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14
Gibbs distribution analysis of temporal correlation structure on multicell spike trains from retina ganglion cells
, 2012
"... We present a method to estimate Gibbs distributions with spatiotemporal constraints on spike trains statistics. We apply this method to spike trains recorded from ganglion cells of the salamander retina, in response to natural movies. Our analysis, restricted to a few neurons, performs more accura ..."
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Cited by 11 (5 self)
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We present a method to estimate Gibbs distributions with spatiotemporal constraints on spike trains statistics. We apply this method to spike trains recorded from ganglion cells of the salamander retina, in response to natural movies. Our analysis, restricted to a few neurons, performs more accurately than pairwise synchronization models (Ising) or the 1time step Markov models (Marre et al. (2009)) to describe the statistics of spatiotemporal spike patterns and emphasizes the role of higher order spatiotemporal interactions.
Statistics of spike trains in conductancebased neural networks: Rigorous results
 J. Mathemat. Neurosci
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 8 (5 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
A view of Neural Networks as dynamical systems
 in "International Journal of Bifurcations and Chaos", 2009, http://lanl.arxiv.org/abs/0901.2203
"... We present some recent investigations resulting from the modelling of neural networks as dynamical systems, and dealing with the following questions, adressed in the context of specific models. (i). Characterizing the collective dynamics; (ii). Statistical analysis of spikes trains; (iii). Interplay ..."
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Cited by 4 (2 self)
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We present some recent investigations resulting from the modelling of neural networks as dynamical systems, and dealing with the following questions, adressed in the context of specific models. (i). Characterizing the collective dynamics; (ii). Statistical analysis of spikes trains; (iii). Interplay between dynamics and network structure; (iv). Effects of synaptic plasticity.
Spike trains statistics in Integrate and Fire Models: exact results
 in "Proceedings of the NeuroComp2010 Conference
, 2010
"... ABSTRACT We briefly review and highlight the consequences of rigorous and exact results obtained in [1], characterizing the statistics of spike trains in a network of leaky IntegrateandFire neurons, where time is discrete and where neurons are subject to noise, without restriction on the synapti ..."
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Cited by 2 (0 self)
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ABSTRACT We briefly review and highlight the consequences of rigorous and exact results obtained in [1], characterizing the statistics of spike trains in a network of leaky IntegrateandFire neurons, where time is discrete and where neurons are subject to noise, without restriction on the synaptic weights connectivity. The main result is that spike trains statistics are characterized by a Gibbs distribution, whose potential is explicitly computable. This establishes, on one hand, a rigorous ground for the current investigations attempting to characterize real spike trains data with Gibbs distributions, such as the Isinglike distribution [2], using the maximal entropy principle. However, it transpires from the present analysis that the Ising model might be a rather weak approximation. Indeed, the Gibbs potential (the formal “Hamiltonian”) is the log of the socalled “conditional intensity ” (the probability that a neuron fires given the past of the whole network [3, 4, 5, 6, 7, 8, 9, 10]). But, in the present example, this probability has an infinite memory, and the corresponding process is nonMarkovian (resp. the Gibbs potential has infinite range). Moreover, causality implies that the conditional intensity does not depend on the state of the neurons at the same time, ruling out the Ising model as a candidate for an exact characterization of spike trains statistics. However, Markovian approximations can be proposed whose degree of approximation can be rigorously controlled. In this setting, Ising model appears as the “next step ” after the Bernoulli model (independent neurons) since it introduces spatial pairwise correlations, but not time correlations. The range of validity of this approximation is discussed together with possible approaches allowing to introduce time correlations, with algorithmic extensions.
unknown title
, 2012
"... Author manuscript, published in "NeuroComp/KEOpS'12 workshop beyond the retina: from computational models to outcomes in bioengineering. Focus on architecture and dynamics sustaining information flows in the visuomotor system. (2012)" Analyzing largescale spike trains data with spati ..."
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Author manuscript, published in "NeuroComp/KEOpS'12 workshop beyond the retina: from computational models to outcomes in bioengineering. Focus on architecture and dynamics sustaining information flows in the visuomotor system. (2012)" Analyzing largescale spike trains data with spatiotemporal constraints
Creative Commons Attribution License
"... Abstract We consider a conductancebased neural network inspired by the generalized Integrate and Fire model introduced by Rudolph and Destexhe in 1996. We show the existence and uniqueness of a unique Gibbs distribution characterizing spike train statistics. The corresponding Gibbs potential is exp ..."
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Abstract We consider a conductancebased neural network inspired by the generalized Integrate and Fire model introduced by Rudolph and Destexhe in 1996. We show the existence and uniqueness of a unique Gibbs distribution characterizing spike train statistics. The corresponding Gibbs potential is explicitly computed. These results hold in the presence of a timedependent stimulus and apply therefore to nonstationary dynamics. 1
unknown title
, 2009
"... How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A modelbased argumentation. ..."
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How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A modelbased argumentation.
unknown title
, 2012
"... Author manuscript, published in "NeuroComp/KEOpS'12 workshop beyond the retina: from computational models to outcomes in bioengineering. Focus on architecture and dynamics sustaining information flows in the visuomotor system. (2012)" Analyzing largescale spike trains data with spati ..."
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Author manuscript, published in "NeuroComp/KEOpS'12 workshop beyond the retina: from computational models to outcomes in bioengineering. Focus on architecture and dynamics sustaining information flows in the visuomotor system. (2012)" Analyzing largescale spike trains data with spatiotemporal constraints