Section: New Results

Spike trains statistics

Natural image identification from spike train analysis

Participants : Geoffrey Portelli, Olivier Marre [Institution de la Vision, Paris, France] , Marc Antonini [Laboratoire I3S, UMR CNRS, Université Nice Sophia Antipolis, France] , Michael Berry II [Princeton Neuroscience Institute, Department of Molecular Biology, Princeton University, Princeton, NJ 08544, USA] , Pierre Kornprobst [correspondent] .

We started a new activity to analyse how natural images are encoded in retinal output. This work is related to [67] , [72] where synthetic stimuli are used. Here, we recorded a population of 100-200 ganglion cells of a salamander retina, while flashing 720 natural images from the Torralba database [71] plus one control image, each repeated 10 times. We characterized the response of each cell by two parameters : the latency of the first spike after the stimulus onset, and the firing rate. A distribution of these two features was then estimated for each neuron and natural image. Pooling the information across all the neurons, a discriminability coefficient between pairs of image is proposed, using either the rate or the latency, or both. We also provide a way to identify a given image among others based on the rate–latency distributions. Preliminary results have been presented in [40] . Results showed that, on average, the discriminability was better based on the latency than on the rate. The most discriminable pairs were different using the rate or the latency, so these two features conveyed complementary information. In addition, we observe a similar evolution of the identification performance when the rate, or the latency, or both are used.

Spike train statistics from empirical facts to theory: the case of the retina

Participants : Bruno Cessac [correspondent] , Adrian Palacios [CINV-Centro Interdisciplinario de Neurociencia de Valparaiso, Universidad de Valparaiso] .

This work 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. This work has been published in Mathematical Problems in Computational Biology and Biomedicine, F. Cazals and P. Kornprobst, Springer [55] .

Gibbs distribution analysis of temporal correlations structure in retina ganglion cells

Participants : Juan-Carlos Vasquez, Olivier Marre [Institution de la Vision, Paris, France] , Adrian Palacios [CINV-Centro Interdisciplinario de Neurociencia de Valparaiso, Universidad de Valparaiso] , Michael Berry II [Princeton Neuroscience Institute, Department of Molecular Biology, Princeton University, Princeton, NJ 08544, USA] , Bruno Cessac [correspondent] .

We present a method to estimate Gibbs distributions with spatio-temporal 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 1-time step Markov models (Marre et al. (2009)) to describe the statistics of spatio-temporal spike patterns and emphasizes the role of higher order spatio-temporal interactions. This work has been presented in several conferences [29] , [30] , [28] and pusblished in J. Physiol. Paris [26] .

Spatio-temporal spike trains analysis for large scale networks using maximum entropy principle and Monte-Carlo method

Participants : Hassan Nasser, Olivier Marre [Institut de la Vision, Paris, France] , Bruno Cessac [correspondent] .

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. 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. We also 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. This work has been presented in several conferences [54] , [51] , [53] , [52] and accepted in Journal of Statistical Mechanics [22] .

Spike train statistics and Gibbs distributions

Participants : Rodrigo Cofré, Bruno Cessac [correspondent] .

We introduce Gibbs distribution in a general setting, including non stationary dynamics, and present then three examples of such Gibbs distributions, in the context of neural networks spike train statistics: (i) Maximum entropy model with spatio-temporal constraints; (ii) Generalized Linear Models; (iii) Conductance based Inte- grate and Fire model with chemical synapses and gap junctions. This leads us to argue that Gibbs distributions might be canonical models for spike train statistics analysis. This work has been presented in several conferences [43] , [31] and submitted to J. Physiol. Paris [12] .