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Neuronal networks, spike trains statistics and Gibbs distributions

Rodrigo Cofré 1 
1 NEUROMATHCOMP - Mathematical and Computational Neuroscience
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
Abstract : Sensory neurons respond to external stimulus using sequences of action potentials (“spikes”). They convey collectively to the brain information about the stimulus using spatio-temporal patterns of spikes (spike trains), that constitute a “neural code”. Since spikes patterns occur irregularly (yet highly structured) both within and over repeated trials, it is reasonable to characterize them using statistical methods and probabilistic descriptions. However, the statistical characterization of experimental data presents several major constraints: apart from those inherent to empirical statistics like finite size sampling, ‘the’ underlying statistical model is unknown. In this thesis we adopt a complementary approach to experiments. We consider neuromimetic models allowing the study of collective spike trains statistics and how it depends on network architecture and history, as well as on the stimulus. First, we consider a conductance-based Integrate-and-Fire model with chemical and electric synapses. We show that the spike train statistics is characterized by non-stationary, infinite memory, distribution consistent with conditional probabilities (Left interval specifications), which is continuous and non null, thus a Gibbs distribution. Then, we present a novel method that allows us to unify spatio-temporal Maximum Entropy models (whose invariant measure are Gibbs distributions in the Bowen sense) and neuro-mimetic models, providing a solid ground towards biophysical explanation of spatio-temporal correlations observed in experimental data. Finally, using these tools, we discuss the stimulus response of retinal ganglion cells, and the possible generalization of the co
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Rodrigo Cofré. Neuronal networks, spike trains statistics and Gibbs distributions. Other. Université Nice Sophia Antipolis, 2014. English. ⟨NNT : 2014NICE4078⟩. ⟨tel-01127093⟩

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