Author: "NEUROMATHCOMP" / Language: undetermined - Searchworks@Jio Institute Digital Library Search Results

Your search keyword '"NEUROMATHCOMP"' showing total 31 results

Start Over Author "NEUROMATHCOMP" Language undetermined

31 results on '"NEUROMATHCOMP"'

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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.

8. 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

9. 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

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

Author: Rodrigo Cofré, Bruno Cessac, 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: Theoretical computer science, Computer science, Entropy, Models, Neurological, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], Action Potentials, FOS: Physical sciences, Information theory, Synaptic Transmission, 01 natural sciences, Random neural network, 010305 fluids & plasmas, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], 0103 physical sciences, Animals, Humans, Entropy (information theory), Computer Simulation, Physics - Biological Physics, 010306 general physics, Neurons, Spiking neural network, Models, Statistical, Computational neuroscience, Quantitative Biology::Neurons and Cognition, Mathematical model, Artificial neural network, business.industry, Principle of maximum entropy, Pattern recognition, Biological Physics (physics.bio-ph), FOS: Biological sciences, Quantitative Biology - Neurons and Cognition, Neurons and Cognition (q-bio.NC), Artificial intelligence, Nerve Net, business
Abstract: Understanding how stimuli and synaptic connectivity in uence the statistics of spike patterns in neural networks is a central question in computational neuroscience. Maximum Entropy approach has been successfully used to characterize the statistical response of simultaneously recorded spiking neurons responding to stimuli. But, in spite of good performance in terms of prediction, the fitting parameters do not explain the underlying mechanistic causes of the observed correlations. On the other hand, mathematical models of spiking neurons (neuro-mimetic models) provide a probabilistic mapping between stimulus, network architecture and spike patterns in terms of conditional proba- bilities. In this paper we build an exact analytical mapping between neuro-mimetic and Maximum Entropy models., arXiv admin note: text overlap with arXiv:1309.5873
Published: 2014

11. Heteroclinic cycles in Hopfield networks

Author: Pascal Chossat, Maciej Krupa, 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), Multiscale dYnamiCs in neuroENdocrine AxEs (Mycenae), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), 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 (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: Hopfield networks, Computer science, network architecture AMS classification: 34C37, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Dynamical Systems (math.DS), Stimulus (physiology), Topology, 01 natural sciences, Hopfield network, 37N25, 0103 physical sciences, Learning rule, FOS: Mathematics, Mathematics - Dynamical Systems, 010306 general physics, Network architecture, Quantitative Biology::Neurons and Cognition, Applied Mathematics, General Engineering, heteroclinic cycles, 68T05, Modeling and Simulation, learning rule, 92B20, 010307 mathematical physics, 34C37, 37N25, 68T05, 92B20
Abstract: It is widely believed that information is stored in the brain by means of the varying strength of synaptic connections between neurons. Stored patterns can be replayed upon the arrival of an appropriate stimulus. Hence, it is interesting to understand how an information pattern can be represented by the dynamics of the system. In this work, we consider a class of network neuron models, known as Hopfield networks, with a learning rule which consists of transforming an information string to a coupling pattern. Within this class of models, we study dynamic patterns, known as robust heteroclinic cycles, and establish a tight connection between their existence and the structure of the coupling.
Published: 2014
Full Text: View/download PDF

12. Motility-induced phase separation of active particles in the presence of velocity alignment

Author: Raphael Chetrite, Julien Barré, Massimiliano Muratori, Fernando Peruani, 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 Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), 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), 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), Université Nice Sophia Antipolis (1965 - 2019) (UNS), Laboratoire Jean Alexandre Dieudonné (LJAD), 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 (LJAD), 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 (1965 - 2019) (UNS)
Subjects: Physics, [PHYS]Physics [physics], Spinodal, Phase transition, Active particles, FOS: Physical sciences, Statistical and Nonlinear Physics, Condensed Matter - Soft Condensed Matter, Active matter, Chemical physics, Biological Physics (physics.bio-ph), Phase (matter), Dissipative system, Soft Condensed Matter (cond-mat.soft), Physics - Biological Physics, Spatial diffusion, Entropy (arrow of time), Mathematical Physics
Abstract: Self-propelled particle (SPP) systems are intrinsically out of equilibrium systems, where each individual particle converts energy into work to move in a dissipative medium. When interacting through a velocity alignment mechanism, and the medium acts as a momentum sink, even momentum is not conserved. In this scenario, a mapping into an equilibrium system seems unlikely. Here, we show that an entropy functional can be derived for SPPs with velocity alignment and density-dependent speed, at least in the (orientationally) disordered phase. This non-trivial result has important physical consequences. The study of the entropy functional reveals that the system can undergo phase separation before the orientational-order phase transition known to occur in SPP systems with velocity alignment.Moreover, we indicate that the spinodal line is a function of the alignment sensitivity and show that density fluctuations as well as the critical spatial diffusion, that leads to phase separation, dramatically increase as the orientational-order transition is approached., Comment: Published in J. Stat. Phys
Published: 2014
Full Text: View/download PDF

13. Particle systems with a singular mean-field self-excitation. Application to neuronal networks

Author: François Delarue, James Inglis, Etienne Tanré, Sylvain Rubenthaler, 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), 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), 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), 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), 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), 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: Statistics and Probability, propagation of chaos, Population, Topology (electrical circuits), Type (model theory), 01 natural sciences, McKean nonlinear diffusion process, integrate-and-fire network, neuroscience, 010104 statistics & probability, Control theory, FOS: Mathematics, 0101 mathematics, education, Mathematics, Particle system, education.field_of_study, Quantitative Biology::Neurons and Cognition, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Probability (math.PR), counting process, Skorohod M1 topology, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Nonlinear system, Mean field theory, Modeling and Simulation, Spike (software development), Mathematics - Probability, Excitation
Abstract: International audience; We discuss the construction and approximation of solutions to a nonlinear McKean-Vlasov equation driven by a singular self-excitatory interaction of the mean-field type. Such an equation is intended to describe an infinite population of neurons which interact with one another. Each time a proportion of neurons 'spike', the whole network instantaneously receives an excitatory kick. The instantaneous nature of the excitation makes the system singular and prevents the application of standard results from the literature. Making use of the Skorohod M1 topology, we prove that, for the right notion of a 'physical' solution, the nonlinear equation can be approximated either by a finite particle system or by a delayed equation. As a by-product, we obtain the existence of 'synchronized' solutions, for which a macroscopic proportion of neurons may spike at the same time.
Published: 2014
Full Text: View/download PDF

14. Interplay between synaptic delays and propagation delays in neural field equations

Author: 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: Hopf bifurcation, Mesoscopic physics, Quantitative Biology::Neurons and Cognition, Mathematical analysis, Space (mathematics), 01 natural sciences, 010305 fluids & plasmas, 010101 applied mathematics, Radio propagation, symbols.namesake, Nonlinear system, Bifurcation theory, Modeling and Simulation, 0103 physical sciences, symbols, Statistical physics, 0101 mathematics, Constant (mathematics), Analysis, Center manifold, Mathematics
Abstract: International audience; Neural field equations describe the activity of neural populations at a mesoscopic level. Although the early derivation of these equations introduced space dependent delays coming from the finite speed of signal propagation along axons, there have been few studies concerning their role in shaping the (nonlinear) dynamics of neural activity. This is mainly due to the lack of analytical tractable models. On the other hand, constant delays have been introduced to model the synaptic transmission and the spike initiation dynamics. By incorporating the two kinds of delays into the neural field equations, we are able to find the Hopf bifurcation curves analytically, which produces many Hopf--Hopf interactions. We use normal theory to study two different types of connectivity that reveal a surprisingly rich dynamical portrait. In particular, the shape of the connectivity strongly influences the spatiotemporal dynamics.
Published: 2013
Full Text: View/download PDF

15. Modeling in Computational Biology and Biomedicine

Author: Frdric Cazals, Pierre Kornprobst, Algorithms, Biology, Structure (ABS), 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), Cazals, Frédéric and 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), 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 and theoretical biology, Computer science, business.industry, media_common.quotation_subject, 0206 medical engineering, 020206 networking & telecommunications, Context (language use), 02 engineering and technology, Computational biology, 020601 biomedical engineering, Variety (cybernetics), Systems biomedicine, Presentation, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], Multidisciplinary approach, 0202 electrical engineering, electronic engineering, information engineering, Added value, business, Biomedicine, media_common
Abstract: International audience; First book that strikes a balance between biology and biomedicine on the one hand, and applied mathematics and computer science on the other hand Presents a panoply of systems ranging from atoms and molecules to organs and biomedicine Three communities are addressed: Bioinformatics, Biomedicine, and Neuroscience Computational biology, mathematical biology, biology and biomedicine are currently undergoing spectacular progresses due to a synergy between technological advances and inputs from physics, chemistry, mathematics, statistics and computer science. The goal of this book is to evidence this synergy by describing selected developments in the following fields: bioinformatics, biomedicine and neuroscience. This work is unique in two respects - first, by the variety and scales of systems studied and second, by its presentation: Each chapter provides the biological or medical context, follows up with mathematical or algorithmic developments triggered by a specific problem and concludes with one or two success stories, namely new insights gained thanks to these methodological developments. It also highlights some unsolved and outstanding theoretical questions, with a potentially high impact on these disciplines. Two communities will be particularly interested in this book. The first one is the vast community of applied mathematicians and computer scientists, whose interests should be captured by the added value generated by the application of advanced concepts and algorithms to challenging biological or medical problems. The second is the equally vast community of biologists. Whether scientists or engineers, they will find in this book a clear and self-contained account of concepts and techniques from mathematics and computer science, together with success stories on their favorite systems. The variety of systems described represents a panoply of complementary conceptual tools. On a practical level, the resources listed at the end of each chapter (databases, software) offer invaluable support for getting started on a specific topic in the fields of biomedicine, bioinformatics and neuroscience.
Published: 2013

16. Simple heteroclinic cycles in R^4

Author: Podvigina, Olga, Chossat, Pascal, Observatoire de la Côte d'Azur (OCA), Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Institute of Earthquake Prediction Theory and Mathematical Geophysics (IEPT), Russian Academy of Sciences [Moscow] (RAS), 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: quaternions, heteroclinic cycle, Mathematics::Dynamical Systems, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], FOS: Physical sciences, Mathematical Physics (math-ph), Chaotic Dynamics (nlin.CD), Nonlinear Sciences - Chaotic Dynamics, Mathematical Physics, equivariant dynamical system
Abstract: In generic dynamical systems heteroclinic cycles are invariant sets of codimension at least one, but they can be structurally stable in systems which are equivariant under the action of a symmetry group, due to the existence of flow-invariant subspaces. For dynamical systems in R^n the minimal dimension for which such robust heteroclinic cycles can exist is n=3. In this case the list of admissible symmetry groups is short and well-known. The situation is different and more interesting when n=4. In this paper we list all finite groups Gamma such that an open set of smooth Gamma-equivariant dynamical systems in R^4 possess a very simple heteroclinic cycle (a structurally stable heteroclinic cycle satisfying certain additional constraints). This work extends the results which were obtained by Sottocornola in the case when all equilibria in the heteroclinic cycle belong to the same Gamma-orbit (in this case one speaks of homoclinic cycles)., Comment: 43 pages; submitted to "Nonlinearity"
Published: 2013
Full Text: View/download PDF

17. Multiscale analysis of slow-fast neuronal learning models with noise

Author: Mathieu Galtier, Gilles Wainrib, 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), School of Engineering and Science [Bremen] (JU-SES), Jacobs University [Bremen], Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), 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), and Université Paris 8 Vincennes-Saint-Denis (UP8)-Université Paris 13 (UP13)-Institut Galilée-Centre National de la Recherche Scientifique (CNRS)
Subjects: Trace (linear algebra), Computer science, Neuroscience (miscellaneous), inhomogeneous Markov process, unsupervised learning, STDP, 03 medical and health sciences, Matrix (mathematics), slow-fast systems, 0302 clinical medicine, model reduction, Statistical physics, 030304 developmental biology, averaging, 0303 health sciences, Cross-correlation, business.industry, Research, stochastic differential equations, Mathematical theory, Noise, Hebbian theory, recurrent networks, Time derivative, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], Artificial intelligence, Focus (optics), business, Hebbian learning, 030217 neurology & neurosurgery
Abstract: International audience; This paper deals with the application of temporal averaging methods to recurrent networks of noisy neurons undergoing a slow and unsupervised modification of their connectivity matrix called learning. Three time-scales arise for these models: (i) the fast neuronal dynamics, (ii) the intermediate external input to the system, and (iii) the slow learning mechanisms. Based on this time-scale separation, we apply an extension of the mathematical theory of stochastic averaging with periodic forcing in order to derive a reduced deterministic model for the connectivity dynamics. We focus on a class of models where the activity is linear to understand the specificity of several learning rules (Hebbian, trace or anti-symmetric learning). In a weakly connected regime, we study the equilibrium connectivity which gathers the entire 'knowledge' of the network about the inputs. We develop an asymptotic method to approximate this equilibrium. We show that the symmetric part of the connectivity post-learning encodes the correlation structure of the inputs, whereas the anti-symmetric part corresponds to the cross correlation between the inputs and their time derivative. Moreover, the time-scales ratio appears as an important parameter revealing temporal correlations.
Published: 2012

18. Streaming an image through the eye: The retina seen as a dithered scalable image coder

Author: Khaled Masmoudi, Pierre Kornprobst, Marc Antonini, Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe IMAGES-CREATIVE, Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), 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 Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), 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), 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 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 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: FOS: Computer and information sciences, Difference of Gaussians, Computer science, media_common.quotation_subject, Computer Vision and Pattern Recognition (cs.CV), Computer Science - Computer Vision and Pattern Recognition, 02 engineering and technology, 03 medical and health sciences, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], 0302 clinical medicine, Perception, 0202 electrical engineering, electronic engineering, information engineering, medicine, Bit allocation, Computer vision, Dither, Neural and Evolutionary Computing (cs.NE), Electrical and Electronic Engineering, media_common, Retina, business.industry, Computer Science - Neural and Evolutionary Computing, medicine.anatomical_structure, Signal Processing, Scalability, 020201 artificial intelligence & image processing, Computer Vision and Pattern Recognition, Artificial intelligence, business, 030217 neurology & neurosurgery, Software, Decoding methods, Coding (social sciences)
Abstract: We propose the design of an original scalable image coder/decoder that is inspired from the mammalians retina. Our coder accounts for the time-dependent and also nondeterministic behavior of the actual retina. The present work brings two main contributions: As a first step, (i) we design a deterministic image coder mimicking most of the retinal processing stages and then (ii) we introduce a retinal noise in the coding process, that we model here as a dither signal, to gain interesting perceptual features. Regarding our first contribution, our main source of inspiration will be the biologically plausible model of the retina called Virtual Retina. The main novelty of this coder is to show that the time-dependent behavior of the retina cells could ensure, in an implicit way, scalability and bit allocation. Regarding our second contribution, we reconsider the inner layers of the retina. We emit a possible interpretation for the non-determinism observed by neurophysiologists in their output. For this sake, we model the retinal noise that occurs in these layers by a dither signal. The dithering process that we propose adds several interesting features to our image coder. The dither noise whitens the reconstruction error and decorrelates it from the input stimuli. Furthermore, integrating the dither noise in our coder allows a faster recognition of the fine details of the image during the decoding process. Our present paper goal is twofold. First, we aim at mimicking as closely as possible the retina for the design of a novel image coder while keeping encouraging performances. Second, we bring a new insight concerning the non-deterministic behavior of the retina., Comment: arXiv admin note: substantial text overlap with arXiv:1104.1550
Published: 2012
Full Text: View/download PDF

19. Mean Field description of and propagation of chaos in recurrent multipopulation networks of Hodgkin-Huxley and Fitzhugh-Nagumo neurons

Author: Baladron, Javier, Fasoli, Diego, Faugeras, Olivier, Touboul, Jonathan, 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), Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Nice Sophia Antipolis (... - 2019) (UNS)
Subjects: [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Quantitative Biology::Neurons and Cognition, Quantitative Biology - Neurons and Cognition, FOS: Biological sciences, Probability (math.PR), FOS: Mathematics, Neurons and Cognition (q-bio.NC), 60F99, 60B10, 92B20, 82C32, 82C80, 35Q80, Mathematics - Probability
Abstract: We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are represented either by the Hodgkin-Huxley model or by one of its simplified version, the Fitzhugh-Nagumo model. The synapses between neurons are either electrical or chemical. The network is assumed to be fully connected. The maximum conductances vary randomly. Under the condition that all neurons initial conditions are drawn independently from the same law that depends only on the population they belong to, we prove that a propagation of chaos phenomenon takes places, namely that in the mean-field limit, any finite number of neurons become independent and, within each population, have the same probability distribution. This probability distribution is solution of a set of implicit equations, either nonlinear stochastic differential equations resembling the McKean-Vlasov equations, or non-local partial differential equations resembling the McKean-Vlasov-Fokker- Planck equations. We prove the well-posedness of these equations, i.e. the existence and uniqueness of a solution. We also show the results of some preliminary numerical experiments that indicate that the mean-field equations are a good representation of the mean activity of a finite size network, even for modest sizes. These experiment also indicate that the McKean-Vlasov-Fokker- Planck equations may be a good way to understand the mean-field dynamics through, e.g., a bifurcation analysis., Comment: 55 pages, 9 figures
Published: 2011
Full Text: View/download PDF

20. Hebbian learning of recurrent connections: a geometrical perspective

Author: Paul C. Bressloff, Olivier Faugeras, Mathieu Galtier, School of Engineering and Science [Bremen] (JU-SES), Jacobs University [Bremen], 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), Department of Mathematics - University of Utah, University of Utah, 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, Cognitive Neuroscience, Models, Neurological, FOS: Physical sciences, Euclidean distance matrix, Topology, Projection (linear algebra), Membrane Potentials, Hopfield network, 03 medical and health sciences, 0302 clinical medicine, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], Arts and Humanities (miscellaneous), Position (vector), Orientation, Leabra, Neural Pathways, Animals, Humans, Learning, Computer Simulation, 030304 developmental biology, Mathematics, Cerebral Cortex, 0303 health sciences, Orientation column, Neuronal Plasticity, Nonlinear Sciences - Adaptation and Self-Organizing Systems, Orientation (vector space), Hebbian theory, Quantitative Biology - Neurons and Cognition, FOS: Biological sciences, Synapses, Neurons and Cognition (q-bio.NC), Neural Networks, Computer, Adaptation and Self-Organizing Systems (nlin.AO), 030217 neurology & neurosurgery
Abstract: International audience; We show how a Hopfield network with modifiable recurrent connections undergoing slow Hebbian learning can extract the underlying geometry of an input space. First, we use a slow and fast analysis to derive an averaged system whose dynamics derives from an energy function and therefore always converges to equilibrium points. The equilibria reflect the correlation structure of the inputs, a global object extracted through local recurrent interactions only. Second, we use numerical methods to illustrate how learning extracts the hidden geometrical structure of the inputs. Indeed, multidimensional scaling methods make it possible to project the final connectivity matrix onto a Euclidean distance matrix in a high-dimensional space, with the neurons labeled by spatial position within this space. The resulting network structure turns out to be roughly convolutional. The residual of the projection defines the nonconvolutional part of the connectivity, which is minimized in the process. Finally, we show how restricting the dimension of the space where the neurons live gives rise to patterns similar to cortical maps. We motivate this using an energy efficiency argument based on wire length minimization. Finally, we show how this approach leads to the emergence of ocular dominance or orientation columns in primary visual cortex via the self-organization of recurrent rather than feedforward connections. In addition, we establish that the nonconvolutional (or long-range) connectivity is patchy and is co-aligned in the case of orientation learning.
Published: 2011
Full Text: View/download PDF

21. Finite-size and correlation-induced effects in mean-field dynamics

Author: G. Bard Ermentrout, 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), Department of Mathematics, University of Pittsburgh (PITT), Pennsylvania Commonwealth System of Higher Education (PCSHE)-Pennsylvania Commonwealth System of Higher Education (PCSHE), 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: Dynamical systems theory, Cognitive Neuroscience, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Models, Neurological, Statistics as Topic, FOS: Physical sciences, Dynamical Systems (math.DS), 01 natural sciences, Stability (probability), 03 medical and health sciences, Cellular and Molecular Neuroscience, 0302 clinical medicine, 0103 physical sciences, Master equation, FOS: Mathematics, Animals, Humans, Limit (mathematics), Statistical physics, Mathematics - Dynamical Systems, 010306 general physics, [NLIN.NLIN-AO]Nonlinear Sciences [physics]/Adaptation and Self-Organizing Systems [nlin.AO], Mathematics, Variable (mathematics), Neurons, Mesoscopic physics, Behavior, Stochastic Processes, Large numbers, Nonlinear Sciences - Adaptation and Self-Organizing Systems, Sensory Systems, Mean field theory, Nonlinear Dynamics, Quantitative Biology - Neurons and Cognition, FOS: Biological sciences, Neurons and Cognition (q-bio.NC), Neural Networks, Computer, Nerve Net, Adaptation and Self-Organizing Systems (nlin.AO), 030217 neurology & neurosurgery
Abstract: International audience; The brain's activity is characterized by the interaction of a very large number of neurons that are strongly affected by noise. However, signals often arise at macroscopic scales integrating the effect of many neurons into a reliable pattern of activity. In order to study such large neuronal assemblies, one is often led to derive mean-field limits summarizing the effect of the interaction of a large number of neurons into an effective signal. Classical mean-field approaches consider the evolution of a deterministic variable, the mean activity, thus neglecting the stochastic nature of neural behavior. In this article, we build upon two recent approaches that include correlations and higher order moments in mean-field equations, and study how these stochastic effects influence the solutions of the mean-field equations, both in the limit of an infinite number of neurons and for large yet finite networks. We introduce a new model, the infinite model, which arises from both equations by a rescaling of the variables and, which is invertible for finite-size networks, and hence, provides equivalent equations to those previously derived models. The study of this model allows us to understand qualitative behavior of such large-scale networks. We show that, though the solutions of the deterministic mean-field equation constitute uncorrelated solutions of the new mean-field equations, the stability properties of limit cycles are modified by the presence of correlations, and additional non-trivial behaviors including periodic orbits appear when there were none in the mean field. The origin of all these behaviors is then explored in finite-size networks where interesting mesoscopic scale effects appear. This study leads us to show that the infinite-size system appears as a singular limit of the network equations, and for any finite network, the system will differ from the infinite system.
Published: 2010

22. Evaluating motion estimation models from behavioural and psychophysical data

Author: Heiko Neumann, Jan D. Bouecke, Guillaume S. Masson, Pierre Kornprobst, Émilien Tlapale, 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), Institute of Neural Information Processing [Ulm], Universität Ulm - Ulm University [Ulm, Allemagne], DyVa Team, Institut de neurosciences cognitives de la méditerranée - UMR 6193 (INCM), Université de la Méditerranée - Aix-Marseille 2-Centre National de la Recherche Scientifique (CNRS)-Université de la Méditerranée - Aix-Marseille 2-Centre National de la Recherche Scientifique (CNRS)-Université de la Méditerranée - Aix-Marseille 2, Junichi Suzuki and Tadashi Nakano, 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: Computer science, biologically inspired artificial vision models, Optical flow, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Machine learning, computer.software_genre, 050105 experimental psychology, Motion (physics), optical flow, motion estimation, 03 medical and health sciences, 0302 clinical medicine, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], Motion estimation, Psychophysics, 0501 psychology and cognitive sciences, Motion perception, Set (psychology), business.industry, 05 social sciences, Information processing, Experimental data, motion perception, eye movements, Artificial intelligence, business, computer, 030217 neurology & neurosurgery, evaluation methodology
Abstract: International audience; Offering proper evaluation methodology is essential to continue progress in modelling the neural mechanisms involved in vision information processing. Currently the evaluation of biologically inspired motion estimation models lacks a proper methodology for comparing their performance against behavioural and psychophysical data. Here we set the basis for such a new benchmark methodology based on human visual performance and designed a database of image sequences taken from neuroscience and psychophysics literature. In this article we focused on two fundamental aspects of motion estimation, which are the respective influence between 1d versus 2d cues and the dynamics of motion integration. Since motion models deal with many kinds of motion representations and scales, we defined two general readouts based on a global motion estimation. Such readouts, namely eye movements and perceived motion, will serve as a reference to compare simulated and experimental data. Baseline results are provided for biologically inspired artificial vision models but also for computer vision models. As a whole we provide here the basis for a valuable evaluation methodology to unravel the fundamental mechanisms of motion perception in the visual cortex. Our database is freely available on the web together with scoring instructions and results at: http://www-sop.inria.fr/neuromathcomp/psymotionbench
Published: 2010

23. Parametric estimation of spike train statistics

Author: Thierry Viéville, Bruno Cessac, 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), 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), 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), 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), 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), 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 (1965 - 2019) (UNS)
Subjects: Kullback–Leibler divergence, Quantitative Biology::Neurons and Cognition, Computer science, General Neuroscience, Spike train, lcsh:QP351-495, Conditional probability, Statistical model, 01 natural sciences, Boltzmann distribution, lcsh:RC321-571, 010305 fluids & plasmas, 03 medical and health sciences, Cellular and Molecular Neuroscience, lcsh:Neurophysiology and neuropsychology, 0302 clinical medicine, 0103 physical sciences, Statistics, Ergodic theory, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], Neural coding, lcsh:Neurosciences. Biological psychiatry. Neuropsychiatry, ComputingMilieux_MISCELLANEOUS, 030217 neurology & neurosurgery, Parametric statistics
Abstract: We consider the evolution of a network of neurons, focusing on the asymptotic behavior of spikes dynamics instead of membrane potential dynamics. The spike response is not sought as a deterministic response in this context, but as a conditional probability: "Reading the code" consists in inferring such a probability. This probability is computed from empirical raster plots, by using the framework of thermodynamic formalism in ergodic theory. This provides us a parametric statistical model where the probability has the form of a Gibbs distribution. In this respect, this approach generalizes the seminal and profound work of Schneidman and collaborators . A minimal presentation of the formalism is reviewed here, while a general algorithmic estimation method is proposed, minimizing the relative entropy, yielding fast convergent implementations. It is also made explicit how several spike observables (entropy, rate, synchronizations, correlations) are given in closed-form from the parametric estimation. This paradigm does not only allow us to estimate the spike statistics, given a design choice, but also to compare different models, thus answering comparative questions about the neural code such as : are correlations (or time synchrony or a given set of spike patterns, ..) significant with respect to rate coding ? A numerical validation of the method is proposed and the perspectives regarding spike-train code analysis are also discussed.
Published: 2009

24. A view of Neural Networks as dynamical systems

Author: Bruno Cessac, Institut Non Linéaire de Nice Sophia-Antipolis (INLN), 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), 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), Université Nice Sophia Antipolis (... - 2019) (UNS), Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Nice Sophia Antipolis (... - 2019) (UNS)
Subjects: Dynamical systems theory, Computer science, [PHYS.PHYS.PHYS-BIO-PH]Physics [physics]/Physics [physics]/Biological Physics [physics.bio-ph], Network structure, FOS: Physical sciences, Context (language use), 01 natural sciences, 03 medical and health sciences, 0302 clinical medicine, 0103 physical sciences, Statistical analysis, Statistical physics, Physics - Biological Physics, Collective dynamics, [NLIN.NLIN-AO]Nonlinear Sciences [physics]/Adaptation and Self-Organizing Systems [nlin.AO], 010306 general physics, Engineering (miscellaneous), Artificial neural network, Quantitative Biology::Neurons and Cognition, Applied Mathematics, Nonlinear Sciences - Adaptation and Self-Organizing Systems, Biological Physics (physics.bio-ph), Modeling and Simulation, Quantitative Biology - Neurons and Cognition, FOS: Biological sciences, Spike (software development), Neurons and Cognition (q-bio.NC), Adaptation and Self-Organizing Systems (nlin.AO), 030217 neurology & neurosurgery
Abstract: We consider neural networks from the point of view of dynamical systems theory. In this spirit we review recent results dealing with the following questions, adressed in the context of specific models. 1. Characterizing the collective dynamics; 2. Statistical analysis of spikes trains; 3. Interplay between dynamics and network structure; 4. Effects of synaptic plasticity., Comment: Review paper, 51 pages, 10 figures. submitted
Published: 2009
Full Text: View/download PDF

25. How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A model-based argumentation

Author: Thierry Viéville, Bruno Cessac, Juan Carlos Vasquez, Horacio Rostro, 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), Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (... - 2019) (UNS), Neuromimetic intelligence (CORTEX), INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP), ANR MACCAC, ANR-07-BLAN-0335,MAPS,Mappings, Adaptation, Plasticity and Spatial computation(2007), 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), Université Nice Sophia Antipolis (1965 - 2019) (UNS), and Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Dynamical systems theory, Computer science, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, Dynamical Systems (math.DS), Argumentation theory, 03 medical and health sciences, Neurons dynamics, 0302 clinical medicine, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], FOS: Mathematics, Ergodic theory, Physics - Biological Physics, Statistical physics, Mathematics - Dynamical Systems, Mathematical Physics, 030304 developmental biology, Probability measure, 0303 health sciences, Spike coding, Quantitative Biology::Neurons and Cognition, Statistical and Nonlinear Physics, Nonlinear Sciences - Adaptation and Self-Organizing Systems, Formalism (philosophy of mathematics), Biological Physics (physics.bio-ph), Synaptic plasticity, Gibbs distributions, Thermodynamic formalism, Adaptation and Self-Organizing Systems (nlin.AO), 030217 neurology & neurosurgery, Coding (social sciences)
Abstract: This paper addresses two questions in the context of neuronal networks dynamics, using methods from dynamical systems theory and statistical physics: (i) How to characterize the statistical properties of sequences of action potentials ("spike trains") produced by neuronal networks ? and; (ii) what are the effects of synaptic plasticity on these statistics ? We introduce a framework in which spike trains are associated to a coding of membrane potential trajectories, and actually, constitute a symbolic coding in important explicit examples (the so-called gIF models). On this basis, we use the thermodynamic formalism from ergodic theory to show how Gibbs distributions are natural probability measures to describe the statistics of spike trains, given the empirical averages of prescribed quantities. As a second result, we show that Gibbs distributions naturally arise when considering "slow" synaptic plasticity rules where the characteristic time for synapse adaptation is quite longer than the characteristic time for neurons dynamics., Comment: 39 pages, 3 figures
Published: 2008
Full Text: View/download PDF

26. Perceptual transition dynamics of a multi-stable visual motion stimulus II: modelling

Author: James Rankin, Andrew Isaac Meso, Olivier Faugeras, Guillaume S. Masson, Pierre Kornprobst, 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 de Neurosciences de la Timone (INT), Aix Marseille Université (AMU)-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), 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: media_common.quotation_subject, 05 social sciences, Diagonal, Mathematical analysis, Neural fields, Biology, Stimulus (physiology), 050105 experimental psychology, Sensory Systems, Visual motion, 03 medical and health sciences, Ophthalmology, 0302 clinical medicine, Bifurcation analysis, Numerical continuation, Perception, 0501 psychology and cognitive sciences, Percept, Neuroscience, 030217 neurology & neurosurgery, media_common
Abstract: International audience; We studied the temporal dynamics of perceptual switches that are known to occur during prolonged presentations of a multi-stable visual motion stimulus using a neural fields, population-level representation of cortical activity in the middle temporal (MT) visual area. The so-called 'barber pole'' stimulus is considered with an aperture configuration that supports horizontal (H), diagonal (D) or vertical (V) perceived directions for the same input. It was established in previous modelling work and psychophysical experiments that, for short presentations, there is a shift in perceptual dominance from D to either H or V with increasing duration. The experiments described in the companion experimental abstract (I) show that for longer term presentations on the order of tens of seconds, the perceived direction remains multi-stable, with perception switching every few seconds between H and V. Here, we present an extension our previous motion integration model with the addition of a firing rate (spike frequency) adaptation dynamic that enables switching between the mutually inhibitory representations of H and V. A parameter study is performed using the tools of bifurcation analysis and numerical continuation that shows the model supports two different switching characteristics. In the bump oscillation case, with more weight given to the local input, switches between H and V occur at regular intervals with a very fast transition between the two states. In the travelling wave case, with more weight given to lateral connections, switches also occur at regular intervals but the transition is slower and a wave propagates from H to V (or vice-versa) via the diagonal percept D. Interestingly, the experimental results (I) also show a range of subject responses with respect to the switching characteristic involving D as an intermediate percept; this suggests variable dynamical interplay between intracortical connections in MT and the input received from lower cortical areas.
Published: 2012

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

Author: Bruno Cessac, Horacio Rostro-Gonzalez, Thierry Viéville, 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), Laboratoire Jean Alexandre Dieudonné (LJAD), Neuromimetic intelligence (CORTEX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Complex Systems, Artificial Intelligence & Robotics (LORIA - AIS), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), ANR-07-BLAN-0335,MAPS,Mappings, Adaptation, Plasticity and Spatial computation(2007), 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 Laboratoire Jean Alexandre Dieudonné (JAD)
Subjects: Theoretical computer science, Linear programming, Computer science, Generalization, Models, Neurological, Biomedical Engineering, Action Potentials, 02 engineering and technology, Spiking network, Random neural network, Membrane Potentials, Neurons dynamics, 03 medical and health sciences, Cellular and Molecular Neuroscience, Engineering, [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], 0302 clinical medicine, Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, Spike trains, Time complexity, Spiking neural network, Spike coding, Quantitative Biology::Neurons and Cognition, Artificial neural network, Estimation theory, neural networks, Electric Stimulation, Electrophysiology, Hebbian theory, Linear Models, 020201 artificial intelligence & image processing, Neural Networks, Computer, Algorithm, Algorithms, Software, 030217 neurology & neurosurgery
Abstract: International audience; This paper presents a reverse engineering approach for parameter estimation in spiking neural networks (SNNs). We consider the deterministic evolution of a time-discretized network with spiking neurons, where synaptic transmission has delays, modeled as a neural network of the generalized integrate and fire type. Our approach aims at by-passing the fact that the parameter estimation in SNN results in a non-deterministic polynomial-time hard problem when delays are to be considered. Here, this assumption has been reformulated as a linear programming (LP) problem in order to perform the solution in a polynomial time. Besides, the LP problem formulation makes the fact that the reverse engineering of a neural network can be performed from the observation of the spike times explicit. Furthermore, we point out how the LP adjustment mechanism is local to each neuron and has the same structure as a 'Hebbian' rule. Finally, we present a generalization of this approach to the design of input―output (I/O) transformations as a practical method to 'program' a spiking network, i.e. find a set of parameters allowing us to exactly reproduce the network output, given an input. Numerical verifications and illustrations are provided.
Published: 2012

28. Another look at the retina as an image dithered scalar quantizer

Author: Masmoudi, K., Antonini, M., Pierre Kornprobst, Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), 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), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia-Antipolis (I3S) / Equipe IMAGES-CREATIVE, Signal, Images et Systèmes (Laboratoire I3S - SIS), 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 Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), 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), 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), 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: Quantitative Biology::Neurons and Cognition, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Abstract: International audience; We explore, in this paper, the behavior of the mammalians retina considered as an analog-to-digital converter for the incoming light stimuli. This work extends our previous effort towards combining results in neurosciences with image processing techniques [1]. We base our study on a biologically realistic model that reproduces the neural code as generated by the retina. The neural code, that we consider here, consists of non-deterministic temporal sequences of uniformly shaped electrical impulses, also termed as spikes. We describe, starting from this spike-based code, a dynamic quantization scheme that relies on the so-called rate coding hypothesis. We, then, propose a possible decoding procedure. This yields an original quantizing/de-quantizing system which evolves dynamically from coarse to fine, and from uniform to non-uniform. Furthermore, we emit a possible interpretation for the non-determinism observed in the spike timings. In order to do this, we implement a three-staged processing system mapping the anatomical architecture of the retina. We, then, model the retinal noise by a dither signal which permits us to define the retina behavior as a non-subtractive dithered quantizer. The quantizing/de-quantizing system, that we propose, offers several interesting features as time scalability as well as reconstruction error whitening and de-correlation from the input stimuli.

29. Spike trains statistics in integrate and fire models: exact results

Author: Bruno Cessac, Hassan Roland Nasser, Juan Carlos Vasquez, 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: Quantitative Biology::Neurons and Cognition, Action selection, Neuron models, [SCCO.NEUR]Cognitive science/Neuroscience, FOS: Physical sciences, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], System dynamics, Adaptation and Self-Organizing Systems (nlin.AO), Nonlinear Sciences - Adaptation and Self-Organizing Systems
Abstract: We briefly review and highlight the consequences of rigorous and exact results obtained in \cite{cessac:10}, characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where neurons are subject to noise, without restriction on the synaptic weights connectivity. The main result is that spike trains statistics are characterized by a Gibbs distribution, whose potential is explicitly computable. This establishes, on one hand, a rigorous ground for the current investigations attempting to characterize real spike trains data with Gibbs distributions, such as the Ising-like distribution, using the maximal entropy principle. However, it transpires from the present analysis that the Ising model might be a rather weak approximation. Indeed, the Gibbs potential (the formal "Hamiltonian") is the log of the so-called "conditional intensity" (the probability that a neuron fires given the past of the whole network). But, in the present example, this probability has an infinite memory, and the corresponding process is non-Markovian (resp. the Gibbs potential has infinite range). Moreover, causality implies that the conditional intensity does not depend on the state of the neurons at the \textit{same time}, ruling out the Ising model as a candidate for an exact characterization of spike trains statistics. However, Markovian approximations can be proposed whose degree of approximation can be rigorously controlled. In this setting, Ising model appears as the "next step" after the Bernoulli model (independent neurons) since it introduces spatial pairwise correlations, but not time correlations. The range of validity of this approximation is discussed together with possible approaches allowing to introduce time correlations, with algorithmic extensions., Comment: 6 pages, submitted to conference NeuroComp2010 http://2010.neurocomp.fr/; Bruno Cessac http://www-sop.inria.fr/neuromathcomp/

30. Parameters estimation for spatio-temporal maximum entropy distributions: application to neural spike trains

Author: Hassan Roland Nasser, Bruno Cessac, 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: Quantitative Biology::Neurons and Cognition, [SCCO.NEUR]Cognitive science/Neuroscience
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 (Dudik et al 04 and Broderick et al 07) 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.

31. A new twist for the simulation of hybrid systems using the true jump method

Author: 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: FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: The use of stochastic models, in effect piecewise deterministic Markov processes (PDMP), has become increasingly popular especially for the modeling of chemical reactions and cell biophysics. Yet, exact simulation methods, for the simulation of these models in evolving environments, are limited by the need to find the next jumping time at each recursion of the algorithm. Here, we report on a new general method to find this jumping time for the True Jump Method. It is based on an expression in terms of ordinary differential equations for which efficient numerical methods are available. As such, our new result makes it possible to study numerically stochastic models for which analytical formulas are not available thereby providing a way to approximate the state distribution for example. We conclude that the wide use of event detection schemes for the simulation of PDMPs should be strongly reconsidered. The only relevant remaining question being the efficiency of our method compared to the Fictitious Jump Method, question which is strongly case dependent.

Catalog

Books, media, physical & digital resources

See catalog results

Searchworks

Select search scope, currently: Articles

Catalog

books, media & more in Jio Institute collections

Articles

journal articles & other e-resources

Refine your results

31 results on '"NEUROMATHCOMP"'

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

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

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

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

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

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

7. Toward a realistic input for visual cortex models

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

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

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

11. Heteroclinic cycles in Hopfield networks

12. Motility-induced phase separation of active particles in the presence of velocity alignment

13. Particle systems with a singular mean-field self-excitation. Application to neuronal networks

14. Interplay between synaptic delays and propagation delays in neural field equations

15. Modeling in Computational Biology and Biomedicine

16. Simple heteroclinic cycles in R^4

17. Multiscale analysis of slow-fast neuronal learning models with noise

18. Streaming an image through the eye: The retina seen as a dithered scalable image coder

19. Mean Field description of and propagation of chaos in recurrent multipopulation networks of Hodgkin-Huxley and Fitzhugh-Nagumo neurons

20. Hebbian learning of recurrent connections: a geometrical perspective

21. Finite-size and correlation-induced effects in mean-field dynamics

22. Evaluating motion estimation models from behavioural and psychophysical data

23. Parametric estimation of spike train statistics

24. A view of Neural Networks as dynamical systems

25. How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A model-based argumentation

26. Perceptual transition dynamics of a multi-stable visual motion stimulus II: modelling

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

28. Another look at the retina as an image dithered scalar quantizer

29. Spike trains statistics in integrate and fire models: exact results

30. Parameters estimation for spatio-temporal maximum entropy distributions: application to neural spike trains

31. A new twist for the simulation of hybrid systems using the true jump method

Catalog

Searchworks

Select search scope, currently: Articles Catalog books, media & more in Jio Institute collections Articles journal articles & other e-resources

Search

Search Constraints

Refine your results

Search Limiters

Topic

Publication Year Range

Journal

Database

Publisher

31 results on '"NEUROMATHCOMP"'

Search Results

Catalog

Select search scope, currently: Articles

Catalog

books, media & more in Jio Institute collections

Articles

journal articles & other e-resources