Lapicque's introduction of the integrate-and-fire model neuron, 1907. ,
Efficient Markov Chain Monte Carlo Methods for Decoding Neural Spike Trains, Neural Computation, vol.79, issue.1, pp.46-96, 2011. ,
DOI : 10.1152/jn.90941.2008
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4740351
Geometrical Methods in the Theory of Ordinary Differential Equations, 1983. ,
Asymptotics of hitting probabilities for general onedimensional pinned diffusions, The Annals of Applied Probability, vol.12, issue.3, pp.1071-1095, 2002. ,
A network of electrically coupled interneurons drives synchronized inhibition in neocortex, Nature Neuroscience, vol.3, issue.9, pp.904-910, 2000. ,
Electrical Coupling and Neuronal Synchronization in the Mammalian Brain, Neuron, vol.41, issue.4, pp.495-511, 2004. ,
DOI : 10.1016/S0896-6273(04)00043-1
Spatial interaction and the statistical analysis of lattice systems, Journal of the Royal Statistical Society, vol.36, pp.192-236, 1974. ,
Rediscovering the power of pairwise interactions. arXiv.org:0712.4397 [q?bio, 2007. ,
The diverse functional roles and regulation of neuronal gap junctions in the retina, Nature Reviews Neuroscience, vol.492, issue.7, pp.495-506, 2009. ,
DOI : 10.1038/nrn2636
Equilibrium states and the ergodic theory of Anosov diffeomorphisms, Lect. Notes.in Math, vol.470, pp.35-36, 1975. ,
DOI : 10.1007/BFb0081279
Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues, pp.22-27, 1999. ,
DOI : 10.1007/978-1-4757-3124-8
Maximum likelihood analysis of spike trains of interacting nerve cells, Biological Cybernetics, vol.56, issue.3, pp.189-200, 1988. ,
DOI : 10.1007/BF00318010
Nerve Cell Spike Train Data Analysis: A Progression of Technique, Journal of the American Statistical Association, vol.119, issue.418, pp.260-271, 1992. ,
DOI : 10.1080/01621459.1987.10478466
Finite Dimensional Linear Systems, 1970. ,
DOI : 10.1137/1.9781611973884
Faster solutions of the inverse pairwise ising problem. Submitted (see http ,
Likelihood Methods for Neural Spike Train Data Analysis, Computational Neuroscience: A Comprehensive Approach, 2003. ,
DOI : 10.1201/9780203494462.ch9
Dynamics of the firing probability of noisy integrateand-fire neurons, Neural Computation, vol.14, issue.112, pp.2057-2110, 2002. ,
Fast Global Oscillations in Networks of Integrate-and-Fire Neurons with Low Firing Rates, Neural Computation, vol.15, issue.7, pp.1621-1671, 1999. ,
DOI : 10.1038/373612a0
A Review of the Integrate-and-fire Neuron Model: I. Homogeneous Synaptic Input, Biological Cybernetics, vol.68, issue.1, pp.1-19, 2006. ,
DOI : 10.1007/s00422-006-0068-6
A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties, Biological Cybernetics, vol.16, issue.60, pp.97-112, 2006. ,
DOI : 10.1007/s00422-006-0082-8
A Generalized Linear Model for Estimating Spectrotemporal Receptive Fields from Responses to Natural Sounds, PLoS ONE, vol.102, issue.2, pp.470-484, 2011. ,
DOI : 10.1371/journal.pone.0016104.g009
A discrete time neural network model with spiking neurons, Journal of Mathematical Biology, vol.18, issue.26, pp.311-345, 2008. ,
DOI : 10.1007/s00285-007-0117-3
URL : https://hal.archives-ouvertes.fr/inria-00530115
A VIEW OF NEURAL NETWORKS AS DYNAMICAL SYSTEMS, International Journal of Bifurcation and Chaos, vol.20, issue.06, pp.1585-1629, 2010. ,
DOI : 10.1142/S0218127410026721
URL : https://hal.archives-ouvertes.fr/inria-00534326
A discrete time neural network model with spiking neurons: II: Dynamics with noise, Journal of Mathematical Biology, vol.19, issue.1???3, pp.863-900 ,
DOI : 10.1007/s00285-010-0358-4
URL : https://hal.archives-ouvertes.fr/inria-00530115
Statistics of spike trains in conductance-based neural networks: Rigorous results, The Journal of Mathematical Neuroscience, vol.1, issue.1, pp.52-53 ,
DOI : 10.1038/nature05534
URL : https://hal.archives-ouvertes.fr/hal-00640501
Estimating maximum entropy distributions from periodic orbits in spike trains, INRIA Research Report Number, vol.8329, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00842776
Spike Train Statistics from Empirical Facts to Theory: The Case of the Retina, Current Mathematical Problems in Computational Biology and Biomedicine, vol.102, p.43, 2012. ,
DOI : 10.1007/978-3-642-31208-3_8
URL : https://hal.archives-ouvertes.fr/hal-00640507
On dynamics of integrate-and-fire neural networks with adaptive conductances, Frontiers in neuroscience, vol.2, issue.2, pp.53-56, 2008. ,
URL : https://hal.archives-ouvertes.fr/inria-00338369
Pressure and equilibrium states in ergodic theory, Israel Journal of Mathematics, vol.131, issue.1, pp.35-37, 2008. ,
A simple white noise analysis of neuronal light responses, Network: Computation in Neural Systems, vol.12, issue.2, p.48, 2001. ,
DOI : 10.1080/713663221
Evolution semigroups in dynamical systems, page 61 URL http://books.google.fr/books, 1999. ,
Dynamics of Spiking Neurons with Electrical Coupling, Neural Computation, vol.18, issue.7, pp.1643-1678, 2000. ,
DOI : 10.1023/A:1008841325921
The Computational Brain, 2002. ,
Neuronal couplings between retinal ganglion cells inferred by efficient inverse statistical physics methods, Proceedings of the National Academy of Sciences, vol.106, issue.33, pp.14058-14062, 2009. ,
DOI : 10.1073/pnas.0906705106
Dynamics and spike trains statistics in conductance-based integrate-and-fire neural networks with chemical and electric synapses, Chaos, Solitons & Fractals, vol.50, issue.8, pp.13-31, 2013. ,
DOI : 10.1016/j.chaos.2012.12.006
Exact computation of the maximum-entropy potential of spiking neural-network models, Physical Review E, vol.89, issue.5, pp.368-368 ,
DOI : 10.1103/PhysRevE.89.052117
ELECTRICAL SYNAPSES IN THE MAMMALIAN BRAIN, Annual Review of Neuroscience, vol.27, issue.1, pp.393-418, 2004. ,
DOI : 10.1146/annurev.neuro.26.041002.131128
Neuronal Networks with Gap Junctions: A Study of Piecewise Linear Planar Neuron Models, SIAM Journal on Applied Dynamical Systems, vol.7, issue.3, pp.1101-1129, 2008. ,
DOI : 10.1137/070707579
Gap Junctions and Emergent Rhythms, pp.77-94, 2007. ,
DOI : 10.1007/978-1-4419-0389-1_5
URL : http://eprints.nottingham.ac.uk/894/1/COBENN.pdf
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems, 2005. ,
Kinetic models of synaptic transmission, 1998. ,
Performance Guarantees for Regularized Maximum Entropy Density Estimation, Proceedings of the 17th Annual Conference on Computational Learning Theory, 2004. ,
DOI : 10.1007/978-3-540-27819-1_33
Mathematical Foundations of Neuroscience, 2010. ,
DOI : 10.1007/978-0-387-87708-2
Chains with complete connections : General theory, uniqueness, loss of memory and mixing properties, J. Stat. Phys, vol.118, pp.3-4555, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-01296844
A network of fast-spiking cells in the neocortex connected by electrical synapses, Nature, vol.402, issue.6757, pp.72-75, 1999. ,
Electrical synapses between Gaba-Releasing interneurons, Nature Reviews Neuroscience, vol.235, issue.6, pp.425-433, 2001. ,
DOI : 10.1038/35077566
Infinite Systems of Interacting Chains with Memory of Variable Length???A Stochastic Model for Biological Neural Nets, Journal of Statistical Physics, vol.5, issue.2, pp.896-921 ,
DOI : 10.1007/s10955-013-0733-9
The Architecture of Functional Interaction Networks in the Retina, Journal of Neuroscience, vol.31, issue.8, pp.313044-3054, 2011. ,
DOI : 10.1523/JNEUROSCI.3682-10.2011
Sparse low-order interaction network underlies a highly correlated and learnable neural population code, Proceedings of the National Academy of Sciences, vol.108, issue.23, pp.9679-9684, 2011. ,
DOI : 10.1073/pnas.1019641108
The theory of matrices, 1998. ,
On the dynamics of electrically-coupled neurons with inhibitory synapses, Journal of Computational Neuroscience, vol.22, issue.1, pp.39-61, 2007. ,
DOI : 10.1007/s10827-006-9676-3
Receptive Fields in Primate Retina Are Coordinated to Sample Visual Space More Uniformly, PLoS Biology, vol.17, issue.4, 2009. ,
DOI : 10.1371/journal.pbio.1000063.g006
Gibbs measures and phase transitions De Gruyter Studies in Math- ematics:9. Berlin, pp.30-39, 1988. ,
Spiking Neuron Models, 2002. ,
Explicit Stability Conditions for Continuous Systems: A Functional Analytic Approach, Lecture Notes in Control and Information Sciences, vol.314, 2005. ,
DOI : 10.1007/b99808
Eye Smarter than Scientists Believed: Neural Computations in Circuits of the Retina, Neuron, vol.65, issue.2, pp.150-164, 2010. ,
DOI : 10.1016/j.neuron.2009.12.009
Stimulus-dependent Maximum Entropy Models of Neural Population Codes, PLoS Computational Biology, vol.012020, issue.3, p.2013 ,
DOI : 10.1371/journal.pcbi.1002922.g010
A Theorem about Random Fields, Bulletin of the London Mathematical Society, vol.5, issue.1, pp.81-84, 1973. ,
DOI : 10.1112/blms/5.1.81
Markov fields on finite graphs and lattices. unpublished, pp.76-81, 1971. ,
Thermodynamic formalism, multifractal analysis of conformal infinite iterated function, Acta Mathematica Hungarica, vol.96, issue.1/2, pp.27-98, 2002. ,
DOI : 10.1023/A:1015613628175
Encoding Through Patterns: Regression Tree???Based Neuronal Population Models, Neural Computation, vol.5, issue.8 ,
DOI : 10.1093/cercor/bhn047
Perception lecture Notes, 2006. ,
A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology, vol.117, issue.4, pp.500-544, 1952. ,
DOI : 10.1113/jphysiol.1952.sp004764
Electrical synapses: a dynamic signaling system that shapes the activity of neuronal networks, Biochimica et Biophysica Acta (BBA) - Biomembranes, vol.1662, issue.1-2, pp.113-137, 2004. ,
DOI : 10.1016/j.bbamem.2003.10.023
Light increases the gap junctional coupling of retinal ganglion cells, The Journal of Physiology, vol.405, issue.21, pp.4145-4163, 2010. ,
DOI : 10.1113/jphysiol.2010.193268
Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, 2007. ,
Information Theory and Statistical Mechanics, Physical Review, vol.106, issue.4, pp.13-35, 1957. ,
DOI : 10.1103/PhysRev.106.620
Unstable Solutions of Nonautonomous Linear Differential Equations, SIAM Review, vol.50, issue.3, pp.570-584, 2008. ,
DOI : 10.1137/060677057
Mathematical Physiology, Interdisciplinary Applied Mathematics, vol.8, issue.1, 1998. ,
DOI : 10.1007/978-0-387-75847-3
Equilibrium States in Ergodic Theory, p.30, 1998. ,
DOI : 10.1017/CBO9781107359987
How precise is the timing of action potentials?, Frontiers in Neuroscience, vol.3, issue.1, pp.2-3, 2009. ,
DOI : 10.3389/neuro.01.009.2009
Symbolic Dynamics: One-sided, Two-sided and Countable State Markov Shifts, 1998. ,
DOI : 10.1007/978-3-642-58822-8
Understanding visual population codes -towards a common multivariate framework for cell recording and functional imaging, 2010. ,
Recherches quantitatives sur l'excitation électrique des nerfs traitée comme une polarisation, J. Physiol. Pathol. Gen, vol.9, pp.620-635, 1907. ,
Stochastic Methods in Neuroscience., chapter A brief introduction to some simple stochastic processes, pp.1-28, 2009. ,
Maximizing spike train coherence or incoherence in the leaky integrate-and-fire model, Physical Review E, vol.66, issue.3, p.31916, 2002. ,
DOI : 10.1103/PhysRevE.66.031916
Effects of noise in excitable systems, Physics Reports, vol.392, issue.6, pp.321-424, 2004. ,
DOI : 10.1016/j.physrep.2003.10.015
COHOMOLOGY OF DYNAMICAL SYSTEMS, Mathematics of the USSR-Izvestiya, vol.6, issue.6, pp.1278-1371, 1972. ,
DOI : 10.1070/IM1972v006n06ABEH001919
Receptive fields without spike-triggering, 21th Neural Information Processing Systems Conference, pp.280-286, 2008. ,
Empirical models of spiking in neural populations, Advances in Neural Information Processing Systems 24, pp.1350-1358, 2011. ,
Prediction of spatiotemporal patterns of neural activity from pairwise correlations. Physical review letters, pp.13-43, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00444939
Interactions between ganglion cells in cat retina, J Neurophysiol, vol.49, issue.2, pp.350-65, 1983. ,
Generalized linear models, 1989. ,
Dendritic synchrony and transient dynamics in a coupled oscillator model of the dopaminergic neuron, Journal of Neuroscience, vol.15, pp.53-69, 2003. ,
Electrical Coupling Promotes Fidelity of Responses in the Networks of Model Neurons, Neural Computation, vol.21, issue.23, pp.3057-3078, 2009. ,
DOI : 10.1038/373033a0
The Neural Code of the Retina, Neuron, vol.22, issue.3, pp.435-450, 1999. ,
DOI : 10.1016/S0896-6273(00)80700-X
Parameter Estimation for Spatio-Temporal Maximum Entropy Distributions: Application to Neural Spike Trains, Entropy, vol.16, issue.4, p.2014 ,
DOI : 10.3390/e16042244
URL : https://hal.archives-ouvertes.fr/hal-01096213
Spatio-temporal spike train analysis for large scale networks using the maximum entropy principle and Monte Carlo method, Journal of Statistical Mechanics: Theory and Experiment, vol.2013, issue.03, pp.43-45, 2013. ,
DOI : 10.1088/1742-5468/2013/03/P03006
URL : https://hal.archives-ouvertes.fr/hal-00846160
Population coding in the retina, Current Opinion in Neurobiology, vol.8, issue.4, pp.488-493, 1998. ,
DOI : 10.1016/S0959-4388(98)80036-6
Decoding neuronal spike trains: How important are correlations?, Proceedings of the National Academy of Sciences, vol.100, issue.12, pp.7348-7353, 2003. ,
DOI : 10.1073/pnas.1131895100
URL : http://www.ncbi.nlm.nih.gov/pmc/articles/PMC165878
Sparse coding and high-order correlations in fine-scale cortical networks, Nature, vol.17, issue.7306, pp.617-621, 2010. ,
DOI : 10.1038/nature09178
Synchronization properties of networks of electrically coupled neurons in the presence of noise and heterogeneities, Journal of Computational Neuroscience, vol.97, issue.3, pp.369-392, 2009. ,
DOI : 10.1007/s10827-008-0117-3
Connexin36 is required for gap junctional coupling of most ganglion cell subtypes in the mouse retina, The Journal of Comparative Neurology, vol.17, issue.6, pp.911-927, 2010. ,
DOI : 10.1002/cne.22254
Spontaneous neuronal network remodeling takes place along sloppy parameter dimensions. preprint, p.2014 ,
Maximum likelihood estimation of cascade point-process neural encoding models, Network: Computation in Neural Systems, vol.15, issue.4, pp.243-2620954, 2004. ,
DOI : 10.1088/0954-898X_15_4_002
Superlinear Population Encoding of Dynamic Hand Trajectory in Primary Motor Cortex, Journal of Neuroscience, vol.24, issue.39, pp.8551-8561, 2004. ,
DOI : 10.1523/JNEUROSCI.0919-04.2004
A Unified Approach to the Study of Temporal, Correlational, and Rate Coding, Neural Computation, vol.80, issue.10, pp.1311-1349, 2001. ,
DOI : 10.1088/0954-898X/8/2/003
An efficient algorithm for continuous-time cross correlation spike trains, J. Neurosci. Methods, vol.128, issue.2, 2008. ,
The Combined Effects of Inhibitory and Electrical Synapses in Synchrony, Neural Computation, vol.16, issue.3, pp.633-670, 2005. ,
DOI : 10.2170/jjphysiol.8.305
URL : https://hal.archives-ouvertes.fr/hal-00094743
Prediction and Decoding of Retinal Ganglion Cell Responses with a Probabilistic Spiking Model, Journal of Neuroscience, vol.25, issue.47, pp.11003-11013, 2005. ,
DOI : 10.1523/JNEUROSCI.3305-05.2005
Model-Based Decoding, Information Estimation, and Change-Point Detection Techniques for Multineuron Spike Trains, Neural Computation, vol.79, issue.1, pp.1-45, 2011. ,
DOI : 10.1109/TNSRE.2009.2023307
Spatio-temporal correlations and visual signalling in a complete neuronal population, Nature, vol.22, issue.7207, pp.995-999, 2008. ,
DOI : 10.1038/nature07140
Free Energy as a Dynamical Invariant (or Can You Hear the Shape of a Potential?), Communications in Mathematical Physics, vol.109, issue.3, pp.457-482, 2003. ,
DOI : 10.1007/s00220-003-0905-6
Information processing with population codes, Nature Reviews Neuroscience, vol.1, issue.2, pp.125-132, 2000. ,
DOI : 10.1038/35039062
Spikes, Exploring the Neural Code. The M.I, 1996. ,
Information and Its Role in Nature, 2005. ,
Neural Networks: A Systematic Introduction, 1996. ,
DOI : 10.1007/978-3-642-61068-4
Pairwise Maximum Entropy Models for Studying Large Biological
Systems: When They Can Work and When They Can't, PLoS Computational Biology, vol.9, issue.5, p.123, 2009. ,
DOI : 10.1371/journal.pcbi.1000380.g007
Analytical Integrate-and-Fire Neuron Models with Conductance-Based Dynamics for Event-Driven Simulation Strategies, Neural Computation, vol.18, issue.9, pp.2146-2210, 2006. ,
DOI : 10.1103/PhysRevLett.71.1280
URL : https://hal.archives-ouvertes.fr/hal-00120630
Thermodynamic formalism, 1978. ,
DOI : 10.1017/CBO9780511617546
Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics, Journal of Statistical Physics, vol.95, issue.1/2, pp.393-468, 1999. ,
DOI : 10.1023/A:1004593915069
Synergy, redundancy, and independence in population codes, J Neurosci, vol.23, issue.37, pp.11539-53, 2003. ,
Weak pairwise correlations imply strongly correlated network states in a neural population, Nature, vol.37, issue.7087, pp.1007-1012, 2006. ,
DOI : 10.1038/nature04701
How Noisy Adaptation of Neurons Shapes Interspike Interval Histograms and Correlations, PLoS Computational Biology, vol.81, issue.12 ,
DOI : 10.1371/journal.pcbi.1001026.g014
The variable discharge of cortical neurons: implications for connectivity, computation, and information coding, J. Neurosci, vol.18, issue.10, pp.3870-3896, 1998. ,
Rod pathways: the importance of seeing nothing, Trends in Neurosciences, vol.22, issue.11, pp.497-504, 1999. ,
DOI : 10.1016/S0166-2236(99)01458-7
Analyzing Neural Responses to Natural Signals: Maximally Informative Dimensions, Neural Computation, vol.22, issue.2, pp.223-250, 2004. ,
DOI : 10.1016/S0896-6273(03)00022-9
The structure of multi-neuron firing patterns in primate retina, J Neurosci, vol.26, issue.32, pp.8254-66, 2006. ,
The Structure of Large-Scale Synchronized Firing in Primate Retina, Journal of Neuroscience, vol.29, issue.15, pp.5022-5031, 2009. ,
DOI : 10.1523/JNEUROSCI.5187-08.2009
Characterization of Neural Responses with Stochastic Stimuli. The cognitive neurosciences, 2004. ,
Spontaneous Dynamics of Asymmetric Random Recurrent Spiking Neural Networks, Neural Computation, vol.18, issue.1, 2006. ,
DOI : 10.1214/aoms/1177731118
URL : https://hal.archives-ouvertes.fr/hal-00119755
Higher-order correlations in non-stationary parallel spike trains: statistical modeling and inference, Frontiers in computational neuroscience, vol.4, issue.16, p.2010 ,
A Maximum Entropy Model Applied to Spatial and Temporal Correlations from Cortical Networks In Vitro, Journal of Neuroscience, vol.28, issue.2, pp.505-518, 2008. ,
DOI : 10.1523/JNEUROSCI.3359-07.2008
Estimating spatio-temporal receptive fields of auditory and visual neurons from their responses to natural stimuli, Network: Computation in Neural Systems, vol.10, issue.3, pp.289-316, 2001. ,
DOI : 10.1126/science.287.5456.1273
Ising models for networks of real neurons. arXiv, q-bio/0611072, 2006. ,
Spin glass models for a network of real neurons, pp.45-53 ,
Optimal population coding by noisy spiking neurons, Proceedings of the National Academy of Sciences, vol.107, issue.32, pp.14419-14424, 2010. ,
DOI : 10.1073/pnas.1004906107
Thermodynamics and signatures of criticality in a network of neurons, Proceedings of the National Academy of Sciences, vol.112, issue.37, pp.2014-2059 ,
DOI : 10.1073/pnas.1514188112
The spikes trains probability distributions: A stochastic calculus approach, Journal of Physiology-Paris, vol.101, issue.1-3, pp.78-98, 2007. ,
DOI : 10.1016/j.jphysparis.2007.10.008
A Point Process Framework for Relating Neural Spiking Activity to Spiking History, Neural Ensemble, and Extrinsic Covariate Effects, Journal of Neurophysiology, vol.93, issue.2, pp.1074-1089, 2005. ,
DOI : 10.1152/jn.00697.2004
Effect of nonstationarity on models inferred from neural data. preprint http ,
Gibbs distribution analysis of temporal correlation structure on multicell spike trains from retina ganglion cells, J. Physiol. Paris, vol.43, pp.13-53, 2012. ,
Virtual Retina: A biological retina model and simulator, with contrast gain control, Journal of Computational Neuroscience, vol.32, issue.3, pp.219-249, 2009. ,
DOI : 10.1007/s10827-008-0108-4
URL : https://hal.archives-ouvertes.fr/inria-00160716
Evolution systems of measures for non-autonomous stochastic differential equations with levy noise, Communications on Stochastic Analysis, vol.5, issue.65, pp.353-370, 2011. ,
A Small World of Neuronal Synchrony, Cerebral Cortex, vol.18, issue.12, 2008. ,
DOI : 10.1093/cercor/bhn047