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Spike Train Statistics from Empirical Facts to Theory: The Case of the Retina

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Book cover Modeling in Computational Biology and Biomedicine

Abstract

This chapter focuses on methods from statistical physics and probability theory allowing the analysis of spike trains in neural networks. Taking as an example the retina we present recent works attempting to understand how retina ganglion cells encode the information transmitted to the visual cortex via the optical nerve, by analyzing their spike train statistics. We compare the maximal entropy models used in the literature of retina spike train analysis to rigorous results establishing the exact form of spike train statistics in conductance-based Integrate-and-Fire neural networks.

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Notes

  1. 1.

    Fluctuations are not necessarily Gaussian, if the system undergoes a second order phase transition where the topological pressure introduced in Sect. 8.3.1.5 is not twice differentiable.

  2. 2.

    This is an approximation of the exact potential holding when the noise variance is small.

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Acknowledgements

This work has been supported by ERC grant Nervi 227747 (BC), European grant BrainScales (BC), ANR-CONICYT grant (KEOPS), FONDECYT 1110292 (AP) and ICM-IC09-022-P (AP).

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Authors and Affiliations

  1. Inria Sophia Antipolis Méditerranée, Neuromathcomp project-team, 2004 Route des Lucioles, Sophia Antipolis, 06902, France

    Bruno Cessac

  2. CINV-Centro Interdisciplinario de Neurociencia de Valparaiso, Universidad de Valparaiso, Harrington 287, Valparaiso, 2360102, Chile

    Adrian G. Palacios

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  1. Bruno Cessac
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Correspondence to Bruno Cessac .

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  1. , Algorithms-Biology-Structure, INRIA Sophia Antipolis - Méditerranée, Route des Lucioles 2004, Sophia Antipolis, 06902, France

    Frédéric Cazals

  2. , NeuroMathComp project team, INRIA Sophia Antipolis - Méditerranée, Route des Lucioles 2004, Sophia Antipolis, 06902, France

    Pierre Kornprobst

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Cessac, B., Palacios, A.G. (2013). Spike Train Statistics from Empirical Facts to Theory: The Case of the Retina. In: Cazals, F., Kornprobst, P. (eds) Modeling in Computational Biology and Biomedicine. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31208-3_8

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