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Volumn 62, Issue 6, 2011, Pages 863-900

A discrete time neural network model with spiking neurons: II: Dynamics with noise

Author keywords

Gibbs distributions; Neurons dynamics; Spike train statistics; Thermodynamic formalism

Indexed keywords

ACTION POTENTIAL; ARTICLE; BIOLOGICAL MODEL; HUMAN; NERVE CELL; NERVE CELL NETWORK; PHYSIOLOGY; STATISTICAL MODEL; STATISTICS;

EID: 79956132400     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-010-0358-4     Document Type: Article
Times cited : (36)

References (59)
  • 1
    • 84944495616 scopus 로고
    • The impulses produced by sensory nerve endings. Part II: the response of a single end organ
    • Adrian E, Zotterman Y (1926) The impulses produced by sensory nerve endings. Part II: the response of a single end organ. J Physiol (Lond) 61: 151-171.
    • (1926) J Physiol (Lond) , vol.61 , pp. 151-171
    • Adrian, E.1    Zotterman, Y.2
  • 2
    • 0141749203 scopus 로고    scopus 로고
    • A universal model for spike-frequency adaptation
    • Benda J, Herz A (2003) A universal model for spike-frequency adaptation. Neural Computtion 15(11): 2523-2564.
    • (2003) Neural Computtion , vol.15 , Issue.11 , pp. 2523-2564
    • Benda, J.1    Herz, A.2
  • 3
    • 14644428975 scopus 로고    scopus 로고
    • Spike-frequency adaptation separates transient communication signals from background oscillations
    • Benda J, Longtin A, Maler L (2005) Spike-frequency adaptation separates transient communication signals from background oscillations. J Neurosci 25: 2312-2321.
    • (2005) J Neurosci , vol.25 , pp. 2312-2321
    • Benda, J.1    Longtin, A.2    Maler, L.3
  • 4
    • 41849126429 scopus 로고    scopus 로고
    • Equilibrium states and the ergodic theory of Anosov diffeomorphisms, 2nd revised version
    • Springer-Verlag
    • Bowen R (2008) Equilibrium states and the ergodic theory of Anosov diffeomorphisms, 2nd revised version. In: Lecture notes in mathematics, vol 470. Springer-Verlag.
    • (2008) Lecture notes in mathematics , vol.470
    • Bowen, R.1
  • 5
    • 0042160387 scopus 로고    scopus 로고
    • Decay of correlations for non hölderian dynamics. A coupling approach
    • Bressaud X, Fernandez R, Galves A (1999) Decay of correlations for non hölderian dynamics. A coupling approach. Electron J Probab 4(3): 1-19.
    • (1999) Electron J Probab , vol.4 , Issue.3 , pp. 1-19
    • Bressaud, X.1    Fernandez, R.2    Galves, A.3
  • 6
    • 0033210816 scopus 로고    scopus 로고
    • Fast global oscillations in networks of integrate-and-fire neurons with low firing rates
    • Brunel N, Hakim V (1999) Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Comput 11: 1621-1671.
    • (1999) Neural Comput , vol.11 , pp. 1621-1671
    • Brunel, N.1    Hakim, V.2
  • 7
    • 36749004948 scopus 로고    scopus 로고
    • A discrete time neural network model with spiking neurons I. Rigorous results on the spontaneous dynamics
    • Cessac B (2008) A discrete time neural network model with spiking neurons I. Rigorous results on the spontaneous dynamics. J Math Biol 56(3): 311-345.
    • (2008) J Math Biol , vol.56 , Issue.3 , pp. 311-345
    • Cessac, B.1
  • 8
    • 41349089523 scopus 로고    scopus 로고
    • Stable resonances and signal propagation in a chaotic network of coupled units
    • Cessac B, Sepulchre J (2004) Stable resonances and signal propagation in a chaotic network of coupled units. Phys Rev E 70: 056111.
    • (2004) Phys Rev E , vol.70 , pp. 056111
    • Cessac, B.1    Sepulchre, J.2
  • 9
    • 33645679781 scopus 로고    scopus 로고
    • Transmitting a signal by amplitude modulation in a chaotic network
    • Cessac B, Sepulchre J (2006) Transmitting a signal by amplitude modulation in a chaotic network. Chaos 16: 013104.
    • (2006) Chaos , vol.16 , pp. 013104
    • Cessac, B.1    Sepulchre, J.2
  • 10
    • 77049123046 scopus 로고    scopus 로고
    • On dynamics of integrate-and-fire neural networks with adaptive conductances
    • Cessac B, Viéville T (2008) On dynamics of integrate-and-fire neural networks with adaptive conductances. Front Neurosci 2(2): 1-20.
    • (2008) Front Neurosci , vol.2 , Issue.2 , pp. 1-20
    • Cessac, B.1    Viéville, T.2
  • 11
    • 70349309802 scopus 로고    scopus 로고
    • How gibbs distribution may naturally arise from synaptic adaptation mechanisms: a model based argumentation
    • Cessac B, Rostro-Gonzalez H, Vasquez J, Viéville T (2009) How gibbs distribution may naturally arise from synaptic adaptation mechanisms: a model based argumentation. J Stat Phys 136(3): 565-602.
    • (2009) J Stat Phys , vol.136 , Issue.3 , pp. 565-602
    • Cessac, B.1    Rostro-Gonzalez, H.2    Vasquez, J.3    Viéville, T.4
  • 14
    • 22044441901 scopus 로고    scopus 로고
    • Criteria for d-continuity
    • Coelho Z, Quas A (1998) Criteria for d-continuity. Trans Am Math Soc 350(8): 3257-3268.
    • (1998) Trans Am Math Soc , vol.350 , Issue.8 , pp. 3257-3268
    • Coelho, Z.1    Quas, A.2
  • 15
    • 0032523522 scopus 로고    scopus 로고
    • Spike frequency adaptation affects the synchronization properties of networks of cortical oscillators
    • Crook S, Ermentrout G, Bower J (1998) Spike frequency adaptation affects the synchronization properties of networks of cortical oscillators. Neural Comput 10(4): 837-854.
    • (1998) Neural Comput , vol.10 , Issue.4 , pp. 837-854
    • Crook, S.1    Ermentrout, G.2    Bower, J.3
  • 16
    • 0000620132 scopus 로고
    • Sanov property, generalized i-projection and a conditional limit theorem
    • Csiszar I (1984) Sanov property, generalized i-projection and a conditional limit theorem. Ann Prob 12(3): 768-793.
    • (1984) Ann Prob , vol.12 , Issue.3 , pp. 768-793
    • Csiszar, I.1
  • 18
    • 0035374850 scopus 로고    scopus 로고
    • The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators
    • Ermentrout B, Pascal M, Gutkin B (2001) The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators. Neural Comput 13(6): 1285-1310.
    • (2001) Neural Comput , vol.13 , Issue.6 , pp. 1285-1310
    • Ermentrout, B.1    Pascal, M.2    Gutkin, B.3
  • 21
    • 0040744515 scopus 로고    scopus 로고
    • Mathematical formulations of hebbian learning
    • Gerstner W, Kistler WM (2002b) Mathematical formulations of hebbian learning. Biol Cybern 87: 404-415.
    • (2002) Biol Cybern , vol.87 , pp. 404-415
    • Gerstner, W.1    Kistler, W.M.2
  • 22
    • 0032833917 scopus 로고    scopus 로고
    • Precise spike synchronization in monkey motor cortex involved in preparation for movement
    • Grammont F, Riehle A (1999) Precise spike synchronization in monkey motor cortex involved in preparation for movement. Exp Brain Res 128: 118-122.
    • (1999) Exp Brain Res , vol.128 , pp. 118-122
    • Grammont, F.1    Riehle, A.2
  • 23
    • 0142134887 scopus 로고    scopus 로고
    • Spike synchronization and firing rate in a population of motor cortical neurons in relation to movement direction and reaction time
    • Grammont F, Riehle A (2003) Spike synchronization and firing rate in a population of motor cortical neurons in relation to movement direction and reaction time. Biol Cybern 88: 360-373.
    • (2003) Biol Cybern , vol.88 , pp. 360-373
    • Grammont, F.1    Riehle, A.2
  • 24
    • 4344661328 scopus 로고    scopus 로고
    • Which model to use for cortical spiking neurons?
    • Izhikevich E (2004) Which model to use for cortical spiking neurons? IEEE Trans Neural Netw 15(5): 1063-1070.
    • (2004) IEEE Trans Neural Netw , vol.15 , Issue.5 , pp. 1063-1070
    • Izhikevich, E.1
  • 25
    • 11944266539 scopus 로고
    • Information theory and statistical mechanics
    • Jaynes E (1957) Information theory and statistical mechanics. Phys Rev 106: 620.
    • (1957) Phys Rev , vol.106 , pp. 620
    • Jaynes, E.1
  • 26
    • 0742288761 scopus 로고    scopus 로고
    • Square summability of variations of g-functions and uniqueness of g-measure
    • Johansson A, Oberg A (2003) Square summability of variations of g-functions and uniqueness of g-measure. Math Res Lett 10: 587-601.
    • (2003) Math Res Lett , vol.10 , pp. 587-601
    • Johansson, A.1    Oberg, A.2
  • 27
    • 3142666109 scopus 로고    scopus 로고
    • Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy
    • Jolivet R, Lewis T, Gerstner W (2004) Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy. J Neurophysiol 92: 959-976.
    • (2004) J Neurophysiol , vol.92 , pp. 959-976
    • Jolivet, R.1    Lewis, T.2    Gerstner, W.3
  • 28
    • 33745833056 scopus 로고    scopus 로고
    • Predicting spike timing of neocortical pyramidal neurons by simple threshold models
    • Jolivet R, Rauch A, Lscher H-R, Gerstner W (2006) Predicting spike timing of neocortical pyramidal neurons by simple threshold models. J Comput Neurosci 21: 35-49.
    • (2006) J Comput Neurosci , vol.21 , pp. 35-49
    • Jolivet, R.1    Rauch, A.2    Lscher, H.-R.3    Gerstner, W.4
  • 29
    • 0442269813 scopus 로고
    • Strongly mixing g-measures
    • Keane M (1972) Strongly mixing g-measures. Invent Math 16: 309-324.
    • (1972) Invent Math , vol.16 , pp. 309-324
    • Keane, M.1
  • 31
    • 62449249902 scopus 로고    scopus 로고
    • Sequential desynchronization in networks of spiking neurons with partial reset
    • Kirst C, Geisel T, Timme M (2009) Sequential desynchronization in networks of spiking neurons with partial reset. Phys Rev Lett 102: 068101.
    • (2009) Phys Rev Lett , vol.102 , pp. 068101
    • Kirst, C.1    Geisel, T.2    Timme, M.3
  • 33
    • 0001127901 scopus 로고
    • Recherches quantitatives sur l'excitation électrique des nerfs traitée comme une polarisation
    • Lapicque L (1907) Recherches quantitatives sur l'excitation électrique des nerfs traitée comme une polarisation. J Physiol Pathol Gen 9: 620-635.
    • (1907) J Physiol Pathol Gen , vol.9 , pp. 620-635
    • Lapicque, L.1
  • 34
    • 0001483334 scopus 로고
    • Principe variationnel et systèmes dynamiques symboliques
    • Ledrappier F (1974) Principe variationnel et systèmes dynamiques symboliques. Z Wahr verw Gebiete 30(185): 185-202.
    • (1974) Z Wahr Verw Gebiete , vol.30 , Issue.185 , pp. 185-202
    • Ledrappier, F.1
  • 36
    • 64649095157 scopus 로고    scopus 로고
    • Prediction of spatiotemporal patterns of neural activity from pairwise correlations
    • Marre O, Boustani SE, Frégnac Y, Destexhe A (2009) Prediction of spatiotemporal patterns of neural activity from pairwise correlations. Phys Rev Lett 102: 138101.
    • (2009) Phys Rev Lett , vol.102 , pp. 138101
    • Marre, O.1    Boustani, S.E.2    Frégnac, Y.3    Destexhe, A.4
  • 37
    • 0037866386 scopus 로고    scopus 로고
    • Decoding neuronal spike trains: how important are correlations
    • Nirenberg S, Latham P (2003) Decoding neuronal spike trains: how important are correlations. Proc Nat Acad Sci 100(12): 7348-7353.
    • (2003) Proc Nat Acad Sci , vol.100 , Issue.12 , pp. 7348-7353
    • Nirenberg, S.1    Latham, P.2
  • 39
    • 47749151165 scopus 로고    scopus 로고
    • Sparse spike coding: applications of neuroscience to the processing of natural images
    • Proceedings of SPIE, the International Society for Optical Engineering, number ISSN 0277-786X CODEN PSISDG, Bellingham, WA, ETATS-UNIS
    • Perrinet L (2008) Sparse spike coding: applications of neuroscience to the processing of natural images. In: Society of Photo-Optical Instrumentation Engineers (ed) Proceedings of SPIE, the International Society for Optical Engineering, number ISSN 0277-786X CODEN PSISDG, Bellingham, WA, ETATS-UNIS.
    • (2008) Society of Photo-Optical Instrumentation Engineers
    • Perrinet, L.1
  • 42
    • 0034486508 scopus 로고    scopus 로고
    • Dynamical changes and temporal precision of synchronized spiking activity in monkey motor cortex during movement preparation
    • Riehle A, Grammont F, Diesmann M, Grün S (2000) Dynamical changes and temporal precision of synchronized spiking activity in monkey motor cortex during movement preparation. J Physiol (Paris) 94: 569-582.
    • (2000) J Physiol (Paris) , vol.94 , pp. 569-582
    • Riehle, A.1    Grammont, F.2    Diesmann, M.3    Grün, S.4
  • 43
    • 67049119347 scopus 로고    scopus 로고
    • Pairwise maximum entropy models for studying large biological systems: when they can work and when they can't
    • Roudy Y, Nirenberg S, Latham P (2009) Pairwise maximum entropy models for studying large biological systems: when they can work and when they can't. PLOS Comput Biol 5(5): e1000380.
    • (2009) PLOS Comput Biol , vol.5 , Issue.5
    • Roudy, Y.1    Nirenberg, S.2    Latham, P.3
  • 44
    • 33748464002 scopus 로고    scopus 로고
    • Analytical integrate and fire neuron models with conductance-based dynamics for event driven simulation strategies
    • Rudolph M, Destexhe A (2006) Analytical integrate and fire neuron models with conductance-based dynamics for event driven simulation strategies. Neural Comput 18: 2146-2210.
    • (2006) Neural Comput , vol.18 , pp. 2146-2210
    • Rudolph, M.1    Destexhe, A.2
  • 47
    • 0033246861 scopus 로고    scopus 로고
    • Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics
    • Ruelle D (1999) Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics. J Stat Phys 95: 393-468.
    • (1999) J Stat Phys , vol.95 , pp. 393-468
    • Ruelle, D.1
  • 48
    • 0035380719 scopus 로고    scopus 로고
    • Rate coding versus temporal order coding: what the retina ganglion cells tell the visual cortex
    • Rullen RV, Thorpe S (2001) Rate coding versus temporal order coding: what the retina ganglion cells tell the visual cortex. Neural Comput 13(6): 1255-1283.
    • (2001) Neural Comput , vol.13 , Issue.6 , pp. 1255-1283
    • Rullen, R.V.1    Thorpe, S.2
  • 49
    • 33646170322 scopus 로고    scopus 로고
    • Weak pairwise correlations imply string correlated network states in a neural population
    • Schneidman E, Berry M, Segev R, Bialek W (2006) Weak pairwise correlations imply string correlated network states in a neural population. Nature 440: 1007-1012.
    • (2006) Nature , vol.440 , pp. 1007-1012
    • Schneidman, E.1    Berry, M.2    Segev, R.3    Bialek, W.4
  • 51
    • 84956071330 scopus 로고
    • Gibbs measures in ergodic theory
    • Sinai Y (1972) Gibbs measures in ergodic theory. Russ Math Surveys 27(4): 21-69.
    • (1972) Russ Math Surveys , vol.27 , Issue.4 , pp. 21-69
    • Sinai, Y.1
  • 52
    • 33644875527 scopus 로고    scopus 로고
    • Spontaneous dynamics of asymmetric random recurrent spiking neural networks
    • Soula H, Beslon G, Mazet O (2006) Spontaneous dynamics of asymmetric random recurrent spiking neural networks. Neural Comput 18(1): 60-79.
    • (2006) Neural Comput , vol.18 , Issue.1 , pp. 60-79
    • Soula, H.1    Beslon, G.2    Mazet, O.3
  • 53
    • 0002594179 scopus 로고
    • Spike arrival times: a highly efficient coding scheme for neural networks
    • Thorpe S (1990) Spike arrival times: a highly efficient coding scheme for neural networks. In: Parallel processing neural systems and computers, pp 91-94.
    • (1990) Parallel processing neural systems and computers , pp. 91-94
    • Thorpe, S.1
  • 54
    • 0029895137 scopus 로고    scopus 로고
    • Speed of processing in the human visual system
    • Thorpe S, Fize D, Marlot C (1996) Speed of processing in the human visual system. Nature 381: 520-522.
    • (1996) Nature , vol.381 , pp. 520-522
    • Thorpe, S.1    Fize, D.2    Marlot, C.3
  • 56
    • 36749062075 scopus 로고    scopus 로고
    • The spikes trains probability distributions: a stochastic calculus approach
    • Touboul J, Faugeras O (2007) The spikes trains probability distributions: a stochastic calculus approach. J Physiol (Paris) 101(1-3): 78-98.
    • (2007) J Physiol (Paris) , vol.101 , Issue.1-3 , pp. 78-98
    • Touboul, J.1    Faugeras, O.2
  • 58
    • 33847632899 scopus 로고    scopus 로고
    • Optimality model of unsupervised spike-timing dependent plasticity: synaptic memory and weight distribution
    • Toyoizumi T, Pfister J-P, Aihara K, Gerstner W (2007) Optimality model of unsupervised spike-timing dependent plasticity: synaptic memory and weight distribution. Neural Comput 19: 639-671.
    • (2007) Neural Comput , vol.19 , pp. 639-671
    • Toyoizumi, T.1    Pfister, J.-P.2    Aihara, K.3    Gerstner, W.4
  • 59
    • 79956073160 scopus 로고    scopus 로고
    • Vasquez J, Cessac B, Vieville T (2010) Entropy-based parametric estimation of spike train statistics. J Comput Neurosci (submitted).


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