Overall Objectives
Research Program
Highlights of the Year
New Software and Platforms
New Results
Partnerships and Cooperations
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Major publications by the team in recent years
J. 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.
B. Cessac.
A discrete time neural network model with spiking neurons II. Dynamics with noise, in: J. Math. Biol., 2011, vol. 62, pp. 863-900.
P. Chossat, O. Faugeras.
Hyperbolic planforms in relation to visual edges and textures perception, in: Plos Comput Biol, December 2009, vol. 5, no 12, e1000625.
R. 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.
R. Cofre, B. Cessac.
Exact computation of the Maximum Entropy Potential of spiking neural networks models, in: Physical Reviev E, 2014, vol. 89, no 052117, 13 p.
O. 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.
O. 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 ]
J. 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 ]
E. 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.
J. Touboul, O. Faugeras.
A Markovian event-based framework for stochastic spiking neural networks, in: Journal of Computational Neuroscience, April 2011, vol. 30.
R. 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 ]
R. Veltz, O. Faugeras.
A center manifold result for delayed neural fields equations, in: SIAM Journal on Applied Mathematics (under revision), July 2012, RR-8020.
R. Veltz.
Nonlinear analysis methods in neural field models, Université Paris Est, 2011.
A. 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

M. Desroches.
Complex oscillations with multiple timescales - Application to neuronal dynamics , Universite Pierre et Marie Curie, December 2015, Habilitation à diriger des recherches.

Articles in International Peer-Reviewed Journals

P. Beltrame, P. Chossat.
Onset of intermittent octahedral patterns in spherical Bénard convection, in: European Journal of Mechanics - B/Fluids, April 2015, no 50, pp. 156-174. [ DOI : 10.1016/j.euromechflu.2014.11.014 ]
E. Benoît, M. Brøns, M. Desroches, M. Krupa.
Extending the zero-derivative principle for slow–fast dynamical systems, in: Zeitschrift für Angewandte Mathematik und Physik (ZAMP), July 2015. [ DOI : 10.1007/s00033-015-0552-8 ]
M. Bossy, O. Faugeras, D. Talay.
Clarification and Complement to " Mean-Field Description and Propagation of Chaos in Networks of Hodgkin–Huxley and FitzHugh–Nagumo Neurons ", in: Journal of Mathematical Neuroscience, 2015, vol. 5, no 1, 19 p. [ DOI : 10.1186/s13408-015-0031-8 ]
J. Burke, M. Desroches, A. Granados, T. J. Kaper, M. Krupa, T. Vo.
From Canards of Folded Singularities to Torus Canards in a Forced van der Pol Equation, in: Journal of Nonlinear Science, November 2015. [ DOI : 10.1007%2Fs00332-015-9279-0 ]
P. Chossat, M. Krupa.
Heteroclinic cycles in Hopfield networks, in: Journal of Nonlinear Science, January 2016. [ DOI : 10.1007/s00332-015-9276-3 ]
F. Delarue, J. Inglis, S. Rubenthaler, E. Tanré.
Particle systems with a singular mean-field self-excitation. Application to neuronal networks, in: Stochastic Processes and Applications, 2015, vol. 125, pp. 2451–2492. [ DOI : 10.1016/ ]
D. Fasoli, O. Faugeras, S. Panzeri.
A Formalism for Evaluating Analytically the Cross-Correlation Structure of a Firing-Rate Network Model, in: journal of mathematical neurosciences, March 2015. [ DOI : 10.1186/s13408-015-0020-y ]
O. Faugeras, J. Maclaurin.
Asymptotic description of neural networks with correlated synaptic weights, in: Entropy, July 2015, vol. 17(7), 4701-4743, no 7, pp. 4701-4743.
S. Fernández-García, M. Desroches, M. Krupa, A. Teruel.
Canard solutions in planar piecewise linear systems with three zones, in: Dynamical Systems, September 2015. [ DOI : 10.1080/14689367.2015.1079304 ]
O. Podvigina, P. Chossat.
Simple heteroclinic cycles in R4, in: Nonlinearity, 2015, vol. 28, no 4, pp. 901-926. [ DOI : 10.1088/0951-7715/28/4/901 ]
F. Solari, M. Chessa, N. V. K. Medathati, P. Kornprobst.
What can we expect from a V1-MT feedforward architecture for optical flow estimation?, in: Signal Processing: Image Communication, 2015. [ DOI : 10.1016/j.image.2015.04.006 ]
R. Veltz, P. Chossat, O. Faugeras.
On the effects on cortical spontaneous activity of the symmetries of the network of pinwheels in visual area V1, in: Journal of Mathematical Neuroscience, May 2015. [ DOI : 10.1186/s13408-015-0023-8 ]
R. Veltz, O. Faugeras.
ERRATUM: A Center Manifold Result for Delayed Neural Fields Equations, in: SIAM Journal on Mathematical Analysis, 2015. [ DOI : 10.1137/140962279 ]
R. Veltz, T. J. Sejnowski.
Periodic Forcing of Inhibition-Stabilized Networks: Nonlinear Resonances and Phase-Amplitude Coupling, in: Neural Computation, December 2015, vol. 27, no 12. [ DOI : 10.1162/NECO_a_00786 ]

Invited Conferences

B. Cessac.
Confronting mean-field theories to measurements a perspective from neuroscience, in: Confronting mean-field theories to measurements a perspective from neuroscience, Paris, France, January 2015.
B. Cessac.
Mean Field Methods in Neuroscience, in: Dynamics of Multi-Level Systems, Dresde, Germany, June 2015.
B. Cessac.
Mean Field TheoriesNeuroscience, in: QFT methods in stochastic nonlinear dynamics, Bielefeld, Germany, March 2015.
B. Cessac.
Statistical models for spike trains analysis in the retina, in: 12eme Colloque de la société des neurosciences, Montpellier, France, May 2015.
B. Cessac, J. Naudé, H. Berry, B. Delord.
Control of recurrent neural network dynamics byhomeostatic intrinsic plasticity, in: Workshop on neural population dynamics, Gif sur Yvette, France, February 2015.
T. Karvouniari, L. Gil, B. Cessac.
Biophysical reaction-diffusion model for stage II retinal waves and bifurcations analysis, in: MathStatNeuro workshop, Nice, France, September 2015.

Conferences without Proceedings

B. Cessac.
Statistical analysis of spike trains in neuronal networks, in: Neuroscience and modellint, Paris, France, December 2015.
M. Chessa, N. V. K. Medathati, G. S. Masson, F. Solari, P. Kornprobst.
Decoding MT Motion Response For Optical Flow Estimation : An Experimental Evaluation, in: 23rd European Signal Processing Conference (EUSIPCO), Nice, France, August 2015.
R. Cofre, B. Cessac.
Spatio-Temporal Linear Response of Spiking Neuronal Network Models, in: ISCLANE 15, Barcelone, Spain, September 2015.
C. Hilario Gomez, N. V. K. Medathati, P. Kornprobst, V. Murino, D. Sona.
Improving FREAK Descriptor for Image Classification, in: The 10th International Conference on Computer Vision Systems (ICVS 2015), Nice, France, July 2015.

Internal Reports

N. V. K. Medathati, M. Chessa, G. S. Masson, P. Kornprobst, F. Solari.
Adaptive Motion Pooling and Diffusion for Optical Flow, Inria Sophia-Antipolis ; University of Genoa ; INT la Timone, March 2015, no RR-8695, 19 p.
N. V. K. Medathati, M. Chessa, G. S. Masson, P. Kornprobst, F. Solari.
Decoding MT Motion Response for Optical Flow Estimation: An Experimental Evaluation, Inria Sophia-Antipolis, France ; University of Genoa, Genoa, Italy ; INT la Timone, Marseille, France ; Inria, March 2015, no RR-8696, Published in the 23rd European Signal Processing Conference (EUSIPCO).
N. V. K. Medathati, H. Neumann, G. S. Masson, P. Kornprobst.
Bio-Inspired Computer Vision: Setting the Basis for a New Departure, Inria Sophia Antipolis, France ; Institut de Neurosciences de la Timone, Marseille, France ; University of Ulm, Germany ; Inria, March 2015, no RR-8698, 57 p.

Other Publications

D. Avitabile, M. Desroches, E. Knobloch, M. Krupa.
Ducks in space, November 2015, submitted for publication.
P. Bressloff, O. Faugeras.
On the Hamiltonian structure of large deviations in stochastic hybrid systems, September 2015, working paper or preprint.
M. Desroches, S. Fernández-García, M. Krupa.
Canards and spike-adding transitions in a minimal piecewise-linear Hindmarsh-Rose square-wave burster, December 2015, submitted for publication.
M. Desroches, A. Guillamon, E. Ponce, R. Prohens, S. Rodrigues, A. Teruel.
Canards, folded nodes and mixed-mode oscillations in piecewise-linear slow-fast systems, March 2015, accepted for publication in SIAM Review on 13 August 2015.
M. Desroches, M. Krupa, S. Rodrigues.
Spike-adding mechanism in parabolic bursters: the role of folded-saddle canards, December 2015, submitted for publication.
G. Hilgen, S. Softley, D. Pamplona, P. Kornprobst, B. Cessac, E. Sernagor.
The effect of retinal GABA Depletion by Allylglycineon mouse retinal ganglion cell responses to light, October 2015, European Retina Meeting, Poster.
J. Inglis, J. Maclaurin.
A general framework for stochastic traveling waves and patterns, with application to neural field equations, June 2015, 43 pages, 3 figures.
J. Inglis, D. Talay.
Mean-field limit of a stochastic particle system smoothly interacting through threshold hitting-times and applications to neural networks with dendritic component, September 2015, working paper or preprint.
T. Karvouniari, L. Gil, O. Marre, S. Picaud, B. Cessac.
Biophysical modelling of the intrinsic mechanisms of the autonomous starbust cells during stage II retinal waves, January 2016, Modelling the early visual system - Workshop, Poster.
D. Pamplona, B. Cessac, P. Kornprobst.
Shifting stimulus for faster receptive fields estimation of ensembles of neurons, March 2015, Computational and Systems Neuroscience (Cosyne), Poster.
D. Pamplona, G. Hilgen, S. Pirmoradian, M. H. Hennig, B. Cessac, E. Sernagor, P. Kornprobst.
A super-resolution approach for receptive fields estimation of neuronal ensembles, July 2015, Computational Neuroscience (CNS), Poster.
C. Ravello, R. Herzog, B. Cessac, M.-J. Escobar, A. Palacios.
Spectral dimension reduction on parametric models for spike train statistics, May 2015, 12e Colloque de la Société des Neurosciences , Poster.
R. Veltz.
A new twist for the simulation of hybrid systems using the true jump method, December 2015, working paper or preprint.
References in notes
G. Basalyga, M. A. Montemurro, T. Wennekers.
Information coding in a laminar computational model of cat primary visual cortex, in: J. Comput. Neurosci., 2013, vol. 34, pp. 273–83.
J. 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 ]
B. 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.
B. 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 ]
B. Cessac, R. Cofre.
Spike train statistics and Gibbs distributions, in: Journal of Physiology - Paris, 2013, vol. 107, no 5, pp. 360-368.
B. 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 ]
B. Cessac, T. Viéville.
On Dynamics of Integrate-and-Fire Neural Networks with Adaptive Conductances, in: Frontiers in neuroscience, July 2008, vol. 2, no 2.
E. J. Chichilnisky.
A simple white noise analysis of neuronal light responses, in: Network: Comput. Neural Syst., 2001, vol. 12, pp. 199–213.
M. O. Cunningham, M. A. Whittington, A. Bibbig, A. Roopun, F. E. LeBeau, A. Vogt, H. Monyer, E. H. Buhl, R. D. Traub.
A role for fast rhythmic bursting neurons in cortical gamma oscillations in vitro, in: Proceedings of the National Academy of Sciences of the United States of America, 2004, vol. 101, no 18, pp. 7152–7157.
M. Desroches, J. Guckenheimer, B. Krauskopf, C. Kuehn, H. M. Osinga, M. Wechselberger.
Mixed-mode oscillations with multiple time scales, in: SIAM Review, 2012, vol. 54, no 2, pp. 211–288.
M. Desroches, T. J. Kaper, M. Krupa.
Mixed-Mode Bursting Oscillations: Dynamics created by a slow passage through spike-adding canard explosion in a square-wave burster, in: Chaos, October 2013, vol. 23, no 4, 046106. [ DOI : 10.1063/1.4827026 ]
M. Desroches, B. Krauskopf, H. M. Osinga.
The geometry of slow manifolds near a folded node, in: SIAM Journal on Applied Dynamical Systems, 2008, vol. 7, no 4, pp. 1131–1162.
M.-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.
M.-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, pp. 284-301.
P. Foldiak.
Stimulus optimization in primary visual cortex, in: Neurocomputing, 2001, vol. 38, pp. 1217–1222.
M. 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.
M. Galtier, G. Wainrib.
Multiscale analysis of slow-fast neuronal learning models with noise, in: Journal of Mathematical Neuroscience, 2012, vol. 2, no 13.
E. M. Izhikevich.
Neural excitability, spiking and bursting, in: International Journal of Bifurcation and Chaos, 2000, vol. 10, no 06, pp. 1171–1266.
B. 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.
M. Krupa, N. Popović, N. Kopel, H. G. Rotstein.
Mixed-mode oscillations in a three time-scale model for the dopaminergic neuron, in: Chaos: An Interdisciplinary Journal of Nonlinear Science, 2008, vol. 18, no 1, 015106 p.
M. Krupa, P. Szmolyan.
Relaxation oscillation and canard explosion, in: Journal of Differential Equations, 2001, vol. 174, no 2, pp. 312–368.
D. MacKay.
Information-based objective functions for active data selection, in: Neural computation, 1992, vol. 4, no 4, pp. 590–604.
C. K. Machens.
Adaptive sampling by information maximization, in: Physical Review Letters, 2002, vol. 88, no 22.
K. 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.
K. 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.
K. 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.
T. 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, 2012, vol. 32, no 3, pp. 425–441.
A. Mohemmed, G. Lu, N. Kasabov.
Evaluating SPAN Incremental Learning for Handwritten Digit Recognition, in: Neural Information Processing, Berlin, Heidelberg, Springer, 2012, pp. 670–677.
K. Nasrollahi, T. B. Moeslund.
Super-resolution: a comprehensive survey, in: Machine Vision and Applications, 2014, vol. 25, pp. 1423–1468.
J. 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. [ DOI : 10.1007/s10827-012-0409-5 ]
N. Rust, V. Mante, E. Simoncelli, J. Movshon.
How MT cells analyze the motion of visual patterns, in: Nature Neuroscience, 2006, vol. 9, pp. 1421–1431.
E. Simoncelli, D. Heeger.
A Model of Neuronal Responses in Visual Area MT, in: Vision Research, 1998, vol. 38, pp. 743–761.
B. 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.
B. 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.
E. 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.
E. Tlapale.
Modelling the dynamics of contextual motion integration in the primate, Université Nice Sophia Antipolis, January 2011.
J. 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.
P. Vance, S. A. Coleman, D. Kerr, G. Das, T. McGinnity.
Modelling of a retinal ganglion cell with simple spiking models, in: IEEE Int. Jt. Conf. Neural Networks, 2015, pp. 1–8.
R. 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 ]
R. 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.