Project-Team Neuromathcomp
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Overall Objectives
Research Program
Software and Platforms
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Bibliography

Major publications by the team in recent years
  • 1J. Baladron Pezoa, D. Fasoli, O. Faugeras, J. Touboul.
    Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons, in: The Journal of Mathematical Neuroscience, 2012, vol. 2, no 1.
    http://www.mathematical-neuroscience.com/content/2/1/10
  • 2B. Cessac.
    A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics, in: J. Math. Biol., 2008, vol. 56, no 3, pp. 311-345.
    http://lanl.arxiv.org/abs/0706.0077
  • 3B. Cessac.
    A discrete time neural network model with spiking neurons II. Dynamics with noise., in: Journal of Mathematical Biology, 2011, vol. 62, no 6, pp. 863-900. [ DOI : 10.1007/s00285-010-0358-4 ]
    http://lanl.arxiv.org/pdf/1002.3275
  • 4B. Cessac, H. Rostro-Gonzalez, J.-C. Vasquez, T. Viéville.
    How Gibbs distribution may naturally arise from synaptic adaptation mechanisms: a model based argumentation, in: J. Stat. Phys., 2009, vol. 136, no 3, pp. 565-602. [ DOI : 10.1007/s10955-009-9786-1 ]
    http://lanl.arxiv.org/abs/0812.3899
  • 5P. Chossat, O. Faugeras.
    Hyperbolic planforms in relation to visual edges and textures perception, in: Plos Comput Biol, December 2009, vol. 5, no 12.
    http://dx.doi.org/doi:10.1371/journal.pcbi.1000625
  • 6O. Faugeras, F. Grimbert, J.-J. Slotine.
    Abolute stability and complete synchronization in a class of neural fields models, in: SIAM Journal of Applied Mathematics, September 2008, vol. 61, no 1, pp. 205–250.
  • 7O. Faugeras, J. Touboul, B. Cessac.
    A constructive mean field analysis of multi population neural networks with random synaptic weights and stochastic inputs, in: Frontiers in Computational Neuroscience, 2009, vol. 3, no 1. [ DOI : 10.3389/neuro.10.001.2010 ]
    http://arxiv.org/abs/0808.1113
  • 8E. Tlapale, G. S. Masson, P. Kornprobst.
    Modelling the dynamics of motion integration with a new luminance-gated diffusion mechanism, in: Vision Research, August 2010, vol. 50, no 17, pp. 1676–1692.
    http://dx.doi.org/10.1016/j.visres.2010.05.022
  • 9J. Touboul, O. Faugeras.
    A Markovian event-based framework for stochastic spiking neural networks, in: Journal of Computational Neuroscience, April 2011, vol. 30.
    http://www.springerlink.com/content/81736mn03j2221m7/fulltext.pdf
  • 10R. Veltz, O. Faugeras.
    Local/Global Analysis of the Stationary Solutions of Some Neural Field Equations, in: SIAM Journal on Applied Dynamical Systems, August 2010, vol. 9, no 3, pp. 954–998. [ DOI : 10.1137/090773611 ]
    http://arxiv.org/abs/0910.2247
  • 11R. Veltz.
    Nonlinear analysis methods in neural field models, Université Paris Est, 2011.
    ftp://ftp-sop.inria.fr/neuromathcomp/publications/phds/veltz-11.pdf
  • 12A. Wohrer, P. Kornprobst.
    Virtual Retina : A biological retina model and simulator, with contrast gain control, in: Journal of Computational Neuroscience, 2009, vol. 26, no 2, 219 p, DOI 10.1007/s10827-008-0108-4.
Publications of the year

Doctoral Dissertations and Habilitation Theses

  • 13J. Baladron Pezoa.
    Exploring the neural codes using parallel hardware, Université Nice Sophia Antipolis, June 2013.
    http://hal.inria.fr/tel-00847333
  • 14D. Fasoli.
    Traiter le cerveau avec les neurosciences : théorie de champ-moyen, effets de taille finie et capacité de codage des réseaux de neurones stochastiques, Université Nice Sophia Antipolis, September 2013.
    http://hal.inria.fr/tel-00850289

Articles in International Peer-Reviewed Journals

  • 15B. Cessac, R. Cofre.
    Spike train statistics and Gibbs distributions, in: Journal of Physiology - Paris, 2013, vol. 107, no 5, pp. 360-368.
    http://hal.inria.fr/hal-00850155
  • 16P. Chossat, G. Faye.
    Pattern Formation for the Swift-Hohenberg Equation on the Hyperbolic Plane, in: Journal of Dynamics and Differential Equations, 2013, pp. 1–47. [ DOI : 10.1007/s10884-013-9308-3 ]
    http://hal.inria.fr/hal-00845612
  • 17R. Cofré, B. Cessac.
    Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses, in: Chaos, Solitons and Fractals, 2013, vol. 50, pp. 13-31. [ DOI : 10.1016/j.chaos.2012.12.006 ]
    http://hal.inria.fr/hal-00846091
  • 18G. Faye, P. Chossat.
    A spatialized model of textures perception using structure tensor formalism, in: Networks and Heterogeneous Media, 2013.
    http://hal.inria.fr/hal-00807371
  • 19G. Faye, J. Rankin, P. Chossat.
    Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis, in: Journal of Mathematical Biology, 2013, vol. 66, no 6, pp. 1303-1338. [ DOI : 10.1007/s00285-012-0532-y ]
    http://hal.inria.fr/hal-00807366
  • 20H. Nasser, O. Marre, B. Cessac.
    Spatio-temporal spike train analysis for large scale networks using the maximum entropy principle and Monte Carlo method, in: Journal of Statistical Mechanics: Theory and Experiment, 2013, vol. 2013, no 03, 41 p. [ DOI : 10.1088/1742-5468/2013/03/P03006 ]
    http://hal.inria.fr/hal-00846160
  • 21J. Naudé, B. Cessac, H. Berry, B. Delord.
    Effects of Cellular Homeostatic Intrinsic Plasticity on Dynamical and Computational Properties of Biological Recurrent Neural Networks, in: Journal of Neuroscience, 2013, vol. 33, no 38, pp. 15032-15043. [ DOI : 10.1523/JNEUROSCI.0870-13.2013 ]
    http://hal.inria.fr/hal-00844218
  • 22J. Rankin, A. Meso, G. Masson, O. Faugeras, P. Kornprobst.
    Bifurcation Study of a Neural Fields Competition Model with an Application to Perceptual Switching in Motion Integration, in: Journal of Computational Neuroscience, 2013.
    http://hal.inria.fr/hal-00920528
  • 23J. Rankin, E. Tlapale, R. Veltz, O. Faugeras, P. Kornprobst.
    Bifurcation analysis applied to a model of motion integration with a multistable stimulus, in: Journal of Computational Neuroscience, 2013, vol. 34, no 1, pp. 103-124, 10.1007/s10827-012-0409-5. [ DOI : 10.1007/s10827-012-0409-5 ]
    http://hal.inria.fr/hal-00845593
  • 24R. Veltz, O. Faugeras.
    A Center Manifold Result for Delayed Neural Fields Equations, in: SIAM Journal on Mathematical Analysis, 2013, vol. 45, no 3, pp. 1527-1562. [ DOI : 10.1137/110856162 ]
    http://hal.inria.fr/hal-00850382
  • 25R. Veltz.
    Interplay Between Synaptic Delays and Propagation Delays in Neural Field Equations, in: SIAM Journal on Applied Dynamical Systems, 2013, vol. 12, no 3, pp. 1566-1612. [ DOI : 10.1137/120889253 ]
    http://hal.inria.fr/hal-00850391

Invited Conferences

  • 26B. Cessac.
    Spike trains analysis, Gibbs distributions and (Variable Length ?) Markov chains, in: VLMC days, 5-6 March 2013, Dijon, France, 2013.
    http://hal.inria.fr/hal-00845619

International Conferences with Proceedings

  • 27B. Cessac, R. Cofre.
    Can we hear the shape of a Maximum Entropy potential from a spike train?, in: Bernstein Conference, Tübingen, Germany, 2013.
    http://hal.inria.fr/hal-00851436
  • 28N. V. K. Medathati, J. Rankin, P. Kornprobst, G. S. Masson.
    A retinotopic neural fields model of perceptual switching in 2D motion integration, in: Bernstein Conference, Tubingen, Germany, 2013.
    http://hal.inria.fr/hal-00850097

Scientific Books (or Scientific Book chapters)

  • 29B. Cessac, A. Palacios.
    Spike Train Statistics from Empirical Facts to Theory: The Case of the Retina, in: Modeling in Computational Biology and Biomedicine: A Multidisciplinary Endeavor, F. Cazals, P. Kornprobst (editors), Springer, 2013.
    http://hal.inria.fr/hal-00640507

Books or Proceedings Editing

  • 30F. Cazals, P. Kornprobst (editors)
    Modeling in Computational Biology and Medicine: A Multidisciplinary Endeavor, Springer, 2013, 315 p. [ DOI : 10.1007/978-3-642-31208-3 ]
    http://hal.inria.fr/hal-00845616

Internal Reports

  • 31B. Cessac, R. Cofre.
    Estimating maximum entropy distributions from periodic orbits in spike trains, Inria, July 2013, no RR-8329.
    http://hal.inria.fr/hal-00842776
  • 32O. Faugeras, J. Inglis.
    Stochastic neural field equations: A rigorous footing, November 2013, 40 p.
    http://hal.inria.fr/hal-00907555
  • 33O. Faugeras, J. Maclaurin.
    A large deviation principle for networks of rate neurons with correlated synaptic weights, February 2013, 71 p.
    http://hal.inria.fr/hal-00785627
  • 34H. Nasser, B. Cessac.
    Parameters estimation for spatio-temporal maximum entropy distributions: application to neural spike trains, January 2014.
    http://hal.inria.fr/hal-00927080
  • 35J. Rankin, A. Meso, G. Masson, O. Faugeras, P. Kornprobst.
    Bifurcation Study of a Neural Fields Competition Model with an Application to Perceptual Switching in Motion Integration, Inria, February 2013, no RR-8220, 37 p.
    http://hal.inria.fr/hal-00783525
  • 36E. Teftef, M.-J. Escobar, A. Astudillo, C. Carvajal, B. Cessac, A. Palacios, T. Viéville, F. Alexandre.
    Modeling non-standard retinal in/out function using computer vision variational methods, Inria, January 2013, no RR-8217, 28 p.
    http://hal.inria.fr/hal-00783091
  • 37R. Veltz.
    Interplay between synaptic delays and propagation delays in neural fields equations, Inria, January 2013, no RR-8020, 53 p.
    http://hal.inria.fr/hal-00780444

Other Publications

  • 38P. Beltrame, P. Chossat.
    Onset of intermittent octahedral patterns in spherical Bénard convection, February 2014.
    http://hal.inria.fr/hal-00945597
  • 39B. Cessac, R. Cofre.
    Space-time correlations in spike trains and the neural code, in: Mathematics and neuroscience a dialogue, Utrecht, Netherlands, September 2013.
    http://hal.inria.fr/hal-00861405
  • 40R. Cofre, B. Cessac.
    Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses, in: Twenty Second Annual Computational Neuroscience Meeting : CNS 2013, Paris, France, July 2013, 58 p. [ DOI : 10.1186/1471-2202-14-S1-P58 ]
    http://hal.inria.fr/hal-00842297
  • 41R. Cofre, B. Cessac.
    Hearing the Maximum Entropy Potential of neuronal networks, January 2014.
    http://hal.inria.fr/hal-00861397
  • 42O. Faugeras, J. MacLaurin.
    A large deviation principle for networks of rate neurons with correlated synaptic weights, in: Twenty Second Annual Computational Neuroscience Meeting : CNS 2013, Paris, France, July 2013, 252 p. [ DOI : 10.1186/1471-2202-14-S1-P252 ]
    http://hal.inria.fr/hal-00842310
  • 43M. Muratori, B. Cessac.
    Beyond dynamical mean-field theory of neural networks, in: Twenty Second Annual Computational Neuroscience Meeting : CNS 2013, Paris, France, July 2013, 60 p. [ DOI : 10.1186/1471-2202-14-S1-P60 ]
    http://hal.inria.fr/hal-00842309
  • 44H. Nasser, S. Kraria, B. Cessac.
    EnaS: a new software for neural population analysis in large scale spiking networks, in: Twenty Second Annual Computational Neuroscience Meeting : CNS 2013, Paris, France, July 2013, 57 p. [ DOI : 10.1186/1471-2202-14-S1-P57 ]
    http://hal.inria.fr/hal-00842303
  • 45G. Portelli, J. M. Barrett, E. Sernagor, P. Kornprobst.
    Decoding the retina with the first wave of spikes, in: European Retina Meeting - 2013, Alicante, Spain, October 2013.
    http://hal.inria.fr/hal-00920543
  • 46J. Rankin, D. Avitabile, J. Baladron Pezoa, G. Faye, D. J. B. Lloyd.
    Continuation of localised coherent structures in nonlocal neural field equations, 2013, 21 p, submitted for peer review.
    http://hal.inria.fr/hal-00850408
  • 47W. Taouali, B. Cessac.
    A maximum likelihood estimator of neural network synaptic weights, in: Twenty Second Annual Computational Neuroscience Meeting : CNS 2013, Paris, France, July 2013, 59 p. [ DOI : 10.1186/1471-2202-14-S1-P59 ]
    http://hal.inria.fr/hal-00842312
References in notes
  • 48J. Bouecke, E. Tlapale, P. Kornprobst, H. Neumann.
    Neural Mechanisms of Motion Detection, Integration, and Segregation: From Biology to Artificial Image Processing Systems, in: EURASIP Journal on Advances in Signal Processing, 2011, vol. 2011, special issue on Biologically inspired signal processing: Analysis, algorithms, and applications. [ DOI : 10.1155/2011/781561 ]
    http://hal.inria.fr/hal-00784429
  • 49B. Cessac.
    A view of Neural Networks as dynamical systems, in: International Journal of Bifurcations and Chaos, 2010, vol. 20, no 6, pp. 1585-1629. [ DOI : 10.1142/S0218127410026721 ]
    http://lanl.arxiv.org/abs/0901.2203
  • 50B. Cessac.
    Statistics of spike trains in conductance-based neural networks: Rigorous results, in: The Journal of Mathematical Neuroscience, 2011, vol. 1, no 8, pp. 1-42. [ DOI : 10.1186/2190-8567-1-8 ]
    http://www.mathematical-neuroscience.com/content/1/1/8
  • 51B. Cessac, T. Viéville.
    On Dynamics of Integrate-and-Fire Neural Networks with Adaptive Conductances, in: Frontiers in neuroscience, July 2008, vol. 2, no 2.
    http://hal.inria.fr/inria-00338369
  • 52J. M. Cortes, M. Desroches, S. Rodrigues, R. Veltz, M. A. Muñoz, T. J. Sejnowski.
    Short-term synaptic plasticity in the deterministic Tsodyks-Markram model leads to unpredictable network dynamics, in: Proceedings of the National Academy of Sciences, 2013, vol. 110, no 41, pp. 16610–16615.
  • 53M.-J. Escobar, P. Kornprobst.
    Action recognition via bio-inspired features: The richness of center-surround interaction, in: Computer Vision and Image Understanding, 2012, vol. 116, no 5, 593—605 p.
    http://hal.inria.fr/hal-00849935
  • 54M.-J. Escobar, G. S. Masson, T. Viéville, P. Kornprobst.
    Action Recognition Using a Bio-Inspired Feedforward Spiking Network, in: International Journal of Computer Vision, 2009, vol. 82, no 3, 284 p.
    ftp://ftp-sop.inria.fr/neuromathcomp/publications/2009/escobar-masson-etal:09.pdf
  • 55G. Faye.
    Reduction method for studying localized solutions of neural field equations on the Poincaré disk, in: Comptes Rendus de l'Académie des Sciences, Mathématique, February 2012, vol. 350, no 3-4, pp. 161–166.
    http://www.sciencedirect.com/science/article/pii/S1631073X12000337
  • 56G. Faye, J. Rankin, D. J. B. Lloyd.
    Localized radial bumps of a neural field equation on the Euclidean plane and the Poincaré disk, in: Nonlinearity, April 2012.
  • 57M. Galtier, O. Faugeras, P. Bressloff.
    Hebbian Learning of Recurrent Connections: A Geometrical Perspective, in: Neural Computation, September 2012, vol. 24, no 9, pp. 2346–2383.
  • 58M. Galtier, G. Wainrib.
    Multiscale analysis of slow-fast neuronal learning models with noise, in: Journal of Mathematical Neuroscience, 2012, vol. 2, no 13.
    http://www.mathematical-neuroscience.com/content/2/1/13/abstract
  • 59J. Gautrais, S. Thorpe.
    Rate Coding vs Temporal Order Coding : a theorical approach, in: Biosystems, 1998, vol. 48, pp. 57–65.
  • 60T. Gollisch, M. Meister.
    Rapid Neural Coding in the Retina with Relative Spike Latencies, in: Science, 2008, vol. 319, pp. 1108–1111, DOI: 10.1126/science.1149639.
  • 61B. H. Jansen, V. G. Rit.
    Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns, in: Biological Cybernetics, 1995, vol. 73, pp. 357–366.
  • 62K. Masmoudi, M. Antonini, P. Kornprobst.
    Frames for Exact Inversion of the Rank Order Coder, in: IEEE Transactions on Neural Networks and Learning Systems, 2012, vol. 23, no 2, pp. 353–359.
    http://dx.doi.org/10.1109/TNNLS.2011.2179557
  • 63K. Masmoudi, M. Antonini, P. Kornprobst.
    Streaming an image through the eye: The retina seen as a dithered scalable image coder, in: Signal Processing-Image Communication, 2012.
    http://dx.doi.org/10.1016/j.image.2012.07.005
  • 64T. Masquelier.
    Relative spike time coding and STDP-based orientation selectivity in the early visual system in natural continuous and saccadic vision: a computational model, in: Journal of Computational Neuroscience, 2011.
    http://dx.doi.org/10.1007/s10827-011-0361-9
  • 65B. Siri, H. Berry, B. Cessac, B. Delord, M. Quoy.
    Effects of Hebbian learning on the dynamics and structure of random networks with inhibitory and excitatory neurons., in: Journal of Physiology-Paris, 2007.
  • 66B. Siri, H. Berry, B. Cessac, B. Delord, M. Quoy.
    A Mathematical Analysis of the Effects of Hebbian Learning Rules on the Dynamics and Structure of Discrete-Time Random Recurrent Neural Networks, in: Neural Computation, December 2008, vol. 20, no 12, 12 p.
  • 67E. Tlapale, P. Kornprobst, G. S. Masson, O. Faugeras.
    A Neural Field Model for Motion Estimation, in: Mathematical Image Processing, S. Verlag (editor), Springer Proceedings in Mathematics, 2011, vol. 5, pp. 159–180.
    http://dx.doi.org/10.1007/978-3-642-19604-1
  • 68E. Tlapale, G. S. Masson, P. Kornprobst.
    Modelling the dynamics of motion integration with a new luminance-gated diffusion mechanism, in: Vision Research, August 2010, vol. 50, no 17, pp. 1676–1692.
    http://dx.doi.org/10.1016/j.visres.2010.05.022
  • 69E. Tlapale.
    Modelling the dynamics of contextual motion integration in the primate, Université Nice Sophia Antipolis, January 2011.
    ftp://ftp-sop.inria.fr/neuromathcomp/publications/phds/tlapale-11.pdf
  • 70J. Touboul, F. Wendling, P. Chauvel, O. Faugeras.
    Neural Mass Activity, Bifurcations, and Epilepsy, in: Neural Computation, December 2011, vol. 23, no 12, pp. 3232–3286.
  • 71J.-C. Vasquez, A. Palacios, O. Marre, M. J. Berry, B. Cessac.
    Gibbs distribution analysis of temporal correlations structure in retina ganglion cells, in: J. Physiol. Paris, May 2012, vol. 106, no 3-4, pp. 120-127.
    http://arxiv.org/abs/1112.2464
  • 72A. Wohrer, P. Kornprobst.
    Virtual Retina : A biological retina model and simulator, with contrast gain control, in: Journal of Computational Neuroscience, 2009, vol. 26, no 2, 219 p, DOI 10.1007/s10827-008-0108-4.
  • 73A. Wohrer.
    Model and large-scale simulator of a biological retina with contrast gain control, University of Nice Sophia-Antipolis, 2008.

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