Section: New Results
Human vision understanding through joint experimental and modeling studies, for normal and distrophic retinas
Cells characterization from their spike response
A new nonconvex variational approach for sensory neurons receptive field estimation
Participants : Audric Drogoul, Gilles Aubert [UCA, Laboratoire Jean Alexandre Dieudonné, Nice, France] , Bruno Cessac, Pierre Kornprobst.
Determining the receptive field of a visual sensory neuron is a first but crucial step to- wards the characterization of neurons response to local spatio-temporal stimuli. Existing methods are based on convex optimization methods neglecting biophysical constraints of neurons (bounded firing rate), and they are relatively poor in terms of accuracy and running time. We propose a new method to estimate receptive fields by a nonconvex variational approach, thus relaxing the simplifying and unrealistic assumption of convexity made by standard approaches. The method consists in studying a relaxed discrete energy minimized by a proximal alternating minimization algorithm. We compare our approach with the classical spike-triggered-average technique on simulated data, considering a typical retinal ganglion cell. Results show a high improvement in terms of accuracy and convergence with respect to the duration of the experiment.
Pan-retinal characterization of Light Responses from Ganglion Cells in the Developing Mouse Retina
Participants : Gerrit Hilgen [Institute of Neuroscience, Medical School, Newcastle University, Newcastle UK] , Sarah Pirmoradian [ANC - Institute for Adaptive and Neural Computation, Edimburgh, UK] , Daniela Pamplona, Pierre Kornprobst, Bruno Cessac, Matthias Hennig Pirmoradian [ANC - Institute for Adaptive and Neural Computation, Edimburgh, UK] , Evelyne Sernagor [Institute of Neuroscience, Medical School, Newcastle University, Newcastle, UK] .
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 RGC types, but also unveiled differences between dorsal and ventral RGCs. At eye-opening, dorsal RGCs of all types were more responsive to light, perhaps indicating an environmental priority to nest viewing for pre-weaning pups. The developmental profile of ON and OFF RGCs exhibited antagonistic behavior, with the strongest ON responses shortly after eye-opening, followed by an increase in the strength of OFF responses later on. Further, we found that with maturation receptive field (RF) center sizes decrease, responses to light get stronger, and centers become more circular while seeing differences in all of them between RGC types. These findings show that retinal functionality is not spatially homogeneous, likely reflecting ecological requirements that favour the early development of dorsal retina, and reflecting different roles in vision in the mature animal.
This work is under revision, submitted to EScience 
Understanding the role of spatio-temporal correlations in visual scene encoding
Spike train analysis and Gibbs distributions
Participants : Bruno Cessac, Rodrigo Cofré [Département de Physique Théorique, Université de Genève] .
Spikes in sensory neurons are conveyed collectively to the cortex using correlated binary patterns (in space and time) which constitute “the neural code”. Since patterns occur irregularly it is appropriate to characterize them using probabilistic descriptions or statistical models. Two major approaches attempt to characterize the spike train statistics: The Maximum Entropy Principle (MaxEnt) and Neuronal Network modeling (N.N). Remarkably, both approaches are related via the concept of Gibbs distributions. MaxEnt models are restricted to time-invariant Gibbs distributions, via the underlying assumption of stationarity, but this concept extends to non-stationary statistics (not defined via entropy), allowing to handle as well statistics of N.N models and GLM with non-stationary dynamics. We show in this poster that, stationary N.N, GLMmodels and MaxEnt models are equivalent via an explicit mapping. This allows us, in particular, to interpret the so-called "effective interactions" of MaxEnt models in terms of “real connections” models.
This work was presented in the Bernstein Conference 2016  and will be soon submitted to Journal of Statistical Physics.
Dimensionality Reduction in spatio-temporal MaxEnt models and analysis of Retinal Ganglion Cell Spiking Activity in experiments
Participants : Rubén Herzog [CINV - Centro Interdisciplinario de Neurociencia de Valparaíso] , Maria-Jose Escobar [Univ Tecnico Federico Santa María] , Adrian Palacios [CINV - Centro Interdisciplinario de Neurociencia de Valparaíso] , Bruno Cessac.
Retinal spike response to stimuli is constrained, on one hand by short range correlations (receptive field overlap) and on the other hand by lateral connectivity (cells connectivity). This last effect is difficult to handle from statistics because it requires to consider spatio-temporal correlations with a time delay long enough to take into account the time of propagation along synapses. Although MaxEnt model are useful to fit optimal model (maximizing entropy) under the constraints of reproducing observed correlations, they do address spatio-temporal correlations in their classical form (Ising or higher order interactions but without time delay). Binning in such models somewhat integrates propagation effects, but in an implicit form, and increasing binning severely bias data . To resolve this issue we have considered spatio-temporal MaxEnt model formerly developed e.g. by Vasquez et al. . The price to pay, however is a huge set of parameters that must be fitted to experimental data to explain the observed spiking patterns statistics. There is no a priori knowledge of which parameters are relevant and which ones are contributing to overfitting. We propose here a method of dimension reduction, i.e. a projection on a relevant subset of parameters, relying on the so-called Susceptibility matrix closely related to the Fisher information. In contrast to standard methods in information geometry though, this matrix handle space and time correlations. We have applied this method for retina data obtained in a diurnal rodent (Octodon degus, having 30 of cones photoreceptors) and a 252-MEA system. Three types of stimuli were used: spatio-temporal uniform light, white noise and a natural movie. We show the role played by time-delayed pairwise interactions in the neural response to stimuli both for close and distant cells. Our conclusion is that, to explain the population spiking statistics we need both short-distance interactions as well as long-distance interactions, meaning that the relevant functional correlations are mediated not only by common input (i.e. receptive field overlap, electrical coupling; spillover) but also by long range connections.
This work has been presented in the Bernstein 2016 conference  and has been submitted to Plos Comp Bio.
On the mathematical consequences of binning spike trains
Participants : Bruno Cessac, Arnaud Le Ny [LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées] , Eva Loecherbach [AGM - Laboratoire d'Analyse, Géométrie et Modélisation and Département de Mathématiques, [Cergy-Pontoise] .
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 which is not Markovian 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.
This work has been published in Neural Computation, Massachusetts Institute of Technology Press (MIT Press), 2016 .
Mathematical and experimental studies on retinal waves
Participants : Dora Karvouniari, Lionel Gil [INLN -Institut Non Linéaire de Nice Sophia-Antipolis] , Olivier Marre [Institut de la Vision] , Serge Picaud [Institut de la Vision] , Bruno Cessac.
We reproduce the spontaneous intrinsic cell-autonomous rhythmic bursting in Starbust Amacrine Cells (SACs) and the slow After Hyperpolarisation Current (sAHP), which modulates the refractory process inbetween two consecutive bursts, observed experimentally in . We describe the dynamical influence of cholinergic synapses, ensuring the level of SAC synchrony necessary for the emergence of waves. We obtain: a) a plausible generic mechanism generating spontaneous retinal waves in development, without any need for external stimulation as opposed to existing models and b) a mathematical characterization of retinal waves. Especially, a biophysical parameter controls the wave arousal and the corresponding shape. The model is accurate enough to reproduce existing experiments, but also to propose new ones.
This work has been presented in the workshop "Modelling the early visual system" , 2nd International Conference on Mathematical Neuroscience (ICMNS) , the AREADNE conference , the Bernstein conference . Two papers are in preparation.
Trajectory anticipation, from retina to V1
This work is just starting. The main work has been done by Selma Souihel in her Master II instership supervised by Bruno Cessac . The aim of the internship is to use and update the software VirtualRetina and Enas in order to reproduce the activity of the retina in response to the stimulus of a moving bar, observed By Mr Berry & al. A form of anticipation of the movement has been demonstrated experimentally by its authors in salamander, rabbit and goldfish retinas. This anticipation can be explained, in the case of a simple trajectory, by the gain control mechanism specific to the ganglion cells, implemented by Virtual-Retina-Enas.
Simulating and analysing retina's response to visual stimuli
ENAS: A new software for spike train analysis and simulation
Participants : Bruno Cessac, Pierre Kornprobst, Selim Kraria, Hassan Nasser, Daniela Pamplona, Geoffrey Portelli, Thierry Vieville [Mnemosyne - Mnemonic Synergy LaBRI - Laboratoire Bordelais de Recherche en Informatique, IMN - Institut des Maladies Neurodégénératives, [Bordeaux] .
Rank order coding: a retinal information decoding strategy revealed by large-scale multielectrode array retinal recordings
Participants : Geoffrey Portelli, John M. Barrett [Institute of Neuroscience, Medical School, Newcastle University, Newcastle UK] , Gerrit Hilgen [Institute of Neuroscience, Medical School, Newcastle University, Newcastle UK] , Timothée Masquelier [CERCO, Toulouse, France] , Alessandro Maccione [NetS3 Lab - NeuroEngineering & bio-arTificial Synergic SystemS Laboratory, Genova, Italy] , Stefano Di Marco [NetS3 Lab - NeuroEngineering & bio-arTificial Synergic SystemS Laboratory, Genova, Italy] , Luca Berdondini [NetS3 Lab - NeuroEngineering & bio-arTificial Synergic SystemS Laboratory, Genova, Italy] , Pierre Kornprobst, Evelyne Sernagor [Institute of Neuroscience, Medical School, Newcastle University, Newcastle, UK] .
How a population of retinal ganglion cells (RGCs) encodes the visual scene remains an open question. Going beyond individual RGC coding strategies, results in salamander suggest that the relative latencies of an RGC pair encodes spatial information. Thus a population code based on this concerted spiking could be a powerful mechanism to transmit visual information rapidly and efficiently. Here, we tested this hypothesis in mouse by recording simultaneous light-evoked responses from hundreds of RGCs, at pan-retinal level, using a new generation of large-scale, high density multielectrode array consisting of 4096 electrodes. Interestingly, we did not find any RGCs exhibiting a clear latency tuning to the stimuli, suggesting that in mouse, individual RGC pairs may not provide sufficient information. We show that a significant amount of information is encoded synergistically in the concerted spiking of large RGC populations. Thus, the RGC population response described with relative activities, or ranks, provides more relevant information than classical independent spike count- or latency- based codes. In particular, we report for the first time that when considering the relative activities across the whole population, the wave of first stimulus-evoked spikes (WFS) is an accurate indicator of stimulus content. We show that this coding strategy co-exists with classical neural codes, and that it is more efficient and faster. Overall, these novel observations suggest that already at the level of the retina, concerted spiking provides a reliable and fast strategy to rapidly transmit new visual scenes.
This work has been published in eNeuro .
Microsaccades enable efficient synchrony-based coding in the retina: a simulation study.
Participants : Timothée Masquelier [CERCO, Toulouse, France] , Geoffrey Portelli, Pierre Kornprobst.
It is now reasonably well established that microsaccades (MS) enhance visual perception, although the underlying neuronal mechanisms are unclear. Here, using numerical simulations, we show that MSs enable efficient synchrony-based coding among the primate retinal ganglion cells (RGC). First, using a jerking contrast edge as stimulus, we demonstrate a qualitative change in the RGC responses: synchronous firing, with a precision in the 10 ms range, only occurs at high speed and high contrast. MSs appear to be sufficiently fast to be able reach the synchronous regime. Conversely, the other kinds of fixational eye movements known as tremor and drift both hardly synchronize RGCs because of a too weak amplitude and a too slow speed respectively. Then, under natural image stimulation, we find that each MS causes certain RGCs to fire synchronously, namely those whose receptive fields contain contrast edges after the MS. The emitted synchronous spike volley thus rapidly transmits the most salient edges of the stimulus, which often constitute the most crucial information. We demonstrate that the readout could be done rapidly by simple coincidence-detector neurons without knowledge of the MS landing time, and that the required connectivity could emerge spontaneously with spike timing-dependent plasticity.
This work has been published in Scientific Reports .
Mean-Field models in neuroscience
Perspectives on Multi-Level Dynamics
Participants : Fatihcan Atay [MPI-MIS - Max Planck Institute for Mathematics in the Sciences] , Sven Banisch [MPI-MIS - Max Planck Institute for Mathematics in the Sciences] , Philippe Blanchard [University of Bielefeld-Departement of physics] , Bruno Cessac, Eckehard Olbrich [MPI-MIS - Max Planck Institute for Mathematics in the Sciences] , Dimitri Volchenkov [University of Bielefeld, Departement of physics] .
As Physics did in previous centuries, there is currently a common dream of extracting generic laws of nature in economics, sociology, neuroscience, by focalising the description of phenomena to a minimal set of variables and parameters, linked together by causal equations of evolution whose structure may reveal hidden principles. This requires a huge reduction of dimensionality (number of degrees of freedom) and a change in the level of description. Beyond the mere necessity of developing accurate techniques affording this reduction, there is the question of the correspondence between the initial system and the reduced one. In this paper, we offer a perspective towards a common framework for discussing and understanding multi-level systems exhibiting structures at various spatial and temporal levels. We propose a common foundation and illustrate it with examples from different fields. We also point out the difficulties in constructing such a general setting and its limitations.
This work has been published in The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity, 2016, 5 .
The relative contribution of noise and adaptation to competition during tri-stable motion perception
Participants : Andrew Isaac Meso [Institut de Neurosciences de la Timone, Team InVibe, France] , James Rankin [Center for Neural Science, New York UniversityNew York, NY] , Pierre Kornprobst, Olivier Faugeras [Université Côte d’Azur, Inria, MathNeuro team, France] , Guillaume S. Masson [Institut de Neurosciences de la Timone, Team InVibe, France] .
Animals exploit antagonistic interactions for sensory processing and these can cause oscillations between competing states. Ambiguous sensory inputs yield such perceptual multistability. Despite numerous empirical studies using binocular rivalry or plaid pattern motion, the driving mechanisms behind the spontaneous transitions between alternatives remain unclear. In the current work, we used a tristable barber pole motion stimulus combining empirical and modeling approaches to elucidate the contributions of noise and adaptation to underlying competition. We first robustly characterized the coupling between perceptual reports of transitions and continuously recorded eye direction, identifying a critical window of 480 ms before button presses, within which both measures were most strongly correlated. Second, we identified a novel nonmonotonic relationship between stimulus contrast and average perceptual switching rate with an initially rising rate before a gentle reduction at higher contrasts. A neural fields model of the underlying dynamics introduced in previous theoretical work and incorporating noise and adaptation mechanisms was adapted, extended, and empirically validated. Noise and adaptation contributions were confirmed to dominate at the lower and higher contrasts, respectively. Model simulations, with two free parameters controlling adaptation dynamics and direction thresholds, captured the measured mean transition rates for participants. We verified the shift from noise-dominated toward adaptation-driven in both the eye direction distributions and intertransition duration statistics. This work combines modeling and empirical evidence to demonstrate the signal-strength–dependent interplay between noise and adaptation during tristability. We propose that the findings generalize beyond the barber pole stimulus case to ambiguous perception in continuous feature spaces.
Understanding the impact of recurrent interactions on MT population tuning: a simulation study.
Participants : Kartheek Medathati, Andrew Isaac Meso [Institut de Neurosciences de la Timone, Team InVibe, France] , Guillaume S. Masson [Institut de Neurosciences de la Timone, Team InVibe, France] , Pierre Kornprobst, James Rankin [Center for Neural Science, New York University, USA] .
In sensory systems, different computational rules are often evident in different neuronal subpopulations. Most previous models of motion estimation by MT cells explain their specific tuning functions by having multiple feedforward inputs, largely ignoring the role of recurrent connectivity, a hallmark of cortical circuits. Therefore they fail to explain the dynamics of these tuning functions and the fact that different behaviour can be achieved by a single subpopulation when varying the spatiotemporal properties of the input. Here, using numerical simulations, we focus on a ring network that models visual motion processing at the level of MT cells. We show how excitatory and inhibitory recurrent connections shape motion direction tuning, thus resulting in different computational rules such as vector averaging, winner-take-all or bimodal representations. In particular, depending on the inhibition regime the ring network can switch from motion integration to motion segmentation, being able to compute either a single pattern motion or to superpose multiple inputs as in motion transparency. Such feature space centre-surround recurrent mechanisms may be widely applicable to explain context-modulation of sensory processing.
This work has been presented at AREADNE conference  and a paper is in preparation.
Bio-Inspired Computer Vision
Bio-Inspired Computer Vision: Towards a Synergistic Approach of Artificial and Biological Vision
Participants : Pierre Kornprobst, Guillaume S. Masson [Institut de Neurosciences de la Timone, Team InVibe] , Kartheek Medathati [correspondent] , Heiko Neumann [Ulm University, Germany] .
Studies in biological vision have always been a great source of inspiration for design of computer vision algorithms. In the past, several successful methods were designed with varying degrees of correspondence with biological vision studies, ranging from purely functional inspiration to methods that utilise models that were primarily developed for explaining biological observations. Even though it seems well recognised that computational models of biological vision can help in design of computer vision algorithms, it is a non-trivial exercise for a computer vision researcher to mine relevant information from biological vision literature as very few studies in biology are organised at a task level.
In , we aim to bridge this gap by providing a computer vision task centric presentation of models primarily originating in biological vision studies. Not only we revisit some of the main features of biological vision and discuss the foundations of existing computational studies modelling biological vision, but also consider three classical computer vision tasks from a biological perspective: image sensing, segmentation and optical flow. Using this task-centric approach, we discuss well-known biological functional principles and compare them with approaches taken by computer vision. Based on this comparative analysis of computer and biological vision, we present some recent models in biological vision and highlight a few models that we think are promising for future investigations in computer vision. To this extent, this paper provides new insights and a starting point for investigators interested in the design of biology-based computer vision algorithms and pave a way for much needed interaction between the two communities leading to the development of synergistic models of artificial and biological vision.
This work has been published in Computer Vision and Image Understanding Journal (CVIU) .
Retina-inspired tone mapping
Participants : Marco Benzi, Maria-Jose Escobar [Universidad Técnica Federico Santa María, Valparaíso, Chile] , Adrien Bousseau [Inria, GraphDeco project-team] , Pierre Kornprobst [correspondent] .
Real-world radiance values span several orders of magnitudes which have to be processed by biological and artificial systems in order to maintain high visual sensitivity.
In biological systems, process starts at the retina level, where adaptation is absolutely crucial since retinas must maintain high contrast sensitivity over a very broad range of luminance, from starlight to direct sunlight. Adaptation is both global through neuromodulatory feedback loops and local through adaptive gain control mechanisms so that retinal networks can be adapted to the whole scene luminance level while maintaining high contrast sensitivity in different regions of the image, despite their considerable differences in luminance. Adaptation is present at different levels, e.g., at the photoreceptor level where sensitivity is a function of the recent mean intensity, and at the bipolar level where slow and fast contrast adaptation mechanisms are found. These multiple adaptational mechanisms act together, with lighting conditions dictating which mechanisms dominate.
In artificial systems, the process of compressing the range of intensities in High-Dynamic Range (HDR) images is know as tone mapping. It is a necessary step to properly visualize captured natural scenes as common displays are Low-Dynamic Range, spanning up to two orders of magnitude. There is a large body of literature in this area on static images, with approaches which combine luminance adaptation (using empirical laws such as the Naka-Rushton equation) and local contrast enhancement sometimes closely inspired from retinal principles , . Recent developments concern video-tone mapping where a few approaches have been developed .
In this work, we investigate if the Virtual Retina simulator  could serve as a goof basis to develop a new tone mapping operator for videos. One strength of this simulator is its model of fast contrast gain control which has been validated on experimental data. However this model was not designed to deal with color and HDR images. This requires some pre- and post-processing but also changes in the Virtual Retina to account for other adaptation phenomena. Preliminary encouraging results have been obtained and we plan to continue that project in 2017.