How Does the Inner Retinal Network Shape the Ganglion Cells Receptive Field? A Computational Study.

We consider a model of basic inner retinal connectivity where bipolar and amacrine cells interconnect and both cell types project onto ganglion cells, modulating their response output to the brain visual areas. We derive an analytical formula for the spatiotemporal response of retinal ganglion cells to stimuli, taking into account the effects of amacrine cells inhibition. This analysis reveals two important functional parameters of the network: (1) the intensity of the interactions between bipolar and amacrine cells and (2) the characteristic timescale of these responses.

A novel approach to the functional classification of retinal ganglion cells.

Retinal neurons are remarkedly diverse based on structure, function and genetic identity. Classifying these cells is a challenging task, requiring multimodal methodology. Here, we introduce a novel approach for retinal ganglion cell (RGC) classification, based on pharmacogenetics combined with immunohistochemistry and large-scale retinal electrophysiology.

Receptive field estimation in large visual neuron assemblies using a super-resolution approach.

Computing the spike-triggered average (STA) is a simple method to estimate linear receptive fields (RFs) in sensory neurons. For random, uncorrelated stimuli, the STA provides an unbiased RF estimate, but in practice, white noise at high resolution is not an optimal stimulus choice as it usually evokes only weak responses. Therefore, for a visual stimulus, images of randomly modulated blocks of pixels are often used.

Retinal Processing: Insights from Mathematical Modelling.

The retina is the entrance of the visual system. Although based on common biophysical principles, the dynamics of retinal neurons are quite different from their cortical counterparts, raising interesting problems for modellers. In this paper, I address some mathematically stated questions in this spirit, discussing, in particular: (1) How could lateral amacrine cell connectivity shape the spatio-temporal spike response of retinal ganglion cells? (2) How could spatio-temporal stimuli correlations and retinal network dynamics shape the spike train correlations at the output of the retina? These questions are addressed, first, introducing a mathematically tractable model of the layered retina, integrating amacrine cells' lateral connectivity and piecewise linear rectification, allowing for computing the retinal ganglion cells receptive field together with the voltage and spike correlations of retinal ganglion cells resulting from the amacrine cells networks.

Linear Response of General Observables in Spiking Neuronal Network Models.

We establish a general linear response relation for spiking neuronal networks, based on chains with unbounded memory. This relation allow 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 the linear response is explicitly related to the collective effect of the stimuli, intrinsic neuronal dynamics, and network connectivity on spike train statistics.

On the potential role of lateral connectivity in retinal anticipation.

We analyse the potential effects of lateral connectivity (amacrine cells and gap junctions) on motion anticipation in the retina. Our main result is that lateral connectivity can-under conditions analysed in the paper-trigger a wave of activity enhancing the anticipation mechanism provided by local gain control (Berry et al. in Nature 398(6725):334-338, 1999; Chen et al.

Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics.

The Thermodynamic Formalism provides a rigorous mathematical framework for studying quantitative and qualitative aspects of dynamical systems. At its core, there is a variational principle that corresponds, in its simplest form, to the Maximum Entropy principle. It is used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems.

Ghost Attractors in Spontaneous Brain Activity: Recurrent Excursions Into Functionally-Relevant BOLD Phase-Locking States.

Functionally relevant network patterns form transiently in brain activity during rest, where a given subset of brain areas exhibits temporally synchronized BOLD signals. To adequately assess the biophysical mechanisms governing intrinsic brain activity, a detailed characterization of the dynamical features of functional networks is needed from the experimental side to constrain theoretical models. In this work, we use an open-source fMRI dataset from 100 healthy participants from the Human Connectome Project and analyze whole-brain activity using Leading Eigenvector Dynamics Analysis (LEiDA), which serves to characterize brain activity at each time point by its whole-brain BOLD phase-locking pattern.

Linear response in neuronal networks: From neurons dynamics to collective response.

We review two examples where the linear response of a neuronal network submitted to an external stimulus can be derived explicitly, including network parameters dependence. This is done in a statistical physicslike approach where one associates, to the spontaneous dynamics of the model, a natural notion of Gibbs distribution inherited from ergodic theory or stochastic processes. These two examples are the Amari-Wilson-Cowan model [S.

A biophysical model explains the spontaneous bursting behavior in the developing retina.

During early development, waves of activity propagate across the retina and play a key role in the proper wiring of the early visual system. During a particular phase of the retina development (stage II) these waves are triggered by a transient network of neurons, called Starburst Amacrine Cells (SACs), showing a bursting activity which disappears upon further maturation. The underlying mechanisms of the spontaneous bursting and the transient excitability of immature SACs are not completely clear yet.

PRANAS: A New Platform for Retinal Analysis and Simulation.

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.

Pan-retinal characterisation of Light Responses from Ganglion Cells in the Developing Mouse Retina.

We have investigated the ontogeny of light-driven responses in mouse retinal ganglion cells (RGCs). Using a large-scale, high-density multielectrode array, we recorded from hundreds to thousands of RGCs simultaneously at pan-retinal level, including dorsal and ventral locations. Responses to different contrasts not only revealed a complex developmental profile for ON, OFF and ON-OFF responses, but also unveiled differences between dorsal and ventral RGC responses.

On the Mathematical Consequences of Binning Spike Trains.

We 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 stochastic process that is no longer Markov 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.

Exact computation of the maximum-entropy potential of spiking neural-network models.

Understanding how stimuli and synaptic connectivity influence the statistics of spike patterns in neural networks is a central question in computational neuroscience. The maximum-entropy approach has been successfully used to characterize the statistical response of simultaneously recorded spiking neurons responding to stimuli. However, in spite of good performance in terms of prediction, the fitting parameters do not explain the underlying mechanistic causes of the observed correlations.

Effects of cellular homeostatic intrinsic plasticity on dynamical and computational properties of biological recurrent neural networks.

Homeostatic intrinsic plasticity (HIP) is a ubiquitous cellular mechanism regulating neuronal activity, cardinal for the proper functioning of nervous systems. In invertebrates, HIP is critical for orchestrating stereotyped activity patterns. The functional impact of HIP remains more obscure in vertebrate networks, where higher order cognitive processes rely on complex neural dynamics.

Spike train statistics and Gibbs distributions.

This paper is based on a lecture given in the LACONEU summer school, Valparaiso, January 2012. 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; and (iii) conductance based integrate and fire model with chemical synapses and gap junctions.

Parameter estimation in spiking neural networks: a reverse-engineering approach.

This paper presents a reverse engineering approach for parameter estimation in spiking neural networks (SNNs). We consider the deterministic evolution of a time-discretized network with spiking neurons, where synaptic transmission has delays, modeled as a neural network of the generalized integrate and fire type. Our approach aims at by-passing the fact that the parameter estimation in SNN results in a non-deterministic polynomial-time hard problem when delays are to be considered.

Gibbs distribution analysis of temporal correlations structure in retina ganglion cells.

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.

The role of the asymptotic dynamics in the design of FPGA-based hardware implementations of gIF-type neural networks.

This paper presents a numerical analysis of the role of asymptotic dynamics in the design of hardware-based implementations of the generalised integrate-and-fire (gIF) neuron models. These proposed implementations are based on extensions of the discrete-time spiking neuron model, which was introduced by Soula et al., and have been implemented on Field Programmable Gate Array (FPGA) devices using fixed-point arithmetic.

Statistics of spike trains in conductance-based neural networks: Rigorous results.

We consider a conductance-based 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.

A discrete time neural network model with spiking neurons: II: dynamics with noise.

We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic weights. We show the existence and uniqueness of an invariant measure of Gibbs type and discuss its properties. We also discuss Markovian approximations and relate them to the approaches currently used in computational neuroscience to analyse experimental spike trains statistics.

Overview of facts and issues about neural coding by spikes.

In the present overview, our wish is to demystify some aspects of coding with spike-timing, through a simple review of well-understood technical facts regarding spike coding. Our goal is a better understanding of the extent to which computing and modeling with spiking neuron networks might be biologically plausible and computationally efficient. We intentionally restrict ourselves to a deterministic implementation of spiking neuron networks and we consider that the dynamics of a network is defined by a non-stochastic mapping.

A constructive mean-field analysis of multi-population neural networks with random synaptic weights and stochastic inputs.

We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the time variations of their membrane potentials. They are coupled by synaptic connections acting on their resulting activity, a nonlinear function of their membrane potential.

On dynamics of integrate-and-fire neural networks with conductance based synapses.

We present a mathematical analysis of networks with integrate-and-fire (IF) neurons with conductance based synapses. Taking into account the realistic fact that the spike time is only known within some finite precision, we propose a model where spikes are effective at times multiple of a characteristic time scale delta, where delta can be arbitrary small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the model-dynamics and obtain the following results.