Abstract
We consider the evolution of a network of neurons, focusing on the asymptotic behavior of spikes dynamics instead of membrane potential dynamics. The spike response is not sought as a deterministic response in this context, but as a conditional probability: Reading the consists in inferring such a probability. This probability is computed from empirical raster plots, by using the framework of thermodynamic formalism in ergodic theory. This provides us a parametric statistical model where the probability has the form of a Gibbs distribution. In this respect, this approach generalizes the seminal and profound work of Schneidman and collaborators . A minimal presentation of the formalism is reviewed here, while a general algorithmic estimation method is proposed, minimizing the relative entropy, yielding fast convergent implementations. It is also made explicit how several spike observables (entropy, rate, synchronizations, correlations) are given in closed-form from the parametric estimation. This paradigm does not only allow us to estimate the spike statistics, given a design choice, but also to compare different models, thus answering comparative questions about the neural code such as : are correlations (or time synchrony or a given set of spike patterns, ..) significant with respect to rate coding ? A numerical validation of the method is proposed and the perspectives regarding spike-train code analysis are also discussed.
Highlights
We consider the evolution of a network of neurons, focusing on the asymptotic behavior of spikes dynamics instead of membrane potential dynamics
The spike response is not sought as a deterministic response in this context, but as a conditional probability: "Reading the code" consists in inferring this probability [1]
The natural candidate for spike train statistics is a Gibbs measure [2]. Our work generalizes this seminal and profound work of Bialek and collaborators. This model allows us to predict the conditional probability of rank R Markovian spike patterns and is strongly linked with the thermodynamic formalism [3]
Summary
Eighteenth Annual Computational Neuroscience Meeting: CNS*2009 Don H Johnson Meeting abstracts – A single PDF containing all abstracts in this Supplement is available here. http://www.biomedcentral.com/content/pdf/1471-2202-10-S1-info.pdf We consider the evolution of a network of neurons, focusing on the asymptotic behavior of spikes dynamics instead of membrane potential dynamics. The spike response is not sought as a deterministic response in this context, but as a conditional probability: "Reading the code" consists in inferring this probability [1].
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