Project-Team Neuromathcomp
Members
Overall Objectives
Research Program
New Software and Platforms
New Results
Partnerships and Cooperations
Dissemination
Bibliography
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Bibliography

Major publications by the team in recent years
  • 1J. Baladron, D. Fasoli, O. Faugeras, J. Touboul.
    Mean-field description and propagation of chaos in networks of Hodgkin-Huxley 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 II. Dynamics with noise, in: J. Math. Biol., 2011, vol. 62, pp. 863-900.
  • 3P. Chossat, O. Faugeras.
    Hyperbolic planforms in relation to visual edges and textures perception, in: Plos Comput Biol, December 2009, vol. 5, no 12, e1000625.
    http://dx.doi.org/doi:10.1371/journal.pcbi.1000625
  • 4R. Cofre, 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, 2012, submitted.
    http://lanl.arxiv.org/abs/1212.3577
  • 5R. Cofre, B. Cessac.
    Exact computation of the Maximum Entropy Potential of spiking neural networksmodels, in: Physical Reviev E, 2014, vol. 89, no 052117, 13 p.
    https://hal.inria.fr/hal-01095599
  • 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
  • 8J. 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 ]
    https://hal.inria.fr/hal-00844218
  • 9E. 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
  • 10J. 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
  • 11R. 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
  • 12R. Veltz, O. Faugeras.
    A center manifold result for delayed neural fields equations, in: SIAM Journal on Applied Mathematics (under revision), July 2012, RR-8020.
    http://hal.inria.fr/hal-00719794
  • 13R. Veltz.
    Nonlinear analysis methods in neural field models, Université Paris Est, 2011.
    ftp://ftp-sop.inria.fr/neuromathcomp/publications/phds/veltz-11.pdf
  • 14A. 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

  • 15R. Cofre.
    Neuronal Networks, Spike Trains Statistics and Gibbs Distributions, Université de Nice Sophia Antipolis, November 2014.
    https://hal.inria.fr/tel-01095575
  • 16H. Nasser.
    Analysis of large scale spiking networks dynamics with spatio-temporal constraints : application to multi-electrodes acquisitions in the retina, Université Nice Sophia Antipolis, March 2014.
    https://tel.archives-ouvertes.fr/tel-00990744

Articles in International Peer-Reviewed Journals

  • 17J. Barré, R. Chétrite, M. Muratori, F. Peruani.
    Motility-Induced Phase Separation of Active Particles in the Presence of Velocity Alignment, in: Journal of Statistical Physics, 2014, 15 p. [ DOI : 10.1007/s10955-014-1008-9 ]
    https://hal.archives-ouvertes.fr/hal-01086368
  • 18R. Cofre, B. Cessac.
    Exact computation of the Maximum Entropy Potential of spiking neural networksmodels, in: Physical Reviev E, 2014, vol. 89, no 052117, 13 p.
    https://hal.inria.fr/hal-01095599
  • 19O. Faugeras, J. Inglis.
    Stochastic neural field equations: A rigorous footing, in: Journal of Mathematical Biology, July 2014, 40 p.
    https://hal.inria.fr/hal-00907555
  • 20O. Faugeras, J. Maclaurin.
    A Large Deviation Principle and an Expression of the Rate Function for a Discrete Stationary Gaussian Process, in: Entropy, 2014, 21 p. [ DOI : 10.3390/e16126722 ]
    https://hal.inria.fr/hal-01096758
  • 21O. Faugeras, J. Maclaurin.
    A representation of the relative entropy with respect to a diffusion process in terms of its infinitesimal-generator, in: Entropy, 2014, vol. 16, 17 p. [ DOI : 10.3390/e16126705 ]
    https://hal.inria.fr/hal-01096777
  • 22O. Faugeras, J. Maclaurin.
    Asymptotic description of stochastic neural networks. I. Existence of a large deviation principle, in: Comptes Rendus de l'Academie des Sciences. Serie 1, Mathematique, October 2014, vol. 352, pp. 841 - 846. [ DOI : 10.1016/j.crma.2014.08.018 ]
    https://hal.inria.fr/hal-01074827
  • 23O. Faugeras, J. Maclaurin.
    Asymptotic description of stochastic neural networks. II. Characterization of the limit law, in: Comptes Rendus de l'Academie des Sciences. Serie 1, Mathematique, October 2014, vol. 352, pp. 847 - 852. [ DOI : 10.1016/j.crma.2014.08.017 ]
    https://hal.inria.fr/hal-01074836
  • 24T. Masquelier, G. Portelli, P. Kornprobst.
    Microsaccades enable efficient synchrony-based visual feature learning and detection, in: BMC Neuroscience, 2014, vol. 15, no Suppl 1, P121.
    https://hal.inria.fr/hal-01026508
  • 25H. Nasser, B. Cessac.
    Parameter Estimation for Spatio-Temporal Maximum Entropy Distributions: Application to Neural Spike Trains, in: Entropy, April 2014, vol. 16, no 4, pp. 2244-2277. [ DOI : 10.3390/e16042244 ]
    https://hal.inria.fr/hal-01096213
  • 26G. Portelli, J. Barrett, E. Sernagor, T. Masquelier, P. Kornprobst.
    Rapid neural coding in the mouse retina with the first wave of spikes, in: BMC Neuroscience, 2014, vol. 15, no Suppl 1, P120.
    https://hal.inria.fr/hal-01026507

Invited Conferences

  • 27B. Cessac.
    De la rétine à la physique statistique, in: 4 ème journée de la physique niçoise, Sophia Antipolis, France, June 2014.
    https://hal.inria.fr/hal-01095605
  • 28B. Cessac.
    Neural Networks Dynamics, in: LACONEU 2014, Valparaiso, Chile, January 2014.
    https://hal.inria.fr/hal-01095600
  • 29B. Cessac.
    Spike train statistics: from mathematical models to software to experiments, in: 6th Workshop in Computational Neuroscience in Marseille, Marseille, France, March 2014.
    https://hal.inria.fr/hal-01095746
  • 30B. Cessac, R. Cofre.
    Statistical analysis of spike trains in neuronal networks, in: MATHSTATNEURO Workshop, Copenhague, Denmark, June 2014.
    https://hal.inria.fr/hal-01095606
  • 31J. Naudé, B. Cessac, H. Berry, B. Delord.
    Effects of Cellular Homeostatic Intrinsic Plasticity on Dynamical and Computational Properties of Biological Recurrent Neural Networks, in: LACONEU 2014, Valparaiso, Chile, January 2014, vol. 33. [ DOI : 10.1523/JNEUROSCI.0870-13.2013 ]
    https://hal.inria.fr/hal-01095601

Internal Reports

  • 32O. Faugeras, J. Maclaurin.
    Asymptotic description of neural networks with correlated synaptic weights, March 2014, no RR-8495, 47 p.
    https://hal.inria.fr/hal-00955770
  • 33H. Nasser, B. Cessac.
    Parameters estimation for spatio-temporal maximum entropy distributions: application to neural spike trains, January 2014.
    https://hal.inria.fr/hal-00927080
  • 34G. Portelli, J. Barrett, E. Sernagor, T. Masquelier, P. Kornprobst.
    The wave of first spikes provides robust spatial cues for retinal information processing, July 2014, no RR-8559.
    https://hal.inria.fr/hal-01019953
  • 35F. Solari, M. Chessa, K. Medathati, P. Kornprobst.
    What can we expect from a classical V1-MT feedforward architecture for optical flow estimation?, Inria Sophia Antipolis ; University of Genoa - DIBRIS, Italy, October 2014, no RR-8618, 22 p.
    https://hal.inria.fr/hal-01078117
  • 36R. Veltz, P. Chossat, O. Faugeras.
    On the effects on cortical spontaneous activity of the symmetries of the network of pinwheels in visual area V1, Inria Sophia Antipolis, 2014.
    https://hal.inria.fr/hal-01079055
  • 37R. Veltz, O. Faugeras.
    ERRATUM: A center manifold result for delayed neural fields equations, Inria Sophia Antipolis, 2014.
    https://hal.inria.fr/hal-01096598
  • 38R. Veltz, T. J. Sejnowski.
    Periodic forcing of stabilized E-I networks: Nonlinear resonance curves and dynamics, Inria Sophia Antipolis, 2014.
    https://hal.inria.fr/hal-01096590

Other Publications

References in notes
  • 51A. Alahi, R. Ortiz, P. Vandergheynst.
    Freak: Fast retina keypoint, in: CVPR, 2012, 510—517 p.
  • 52J. 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://asp.eurasipjournals.com/content/2011/1/781561
  • 53B. Cessac.
    A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics, in: J. Math. Biol., 2008, vol. 56, pp. 311-345.
  • 54B. 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
  • 55B. Cessac, R. Cofre.
    Spike train statistics and Gibbs distributions, in: Journal of Physiology - Paris, 2013, vol. 107, no 5, pp. 360-368.
    https://hal.inria.fr/hal-00850155
  • 56B. 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
  • 57B. Cessac, T. Viéville.
    On Dynamics of Integrate-and-Fire Neural Networks with Adaptive Conductances, in: Frontiers in neuroscience, July 2008, vol. 2, no 2.
    https://hal.inria.fr/inria-00338369
  • 58E. J. Chichilnisky.
    A simple white noise analysis of neuronal light responses, in: Network: Comput. Neural Syst., 2001, vol. 12, pp. 199–213.
  • 59R. Engbert, K. Mergenthaler, P. Sinn, A. Pikovsky.
    An integrated model of fixational eye movements and microsaccades, in: Proc Natl Acad Sci USA, 2011, vol. 108, pp. 765–770.
  • 60M.-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
  • 61M.-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
  • 62P. Foldiak.
    Stimulus optimization in primary visual cortex, in: Neurocomputing, 2001, vol. 38, pp. 1217–1222.
  • 63M. 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.
  • 64M. 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
  • 65M. Gilson, T. Masquelier, E. Hugues.
    STDP allows fast rate-modulated coding with Poisson-like spike trains, in: PLoS Comput Biol, 2011.
  • 66T. 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.
  • 67B. 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.
  • 68D. MacKay.
    Information-based objective functions for active data selection, in: Neural computation, 1992, vol. 4, no 4, pp. 590–604.
  • 69C. K. Machens.
    Adaptive sampling by information maximization, in: Physical Review Letters, 2002, vol. 88, no 22.
  • 70S. Martinez-Conde, J. Otero-Millan, S. L. Macknik.
    The impact of microsaccades on vision: towards a unified theory of saccadic function, in: Nature Reviews Neuroscience, February 2013, vol. 14, no 2, pp. 83–96.
  • 71K. 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
  • 72K. 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
  • 73T. Masquelier, R. Guyonneau, S. Thorpe.
    Competitive STDP-Based Spike Pattern Learning, in: Neural Comput, 2009, vol. 21, pp. 1259–1276.
  • 74T. 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
  • 75L. Paninski.
    Convergence properties of three spike-triggered analysis techniques, in: Network: Comput. Neural Syst., 2003, vol. 14, 437—464 p.
  • 76J. 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 ]
    https://hal.inria.fr/hal-00845593
  • 77B. 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.
  • 78B. 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.
  • 79E. 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
  • 80E. 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
  • 81J. 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.
  • 82R. 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 ]
    https://hal.inria.fr/hal-00850382
  • 83R. Veltz, O. Faugeras.
    A Center Manifold Result for Delayed Neural Fields Equations, in: SIAM Journal on Mathematical Analysis, 2013, vol. 45, no 3, pp. 1527-562.
  • 84A. 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.
  • 85A. Wohrer.
    Model and large-scale simulator of a biological retina with contrast gain control, University of Nice Sophia-Antipolis, 2008.

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