, Olivier Marre, INSERM- Institut de la Vision, Paris

A bound on the efficiency of some frictional Brownian motors,
Pierre Collet

I will first discuss the general question of Brownian motors which are used to model various biological motors. Using the example of a new purely frictional motor with Langevin dynamics I will explain the genericity of these motors. Using Heisenberg’s uncertainty principle I will derive a lower bound on the average kinetic energy and draw some consequences. In particular upper bounds on the efficiency are obtained which are similar to the Carnot bound and the Curzon Ahlborn bound of macroscopic thermodynamic.

Alain Destexhe (to be announced)

Regular non-Markovian processes may not be Gibbsian measures,
Roberto Fernandez

(Work in collaboration with S. Gallo (Federal University of Rio de Janeiro) and G. Maillard (Aix-Marseille))
Processes are determined by conditional expectations with respect to the past. In contrast, one-dimensional Gibbs measures are determined by si- multaneous conditioning on past and future. For the Markovian and expo- nentially continuous cases both theories are known to be equivalent. We present an example showing this not to be the case in the non-Markovian setup : some rather regular non-Markovian processes may fail to be Gibb- sian. Our example belongs to a well-studied family of processes with rather nice attributes : It is a chain with variable-length memory, characterized by the absence of phase coexistence and the existence of a visible renewal scheme.

Dynamical criticality in the collective activity of a population of retinal neurons,
Olivier Marre

(Joint work with Thierry Mora and Stéphane Deny)
Recent experimental results based on multi-electrode and imaging tech- niques have reinvigorated the idea that large neural networks operate near a critical point, between order and disorder. However, evidence for criticality has relied on the definition of arbitrary order parameters, or on models that do not address the dynamical nature of network activity. Here we introduce a novel approach to assess criticality that overcomes these limitations, while encompassing and generalizing previous criteria. We find a simple model to describe the global activity of large populations of ganglion cells in the rat retina, and show that their statistics are poised near a critical point.
Taking into account the temporal dynamics of the activity greatly en- hances the evidence for criticality, revealing it where previous methods would not. The approach is general and could be used in other biological networks.

Fred Wolf, (to be announced)