6 research outputs found
Handling spatio-temporal correlations in neuronal systems
International audienc
Gibbs distribution: from neural network dynamics to spike train statistics estimation
International audienc
Linear response for spiking neuronal networks with unbounded memory
We establish a general linear response relation for spiking neuronal
networks, based on chains with unbounded memory. This relation allows us to
predict the influence of a weak amplitude time-dependent external stimuli on
spatio-temporal spike correlations, from the spontaneous statistics (without
stimulus) in a general context where the memory in spike dynamics can extend
arbitrarily far in the past. Using this approach, we show how linear response
is explicitly related to neuronal dynamics with an example, the gIF model,
introduced by M. Rudolph and A. Destexhe. This example illustrates the
collective effect of the stimuli, intrinsic neuronal dynamics, and network
connectivity on spike statistics. We illustrate our results with numerical
simulations.Comment: 60 pages, 8 figure
Gibbs Measures for Long-Range Ising Models
This review-type paper is based on a talk given at the conference États de la Recherche en Mécanique statistique, which took place at IHP in Paris (December 10-14, 2018). We revisit old results from the 80's about one dimensional long-range polynomially decaying Ising models (often called Dyson models in dimension one) and describe more recent results about interface fluctuations and interface states in dimensions one and two
On the mathematical consequences of binning spike trains
International audienceWe initiate a mathematical analysis of hidden effects induced by binning spike trains of neurons. Assuming that the original spike train has been generated by a discrete Markov process, we show that binning generates a stochas-tic process which is not Markov any more, but is instead a Variable Length Markov Chain (VLMC) with unbounded memory. We also show that the law of the binned raster is a Gibbs measure in the DLR (Dobrushin-Lanford-Ruelle) sense coined in mathematical statistical mechanics. This allows the derivation of several important consequences on statistical properties of binned spike trains. In particular, we introduce the DLR framework as a natural setting to mathematically formalize anticipation, i.e. to tell "how good" our nervous system is at making predictions. In a probabilistic sense, this corresponds to condition a process by its future and we discuss how binning may affect our conclusions on this ability. We finally comment what could be the consequences of binning in the detection of spurious phase transitions or in the detection of wrong evidences of criticality