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249 results on '"NEUROMATHCOMP"'

1. The relative contribution of noise and adaptation to competition during tri-stable motion perception

Author: Meso, Andrew Isaac, Rankin, James, Faugeras, Olivier, Kornprobst, Pierre, Masson, Guillaume, Bournemouth University [Poole] (BU), Institut de Neurosciences de la Timone (INT), Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS), Center for Neural Science [New York] (CNS), New York University [New York] (NYU), NYU System (NYU)-NYU System (NYU), Mathématiques pour les Neurosciences (MATHNEURO), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Biologically plausible Integrative mOdels of the Visual system : towards synergIstic Solutions for visually-Impaired people and artificial visiON (BIOVISION), ANR-10-BLAN-1432,VISAFIX,Instabilité fonctionnelle durant la fixation oculaire : conséquences motrices et perceptives(2010), ANR-13-SHS2-0006,SPEED,Traitement de la vitesse dans les scènes visuelles naturelles, European Project: 227747,EC:FP7:ERC,ERC-2008-AdG,NERVI(2009), European Project: 318723,EC:FP7:ICT,FP7-ICT-2011-8,MATHEMACS(2012), European Project: 269921,EC:FP7:ICT,FP7-ICT-2009-6,BRAINSCALES(2011), ANR-13-BSH2-0006,SPEED,Traitement de la vitesse dans les scènes visuelles naturelles(2013), Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU), Mathematical and Computational Neuroscience (NEUROMATHCOMP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), NEUROMATHCOMP, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-INRIA Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris)-Université Nice Sophia Antipolis (... - 2019) (UNS), Kornprobst, Pierre, BLANC - Instabilité fonctionnelle durant la fixation oculaire : conséquences motrices et perceptives - - VISAFIX2010 - ANR-10-BLAN-1432 - BLANC - VALID, Blanc 2013 - Traitement de la vitesse dans les scènes visuelles naturelles - - SPEED2013 - ANR-13-BSH2-0006 - Blanc 2013 - VALID, From single neurons to visual perception - NERVI - - EC:FP7:ERC2009-01-01 - 2013-12-31 - 227747 - VALID, MATHEmatics of Multi-level Anticipatory Complex Systems - MATHEMACS - - EC:FP7:ICT2012-10-01 - 2015-09-30 - 318723 - VALID, and Brain-inspired multiscale computation in neuromorphic hybrid systems - BRAINSCALES - - EC:FP7:ICT2011-01-01 - 2015-03-31 - 269921 - VALID
Subjects: [SCCO]Cognitive science, Eye movements, Competition model, Multistable motion perception, [SCCO.NEUR]Cognitive science/Neuroscience, [SCCO.NEUR] Cognitive science/Neuroscience, [SCCO.PSYC]Cognitive science/Psychology, [SDV.NEU.SC]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]/Cognitive Sciences, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], Adaptation, Noise, [SDV.NEU.SC] Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]/Cognitive Sciences, ComputingMilieux_MISCELLANEOUS
Abstract: International audience; Animals exploit antagonistic interactions for sensory processing and these can cause oscillations between competing states. Ambiguous sensory inputs yield such perceptual multi-stability. 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 tri-stable barberpole motion stimulus combining empirical and modelling approaches to elucidate the contributions of noise and adaptation to underlying competition. We first robustly characterised the coupling between perceptual reports of transitions and continuously recorded eye direction, identifying a critical window of 480ms before button presses within which both measures were most strongly correlated. Second, we identified a novel non monotonic 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 towards adaptation-driven in both the eye direction distributions and inter-transition duration statistics. This work combines modelling and empirical evidence to demonstrate the signal strength dependent interplay between noise and adaptation during tri- stability. We propose that the findings generalise beyond the barberpole stimulus case to ambiguous perception in continuous feature spaces.
Published: 2016

2. Noise-induced behaviors in neural mean field dynamics

Author: Olivier Faugeras, Jonathan Touboul, Geoffroy Hermann, NEUROMATHCOMP, Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-INRIA Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Mathematical and Computational Neuroscience (NEUROMATHCOMP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Nice Sophia Antipolis (... - 2019) (UNS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS)
Subjects: neural mass models, Collective behavior, noise, Dynamical systems theory, Gaussian, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Dynamical Systems (math.DS), 01 natural sciences, Noise (electronics), 010305 fluids & plasmas, mean field equations, 03 medical and health sciences, symbols.namesake, 0302 clinical medicine, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], 0103 physical sciences, FOS: Mathematics, Applied mathematics, Mathematics - Dynamical Systems, Empirical process, Mathematics, Quantitative Biology::Neurons and Cognition, Ode, dynamical systems, Mean field theory, Quantitative Biology - Neurons and Cognition, FOS: Biological sciences, Modeling and Simulation, symbols, Probability distribution, Neurons and Cognition (q-bio.NC), bifurcations, 030217 neurology & neurosurgery, Analysis
Abstract: International audience; The collective behavior of cortical neurons is strongly affected by the presence of noise at the level of individual cells. In order to study these phenomena in large-scale assemblies of neurons, we consider networks of firing-rate neurons with linear intrinsic dynamics and nonlinear coupling, belonging to a few types of cell populations and receiving noisy currents. Asymptotic equations as the number of neurons tends to infinity (mean field equations) are rigorously derived based on a probabilistic approach. These equations are implicit on the probability distribution of the solutions which generally makes their direct analysis difficult. However, in our case, the solutions are Gaussian, and their moments satisfy a closed system of nonlinear ordinary differential equations (ODEs), which are much easier to study than the original stochastic network equations, and the statistics of the empirical process uniformly converge towards the solutions of these ODEs. Based on this description, we analytically and numerically study the influence of noise on the collective behaviors, and compare these asymptotic regimes to simulations of the network. We observe that the mean field equations provide an accurate description of the solutions of the network equations for network sizes as small as a few hundreds of neurons. In particular, we observe that the level of noise in the system qualitatively modifies its collective behavior, producing for instance synchronized oscillations of the whole network, desynchronization of oscillating regimes, and stabilization or destabilization of stationary solutions. These results shed a new light on the role of noise in shaping collective dynamics of neurons, and gives us clues for understanding similar phenomena observed in biological networks.
Published: 2012

3. Some theoretical and numerical results for delayed neural field equations

Author: Olivier Faugeras, Grégory Faye, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), NEUROMATHCOMP, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-INRIA Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Nice Sophia Antipolis (... - 2019) (UNS), Kornprobst, Pierre, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Nice Sophia Antipolis (1965 - 2019) (UNS)
Subjects: Lyapunov function, Quantitative Biology::Neurons and Cognition, Differential equation, Mathematical analysis, Statistical and Nonlinear Physics, [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], Delay differential equation, Condensed Matter Physics, 01 natural sciences, 010305 fluids & plasmas, Nonlinear system, symbols.namesake, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], Simultaneous equations, Stability theory, 0103 physical sciences, symbols, 010306 general physics, Mathematics, Numerical stability, Numerical partial differential equations
Abstract: Special issue on Mathematical Neuroscience; International audience; In this paper we study neural field models with delays which define a useful framework for modeling macroscopic parts of the cortex involving several populations of neurons. Nonlinear delayed integrodifferential equations describe the spatio-temporal behavior of these fields. Using methods from the theory of delay differential equations, we show the existence and uniqueness of a solution of these equations. A Lyapunov analysis gives us sufficient conditions for the solutions to be asymptotically stable. We also present a fairly detailed study of the numerical computation of these solutions. This is, to our knowledge, the first time that a serious analysis of the problem of the existence and uniqueness of a solution of these equations has been performed. Another original contribution of ours is the definition of a Lyapunov functional and the result of stability it implies. We illustrate our numerical schemes on a variety of examples that are relevant to modeling in neuroscience.
Published: 2010

4. La dynamique récurrente de réseaux permet de réconcilier la segmentation et l’intégration du mouvement visuel

Author: Pierre Kornprobst, James Rankin, N. V. Kartheek Medathati, Guillaume S. Masson, Andrew Isaac Meso, Biologically plausible Integrative mOdels of the Visual system : towards synergIstic Solutions for visually-Impaired people and artificial visiON (BIOVISION), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mathematical and Computational Neuroscience (NEUROMATHCOMP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut de Neurosciences de la Timone (INT), Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS), Bournemouth University [Poole] (BU), GSM and AIM are supported by a grant from the Agence Nationale de la Recherche (SPEED, ANR-13- SHS2–0006) and by the Centre National de la Recherche Scientifique. NVKM and PK were supported by the European Union Seventh Framework Programme (FP7/2007-2013, grant agreement n° 318723, MATHEMACS). JR was partially funded by a Swartz Foundation postdoc grant., ANR-13-BSH2-0006,SPEED,Traitement de la vitesse dans les scènes visuelles naturelles(2013), European Project: 318723,EC:FP7:ICT,FP7-ICT-2011-8,MATHEMACS(2012), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Kornprobst, Pierre, Blanc 2013 - Traitement de la vitesse dans les scènes visuelles naturelles - - SPEED2013 - ANR-13-BSH2-0006 - Blanc 2013 - VALID, MATHEmatics of Multi-level Anticipatory Complex Systems - MATHEMACS - - EC:FP7:ICT2012-10-01 - 2015-09-30 - 318723 - VALID, Mathématiques pour les Neurosciences (MATHNEURO), Center for Neural Science [New York] (CNS), New York University [New York] (NYU), NYU System (NYU)-NYU System (NYU), Inria Sophia Antipolis, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), College of Engineering, Mathematics and Physical Sciences [Exeter] (EMPS), University of Exeter, Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU), Psychology [Bournemouth, UK] (Faculty of Science and Technology), and ANR-13-SHS2-0006,SPEED,Traitement de la vitesse dans les scènes visuelles naturelles
Subjects: Visual motion integration, Dynamical systems theory, Computer science, Models, Neurological, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Motion Perception, [SCCO.COMP]Cognitive science/Computer science, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], lcsh:Medicine, Sensory system, Systèmes dynamiques, 050105 experimental psychology, Motion (physics), Article, 03 medical and health sciences, Superposition principle, Motion, 0302 clinical medicine, direction selectivity, Animals, 0501 psychology and cognitive sciences, Computer vision, Segmentation, Motion perception, [SDV.NEU] Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], lcsh:Science, Network model, Neurons, Intégration du mouvement, Multidisciplinary, Quantitative Biology::Neurons and Cognition, business.industry, [SCCO.NEUR]Cognitive science/Neuroscience, 05 social sciences, [SCCO.NEUR] Cognitive science/Neuroscience, lcsh:R, Ring network, Pattern recognition, dynamical systems, Network dynamics, ring model, sélectivité à l’orientation, Macaca, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], lcsh:Q, Artificial intelligence, business, 030217 neurology & neurosurgery, Photic Stimulation
Abstract: In sensory systems, different computational rules are postulated to be implemented by different neuronal subpopulations, each one being characterised by a particular tuning function. For instance, in primate cortical area MT, different classes of direction-selective cells have been identified and related to either motion integration, segmentation or transparency. Still, how such different tuning properties are constructed is unclear. The dominant theoretical viewpoint postulates that differential weighting of MT inputs along the linear-nonlinear feedforward cascade is sufficient to build these different cell classes but it does not account for their complex temporal dynamics and their versatility when facing different input statistics. Here, we demonstrate that a recurrent network model of visual motion processing can reconcile these different properties. We show how excitatory and inhibitory recurrent connections, within a direction representation space, shape neuronal motion direction tuning and implement different computational rules such as vector averaging, winner-take-all or superposition. The model also captures ordered temporal transitions between these behaviours. In particular, depending on the inhibition regime the ring network can switch from motion integration to motion segmentation, thus being able to compute either a single pattern motion or to superpose multiple inputs as in motion transparency. We thus demonstrate that recurrent architectures can adaptively give rise to different cortical computational regimes depending upon the input statistics, thus reconciling the two facets of sensory processing: integration and segmentation.; Dans les systèmes sensoriels, différentes règles computationnelles sont supposées être implémentées par différentes sous-populations neuronales, chacune étant caractérisée par une fonction de sélectivité. Par exemple, dans la zone corticale des primates MT, différentes classes de cellules sélectives à la direction ont été identifiées et liées à l’intégration du mouvement, à la segmentation ou à la transparence. Cependant, la façon dont ces fonction de sélectivité sont construites n’est pas claire. Le point de vue théorique dominant postule que la pondération différentielle des entrées de MT le long de la cascade montante linéaire non linéaire est suffisante pour construire ces différentes classes de cellules, mais ne tient pas compte de leur dynamique temporelle complexe et leur versatilité face à différentes statistiques d’entrée. Ici, nous démontrons qu’un modèle de réseau récurrent de traitement du mouvement visuel peut réconcilier ces différentes propriétés. Nous montrons comment les connexions récurrentes excitatrices et inhibitrices, au sein d’un espace de représentation de direction, forment la sélectivité neuronale à la direction du mouvement et implémentent des règles de calcul différentes telles que la moyenne des vecteurs, le "tout au vainqueur" (winner-take-all) ou la superposition. Le modèle capture également les transitions temporelles ordonnées entre ces comportements. En particulier, en fonction du régime d’inhibition, le réseau en anneau (ring model) peut passer d’une intégration de mouvement à une segmentation de mouvement, ce qui permet de calculer soit un seul mouvement de motif, soit de superposer des entrées multiples comme dans les mouvements transparents. Nous démontrons ainsi que les architectures récurrentes peuvent adapter de façon adaptative des régimes de calculs corticaux différents en fonction des statistiques d’entrée, afin de réconcilier les deux facettes du traitement sensoriel: l’intégration et la segmentation.
Published: 2017

5. Vers des modèles synergiques de l'estimation du mouvement en vision biologique et artificielle

Author: Medathati, Naga Venkata Kartheek, Biologically plausible Integrative mOdels of the Visual system : towards synergIstic Solutions for visually-Impaired people and artificial visiON (BIOVISION), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mathematical and Computational Neuroscience (NEUROMATHCOMP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015 - 2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Inria, UCA, Inria, Pierre Kornprobst, Guillaume S. Masson, and European Project: 318723,EC:FP7:ICT,FP7-ICT-2011-8,MATHEMACS(2012)
Subjects: Théorie de la bifurcation, Vision biologique, Optical flow, MT neuronal dynamics, biological vision, Bifurcation theory, Dynamique neuronale MT, [INFO]Computer Science [cs], Perception du mouvement, motion perception, Flux optique
Abstract: This thesis addresses the study of the motion perception in primates. We propose that scaling up the models rooted in biological vision by taking a task centric approach would gives us further insights to probe biological vision and better constraints to design models. The first part of this thesis relates to a feedforward view of how the motion information is processed in the mammalian brains with specific focus on areas V1 and MT. Based on a standard physiological model describing the activity of motion sensitive neurons in areas V1 and MT, we propose a feedforward model for dense optical flow estimation. This feedforward V1-MT model is benchmarked with modern computer vision datasets and results form a basis to study multiple aspects of dense motion estimation. Benchmarking results demonstrated that a sharp optical flow map cannot be obtained by considering isotropic pooling and motion estimation is disrupted in regions close to object or motion boundaries. It also shows a blindspot in the modelling literature that spatial association of the extracted motion information has not been attempted or has beenlimited to recovering coarser attributes. In order to improve the motion estimation, we investigated the pooling by MT neurons in terms of spatial-extent and selectivity for integration as well as the decoding strategy in order to obtain a spatially dense optical flow map. We show that by incorporating a pooling strategy that is regulated by form-based cues and considering lateral propagation of the activity, the motion estimation quality is improved. Interestingly, incorporating the form based cues amounts to addition of neurons with different kinds of selectivity to thenetwork. This raises a question, whether or not a minimal network with recurrent interactions in feature domain can exhibit different kinds of feature selectivities or we need to consider explicitly cells with different kinds of selectivity? This question relates to the second part of the thesis. We investigated this question using a ring network model under neural fields formalism with motion direction as feature space, closely mimicing MT physiological experiments. Our model produced a rich variety of results. Our results indicate that a variety of tuning behaviors foundin MT area can be reproduced by a minimal network of directionally tuned cells, explicit 2D cues need not be required for motion integration, dynamical changes inthe MT neuronal tuning reported in the literature can be explained through feature domain recurrent interactions and also open the door for accounting transparency by challenging the high inhibition regimes considered by many models in the literature for motion integration. To conclude, we re-emphasize on task-centric modelling approaches and several directions for interfacing studies in biological andcomputer vision.; Cette thèse porte sur l'étude de la perception du mouvement chez les primates. Nous proposons que la mise à l'échelle des modèles enracinés dans la vision biologique en adoptant une approche centrée sur les tâches nous permettrait de mieux comprendre la vision biologique et de meilleures contraintes pour concevoir des modèles. La première partie de cette thèse concerne une vue d'avance sur la façon dont les informations sur les mouvements sont traitées dans les cerveaux des mammifères avec un accent particulier sur les zones V1 et MT. Sur la base d'un modèle physiologique standard décrivant l'activité des neurones sensibles aux mouvements dans les zones V1 et MT, nous proposons un modèle feedforward pour l'estimation du débit optique dense. Ce modèle feed-forward V1-MT est comparé aux ensembles de données modernes sur la vision par ordinateur et les résultats constituent une base pour étudier plusieurs aspects de l'estimation du mouvement dense. Les résultats de l'analyse comparative ont démontré qu'une carte de flux optique nette ne peut être obtenue en considérant le regroupement isotrope et l'estimation de mouvement est perturbée dans des régions proches des limites d'objet ou de mouvement. Il montre également un point mort dans la littérature de modélisation selon laquelle l'association spatiale de l'information de mouvement extraite n'a pas été tentée ou s'est limitée à récupérer des attributs plus grossiers. Afin d'améliorer l'estimation du mouvement, nous avons étudié la mise en commun par les neurones MT en termes d'étendue spatiale et de sélectivité pour l'intégration ainsi que la stratégie de décodage afin d'obtenir une carte de flux optique spatialement dense. Nous montrons qu'en incorporant une stratégie de mise en commun qui est réglementée par des indices formés et en considérant la propagation latérale de l'activité, la qualité de l'estimation du mouvement est améliorée. Fait intéressant, l'incorporation des indices basés sur la forme équivaut à l'ajout de neurones avec différents types de sélectivité au réseau. Cela soulève une question, qu'un réseau minimal ou non possédant des interactions récurrentes dans un domaine de fonctionnalité puisse-t-il présenter différents types de sélectivité d'entités ou il faut considérer explicitement des cellules avec différents types de sélectivité? Cette question concerne la deuxième partie de la thèse. Nous avons étudié cette question à l'aide d'un modèle de réseau en anneau dans le formalisme des champs neural avec la direction du mouvement comme espace caractéristique, imitant de près les expériences physiologiques du MT. Notre modèle a produit une grande variété de résultats. Nos résultats indiquent qu'une variété de comportements d'accord trouvés dans la zone MT peut être reproduit par un réseau minimal de cellules délocalisées de manière directe, des indices 2D explicites ne doivent pas être nécessaires pour l'intégration du mouvement, les changements dynamiques dans l'accord neuronal MT rapporté dans la littérature peuvent s'expliquer par Les interactions récurrentes de domaine caractéristique et ouvrent la porte à la transparence comptable en mettant au défi les régimes d'inhibition élevés considérés par de nombreux modèles dans la littérature pour l'intégration de mouvement. Pour conclure, nous insistons sur les approches de modélisation axées sur les tâches et sur plusieurs directions pour l'interfaçage des études en vision biologique et informatique.
Published: 2017

6. Canard solutions in planar piecewise linear systems with three zones

Author: Mathieu Desroches, Antonio E. Teruel, Martin Krupa, Soledad Fernández-García, Multiscale dYnamiCs in neuroENdocrine AxEs (Mycenae), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Departament de Ciències Matemàtiques et Informàtica, Universitat de les Illes Balears (UIB), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: Class (set theory), Singular perturbation, Mathematics::Dynamical Systems, Quantitative Biology::Neurons and Cognition, Continuum (topology), [SCCO.NEUR]Cognitive science/Neuroscience, General Mathematics, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Mathematical analysis, Topology, 01 natural sciences, Stability (probability), 010305 fluids & plasmas, Computer Science Applications, 010101 applied mathematics, Piecewise linear function, Planar, Intersection, 0103 physical sciences, Limit (mathematics), 0101 mathematics, Mathematics
Abstract: International audience; In this work, we analyze the existence and stability of canard solutions in a class of planar piecewise linear systems with three zones, using a singular perturbation theory approach. To this aim, we follow the analysis of the classical canard phenomenon in smooth planar slow–fast systems and adapt it to the piecewise-linear framework. We first prove the existence of an intersection between repelling and attracting slow manifolds, which defines a maximal canard, in a non-generic system of the class having a continuum of periodic orbits. Then, we perturb this situation and we prove the persistence of the maximal canard solution, as well as the existence of a family of canard limit cycles in this class of systems. Similarities and differences between the piecewise linear case and the smooth one are highlighted.
Published: 2015

7. A Representation of the Relative Entropy with Respect to a Diffusion Process in Terms of Its Infinitesimal Generator

Author: James MacLaurin, Olivier Faugeras, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: Kullback–Leibler divergence, General Physics and Astronomy, lcsh:Astrophysics, 01 natural sciences, Kullback-Leibler, 010104 statistics & probability, lcsh:QB460-466, Statistical inference, Infinitesimal generator, 0101 mathematics, lcsh:Science, Mathematics, Weak solution, [SCCO.NEUR]Cognitive science/Neuroscience, 010102 general mathematics, Mathematical analysis, relative entropy, diffusion, Empirical measure, lcsh:QC1-999, Exponential function, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], martingale formulation, Rate of convergence, Kullback–Leibler, lcsh:Q, Martingale (probability theory), lcsh:Physics
Abstract: In this paper we derive an integral (with respect to time) representation of the relative entropy (or Kullback–Leibler Divergence) R(μ||P), where μ and P are measures on C([0,T], Rd). The underlying measure P is a weak solution to a martingale problem with continuous coefficients. Our representation is in the form of an integral with respect to its infinitesimal generator. This representation is of use in statistical inference (particularly involving medical imaging). Since R(μ||P) governs the exponential rate of convergence of the empirical measure (according to Sanov’s theorem), this representation is also of use in the numerical and analytical investigation of finite-size effects in systems of interacting diffusions.
Published: 2014

8. Parameter Estimation for Spatio-Temporal Maximum Entropy Distributions: Application to Neural Spike Trains

Author: Bruno Cessac, Hassan Nasser, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), ANR-10-INTB-0204,KEOpS,Algorithmes pour la modélisation du système visuel: de la vision naturelle aux applications numériques.(2010), European Project: 600847,EC:FP7:ICT,FP7-ICT-2011-9,RENVISION(2013), European Project: 318723,EC:FP7:ICT,FP7-ICT-2011-8,MATHEMACS(2012), European Project: 269921,EC:FP7:ICT,FP7-ICT-2009-6,BRAINSCALES(2011), European Project: 227747,EC:FP7:ERC,ERC-2008-AdG,NERVI(2009), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: maximum entropy, Computer science, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, General Physics and Astronomy, neural coding, lcsh:Astrophysics, 01 natural sciences, spike train, spatio-temporal constraints, 010305 fluids & plasmas, lcsh:QB460-466, 0103 physical sciences, Gibbs distribution, convex duality, large-scale analysis, MEA recordings, Physics - Biological Physics, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], lcsh:Science, 010306 general physics, Quantitative Biology::Neurons and Cognition, Artificial neural network, Principle of maximum entropy, Numerical analysis, Extension (predicate logic), lcsh:QC1-999, Biological Physics (physics.bio-ph), Quantitative Biology - Neurons and Cognition, FOS: Biological sciences, lcsh:Q, Neurons and Cognition (q-bio.NC), [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], Train, Spike (software development), Algorithm, lcsh:Physics
Abstract: 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] who proposed the estimation of parameters where only spatial constraints were taken into account. The extension we propose allows to properly handle memory effects in spike statistics, for large sized neural networks., Comment: 34 pages, 33 figures
Published: 2014

9. Exact Event-Driven Implementation for Recurrent Networks of Stochastic Perfect Integrate-and-Fire Neurons

Author: Jonathan Touboul, Marcelo O. Magnasco, Thibaud Taillefumier, Laboratory of Mathematical Physics, Rockefeller University [New York], NEUROMATHCOMP, Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-INRIA Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Nice Sophia Antipolis (1965 - 2019) (UNS)
Subjects: Theoretical computer science, Discretization, Computer science, Nerve net, Cognitive Neuroscience, Models, Neurological, 03 medical and health sciences, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], 0302 clinical medicine, Arts and Humanities (miscellaneous), Neural ensemble, medicine, Animals, Humans, Stochastic neural network, 030304 developmental biology, Neurons, 0303 health sciences, Quantitative Biology::Neurons and Cognition, Brain, Models, Theoretical, Highly sensitive, medicine.anatomical_structure, Neuronal interaction, Neural Networks, Computer, Nerve Net, Algorithms, 030217 neurology & neurosurgery, Coding (social sciences)
Abstract: International audience; In vivo cortical recording reveals that indirectly driven neural assemblies can produce reliable and temporally precise spiking patterns in response to stereotyped stimulation. This suggests that despite being fundamentally noisy, the collective activity of neurons conveys information through temporal coding. Stochastic integrate-and-fire models delineate a natural theoretical framework to study the interplay of intrinsic neural noise and spike timing precision. However, there are inherent difficulties in simulating their networks' dynamics in silico with standard numerical discretization schemes. Indeed, the well-posedness of the evolution of such networks requires temporally ordering every neuronal interaction, whereas the order of interactions is highly sensitive to the random variability of spiking times. Here, we answer these issues for perfect stochastic integrate-and-fire neurons by designing an exact event-driven algorithm for the simulation of recurrent networks, with delayed Dirac-like interactions. In addition to being exact from the mathematical standpoint, our proposed method is highly efficient numerically. We envision that our algorithm is especially indicated for studying the emergence of polychronized motifs in networks evolving under spike-timing-dependent plasticity with intrinsic noise.
Published: 2012

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

Author: Hilgen, Gerrit, Pirmoradian, Sahar, Pamplona, Daniela, Kornprobst, Pierre, Cessac, Bruno, Hennig, Matthias, Sernagor, Evelyne, Institute of Neuroscience [Newcastle] (ION), Newcastle University [Newcastle], Institute for Adaptive and Neural Computation (ANC), University of Edinburgh, Biologically plausible Integrative mOdels of the Visual system : towards synergIstic Solutions for visually-Impaired people and artificial visiON (BIOVISION), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), The research received financial support from the 7th Framework Program for Research of theEuropean Commission (Grant agreement no 600847: RENVISION, project of the Future andEmerging Technologies (FET) program Neuro-bio-inspired systems (NBIS) FET-ProactiveInitiative)), Institute of Neuroscience, Newcastle University, Institute for Adaptive and Neural Computation, University of Edinburgh, Inria, Neuromathcomp Team, and European Project: 600847,EC:FP7:ICT,FP7-ICT-2011-9,RENVISION(2013)
Subjects: [STAT.AP]Statistics [stat]/Applications [stat.AP], genetic structures, [SCCO.NEUR]Cognitive science/Neuroscience, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], sense organs, Development, Retinal ganglion cells, eye diseases, Dorsal and ventral
Abstract: 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 ofRGCs simultaneously at pan-retinal level, including dorsal and ventral locations. Responses to differentcontrasts 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 alltypes were more responsive to light, perhaps indicating an environmental priority to nest viewing forpre-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 ofOFF responses later on. Further, we found that with maturation receptive field (RF) center sizesdecrease, responses to light get stronger, and centers become more circular while seeing differences inall of them between RGC types. These findings show that retinal functionality is not spatiallyhomogeneous, likely reflecting ecological requirements that favour the early development of dorsalretina, and reflecting different roles in vision in the mature animal.
Published: 2016

11. A general framework for stochastic traveling waves and patterns, with application to neural field equations

Author: James Inglis, James MacLaurin, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), TO Simulate and CAlibrate stochastic models (TOSCA), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), European Project: 269921,EC:FP7:ICT,FP7-ICT-2009-6,BRAINSCALES(2011), European Project: 284941,EC:FP7:ICT,FP7-ICT-2011-FET-F,HBP(2011), European Project: 318723,EC:FP7:ICT,FP7-ICT-2011-8,MATHEMACS(2012), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: Mathematical optimization, Stochastic neural field equation, Pattern formation, 01 natural sciences, Noise (electronics), Stability (probability), 010305 fluids & plasmas, Stochastic differential equation, pattern formation, Position (vector), 0103 physical sciences, FOS: Mathematics, 0101 mathematics, [MATH]Mathematics [math], Mathematics, 60H20, 92B99, 010102 general mathematics, Mathematical analysis, Probability (math.PR), Stochastic partial differential equation, Discontinuity (linguistics), traveling waves, Modeling and Simulation, Jump, Mathematics - Probability, Analysis
Abstract: In this paper we present a general framework in which to rigorously study the effect of spatio-temporal noise on traveling waves and stationary patterns. In particular the framework can incorporate versions of the stochastic neural field equation that may exhibit traveling fronts, pulses or stationary patterns. To do this, we first formulate a local SDE that describes the position of the stochastic wave up until a discontinuity time, at which point the position of the wave may jump. We then study the local stability of this stochastic front, obtaining a result that recovers a well-known deterministic result in the small-noise limit. We finish with a study of the long-time behavior of the stochastic wave., Comment: 43 pages, 3 figures
Published: 2016

12. Complex oscillations with multiple timescales - Application to neuronal dynamics

Author: Desroches, Mathieu, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Universite Pierre et Marie Curie, Jean-Pierre Françoise (UPMC), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: Canard solutions, Mixed-Mode Oscillations, Neuronal activity, Quantitative Biology::Neurons and Cognition, [SCCO.NEUR]Cognitive science/Neuroscience, Slow-fast dynamical systems, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Bifurcation theory, Bursting Oscillations, Neurosciences mathématiques, Numerical continuation methods
Abstract: The results gathered in this thesis deal with multiple time scale dynamical systems near non-hyperbolic points, giving rise to canard-type solutions, in systems of dimension 2, 3 and 4. Bifurcation theory and numerical continuation methods adapted for such systems are used to analyse canard cycles as well as canard-induced complex oscillations in three-dimensional systems. Two families of such complex oscillations are considered: mixed-mode oscillations (MMOs) in systems with two slow variables, and bursting oscillations in systems with two fast variables. In the last chapter, we present recent results on systems with two slow and two fast variables, where both MMO-type dynamics and bursting-type dynamics can arise and where complex oscillations are also organised by canard solutions. The main application area that we consider here is that of neuroscience, more precisely low-dimensional point models of neurons displaying both sub-threshold and spiking behaviour. We focus on analysing how canard objects allow to control the oscillatory patterns observed in these neuron models, in particular the crossings of excitability thresholds.
Published: 2015

13. Statistical analysis of spike trains in neuronal networks

Author: Cessac, Bruno, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn]
Abstract: International audience; Recent advances in multi-electrodes array acquisition has made it possible torecord the activity of up to several hundreds of neurons at the same time andto register their collective activity (spike trains). This opens up new perspectivesin understanding how a neuronal network encodes the response to a stimulus, andwhat a spike train tells up about the network structure and nonlinear dynamics.For this, one has to develop statistical models properly handling thespatio-temporal aspects of spike trains, including memory effects. In thistalk, I will review several such statistical models, including Maximum EntropyModels, Generalized Linear Model or neuromimetic models, and their application for the analysis of retina data.
Published: 2015

14. Periodic Forcing of Inhibition-Stabilized Networks: Nonlinear Resonances and Phase-Amplitude Coupling

Author: Terrence J. Sejnowski, Romain Veltz, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Computational Neurobiology Laboratory, The Salk Institute for Biological Studies, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: gamma band, Cognitive Neuroscience, Models, Neurological, Population, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Phase (waves), Action Potentials, Topology, Article, Arts and Humanities (miscellaneous), Control theory, Interneurons, Models, Negative feedback, Gamma Rhythm, Computer Simulation, Artificial Intelligence & Image Processing, education, Positive feedback, Physics, education.field_of_study, Quantitative Biology::Neurons and Cognition, Oscillation, Pyramidal Cells, Neurosciences, Resonance, Neural Inhibition, Coupling (electronics), theta band, Nonlinear system, Nonlinear Dynamics, Neurological, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; Inhibition stabilized networks (ISNs) are neural architectures with strong positive feedback among pyramidal neurons balanced by strong negative feedback from in-hibitory interneurons, a circuit element found in the hippocampus and the primary vi-sual cortex. In their working regime, ISNs produce damped oscillations in the γ-range in response to inputs to the inhibitory population. In order to understand the proper-ties of interconnected ISNs, we investigated periodic forcing of ISNs. We show that ISNs can be excited over a range of frequencies and derive properties of the resonance peaks. In particular, we studied the phase-locked solutions, the torus solutions and the resonance peaks. More particular, periodically forced ISNs respond with (possibly multi-stable) phase-locked activity whereas networks with sustained intrinsic oscilla-tions respond more dynamically to periodic inputs with tori. Hence, the dynamics are surprisingly rich and phase effects alone do not adequately describe the network re-sponse. This strengthens the importance of phase-amplitude coupling as opposed to phase-phase coupling in providing multiple frequencies for multiplexing and routing information. You can use \terry{text to print}essai
Published: 2015

15. An analytical method for computing Hopf bifurcation curves in neural field networks with space-dependent delays

Author: Romain Veltz, Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), imagine [Marne-la-Vallée], Centre Scientifique et Technique du Bâtiment (CSTB)-École des Ponts ParisTech (ENPC)-Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM)-Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-Université Paris-Est Marne-la-Vallée (UPEM), Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS)-Centre Scientifique et Technique du Bâtiment (CSTB), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: Hopf bifurcation, Plane (geometry), Mathematical analysis, Saddle-node bifurcation, 02 engineering and technology, General Medicine, Bifurcation diagram, 01 natural sciences, 010305 fluids & plasmas, symbols.namesake, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], Bounded function, 0103 physical sciences, Family of curves, 0202 electrical engineering, electronic engineering, information engineering, symbols, 020201 artificial intelligence & image processing, Parametrization, Eigenvalues and eigenvectors, Mathematics
Abstract: International audience; We give an analytical parametrization of the curves of purely imaginary eigenvalues in the delay-parameter plane of the linearized neural field network equations with space-dependent delays. In order to determine if the rightmost eigenvalue is purely imaginary, we have to compute a finite number of such curves; the number of curves is bounded by a constant for which we give an expression. The Hopf bifurcation curve lies on these curves.
Published: 2011

16. A Markovian event-based framework for stochastic spiking neural networks

Author: Olivier Faugeras, Jonathan Touboul, NEUROMATHCOMP, Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-INRIA Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Nice Sophia Antipolis (1965 - 2019) (UNS)
Subjects: FOS: Computer and information sciences, Refractory period, Computer science, Spike train, Action Potentials, Synaptic Transmission, Synapse, 0302 clinical medicine, Neurons, Membrane potential, 0303 health sciences, Artificial neural network, Markov Chains, Sensory Systems, medicine.anatomical_structure, symbols, Excitatory postsynaptic potential, Probability distribution, Neurons and Cognition (q-bio.NC), Spike (software development), Algorithm, Cognitive Neuroscience, Markov process, Mathematics - Statistics Theory, Statistics Theory (math.ST), Inhibitory postsynaptic potential, Statistics - Applications, 03 medical and health sciences, Cellular and Molecular Neuroscience, symbols.namesake, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], FOS: Mathematics, medicine, Animals, Humans, Applications (stat.AP), Stochastic neural network, 030304 developmental biology, Spiking neural network, Stochastic Processes, Quantitative Biology::Neurons and Cognition, Markov chain, Synaptic integration, Neural Inhibition, Quantitative Biology - Neurons and Cognition, FOS: Biological sciences, Linear Models, Neural Networks, Computer, Neuron, Nerve Net, 030217 neurology & neurosurgery
Abstract: International audience; In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature of the sequence of spike times in stochastic neural networks, and in particular the ability to deduce from a spike train the next spike time, and therefore produce a description of the network activity only based on the spike times regardless of the membrane potential process. To study this question in a rigorous manner, we introduce and study an event-based description of networks of noisy integrate-and-fire neurons, i.e. that is based on the computation of the spike times. We show that the firing times of the neurons in the networks constitute a Markov chain, whose transition probability is related to the probability distribution of the interspike interval of the neurons in the network. In the cases where the Markovian model can be developed, the transition probability is explicitly derived in such classical cases of neural networks as the linear integrate-and-fire neuron models with excitatory and inhibitory interactions, for different types of synapses, possibly featuring noisy synaptic integration, transmission delays and absolute and relative refractory period. This covers most of the cases that have been investigated in the event-based description of spiking deterministic neural networks.
Published: 2011

17. The effect of retinal GABA Depletion by Allylglycineon mouse retinal ganglion cell responses to light

Author: Hilgen, Gerrit, Softley, Samantha, Pamplona, Daniela, Kornprobst, Pierre, Cessac, Bruno, Sernagor, Evelyne, Institute of Neuroscience [Newcastle] (ION), Newcastle University [Newcastle], Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), European Project: 600847,EC:FP7:ICT,FP7-ICT-2011-9,RENVISION(2013), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn]
Abstract: International audience; The inhibitory neurotransmitter GABA (γ-aminobutyric acid) is metabolized by glutamic acid decarboxylase (GAD) which exists in two iso-forms in the mature CNS, GAD65 and GAD67. Allylglycine, a glycine derivative, is a nonspecific inhibitor of both GAD isoforms. Prolongedexposure to allylgycine can therefore deplete the tissue of endogenous GABA over time (Orlowski et al, 1977; Chabrol et al., 2012). Herewe applied Allylglycine (ALLYL) in vitro over several hours to gradually deplete GABA in the adult mouse retina and compared the effectsof GABA depletion on retinal ganglion cells (RGCs) receptive fields with those obtained by simultaneously blocking all GABAergic recep-tors (type A, B and C).
Published: 2015

18. Decoding MT motion response for optical flow estimation: An experimental evaluation

Author: Guillaume S. Masson, Fabio Solari, Pierre Kornprobst, N. V. Kartheek Medathati, Manuela Chessa, Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi [Genova] (DIBRIS), Universita degli studi di Genova, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut de Neurosciences de la Timone (INT), Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS), European Project: 318723,EC:FP7:ICT,FP7-ICT-2011-8,MATHEMACS(2012), Università degli studi di Genova = University of Genoa (UniGe), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), INRIA Sophia-Antipolis, France, University of Genoa, Genoa, Italy, INT la Timone, Marseille, France, and INRIA
Subjects: Computer science, Optical flow, [SCCO.COMP]Cognitive science/Computer science, Middlebury dataset, Motion (physics), [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], motion energy, Bio-inspired approach, Media Technology, [INFO.INFO-DL]Computer Science [cs]/Digital Libraries [cs.DL], Computer vision, Representation (mathematics), V1, spatio-temporal filters, Signal processing, Artificial neural network, business.industry, Intersection (set theory), [SCCO.NEUR]Cognitive science/Neuroscience, [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], Optical flow estimation, population code, [INFO.INFO-IR]Computer Science [cs]/Information Retrieval [cs.IR], MT, Signal Processing, Benchmark (computing), Artificial intelligence, 1707, business, Algorithm, Decoding methods
Abstract: Published in the 23rd European Signal Processing Conference (EUSIPCO); Motion processing in primates is an intensely studied problem in visual neurosciences and after more than two decades of research, representation of motion in terms of motion energies computed by V1-MT feedforward interactions remains a strong hypothesis. Thus, decoding the motion energies is of natural interest for developing biologically inspired computer vision algorithms for dense optical flow estimation. Here, we address this problem by evaluating four strategies for motion decoding: intersection of constraints, maximum likelihood, linear regression on MT responses and neural network based regression using multi scale-features. We characterize the performances and the current limitations of the different strategies, in terms of recovering dense flow estimation using Middlebury benchmark dataset widely used in computer vision, and we highlight key aspects for future developments.
Published: 2015

19. A super-resolution approach for receptive fields estimation of neuronal ensembles

Author: Pamplona, Daniela, Hilgen, Gerrit, Pirmoradian, Sahar, Hennig, Matthias, Cessac, Bruno, Sernagor, E, Kornprobst, Pierre, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Institute of Neuroscience [Newcastle] (ION), Newcastle University [Newcastle], University of Edinburgh, European Project: 600847,EC:FP7:ICT,FP7-ICT-2011-9,RENVISION(2013), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]
Abstract: International audience; The Spike Triggered Average (STA) is a classical technique to find a discrete approximation of the Receptive Fields (RFs) of sensory neurons [1], a required analysis in most experimental studies. One important parameter of the STA is the spatial resolution of the estimation, corresponding to the size of the blocks of the checkerboard stimulus images. In general, it is experimentally fixed to reach a compromise: If too small, neuronal responses might be too weak thus leading to RF with low Signal-to-Noise-Ratio; on the contrary, if too large, small RF will be lost, or not described with enough details, because of the coarse approximation. Other solutions were proposed consisting in starting from a small block size and updating it following the neuron response in a closed-loop to increase its response [2; 3; 4]. However, these solutions were designed for single cells and cannot be applied to simultaneous recordings of ensembles of neurons (since each RF has its own size and preferred stimulus). To solve this problem, we introduced a modified checkerboard stimulus where blocks are shifted randomly in space at fixed time steps. This idea is inspired from super-resolution techniques developed in image processing [4]. The main interest is that the block size can be large, enabling strong responses, while the resolution can be finer since it depends on the shift minimum size. In [5] was shown that the STA remains an unbiased RF estimator and, using simulated spike trains from an ensemble of Linear Nonlinear Poisson cascade neurons, it was predicted that this approach improves RF estimation over the neuron ensemble. Here, we test these predictions experimentally on the RFs estimation of 8460 ganglion cells from two mouse retinas, using recordings performed with a large scale high-density multielectrode array. To illustrate the main interest of the approach, in Figure 1 we show a representative example of STA for one neuron where RFs have been obtained using the three following stimuli (all presented during 15min, for one retina displayed at 10 Hz, for the other at 30 Hz): (A) standard checkerboard stimulus with block size of 160μm, (B) standard checkerboard stimulus with block size of 40μm, (C) checkerboard stimulus with block size of 160μm and arbitrary shifts of 40μm in x and y-directions. Results show spatial resolution can be improved in case (C), while nothing could be obtained in (B) by changing only the block size of the standard stimulus. At the population level, plot (D) shows the number of the RFs that could be recovered for each stimuli, using a decision criteria based of the RFs value distribution. Most of the RFs were mapped with both methods (A) and (C) (49.9%). However, the proposed case (C) allows to recover 51% of the mapped RFs at a resolution of 40μm, while in the classical case (A), 41% of the RFs could be found at a resolution of only 160μm. Thus, the method does improve the quality of the RF estimation and the amount of successfully mapped RFs in neural ensembles.
Published: 2015

20. Extending the zero-derivative principle for slow–fast dynamical systems

Author: Eric Benoit, Mathieu Desroches, Martin Krupa, Morten Brøns, Mathématiques, Image et Applications - EA 3165 (MIA), Université de La Rochelle (ULR), Department of Mathematics, Department of Mathematics (Kongens Lyngby, Denmark), Technical University of Denmark [Lyngby] (DTU)-Technical University of Denmark [Lyngby] (DTU), Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), La Rochelle Université (ULR), Danmarks Tekniske Universitet = Technical University of Denmark (DTU)-Danmarks Tekniske Universitet = Technical University of Denmark (DTU), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: Ghosts, Templator, Dynamical systems theory, Curvature, Applied Mathematics, General Mathematics, [SCCO.NEUR]Cognitive science/Neuroscience, Mathematical analysis, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], General Physics and Astronomy, Invariant (physics), Slow manifolds, Intrinsic low-dimensional manifolds, Slow time, Scale separation, Zero-derivative principle, Fenichel theory, Statistical physics, Slow–fast dynamics, Spurious relationship, Mathematics
Abstract: International audience; Slow–fast systems often possess slow manifolds, that is invariant or locally invariant sub-manifolds on which the dynamics evolves on the slow time scale. For systems with explicit timescale separation, the existence of slow manifolds is due to Fenichel theory, and asymptotic expansions of such manifolds are easily obtained. In this paper, we discuss methods of approximating slow manifolds using the so-called zero-derivative principle. We demonstrate several test functions that work for systems with explicit time scale separation including ones that can be generalized to systems without explicit timescale separation. We also discuss the possible spurious solutions, known as ghosts, as well as treat the Templator system as an example.
Published: 2015

21. Improving FREAK Descriptor for Image Classification

Author: Kartheek Medathati, Cristina Hilario Gomez, Vittorio Murino, Diego Sona, Pierre Kornprobst, IIT Genoa, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), European Project: 600847,EC:FP7:ICT,FP7-ICT-2011-9,RENVISION(2013), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: scene classification, center-surround ganglion cell organization, Contextual image classification, binary descriptor, Computer science, business.industry, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, FREAK, 020207 software engineering, 02 engineering and technology, Set (abstract data type), bio-inspired descriptor, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Point (geometry), Computer vision, Binary descriptor, Artificial intelligence, business, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Abstract: International audience; In this paper we propose a new set of bio-inspired descrip- tors for image classification based on low-level processing performed by the retina. Taking as a starting point a descriptor called FREAK (Fast Retina Keypoint), we further extend it mimicking the center-surround organization of ganglion receptive fields.To test our approach we com- pared the performance of the original FREAK and our proposal on the 15 scene categories database. The results show that our approach out- performs the original FREAK for the scene classification task.
Published: 2015

22. Asymptotic description of neural networks with correlated synaptic weights

Author: Faugeras, Olivier, Maclaurin, James, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), European Project: 269921,EC:FP7:ICT,FP7-ICT-2009-6,BRAINSCALES(2011), European Project: 318723,EC:FP7:ICT,FP7-ICT-2011-8,MATHEMACS(2012), European Project: 227747,EC:FP7:ERC,ERC-2008-AdG,NERVI(2009), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: stationary gaussian processes, AMS Mathematics Subject Classification: 28C20, 34F05, 34K50, 37L55, 60B11, 60F10, 60G10, 60G15, 60G57, 60G60, 60H10, 62M45, 92C20, Quantitative Biology::Neurons and Cognition, [SDV.NEU.NB]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]/Neurobiology, [SCCO.NEUR]Cognitive science/Neuroscience, Probability (math.PR), lcsh:Astrophysics, spectral representations, neural networks, lcsh:QC1-999, large deviations, 28C20, 34F05, 34K50, 37L55, 60B11, 60F10, 60G10, 60G15, 60G57, 60G60, 60H10, 62M45, 92C20, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], lcsh:QB460-466, firing rate neurons, FOS: Mathematics, lcsh:Q, stationary measures, lcsh:Science, good rate function, lcsh:Physics, correlated synaptic weights, Mathematics - Probability
Abstract: We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. Given a completely connected network of neurons in which the synaptic weights are Gaussian correlated random variables, we describe the asymptotic law of the network when the number of neurons goes to infinity. We introduce the process-level empirical measure of the trajectories of the solutions to the equations of the finite network of neurons and the averaged law (with respect to the synaptic weights) of the trajectories of the solutions to the equations of the network of neurons. The main result of this article is that the image law through the empirical measure satisfies a large deviation principle with a good rate function which is shown to have a unique global minimum. Our analysis of the rate function allows us also to characterize the limit measure as the image of a stationary Gaussian measure defined on a transformed set of trajectories., This paper has been withdrawn by the authors. 50 pages. arXiv admin note: substantial text overlap with arXiv:1302.1029 This paper has been withdrawn because I meant to replace arXiv:1302.1029, not arXiv:1311.4400
Published: 2015

23. Mean Field Methods in Neuroscience

Author: Cessac, Bruno, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), European Project: 318723,EC:FP7:ICT,FP7-ICT-2011-8,MATHEMACS(2012), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Physics::Popular Physics, Quantitative Biology::Neurons and Cognition, Mathematics::History and Overview, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], Computer Science::Digital Libraries, Computer Science::Computers and Society
Abstract: International audience; We review mean Field Methods in Neuroscience
Published: 2015

24. Statistical models for spike trains analysis in the retina

Author: Cessac, Bruno, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), ANR-10-INTB-0204,KEOpS,Algorithmes pour la modélisation du système visuel: de la vision naturelle aux applications numériques.(2010), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn]
Abstract: International audience; Recent advances in multi-electrodes array acquisition have made it possible to record the activity ofup to several hundreds of neurons at the same time and to register their collective activity (spiketrains). For the retina, this opens up new perspectives in understanding how retinal structure and ganglion cells encode information about a visual sceneand what is transmitted to the brain. Especially, two paradigms can be confronted: in the first one, ganglion cells encodeinformation independently of each others; in the second one non linear dynamics and connectivity contributeto produce a population coding where spatio-temporal correlations, although weak, play a significant role inspike coding. Confronting these two paradigms can be done at an experimental and at a theoretical level.On experimental grounds, new methods to analyse the role of weak correlations in spike train statistics are required.On theoretical grounds, mathematical results have been established, in neuronal models, showing how non linear dynamics and connectivity contributeto produce a correlated spike response to stimuli.In the context of the ANR KEOPS project we have been working on these two aspects and we shall presentour main results in this talk.
Published: 2015

25. Spectral dimension reduction on parametric models for spike train statistics

Author: Ravello, Cesar, Herzog, Rubén, Cessac, Bruno, Escobar, Maria-Jose, Palacios, Adrian, Centro Interdisciplinario de Neurociencia de Valparaiso (CINV), Universidad de Valparaiso [Chile], Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Universidad Tecnica Federico Santa Maria [Valparaiso] (UTFSM), ANR-10-INTB-0204,KEOpS,Algorithmes pour la modélisation du système visuel: de la vision naturelle aux applications numériques.(2010), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn]
Abstract: International audience; It has been shown that the neurons of visual system present correlated activity inresponse to dierent stimuli. The role of these correlations is an unresolved subject. Thesecorrelations vary according to the stimulus, specially with natural images. To uncover therole of these correlation and characterize the population code, it is necessary to measure thesimultaneous activity of large neural populations. This has been achieved thanks to the adventof Multi-Electrode Array technology, opening up a way to better characterize how the brainencodes information in the concerted activity of neurons. In parallel, powerful statistical toolshave been developed to accurately characterize spatio-temporal correlations between neurons.Methods based on Maximum Entropy Principle, where statistical entropy is maximized undera set of constraints corresponding to specic assumptions on the relevant statistical quantities,have been proved successfully, specially when they consider spatiotemporal correlations. [ref]They are although limited by (i) the assumption of stationarity, (ii) the many possiblechoice of constraints, and (iii) the huge number of free parameters.In this context, focusing on (ii), (iii), we propose a method of dimensionality reductionallowing to select a model tting data with a minimal number of parameters. This methodis based on the spectral analysis of a symmetric, positive matrix, summing up all relevantspatial-temporal correlations, closely related to the Fisher metric in statistical analysis andinformation geometry, but extended here to the spatio-temporal domain. Based on syntheticand real data - RGC responses to dierent stimuli in a diurnal rodent- we show that thespectrum of this matrix has a cut-o beyond which the corresponding dimensions have anegligible eect on the statistical estimation. This dimensionality reduction reduces the riskof over-tting. The method is used to characterize dierences in response to dierent classesof visual stimuli (white noise, natural images).
Published: 2015

26. Effets des symmétries du réseau de pinwheels de l'aire corticale visuelle V1 sur l'activité corticale spontanée

Author: Veltz, Romain, Chossat, Pascal, Faugeras, Olivier, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), and This work was partially supported by the European Union SeventhFramework Programme (FP7/2007-2013)under grant agreement no. 269921 (BrainScaleS), no. 318723 (Mathemacs),and by the ERC advanced grantNerVi no. 227747 and by the Human Brain Project (HBP).
Subjects: Poincaré-Hopf, tore invariant, hallucinations visuelles, invariant torus, visual hallucinations, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; This paper challenges and significantly extends the seminal work in \cite{ermentrout-cowan:79b,bressloff-cowan-etal:01}. In this work, we improve on the following points the seminal work as in \cite{ermentrout-cowan:79b,bressloff-cowan-etal:01}. We consider the problem of describing mathematically the spontaneous activity of V1 by combining several important experimental observations including 1) the organization of the visual cortex into a spatially periodic network of hypercolumns structured around pinwheels, 2) the difference between short-range and long-range intra-cortical connections, the first ones being rather isotropic and producing naturally doubly-periodic patterns by Turing mechanisms, the second one being patchy and 3) the fact that the Turing patterns spontaneously produced by the short-range connections and the network of pinwheels have similar periods. By analyzing the Preferred Orientation (PO) map, we are able to classify all possible singular points of the PO maps (the pinwheels) as having symmetries described by a small subset of the wallpaper groups. We then propose a description of the spontaneous activity of V1 using a classical voltage-based neural field model that features isotropic short-range connectivities modulated by non-isotropic long-range connectivities. A key observation is that, with only short-range connections and because the problem has full translational invariance in this case, a spontaneous doubly-periodic pattern generates a 2-torus in a suitable functional space which persists as a flow-invariant manifold under small perturbations, hence when turning on the long-range connections. Through a complete analysis of the symmetries of the resulting neural field equation and motivated by a numerical investigation of the bifurcations of their solutions, we conclude that the branches of solutions which are stable over an extended set of parameters are those corresponding to patterns with an hexagonal (or nearly hexagonal) symmetry. The question of which patterns persist when turning on the long-range connections is answered by 1) analyzing the remaining symmetries on the perturbed torus and 2) combining this information with the Poincaré-Hopf theorem. We have developed a numerical implementation of the theory that has allowed us to produce the patterns of activities predicted by the theory, the planforms. In particular we generalize the contoured and non-contoured planforms predicted by previous authors \Modif{\cite{ermentrout-cowan:79b,bressloff-cowan-etal:01} and predict the existence of mixed contoured/non-contoured planforms. We also found that these planforms are most likely to be time evolving.; Cet article étend de manière significative le travail séminal de \cite{Ermentrout-Cowan: 79b, bressloff-Cowan-al: 01}. Dans ce travail, nous améliorons les points suivants dans la théorie \cite{Ermentrout-Cowan: 79b, bressloff-Cowan-al: 01}. Nous considérons le problème de décrire mathématiquement l’activité spontanée de V1 en combinant plusieurs observations expérimentales importantes, notamment 1) l'organisation du cortex visuel selon un réseau spatiallement périodique d'hypercolonnes structurées autour de pinwheels, 2) la différence entre les connexions intra-corticales à courtes et longues portées: les premières étant plutôt isotropes et produisant naturellement des activités doublement périodiques par le mécanisme de Turing, les secondes étant anisotropes et 3) le fait que les activités corticales générées par les connexions locales et le réseau de pinwheels ont des fréquences spatiales similaires. Nous utilisons les groupes de pavages pour produire une classification des cartes d'orientations préférées. Nous proposons ensuite une description de l’activité spontanée de V1 en utilisant un modèle de champ neuronaux avec des connections locales isotropes modulées par des connections à longue portée non-isotropes. Une observation clé est que le tore invariant (conséquence des symétries de translation) produit par le système avec seulement les connections locales, persiste lorsque les connections longues distances sont introduites de façon perturbative. Ainsi, nous analysons d’abord le cas des connections locales et montrons que seules les branches de solutions stationnaires à symétrie presque hexagonale sont stables pour un ensemble de paramètres de mesure non nulle.La persistance de ces solutions est ensuite analysée en utilisant les symétries résiduelles du système et en combinant cette information avec le théorème de Poincaré-Hopf. Des simulations numériques montrent ensuite que les cas les plus simples analysés de façon théorique sont les seuls qui apparaissent numériquement.En conclusion, nous généralisons les hallucinations prédites par les travaux précédents \cite{Ermentrout-Cowan: 79b, bressloff-Cowan-al: 01}. Nous avons également constaté que ces nouvelles hallucinations sont plus susceptibles d’évoluer dans le temps.
Published: 2015

27. Onset of intermittent octahedral patterns in spherical Bénard convection

Author: Pascal Chossat, Philippe Beltrame, Environnement Méditerranéen et Modélisation des Agro-Hydrosystèmes (EMMAH), Avignon Université (AU)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: symétrie sphérique, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], General Physics and Astronomy, Instability, Spherical shell, law.invention, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], cycle hétérocline, law, Intermittency, intermittency, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], [NLIN]Nonlinear Sciences [physics], Invariant (mathematics), Mathematical Physics, Bifurcation, convection, symmetry, Physics, intermittence, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph], Spherical harmonics, Mechanics, 13. Climate action, [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD], bifurcation, Axial symmetry, Center manifold
Abstract: The onset of convection for spherically invariant Rayleigh-Bénard fluid flow is driven by marginal modes associated with spherical harmonics of a certain degree $\ell$, which depends upon the aspect ratio of the spherical shell. At certain critical values of the aspect ratio, marginal modes of degrees $\ell$ and $\ell+1$ coexist. Initially motivated by an experiment of electrophoretic convection between two concentric spheres carried in the International Space Station (GeoFlow project), we analyze the occurrence of intermittent dynamics near bifurcation in the case when marginal modes with $\ell=3, 4$ interact. The situation is by far more complex than in the well studied $\ell=1, 2$ mode interaction, however we show that heteroclinic cycles connecting equilibria with octahedral as well as axial symmetry can exist near bifurcation under certain conditions. Numerical simulations and continuation (using the software AUTO) on the center manifold help understanding these scenarios and show that the dynamics in these cases exhibit intermittent behaviour, even though the heteroclinic cycles may not be asymptotically stable in the usual sense.
Published: 2015

28. Mean Field TheoriesNeuroscience

Author: Cessac, Bruno, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), European Project: 318723,EC:FP7:ICT,FP7-ICT-2011-8,MATHEMACS(2012), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Physics::Popular Physics, Quantitative Biology::Neurons and Cognition, Mathematics::History and Overview, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], Computer Science::Digital Libraries, Computer Science::Computers and Society
Abstract: International audience; We give an overview of mean-field methods in neuroscience.
Published: 2015

29. Shifting stimulus for faster receptive fields estimation of ensembles of neurons

Author: Pamplona, Daniela, Cessac, Bruno, Kornprobst, Pierre, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), European Project: 600847,EC:FP7:ICT,FP7-ICT-2011-9,RENVISION(2013), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]
Abstract: International audience; The spike triggered averaged (STA) technique has been widely used to estimate the receptive fields (RF) of sensory neurons (Chichilnisky, 2001). Theoretically, it has been shown that when the neurons are stimulated with a white noise stimulus the STA is an unbiased estimator of the neuron RF (up to a mul- tiplicative constant). The error decreases with the number of spikes at a rate proportional to the stimulus variance (Paninski, 2003). Experimentally, for visual neurons, the standard stimuli are checkerboards where block size is heuristically tuned. This raises difficulties when dealing with large neurons assemblies: When the block size is too small, neuron’s response might be too weak, and when it is too large, one may miss RFs. Previously online updating the stimulus in the direction of larger stimulus-neural response corre- lation (Foldiak, 2001) or mutual information (Machens, 2002; MacKay, 1992) has been proposed. However, these approaches can not be applied for an ensemble of cells recorded simultaneously since each neuron would update the stimulus in a different direction. We propose an improved checkerboard stimulus where blocks are shifted randomly in space at fixed time steps. Theoretically, we show that the STA remains an unbiased estimator of the RF. Additionally, we show two major properties of this new stimulus: (i) For a fixed block size, RF spatial resolution is improved as a function of the number of possible shifts; (ii) Targeting a given RF spatial resolution, our method converges faster than the standard one. Numerically, we perform an exhaustive analysis of the performance of the approach based on simulated spiked trains from LNP cascades neurons varying RF sizes and positions. Results show global improvements in the RF representation even after short stimulation times. This makes this approach a promising solution to improve RF estimation of large ensemble of neurons.
Published: 2015

30. Adaptive Motion Pooling and Diffusion for Optical Flow

Author: Medathati, N. V. Kartheek, Chessa, Manuela, Masson, Guillaume, Kornprobst, Pierre, Solari, Fabio, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi [Genova] (DIBRIS), Università degli studi di Genova = University of Genoa (UniGe), Institut de Neurosciences de la Timone (INT), Aix Marseille Université (AMU)-Centre National de la Recherche Scientifique (CNRS), INRIA Sophia-Antipolis, University of Genoa, INT la Timone, European Project: 318723,EC:FP7:ICT,FP7-ICT-2011-8,MATHEMACS(2012), European Project: 269921,EC:FP7:ICT,FP7-ICT-2009-6,BRAINSCALES(2011), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), and Universita degli studi di Genova
Subjects: V2, Motion integration, spatio-temporal filters, V1, [SCCO.NEUR]Cognitive science/Neuroscience, Computational Engineering, [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], Middlebury dataset, contrast adaptation, optical flow, V1-MT, motion energy, population code, Bio-inspired approach, MT, Signal Processing, Spatial pooling
Abstract: We study the impact of local context of an image (contrast and 2D structure) on spatial motion integration by MT neurons. To do so, we revisited the seminal work by Heeger and Simoncelli (HS) [4] using spatio-temporal filters to estimate optical flow from V1-MT feedforward interactions. However, the HS model has difficulties to deal with several problems encountered in real scenes (e.g., blank wall problem and motion discontinuities). Here, we propose to extend the HS model with adaptive processing by focussing on the role of local context indicative of the local velocity estimates reliability. We set a network structure representative of V1, V2 and MT areas of the motion stream. We incorporate three functional principles observed in primate visual system: contrast adaptation [3], adaptive afferent pooling [2] and MT diffusion that are adaptive dependent upon the 2D image structure (Adaptive Motion Pooling and Diffusion, AMPD). We evaluated both HS and AMPD models performance on Middlebury optical flow estimation dataset [1]. Our results show that the AMPD model performs better than the HS model and its overall performance is comparable with many modern computer vision methods. The AMPD model could be further improved by integrating feedback to better recover true velocities around motion boundaries. We propose that such adaptive model can serve as a ground for future research in biologically-inspired computer vision.
Published: 2015

31. Control of recurrent neural network dynamics byhomeostatic intrinsic plasticity

Author: Cessac, Bruno, Naudé, Jérémie, Berry, Hugues, Delord, Bruno, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Neurobiologie des processus adaptatifs (NPA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Artificial Evolution and Computational Biology (BEAGLE), Laboratoire d'InfoRmatique en Image et Systèmes d'information (LIRIS), Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Biométrie et Biologie Evolutive - UMR 5558 (LBBE), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS)-VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Centre National de la Recherche Scientifique (CNRS), Institut des Systèmes Intelligents et de Robotique (ISIR), AMAC, Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École Centrale de Lyon (ECL), Université de Lyon-Université Lumière - Lyon 2 (UL2)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), and Université de Lyon-Université Lumière - Lyon 2 (UL2)-Inria Grenoble - Rhône-Alpes
Subjects: [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn]
Abstract: International audience; Homeostatic intrinsic plasticity (HIP) is a ubiquitous cellular mechanism regulating neuronalactivity, cardinal for the proper functioning of nervous systems. Here,we assess how cellular HIP effects translate into collective dynamics and computationalproperties in biological recurrent networks. We develop a realistic multi-scale modelincluding a generic HIP rule regulating the neuronal threshold with actual molecular signalingpathways kinetics, Dale’s principle, sparse connectivity, synaptic balance and Hebbiansynaptic plasticity (SP). Dynamic mean-field analysis and simulations unravel that HIP sets aworking point at which inputs are transduced by large derivative ranges of the transferfunction. This cellular mechanism insures increased network dynamics complexity, robustbalance with SP at the edge of chaos, and improved input separability. Although criticallydependent upon balanced excitatory and inhibitory drives, these effects display strikingrobustness to changes in network architecture, learning rates and input features. Thus, themechanism we unveil might represent a ubiquitous cellular basis for complex dynamics inneural networks. Understanding this robustness is an important challenge to unravel principlesunderlying self-organization around criticality in biological recurrent neural networks.
Published: 2015

32. Confronting mean-field theories to measurements a perspective from neuroscience

Author: Cessac, Bruno, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), European Project: 269921,EC:FP7:ICT,FP7-ICT-2009-6,BRAINSCALES(2011), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn]
Abstract: International audience; Presentation in the conference, Confronting mean-field theories to measurements a perspective from neuroscience, Paris 15-16 January 2015.
Published: 2015

33. ERRATUM: A Center Manifold Result for Delayed Neural Fields Equations

Author: Olivier Faugeras, Romain Veltz, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Lemma (mathematics), Applied Mathematics, [SDV]Life Sciences [q-bio], Mathematical analysis, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Neural fields, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, 010101 applied mathematics, Algebra, 03 medical and health sciences, Computational Mathematics, 0302 clinical medicine, Bifurcation theory, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], 0101 mathematics, 030217 neurology & neurosurgery, Analysis, Center manifold, Mathematics
Abstract: International audience; Lemma C.1 in [R. Veltz and O. Faugeras, SIAM J. Math. Anal., 45(3) (2013), pp. 1527-1562] is wrong. This lemma is used in the proof of the existence of a smooth center manifold, Theorem 4.4 in [5]. An additional assumption is required to prove this existence. We spell out this assumption, correct the proofs and show that the assumption is satisfied for a large class of delay functions τ . We also weaken the general assumptions on τ .
Published: 2015

34. What can we expect from a V1-MT feedforward architecture for optical flow estimation?

Author: Fabio Solari, Manuela Chessa, Pierre Kornprobst, N. V. Kartheek Medathati, Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi [Genova] (DIBRIS), Universita degli studi di Genova, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), European Project: 318723,EC:FP7:ICT,FP7-ICT-2011-8,MATHEMACS(2012), Università degli studi di Genova = University of Genoa (UniGe), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: Scheme (programming language), Computer science, Pooling, Optical flow, Machine learning, computer.software_genre, [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI], Benchmarking, Motion energy, MT, Spatio-temporal filters, V1, 1707, Signal Processing, Software, Electrical and Electronic Engineering, Motion estimation, Code (cryptography), computer.programming_language, business.industry, Feed forward, Scalability, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], Computer Vision and Pattern Recognition, Artificial intelligence, Data mining, business, computer, Decoding methods
Abstract: Motion estimation has been studied extensively in neuroscience in the last two decades. Even though there has been some early interaction between the biological and computer vision communities at a modelling level, comparatively little work has been done on the examination or extension of the biological models in terms of their engineering efficacy on modern optical flow estimation datasets. An essential contribution of this paper is to show how a neural model can be enriched to deal with real sequences. We start from a classical V1-MT feedforward architecture. We model V1 cells by motion energy (based on spatio-temporal filtering), and MT pattern cells (by pooling V1 cell responses). The efficacy of this architecture and its inherent limitations in the case of real videos are not known. To answer this question, we propose a velocity space sampling of MT neurons (using a decoding scheme to obtain the local velocity from their activity) coupled with a multi-scale approach. After this, we explore the performance of our model on the Middlebury dataset. To the best of our knowledge, this is the only neural model in this dataset. The results are promising and suggest several possible improvements, in particular to better deal with discontinuities. Overall, this work provides a baseline for future developments of bio-inspired scalable computer vision algorithms and the code is publicly available to encourage research in this direction. Graphical abstractDisplay Omitted HighlightsWe show how a V1-MT neural model can be adapted to handle real sequences.For the first time, a neural model is benchmarked on a Middlebury dataset.We share our code to encourage research in bio-inspired scalable vision algorithms.
Published: 2015

35. Clarification and Complement to ' Mean-Field Description and Propagation of Chaos in Networks of Hodgkin–Huxley and FitzHugh–Nagumo Neurons '

Author: Denis Talay, Mireille Bossy, Olivier Faugeras, TO Simulate and CAlibrate stochastic models (TOSCA), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Mathematical and Computational Neuroscience (NEUROMATHCOMP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Mean-field limits, Short Report, Neuroscience (miscellaneous), FitzHugh–Nagumo neurons, 01 natural sciences, 010104 statistics & probability, Stochastic differential equation, Neural ensemble, FOS: Mathematics, Applied mathematics, Limit (mathematics), 0101 mathematics, Propagation of chaos, [MATH]Mathematics [math], Hodgkin–Huxley neurons, Complement (set theory), Mathematics, Neural assemblies, Quantitative Biology::Neurons and Cognition, business.industry, Probability (math.PR), 010102 general mathematics, Fitzhugh nagumo, Hodgkin–Huxley model, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mean field theory, [INFO.INFO-IR]Computer Science [cs]/Information Retrieval [cs.IR], Stochastic differential equations, Artificial intelligence, business, Mathematics - Probability, Neural networks
Abstract: International audience; In this note, we clarify the well-posedness of the limit equations to the mean-field N-neuron models proposed in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) and we prove the associated propagation of chaos property. We also complete the modeling issue in (Baladron et al. in J. Math. Neurosci. 2:10, 2012) by discussing the well-posedness of the stochastic differential equations which govern the behavior of the ion channels and the amount of available neurotransmitters.
Published: 2015

36. Toward a realistic input for visual cortex models

Author: Hassan Roland Nasser, Bruno Cessac, Bogdan Kolomiets, Pierre Kornprobst, Serge Picaud, Kornprobst, Pierre, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), NEUROMATHCOMP, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-INRIA Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (LJAD), Institut de la Vision, Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Nice Sophia Antipolis (... - 2019) (UNS), and Laboratoire Jean Alexandre Dieudonné (JAD)
Subjects: retina, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], genetic structures, Spike trains analysis, [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], sense organs, eye diseases
Abstract: International audience; The modelling of the visual system needs to provide realistic retinal responses (spike trains) to visual stimuli. Our team [1] developed a retina simulator that allows a large scale simulation (about 100.000 cells) and provides spikes train output as a response to visual stimuli. This model contains several blocks representing the retina layers. It is able to reproduce realistic individual responses of retinal ganglion cell (RGC). However, as emphasized in the present work, we checked that the collective responses of RGC don't match to real data. Comparing our simulator outputs to real acquisitions data made by B. Kolomiets and S. Picaud (Institut de la Vision) we have shown, using statistical methods developed by our team (EnaS) [3], that real data show a significant synchronization and correlations between RGC outputs, that is absent from our simulator outputs. It is commonly believed that those correlations come from the overlap of RGC receptive fields. However, since, our simulator carefully reproduces this overlap this suggests that synchronization must be explained by other mechanisms such as long range connections from Amacrine to RGC or electrical connections (gap junctions) between RGC which have not been implemented yet in our simulator.

37. A Large Deviation Principle and an Expression of the Rate Function for a Discrete Stationary Gaussian Process

Author: James MacLaurin, Olivier Faugeras, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: General Physics and Astronomy, lcsh:Astrophysics, large deviation principle, Positive-definite matrix, 01 natural sciences, Gaussian random field, 010104 statistics & probability, symbols.namesake, lcsh:QB460-466, 0101 mathematics, lcsh:Science, Gaussian process, Mathematics, stationary Gaussian process, [SCCO.NEUR]Cognitive science/Neuroscience, 010102 general mathematics, Mathematical analysis, Spectral density, Expression (mathematics), lcsh:QC1-999, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], symbols, spectral density, lcsh:Q, Rate function, lcsh:Physics
Abstract: International audience; We prove a Large Deviation Principle for a stationary Gaussian process over R b , indexed by Z d (for some positive integers d and b), with positive definite spectral density and provide an expression of the corresponding rate function in terms of the mean of the process and its spectral density. This result is useful in applications where such an expression is needed.
Published: 2014
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38. Statistique de potentiels d'action et distributions de Gibbs dans les réseaux de neurones

Author: COFRE, RODRIGO, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Université Nice Sophia Antipolis, Bruno Cessac, CESSAC, BRUNO, and UNIVERSITE NICE SOPHIA ANTIPOLIS
Subjects: [SPI.OTHER]Engineering Sciences [physics]/Other, Statistique de potentiels d'action, Gibbs distributions, Réseaux de neurones, Distributions de Gibbs, Spike trains, Neuronal Networks
Abstract: Sensory neurons respond to external stimulus using sequences of action potentials (“spikes”). They convey collectively to the brain information about the stimulus using spatio-temporal patterns of spikes (spike trains), that constitute a “neural code”. Since spikes patterns occur irregularly (yet highly structured) both within and over repeated trials, it is reasonable to characterize them using statistical methods and probabilistic descriptions. However, the statistical characterization of experimental data presents several major constraints: apart from those inherent to empirical statistics like finite size sampling, ‘the’ underlying statistical model is unknown. In this thesis we adopt a complementary approach to experiments. We consider neuromimetic models allowing the study of collective spike trains statistics and how it depends on network architecture and history, as well as on the stimulus. First, we consider a conductance-based Integrate-and-Fire model with chemical and electric synapses. We show that the spike train statistics is characterized by non-stationary, infinite memory, distribution consistent with conditional probabilities (Left interval specifications), which is continuous and non null, thus a Gibbs distribution. Then, we present a novel method that allows us to unify spatio-temporal Maximum Entropy models (whose invariant measure are Gibbs distributions in the Bowen sense) and neuro-mimetic models, providing a solid ground towards biophysical explanation of spatio-temporal correlations observed in experimental data. Finally, using these tools, we discuss the stimulus response of retinal ganglion cells, and the possible generalization of the co; Les neurones sensoriels réagissent à des stimuli externes en émettant des séquences de potentiels d’action (“spikes”). Ces spikes transmettent collectivement de l’information sur le stimulus en formant des motifs spatio-temporels qui constituent le code neural. On observe expérimentalement que ces motifs se produisent de façon irrégulière, mais avec une structure qui peut être mise en évidence par l’utilisation de descriptions probabilistes et de méthodes statistiques. Cependant, la caractérisation statistique des données expérimentales présente plusieurs contraintes majeures: en dehors de celles qui sont inhérentes aux statistiques empiriques comme la taille de l’échantillonnage, ‘le’ modèle statistique sous-jacent est inconnu. Dans cette thèse, nous abordons le problème d’un point de vue complémentaire à l’approche expérimentale. Nous nous intéressons à des modèles neuro-mimétiques permettant d’étudier la statistique collective des potentiels d’action et la façon dont elle dépend de l’architecture et l’histoire du réseau ainsi que du stimulus. Nous considérons tout d’abord un modèle de type Intègre-et-Tire à conductance incluant synapses électriques et chimiques. Nous montrons que la statistique des potentiels d’action est caractérisée par une distribution non stationnaire et de mémoire infinie, compatible avec les probabilités conditionnelles (left interval-specification), qui est non-nulle et continue, donc une distribution de Gibbs. Nous présentons ensuite une méthode qui permet d’unifier les modèles dits d’entropie maximale spatio-temporelle (dont la mesure invariante est une distribution de Gibbs dans le sens de Bowen) et les modèles neuro-mimétiques, en fou
Published: 2014

39. Neuronal networks, spike trains statistics and Gibbs distributions

Author: Cofré, Rodrigo, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Université Nice Sophia Antipolis, Bruno Cessac, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: [SPI.OTHER]Engineering Sciences [physics]/Other, Statistique de potentiels d'action, Gibbs distributions, Distributions de Gibbs, Réseaux de neurones, Spike trains, Neuronal Networks
Abstract: Sensory neurons respond to external stimulus using sequences of action potentials (“spikes”). They convey collectively to the brain information about the stimulus using spatio-temporal patterns of spikes (spike trains), that constitute a “neural code”. Since spikes patterns occur irregularly (yet highly structured) both within and over repeated trials, it is reasonable to characterize them using statistical methods and probabilistic descriptions. However, the statistical characterization of experimental data presents several major constraints: apart from those inherent to empirical statistics like finite size sampling, ‘the’ underlying statistical model is unknown. In this thesis we adopt a complementary approach to experiments. We consider neuromimetic models allowing the study of collective spike trains statistics and how it depends on network architecture and history, as well as on the stimulus. First, we consider a conductance-based Integrate-and-Fire model with chemical and electric synapses. We show that the spike train statistics is characterized by non-stationary, infinite memory, distribution consistent with conditional probabilities (Left interval specifications), which is continuous and non null, thus a Gibbs distribution. Then, we present a novel method that allows us to unify spatio-temporal Maximum Entropy models (whose invariant measure are Gibbs distributions in the Bowen sense) and neuro-mimetic models, providing a solid ground towards biophysical explanation of spatio-temporal correlations observed in experimental data. Finally, using these tools, we discuss the stimulus response of retinal ganglion cells, and the possible generalization of the co; Les neurones sensoriels réagissent à des stimuli externes en émettant des séquences de potentiels d’action (“spikes”). Ces spikes transmettent collectivement de l’information sur le stimulus en formant des motifs spatio-temporels qui constituent le code neural. On observe expérimentalement que ces motifs se produisent de façon irrégulière, mais avec une structure qui peut être mise en évidence par l’utilisation de descriptions probabilistes et de méthodes statistiques. Cependant, la caractérisation statistique des données expérimentales présente plusieurs contraintes majeures: en dehors de celles qui sont inhérentes aux statistiques empiriques comme la taille de l’échantillonnage, ‘le’ modèle statistique sous-jacent est inconnu. Dans cette thèse, nous abordons le problème d’un point de vue complémentaire à l’approche expérimentale. Nous nous intéressons à des modèles neuro-mimétiques permettant d’étudier la statistique collective des potentiels d’action et la façon dont elle dépend de l’architecture et l’histoire du réseau ainsi que du stimulus. Nous considérons tout d’abord un modèle de type Intègre-et-Tire à conductance incluant synapses électriques et chimiques. Nous montrons que la statistique des potentiels d’action est caractérisée par une distribution non stationnaire et de mémoire infinie, compatible avec les probabilités conditionnelles (left interval-specification), qui est non-nulle et continue, donc une distribution de Gibbs. Nous présentons ensuite une méthode qui permet d’unifier les modèles dits d’entropie maximale spatio-temporelle (dont la mesure invariante est une distribution de Gibbs dans le sens de Bowen) et les modèles neuro-mimétiques, en fou
Published: 2014

40. A formalism for evaluating analytically the cross-correlation structure of a firing-rate network model

Author: Olivier Faugeras, Stefano Panzeri, Diego Fasoli, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Neural Computation Laboratory, Istituto Italiano di Tecnologia (IIT), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: Theoretical computer science, Computer science, Population, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Neuroscience (miscellaneous), Background noise, 03 medical and health sciences, Functional connectivity, 0302 clinical medicine, Perturbative theory, Statistical physics, education, Randomness, 030304 developmental biology, Network model, 0303 health sciences, education.field_of_study, Stochastic systems, Cross-correlation, Artificial neural network, Quantitative Biology::Neurons and Cognition, [SCCO.NEUR]Cognitive science/Neuroscience, Research, Firing-rate network model, Graph theory, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Recurrent neural network, 030217 neurology & neurosurgery, Neural networks
Abstract: We introduce a new formalism for evaluating analytically the cross-correlation structure of a finite-size firing-rate network with recurrent connections. The analysis performs a first-order perturbative expansion of neural activity equations that include three different sources of randomness: the background noise of the membrane potentials, their initial conditions, and the distribution of the recurrent synaptic weights. This allows the analytical quantification of the relationship between anatomical and functional connectivity, i.e. of how the synaptic connections determine the statistical dependencies at any order among different neurons. The technique we develop is general, but for simplicity and clarity we demonstrate its efficacy by applying it to the case of synaptic connections described by regular graphs. The analytical equations so obtained reveal previously unknown behaviors of recurrent firing-rate networks, especially on how correlations are modified by the external input, by the finite size of the network, by the density of the anatomical connections and by correlation in sources of randomness. In particular, we show that a strong input can make the neurons almost independent, suggesting that functional connectivity does not depend only on the static anatomical connectivity, but also on the external inputs. Moreover we prove that in general it is not possible to find a mean-field description à la Sznitman of the network, if the anatomical connections are too sparse or our three sources of variability are correlated. To conclude, we show a very counterintuitive phenomenon, which we call stochastic synchronization, through which neurons become almost perfectly correlated even if the sources of randomness are independent. Due to its ability to quantify how activity of individual neurons and the correlation among them depends upon external inputs, the formalism introduced here can serve as a basis for exploring analytically the computational capability of population codes expressed by recurrent neural networks. Electronic Supplementary Material The online version of this article (doi:10.1186/s13408-015-0020-y) contains supplementary material 1.
Published: 2014

41. Asymptotic description of stochastic neural networks. I. Existence of a large deviation principle

Author: Olivier Faugeras, James MacLaurin, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: Quantitative Biology::Neurons and Cognition, Gaussian, [SCCO.NEUR]Cognitive science/Neuroscience, Mathematical analysis, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], General Medicine, Empirical measure, 01 natural sciences, 010305 fluids & plasmas, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, Stochastic differential equation, symbols.namesake, Discrete time and continuous time, 0103 physical sciences, symbols, Applied mathematics, 0101 mathematics, Stochastic neural network, Gaussian process, Random variable, Rate function, Mathematics
Abstract: International audience; We study the asymptotic law of a network of interacting neurons when the number ofneurons becomes infinite. The dynamics of the neurons is described by a set of stochasticdifferential equations in discrete time. The neurons interact through the synaptic weightsthat are Gaussian correlated random variables. We describe the asymptotic law of thenetwork when the number of neurons goes to infinity. Unlike previous works which madethe biologically unrealistic assumption that the weights were i.i.d. random variables, weassume that they are correlated. We introduce the process-level empirical measure of thetrajectories of the solutions into the equations of the finite network of neurons and theaveraged law (with respect to the synaptic weights) of the trajectories of the solutions intothe equations of the network of neurons. The result (Theorem 3.1 below) is that the imagelaw through the empirical measure satisfies a large deviation principle with a good ratefunction. We provide an analytical expression of this rate function in terms of the spectralrepresentation of certain Gaussian processes.; Nous considérons un réseau de neurones décrit par un système d’équations différentiellesstochastiques en temps discret. Les neurones interagissent au travers de poids synaptiquesqui sont des variables aléatoires gaussiennes corrélées. Nous caractérisons la loi asymptotiquede ce réseau lorsque le nombre de neurones tend vers l’infini. Tous les travauxprécédents faisaient l’hypothèse, irréaliste du point de vue de la biologie, de poidsindépendants. Nous introduisons la mesure empirique sur l’espace des trajectoires solutionsdes équations du réseau de neurones de taille finie et la loi moyennée (par rapport auxpoids synaptiques) des trajectoires de ces solutions. Le résultat (théorème 3.1 ci-dessous)est que l’image de cette loi par la mesure empirique satisfait un principe de grandesdéviations avec une bonne fonction de taux, dont nous donnons une expression analytiqueen fonction de la représentation spectrale de certains processus gaussiens.
Published: 2014

42. Asymptotic description of stochastic neural networks. II. Characterization of the limit law

Author: James MacLaurin, Olivier Faugeras, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: [SCCO.NEUR]Cognitive science/Neuroscience, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], General Medicine, Characterization (mathematics), Gaussian measure, 01 natural sciences, Measure (mathematics), 010305 fluids & plasmas, 010101 applied mathematics, Set (abstract data type), [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Covariance operator, 0103 physical sciences, Convergence (routing), Applied mathematics, 0101 mathematics, Stochastic neural network, Rate function, Mathematics
Abstract: International audience; We continue the development, started in [7], of the asymptotic description of certainstochastic neural networks. We use the Large Deviation Principle (LDP) and thegood rate function H announced there to prove that H has a unique minimum e,a stationary measure on the set of trajectories T Z. We characterize this measureby its two marginals, at time 0, and from time 1 to T. The second marginal is astationary Gaussian measure. With an eye on applications, we show that its meanand covariance operator can be inductively computed. Finally we use the LDP toestablish various convergence results, averaged and quenched.; Nous prolongeons le développement, commencé en [8], de la description asymptotique de certains réseaux de neurones stochastiques. Nous utilisons le principe de grandes déviations (PGD) et la bonne fonction de taux H que nous y annoncions pour démontrer l'existence d'un unique minimimum, μe, de H , une mesure stationnaire sur l'ensemble TZ des trajectoires. Nous caractérisons cette mesure par ses deux maginales, à l'instant 0, et du temps 1 au temps T. La seconde marginale est une mesure gaussienne stationnaire. Avec un oeil sur les applications, nous montrons comment calculer de manière inductive sa moyenne et son opérateur de covariance. Nous montrons aussi comment utiliser le PGD pour établir des résultats de convergence en moyenne et presque sûrement.
Published: 2014

43. Que peut-on attendre d'une architecture feedforward classique de V1-MT pour estimer le flot optique?

Author: Solari, Fabio, Chessa, Manuela, Medathati, Kartheek, Kornprobst, Pierre, Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi [Genova] (DIBRIS), Universita degli studi di Genova, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), INRIA Sophia Antipolis, University of Genoa - DIBRIS, Italy, INRIA, European Project: 318723,EC:FP7:ICT,FP7-ICT-2011-8,MATHEMACS(2012), Università degli studi di Genova = University of Genoa (UniGe), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: spatio-temporal filters, motion energy, Optical flow, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], cortical areas V1 and MT, [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], Middlebury dataset, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], benchmarking
Abstract: Motion estimation has been studied extensively in neurosciences in the last two decades. The general consensus that has evolved from the studies in the primate vision is that it is done in a two stage process involving cortical areas V1 and MT in the brain. Spatio temporal filters are leading contenders in terms of models that capture the characteristics exhibited in these areas. Even though there are many models in the biological vision literature covering the optical flow estimation problem based on the spatio-temporal filters little is known in terms of their performance on the modern day computer vision datasets such as Middlebury. In this paper, we start from a mostly classical feedforward V1-MT model introducing a additional decoding step to obtain an optical flow estimation. Two extensions are also discussed using nonlinear filtering of the MT response for a better handling of discontinuities. One essential contribution of this paper is to show how a neural model can be adapted to deal with real sequences and it is here for the first time that such a neural model is benchmarked on the modern computer vision dataset Middlebury. Results are promising and suggest several possible improvements. \code{We think that this work could act as a good starting point for building bio-inspired scalable computer vision algorithms. For that reason we propose to also share the code in order to encourage research in this direction.
Published: 2014

44. Mean-field limit of a stochastic particle system smoothly interacting through threshold hitting-times and applications to neural networks with dendritic component

Author: Denis Talay, James Inglis, TO Simulate and CAlibrate stochastic models (TOSCA), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Mathematical and Computational Neuroscience (NEUROMATHCOMP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), European Project: 318723,EC:FP7:ICT,FP7-ICT-2011-8,MATHEMACS(2012), European Project: 269921,EC:FP7:ICT,FP7-ICT-2009-6,BRAINSCALES(2011), European Project: 284941,EC:FP7:ICT,FP7-ICT-2011-FET-F,HBP(2011), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: McKean-Vlasov equation, noisy integrate-and-fire model, Mathematical optimization, Mean field limit, non-constant synaptic weights, neuroscience, dendritic structure, Component (UML), Convergence (routing), FOS: Mathematics, Statistical physics, Mathematics, Particle system, Artificial neural network, Quantitative Biology::Neurons and Cognition, [SCCO.NEUR]Cognitive science/Neuroscience, Applied Mathematics, Mathematical analysis, Probability (math.PR), mean-field limit, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Computational Mathematics, cable equation, Cable theory, Analysis, Mathematics - Probability
Abstract: pp 3884-3916; International audience; In this article we study the convergence of a stochastic particle system that interacts through threshold hitting times towards a novel equation of McKean-Vlasov type. The particle system is motivated by an original model for the behavior of a network of neurons, in which a classical noisy integrate-and-fire model is coupled with a cable equation to describe the dendritic structure of each neuron.
Published: 2014

45. Can We Hear the Shape of a Maximum Entropy Potential From Spike Trains?

Author: Cofre, Rodrigo, Cessac, Bruno, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), ANR-10-INTB-0204,KEOpS,Algorithmes pour la modélisation du système visuel: de la vision naturelle aux applications numériques.(2010), European Project: 600847,EC:FP7:ICT,FP7-ICT-2011-9,RENVISION(2013), European Project: 318723,EC:FP7:ICT,FP7-ICT-2011-8,MATHEMACS(2012), European Project: 227747,EC:FP7:ERC,ERC-2008-AdG,NERVI(2009), European Project: 269921,EC:FP7:ICT,FP7-ICT-2009-6,BRAINSCALES(2011), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)
Subjects: [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn]
Abstract: International audience; We consider a spike-generating stationary Markov process whose transition probabilities are known. We show that there is a canonicalpotential whose Gibbs distribution, obtained from the MaximumEntropy Principle (MaxEnt), is the equilibrium distribution of thisprocess. We provide a method to compute explicitly and exactly thispotential as a linear combination of spatio-temporal interactions.The method is based on the Hammersley Clifford decomposition andon periodic orbits sampling. An explicit correspondence between theparameters of MaxEnt model and the parameters of Markovianmodels like the Generalized-Linear Model can be established. Wealso provide numerical results.
Published: 2014

46. From Habitat to Retina: Neural Population Coding using Natural Movies

Author: Herzog, Rubén, Araya, Joaquin, Pizarro, Michael, Cessac, Bruno, Ravello, Cesar, Escobar, Maria-Jose, Palacios, Adrian, Centro Interdisciplinario de Neurociencia de Valparaiso (CINV), Universidad de Valparaiso [Chile], Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Universidad Tecnica Federico Santa Maria [Valparaiso] (UTFSM), ANR-10-INTB-0204,KEOpS,Algorithmes pour la modélisation du système visuel: de la vision naturelle aux applications numériques.(2010), European Project: 600847,EC:FP7:ICT,FP7-ICT-2011-9,RENVISION(2013), European Project: 263179,EC:FP7:ERC,ERC-2010-StG_20091209,MATHCONSTRUCTION(2011), European Project: 227747,EC:FP7:ERC,ERC-2008-AdG,NERVI(2009), European Project: 269921,EC:FP7:ICT,FP7-ICT-2009-6,BRAINSCALES(2011), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: genetic structures, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], sense organs, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn]
Abstract: International audience; Population retinal responses to natural stimuli is still anopen research field, nevertheless retinal ganglion cells(RGC) spatio-temporal correlations may be related topopulation coding (1). Here, we use a diurnal rodent retina(O. degus), which has the advantage of present a 3:1proportion of rods and cones (2), respectively, to study theRGC population responses to habitat-based natural stimuli.In order to do this, we have developed a mobile robot thatis capable to record movies in the natural habitat of thisrodent, simulating both his movements and the eye-grounddistance, which allows us to stimulate and record an invitro retina patch using MEA (multi electrode array) with asequence of images taken from the animal natural habitat.The analysis of spike statistics has been done using theEnas software (http://enas.gforge.inria.fr/v3/) allowing tocharacterize spatio-temporal pairwise correlations, incontrast to e.g. Ising models, that analyze onlyinstantaneous spatial correlations.
Published: 2014

47. The wave of first spikes provides robust spatial cues for retinal information processing

Author: Portelli, Geoffrey, Barrett, John, Sernagor, Evelyne, Masquelier, Timothée, Kornprobst, Pierre, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Institute of Neuroscience [Newcastle] (ION), Newcastle University [Newcastle], Institut de la Vision, Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), INRIA, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Pierre et Marie Curie - Paris 6 (UPMC)
Subjects: [SCCO.NEUR]Cognitive science/Neuroscience
Abstract: How a population of retinal ganglion cells (RGCs) encode the visual scene remains an open question. Several coding strategies have been investigated out of which two main views have emerged: considering RGCs as independent encoders or as synergistic encoders, i.e. when the concerted spiking in a RGC population carries more information than the sum of the information contained in the spiking of individual RGCs. Although the RGCs assumed as independent encode the main information, there is currently a growing body of evidence that considering RGCs as synergistic encoders provides complementary and more precise information. Based on salamander retina recordings, it has been suggested [11] that a code based on di erential spike latencies between RGC pairs could be a powerful mechanism. Here, we have tested this hypothesis in the mammalian retina. We recorded responses to stationary gratings from 469 RGCs in 5 mouse retinas. Interestingly, we did not nd any RGC pairs exhibiting clear latency correlations (presumably due to the presence of spontaneous activity), showing that individual RGC pairs do not provide su cient information in our conditions. However considering the whole RGC population, we show that the shape of the wave of rst spikes (WFS) successfully encodes for spatial cues. To quantify its coding capabilities, we performed a discrimination task and we showed that the WFS was more robust to the spontaneous ring than the absolute latencies are. We also investigated the impact of a post-processing neural layer. The recorded spikes were fed into an arti cial lateral geniculate nucleus (LGN) layer. We found that the WFS is not only preserved but even re ned through the LGN-like layer, while classical independent coding strategies become impaired. These ndings suggest that even at the level of the retina, the WFS provides a reliable strategy to encode spatial cues.; Comment une population de cellules ganglionnaires de la rétine (RGC) encode la scène visuelle reste une question ouverte. Plusieurs stratégies de codage ont été étudiés à partir desquelles deux principales vues ont émergé: considérer les RGCs en tant que encodeurs indépendants ou en tant que encodeurs synergique; c'est à dire lorsque la réponse concertée dans une population de RGCs contient plus d'informations que la somme des informations contenues dans les réponses individuelles. Bien que en considérant les RGCs comme des encodeurs indépendants donne accès à l'information principale, il existe actuellement un nombre croissant de preuves qui montrent que considérer les RGCs comme des encodeurs synergiques fournit des informations complémentaires et plus précises. Basé sur des enregistrements de la rétine de salamandre, il a été suggéré [11] qu'un code basé sur les di érences entre les latences des paires de RGCs pourrait être un mécanisme puissant. Ici, nous avons testé cette hypothèse dans la rétine de mammifère. Nous avons enregistré les réponses de 469 RGCs de 5 rétines de souris. Fait intéressant, nous n'avons pas trouvé de paires de RGCs présentant des corrélations de latence claires (probablement en raison de la présence d'une forte activité spontanée). Cela montre que les paires de RGCs individuelles ne fournissent pas su samment d'informations dans nos conditions. Toutefois, en considérant la population de RGCs, nous avons montré que la forme de la première vague de potentiels d'action (WFS) code avec succès des indices spatiaux. Pour quanti er ses capacités de codage, nous avons réalisé une tâche de discrimination et nous avons montré que la WFS était plus robuste à l'activitée spontannée que les latences absolues. Nous avons également étudié l'impact du traitement par une couche de neurones. Les réponses enregistrées ont été introduits dans une couche de corps géniculé latéral arti ciel (LGN). Nous avons constaté que la WFS est non seulement préservée mais mÃame ra née à travers la couche LGN, tandis que les stratégies classiques de codage indépendant deviennent altérées. Ces résultats suggèrent que, même au niveau de la rétine, la WFS propose une stratégie able pour coder l'information visuelle.
Published: 2014

48. Microsaccades enable efficient synchrony-based visual feature learning and detection

Author: Timothée Masquelier, Geoffrey Portelli, Pierre Kornprobst, Institut de la Vision, Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Pierre et Marie Curie - Paris 6 (UPMC), Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), BMC, Ed., Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD)
Subjects: genetic structures, Computer science, Spike train, Retinal ganglion, 03 medical and health sciences, Cellular and Molecular Neuroscience, Synaptic weight, 0302 clinical medicine, Parvocellular cell, [SDV.NEU] Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], 030304 developmental biology, 0303 health sciences, business.industry, General Neuroscience, Eye movement, Pattern recognition, eye diseases, Receptive field, Poster Presentation, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], sense organs, Artificial intelligence, Microsaccade, business, Neuroscience, 030217 neurology & neurosurgery, Coincidence detection in neurobiology
Abstract: Fixational eye movements are common across vertebrates, yet their functional roles, if any, are debated [1]. To investigate this issue, we exposed the Virtual Retina simulator [2] to natural images, generated realistic drifts and microsaccades using the model of ref. [3], and analyzed the output spike trains of the parvocellular retinal ganglion cells (RGC). We first computed cross-correlograms between pairs of RGC that are strongly excited by the image corresponding to the mean eye position. Not surprisingly, in the absence of eye movements, that is when analyzing the tonic (sustained) response to a static image, these cross-correlograms are flat. Adding some slow drift (~20 min/s, self-avoiding random walk) creates long timescale (>1s) correlations because both cells tend to have high firing rates for central positions. Adding microsaccades (~0.5° in 25ms, that is ~20°/s) creates short timescale (tens of ms) correlations: cells that are strongly excited at a particular landing location tend to spike synchronously shortly after the landing. What do the patterns of synchronous spikes represent? To investigate this issue, we fed the RGC spike trains to neurons equipped with spike timing-dependent plasticity (STDP) and lateral inhibitory connections, as in ref. [4]. Neurons self-organized, and each one selected a set of afferents that consistently fired synchronously. We then reconstructed the corresponding visual stimuli by convolving the synaptic weight matrices with the RGC receptive fields. In most cases, we could easily recognize what was learned (e.g. a face), and the neuron was selective (e.g. only responded for microsaccades that landed on a face). Without eye movements, or with only the drift, the STDP-based learning failed, because it needs correlations at a timescale roughly matching the STDP time constants [5]. Microsaccades are thus necessary to generate a synchrony-based coding scheme. More specifically, after each microsaccade landing, cells that are strongly excited by the image corresponding to the landing location tend to fire their first spikes synchronously. Patterns of synchronous spikes can be decoded rapidly – as soon as the first spikes are received – by downstream “coincidence detector” neurons, which do not need to know the landing times. Finally, the required connectivity to do so can spontaneously emerge with STDP. As a whole, these results suggest a new role for microsaccades – to enable efficient visual feature learning and detection thanks to synchronization – that differs from other proposals such as time-to-first spike coding with respect to microsaccade landing times.
Published: 2014

49. De la rétine à la physique statistique

Author: Cessac, Bruno, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), ANR-10-INTB-0204,KEOpS,Algorithmes pour la modélisation du système visuel: de la vision naturelle aux applications numériques.(2010), European Project: 600847,EC:FP7:ICT,FP7-ICT-2011-9,RENVISION(2013), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn]
Abstract: National audience; La rétine est la partie de l'oeil qui transforme les scènes visuelles du monde extérieur en trains d'impulsions (potentiels d'action neuronaux) transmis au cerveau via le nerf optique. Mais c'est bien plus qu'une caméra puisque la rétine est capable de détecter des caractéristiques telles que mouvement différentiel, mouvement d'approche, ...; elle semble même capable d'une forme d'anticipation. Il y a là un (ou plusieurs) mécanismes de codage qui intéressent la communauté des neurosciences. Le développement de techniques d'acquisition telles que MultiElectrode Arrays, Calcium imaging, two photons imaging permettent désormais d'enregistrer l'activité de la rétine tout en cartographiant sa structure. C'est une opportunité pour comprendre les liens entre la structure de la rétine, sa dynamique en réponse à des stimuli visuels et la façon dont elle "encode" ses informations. Mais l'étude de ces mécanismes est encore préliminaire. En particulier, l'analyse même des données obtenues nécessite encore de développer des modèles mathématiques adéquats. Nous montrerons comment des concepts issus de la physique statistique (distributions de Gibbs, réponse linéaire) peuvent être employés pour produire de tels modèles.
Published: 2014

50. Statistical analysis of spike trains in neuronal networks

Author: Cessac, Bruno, Cofre, Rodrigo, Mathematical and Computational Neuroscience (NEUROMATHCOMP), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), ANR-10-INTB-0204,KEOpS,Algorithmes pour la modélisation du système visuel: de la vision naturelle aux applications numériques.(2010), European Project: 600847,EC:FP7:ICT,FP7-ICT-2011-9,RENVISION(2013), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)
Subjects: [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn]
Abstract: International audience; Recent advances in multi-electrodes array acquisition has made it possible to record the activity ofup to several hundreds of neurons at the same time and to register their collective activity (spiketrains). This opens up new perspectives in understanding how a neuronal network encodes theresponse to a stimulus, and what a spike train tells up about the network structure and nonlineardynamics. For this, one has to develop statistical models properly handling the spatio-temporalaspects of spike trains, including memory effects. In this talk, I will review several such statisticalmodels, including Maximum Entropy Models, Generalized Linear Model or neuromimetic models,and their application for the analysis of retina data.
Published: 2014

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