Bibliography

• 1G. Aubert, P. Kornprobst.
  
  Mathematical problems in image processing: partial differential equations and the calculus of variations (Second edition), Applied Mathematical Sciences, Springer-Verlag, 2006, vol. 147.
• 2B. Cessac.
  
  A discrete time neural network model with spiking neurons. Rigorous results on the spontaneous dynamics, in: J. Math. Biol., 2008, vol. 56, n^o 3, p. 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, n^o 6, p. 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, n^o 3, p. 565-602. [ DOI : 10.1007/s10955-009-9786-1 ]
  
  http://lanl.arxiv.org/abs/0812.3899
• 5E. 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, n^o 17, p. 1676–1692.
  
  http://dx.doi.org/10.1016/j.visres.2010.05.022
• 6A. Wohrer, P. Kornprobst.
  
  Virtual Retina : A biological retina model and simulator, with contrast gain control, in: Journal of Computational Neuroscience, 2009, vol. 26, n^o 2, 219 p, DOI 10.1007/s10827-008-0108-4.

Doctoral Dissertations and Habilitation Theses

• 7G. Faye.
  
  Symmetry breaking and pattern formation in some neural field equations, EDSFA, 2012.
• 8G. Hermann.
  
  Some mean field equations in neuroscience, Ecole Polytechnique, January 2012.
  
  ftp://ftp-sop.inria.fr/neuromathcomp/publications/phds/hermann:12.pdf
• 9K. Masmoudi.
  
  Retina-inspired image coding schemes, Université de Nice Sophia Antipolis, 2012.

Articles in International Peer-Reviewed Journals

• 10J. Baladron, D. Fasoli, O. Faugeras.
  
  Three applications of GPU computing in neuroscience, in: Computing in Science and Engineering, 2012.
• 11J. 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, n^o 1.
  
  http://www.mathematical-neuroscience.com/content/2/1/10
• 12B. Cessac, R. Cofré.
  
  Spike train statistics and Gibbs distributions, in: J. Physiol. Paris, 2012, submitted.
• 13R. 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, 2012, submitted.
• 14M.-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, n^o 5, 593—605 p.
  
  http://dx.doi.org/10.1016/j.cviu.2012.01.002
• 15G. 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, n^o 3-4, p. 161–166.
  
  http://www.sciencedirect.com/science/article/pii/S1631073X12000337
• 16G. 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, 2012.
• 17G. 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, 2012, vol. (accepted).
• 18M. Galtier, O. Faugeras, P. Bressloff.
  
  Hebbian Learning of Recurrent Connections: A Geometrical Perspective, in: Neural Computation, September 2012, vol. 24, n^o 9, p. 2346–2383.
• 19M. Galtier, G. Wainrib.
  
  Multiscale analysis of slow-fast neuronal learning models with noise, in: Journal of Mathematical Neuroscience, 2012.
• 20K. 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, n^o 2, p. 353–359.
  
  http://dx.doi.org/10.1109/TNNLS.2011.2179557
• 21K. 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
• 22H. Nasser, O. Marre, B. Cessac.
  
  Spike trains analysis using Gibbs distributions and Monte-Carlo method, in: Journal of Statistical Mechanics, 2012, to appear.
  
  http://lanl.arxiv.org/abs/1209.3886
• 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, 2012, p. 1-22, 10.1007/s10827-012-0409-5.
  
  http://dx.doi.org/10.1007/s10827-012-0409-5
• 24H. Rostro-Gonzalez, B. Cessac, T. Viéville.
  
  Parameters estimation in spiking neural networks: a reverse-engineering approach, in: J. Neural. Eng., 2012, vol. 9, n^o 026024. [ DOI : 10.1088/1741-2560/9/2/026024 ]
  
  http://iopscience.iop.org/1741-2552/9/2/026024/
• 25J. Touboul, G. Hermann, O. Faugeras.
  
  Noise-induced behaviors in neural mean field dynamics, in: SIAM Journal on Applied dynamical Systems, 2012, vol. 11, n^o 1, p. 49–81.
  
  ftp://ftp-sop.inria.fr/neuromathcomp/publications/2012/touboul-hermann-etal:12.pdf
• 26J.-C. Vasquez, A. Palacios, O. Marre, M. J. Berry II, B. Cessac.
  
  Gibbs distribution analysis of temporal correlation structure on multicell spike trains from retina ganglion cells, in: J. Physiol. Paris, May 2012, vol. 106, n^o 3-4, p. 120-127.
  
  http://arxiv.org/abs/1112.2464
• 27R. Veltz, O. Faugeras.
  
  A center manifold result for delayed neural fields equations, in: SIAM Journal on Applied Mathematics, July 2012, under revision.
  
  http://hal.inria.fr/hal-00719794

Invited Conferences

• 28B. Cessac.
  
  Gibbs distributions and statistics of action potentials in neural networks., in: CHAOS, COMPLEXITY and DYNAMICS in BIOLOGICAL NETWORKS, Cargèse May 2012, 2012.
• 29B. Cessac.
  
  Lecture on spike train statistics: beyond the maximal entropy models, in: Neural Coding and Natural Image Statistics 9-13 January 2012, Valparaiso, Chile, 2012.
• 30B. Cessac.
  
  Spike train statistics in neural network: exact results, in: Neural Coding and Natural Image Statistics 9-13 January 2012, Valparaiso, Chile, 2012.
• 31B. Cessac.
  
  Spike trains statistics and Gibbs distributions, in: Probabilistic structures of the brain, Cergy, December 13-14, 2012, 2012.
• 32O. Faugeras.
  
  Neural fields in Action: Mathematical Results and Models of Visual Perception., in: Workshop on "Cognitive Dynamics in Neural Systems: Mathematical and Computational Modeling", March 2012.
• 33O. Faugeras.
  
  Neural fields in action: mathematical results and models of visual perception, in: Progress in Neural Field Theory 2012, April 2012.
• 34O. Faugeras.
  
  Neural fields models of visual areas: principles, successes, and caveats, in: Workshop on Biological and Computer Vision Interfaces, October 2012.
  
  http://www-sop.inria.fr/manifestations/wbcvi2012/program.shtml
• 35O. Faugeras.
  
  Some of the upcoming challenges in computational and mathematical neuroscience, in: IC Colloquium, EPFL, November 2012.
• 36J.-M. Gambaudo, B. Cessac.
  
  Multi-scale analysis of neuronal dynamical systems: the legacy of Poincaré, in: The NeuroComp/KEOpS’12 workshop, "Beyond the retina: from computational models to outcomes in bioengineering. Focus on architecture and dynamics sustaining information flows in the visuomotor system.", Bordeaux, October 10-11 2012., 2012.

International Conferences with Proceedings

• 37K. Masmoudi, M. Antonini, P. Kornprobst.
  
  A perfectly invertible rank order coder, in: International Joint Conference on Biomedical Engineering Systems and Technologies (Biosignals), 2012.
• 38A. Meso, J. Rankin, O. Faugeras, P. Kornprobst, G. S. Masson.
  
  Motion direction integration following the onset of multistable stimuli (I): dynamic shifts in both perception and eye movements depend on signal strength, in: European Conference on Visual Perception, 2012.
• 39A. Meso, J. Rankin, P. Kornprobst, O. Faugeras, G. S. Masson.
  
  Perceptual transition dynamics of a multi-stable visual motion stimulus I: experiments, in: Vision Sciences Society 12th Annual Meeting, 2012.
• 40G. Portelli, O. Marre, M. J. Berry II, M. Antonini, P. Kornprobst.
  
  Rate and latency coding for natural image identification, in: Sensory Coding and Natural Environment 2012, 2012.
• 41J. Rankin, A. Meso, G. S. Masson, O. Faugeras, P. Kornprobst.
  
  Motion direction integration following the onset of multistable stimuli (II): stability properties explain dynamic shifts in the dominant perceived direction, in: European Conference on Visual Perception, September 2012.
• 42J. Rankin, A. Meso, G. S. Masson, O. Faugeras, P. Kornprobst.
  
  Perceptual transition dynamics of a multi-stable visual motion stimulus II: modelling, in: Vision Sciences Society 12th Annual Meeting, 2012.
  
  ftp://ftp-sop.inria.fr/neuromathcomp/publications/2012/rankin-meso-etal:12.pdf

Conferences without Proceedings

• 43B. Cessac, R. Cofré, H. Nasser.
  
  On the ubiquity of Gibbs distributions in spike train statistics, in: 3rd annual meeting of the GDR 2904 "Multi-electroides systems and signal processing to study neural networks", Marseille, October 2012.
• 44B. Cessac, R. Salas, T. Viéville.
  
  Using event-based metric for event-based neural network weight adjustment, in: ESANN12-82, 2012.
• 45R. Cofré, B. Cessac.
  
  Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses, in: AREADNE 2012. Santorini, Greece, July, 2012. Encoding And Decoding of Neural Ensembles, 2012.
• 46R. Cofré, B. Cessac.
  
  Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses, in: SCNE 2012. Wien, Austria, September 2012. Sensory Coding and Natural Environment., 2012.
• 47R. Cofré, B. Cessac.
  
  Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses, in: NEUROCOMP 2012. Bordeaux, France, October, 2012. The NeuroComp/KEOpS 12 workshop, 2012.
• 48R. Cofré, B. Cessac.
  
  Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses, in: GDR MEA 2012. Marseille, France, October, 2012. Encoding And Decoding of Neural Ensembles, 2012.
• 49O. Faugeras.
  
  Biological and Computer Visual Perception, in: Computer Vision and Video Analysis: An international workshop in honor of Prof. Shmuel Peleg, October 2012.
• 50O. Faugeras.
  
  Mean-field methods for networks of rate and spiking neurons, in: Edmond and Lily Safra Center for Brain Sciences seminar, The Hebrew University of Jerusalem, October 2012.
• 51H. Nasser, O. Marre, B. Cessac.
  
  Analyzing large-scale spike trains data with spatio-temporal constraints, in: SCNE 2012. Wien, Austria, September 2012. Sensory Coding and Natural Environment., September 2012.
• 52H. Nasser, O. Marre, B. Cessac.
  
  Analyzing large-scale spike trains data with spatio-temporal constraints, in: NEUROCOMP 2012. Bordeaux, France, October, 2012. The NeuroComp/KEOpS 12 workshop, September 2012.
• 53H. Nasser, O. Marre, B. Cessac.
  
  Spatio-Temporal modeling of large-scale retinal networks using Montecarlo principle, in: Inauguration INT. Marseille, France, Septembre, 2012., September 2012.
• 54H. Nasser, O. Marre, M. J. Berry II, B. Cessac.
  
  Spatio temporal Gibbs distribution analysis of spike trains using Monte Carlo method, in: AREADNE 2012 Research in Encoding And Decoding of Neural Ensembles, 2012.

Scientific Books (or Scientific Book chapters)

• 55B. 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), Lectures Notes in Mathematical and Computational Biology (LNMCB), Springer-Verlag, 2012.

Books or Proceedings Editing

• 56F. Cazals, P. Kornprobst (editors)
  
  Modeling in Computational Biology and Medicine: A Multidisciplinary Endeavor, Springer, 2012, To appear in 2013.

Internal Reports

• 57G. Faye, J. Rankin, P. Chossat.
  
  Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis, Inria Research Report, 2012, n^o RR-7872.
• 58K. Masmoudi, M. Antonini, P. Kornprobst.
  
  Streaming an image through the eye: The retina seen as a dithered scalable image coder, Inria, February 2012, n^o 7877.
  
  http://hal.inria.fr/hal-00668076
• 59A. Rao, A. Legout, B. Cessac, W. Dabbous.
  
  Floor the Ceil and Ceil the Floor: Revisiting AIMD Evaluation, Inria, September 2012.
  
  http://hal.inria.fr/hal-00733890

Other Publications

• 60O. Faugeras, J. Maclaurin.
  
  Mean-field equations for networks of rate neurons with correlated synaptic weights, 2012, Soon to appear on ArXiV.
• 61G. Faye, P. Chossat.
  
  A spatialized model of textures perception using structure tensor formalism, 2012, 49 p, Submitted.

• 62J. 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/
• 63B. Cessac.
  
  Statistics of spike trains in conductance-based neural networks: Rigorous results, in: The Journal of Mathematical Neuroscience, 2011, vol. 1, n^o 8, p. 1-42. [ DOI : 10.1186/2190-8567-1-8 ]
  
  http://www.mathematical-neuroscience.com/content/1/1/8
• 64B. Cessac, T. Viéville.
  
  On Dynamics of Integrate-and-Fire Neural Networks with Adaptive Conductances, in: Frontiers in neuroscience, July 2008, vol. 2, n^o 2.
  
  http://www.frontiersin.org/computational_neuroscience/10.3389/neuro.10/002.2008/abstract
• 65R. 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, 2012, submitted.
• 66M.-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, n^o 3, 284 p.
  
  ftp://ftp-sop.inria.fr/neuromathcomp/publications/2009/escobar-masson-etal:09.pdf
• 67T. Gollisch, M. Meister.
  
  Rapid Neural Coding in the Retina with Relative Spike Latencies, in: Science, 2008, vol. 319, p. 1108–1111, DOI: 10.1126/science.1149639.
• 68K. Masmoudi, M. Antonini, P. Kornprobst.
  
  Another look at the retina as an image scalar quantizer, in: Proceedings of the International Symposium on Circuits and Systems (ISCAS), 2010.
  
  ftp://ftp-sop.inria.fr/neuromathcomp/publications/2010/masmoudi-antonini-etal:10c.pdf
• 69K. Masmoudi, M. Antonini, P. Kornprobst, L. Perrinet.
  
  A novel bio-inspired static image compression scheme for noisy data transmission over low-bandwidth channels, in: Proceedings of the 35th International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2010.
  
  ftp://ftp-sop.inria.fr/neuromathcomp/publications/2010/masmoudi-antonini-etal:10.pdf
• 70T. 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
• 71A. Oliva, A. Torralba.
  
  Modeling the shape of the scene: A holistic representation of the spatial envelope, in: International Journal of Computer Vision, 2001, vol. 42, p. 145–175.
  
  http://dx.doi.org/10.1023/A:1011139631724
• 72G. Schwartz, J. Macke, D. Amodei, H. Tang, M. Berry II.
  
  Low error discrimination using a correlated population code, in: Journal of neurophysiology, August 2012, vol. 108, n^o 4, p. 1069–1088.
• 73B. 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.
• 74B. 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, n^o 12, 12 p.
• 75E. 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, p. 159–180.
  
  http://dx.doi.org/10.1007/978-3-642-19604-1
• 76E. Tlapale.
  
  Modelling the dynamics of contextual motion integration in the primate, Université Nice Sophia Antipolis, January 2011.
• 77J. Touboul, F. Wendling, P. Chauvel, O. Faugeras.
  
  Neural Mass Activity, Bifurcations, and Epilepsy, in: Neural Computation, December 2011, vol. 23, n^o 12, p. 3232–3286.
• 78A. Wohrer, P. Kornprobst.
  
  Virtual Retina : A biological retina model and simulator, with contrast gain control, in: Journal of Computational Neuroscience, 2009, vol. 26, n^o 2, 219 p, DOI 10.1007/s10827-008-0108-4.
• 79A. Wohrer.
  
  Model and large-scale simulator of a biological retina with contrast gain control, University of Nice Sophia-Antipolis, 2008.