Understanding the dynamics of neural networks is a major challenge in experimental neuroscience. For that purpose, a modelling of the recorded activity that reproduces the main statistics of the data is required. In a first part, we present a review on recent results dealing with spike train statistics analysis using maximum entropy models (MaxEnt). Most of these studies have been focusing on modelling synchronous spike patterns, leaving aside the temporal dynamics of the neural activity. However, the maximum entropy principle can be generalized to the temporal case, leading to Markovian models where memory effects and time correlations in the dynamics are properly taken into account. In a second part, we present a new method based on Monte-Carlo sampling which is suited for the fitting of large-scale spatio-temporal MaxEnt models. The formalism and the tools presented here will be essential to fit MaxEnt spatio-temporal models to large neural ensembles. *

We propose a numerical method to learn maximum entropy (MaxEnt) distributions with spatio-temporal constraints from experimental spike trains. This is an extension of two papers, [10] and [4], which proposed the estimation of parameters where only spatial constraints were taken into account. The extension we propose allows one to properly handle memory effects in spike statistics, for large-sized neural networks.

The retina encodes visual scenes by trains of action potentials that are sent to the brain via the optic nerve. In this paper, we describe a new free access user-end software allowing to better understand this coding. It is called PRANAS (https://pranas.inria.fr), standing for Platform for Retinal ANalysis And Simulation. PRANAS targets neuroscientists and modelers by providing a unique set of retina-related tools. PRANAS integrates a retina simulator allowing large scale simulations while keeping a strong biological plausibility and a toolbox for the analysis of spike train population statistics. The statistical method (entropy maximization under constraints) takes into account both spatial and temporal correlations as constraints, allowing to analyze the effects of memory on statistics. PRANAS also integrates a tool computing and representing in 3D (time-space) receptive fields. All these tools are accessible through a friendly graphical user interface. The most CPU-costly of them have been implemented to run in parallel.

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