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Volumn 25, Issue 14, 2015, Pages 2669-2719

Microscopic approach of a time elapsed neural model

Author keywords

Hawkes process; neural network; renewal equation; Wold process

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; NEURAL NETWORKS;

EID: 84944278123     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S021820251550058X     Document Type: Article
Times cited : (76)

References (42)
  • 1
    • 84874565318 scopus 로고    scopus 로고
    • Markov processes and parabolic partial differential equations
    • Wiley
    • M. Bossy et al., Markov processes and parabolic partial differential equations, in Encyclopedia of Quantitative Finance (Wiley, 2010), pp. 1142-1159.
    • (2010) Encyclopedia of Quantitative Finance , pp. 1142-1159
    • Bossy, M.1
  • 4
    • 0030352915 scopus 로고    scopus 로고
    • Stability of nonlinear Hawkes processes
    • P. Brémaud and L. Massoulié, Stability of nonlinear Hawkes processes, Ann. Probab. 24 (1996) 1563-1588.
    • (1996) Ann. Probab. , vol.24 , pp. 1563-1588
    • Brémaud, P.1    Massoulié, L.2
  • 6
    • 0036482863 scopus 로고    scopus 로고
    • The time rescaling theorem and its application to neural spike train analysis
    • E. N. Brown, R. Barbieri, V. Ventura, R. E. Kass and L. M. Frank, The time rescaling theorem and its application to neural spike train analysis, Neural Comput. 14 (2002) 325-346.
    • (2002) Neural Comput. , vol.14 , pp. 325-346
    • Brown, E.N.1    Barbieri, R.2    Ventura, V.3    Kass, R.E.4    Frank, L.M.5
  • 7
    • 0034006515 scopus 로고    scopus 로고
    • Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons
    • N. Brunel, Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons, J. Comput. Neurosci. 8 (2000) 183-208.
    • (2000) J. Comput. Neurosci. , vol.8 , pp. 183-208
    • Brunel, N.1
  • 8
    • 0033210816 scopus 로고    scopus 로고
    • Fast global oscillations in networks of integrate-and-fire neurons with low firing rates
    • N. Brunel and V. Hakim, Fast global oscillations in networks of integrate-and-fire neurons with low firing rates, Neural Comput. 11 (1999) 1621-1671.
    • (1999) Neural Comput. , vol.11 , pp. 1621-1671
    • Brunel, N.1    Hakim, V.2
  • 9
    • 84861627504 scopus 로고    scopus 로고
    • Analysis of nonlinear noisy integrate and fire neuron models: Blow-up and steady states
    • M. J. Cáceres, J. A. Carrillo and B. Perthame, Analysis of nonlinear noisy integrate and fire neuron models: Blow-up and steady states, J. Math. Neurosci. 1 (2011) 1-33.
    • (2011) J. Math. Neurosci. , vol.1 , pp. 1-33
    • Cáceres, M.J.1    Carrillo, J.A.2    Perthame, B.3
  • 10
    • 78650564252 scopus 로고    scopus 로고
    • A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics
    • M. J. Cáceres, J. A. Carrillo and L. Tao, A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics, J. Comput. Phys. 230 (2011) 1084-1099.
    • (2011) J. Comput. Phys. , vol.230 , pp. 1084-1099
    • Cáceres, M.J.1    Carrillo, J.A.2    Tao, L.3
  • 11
    • 84896763570 scopus 로고    scopus 로고
    • Beyond blow-up in excitatory integrate and fire neuronal networks: Refractory period and spontaneous activity
    • M. J. Cáceres and B. Perthame, Beyond blow-up in excitatory integrate and fire neuronal networks: Refractory period and spontaneous activity, J. Theor. Biol. 350 (2014) 81-89.
    • (2014) J. Theor. Biol. , vol.350 , pp. 81-89
    • Cáceres, M.J.1    Perthame, B.2
  • 12
    • 84872609590 scopus 로고    scopus 로고
    • Measure solutions for some models in population dynamics
    • J. A. Cañizo, J. A. Carrillo and S. Cuadrado, Measure solutions for some models in population dynamics, Acta Appl. Math. 123 (2013) 141-156.
    • (2013) Acta Appl. Math. , vol.123 , pp. 141-156
    • Cañizo, J.A.1    Carrillo, J.A.2    Cuadrado, S.3
  • 13
    • 0023688346 scopus 로고
    • Maximum likelihood identification of neural point process systems
    • E. S. Chornoboy, L. P. Schramm and A. F. Karr, Maximum likelihood identification of neural point process systems, Biol. Cybern. 59 (1988) 265-275.
    • (1988) Biol. Cybern. , vol.59 , pp. 265-275
    • Chornoboy, E.S.1    Schramm, L.P.2    Karr, A.F.3
  • 15
    • 0033811553 scopus 로고    scopus 로고
    • Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model
    • A. Compte, N. Brunel, P. S. Goldman-Rakic and X.-J. Wang, Synaptic mechanisms and network dynamics underlying spatial working memory in a cortical network model, Cereb. Cortex 10 (2000) 910-923.
    • (2000) Cereb. Cortex , vol.10 , pp. 910-923
    • Compte, A.1    Brunel, N.2    Goldman-Rakic, P.S.3    Wang, X.-J.4
  • 17
    • 84936791750 scopus 로고    scopus 로고
    • Global solvability of a networked integrate-and-fire model of McKean-Vlasov type
    • F. Delarue, J. Inglis, S. Rubenthaler and E Tanré, Global solvability of a networked integrate-and-fire model of McKean-Vlasov type, Ann. Appl. Probab. 25 (2015) 2096-2133.
    • (2015) Ann. Appl. Probab. , vol.25 , pp. 2096-2133
    • Delarue, F.1    Inglis, J.2    Rubenthaler, S.3    Tanré, E.4
  • 18
    • 84903790443 scopus 로고    scopus 로고
    • Estimation in the partially observed stochastic Morris-Lecar neuronal model with particle filter and stochastic approximation methods
    • S. Ditlevsen and A. Samson, Estimation in the partially observed stochastic Morris-Lecar neuronal model with particle filter and stochastic approximation methods, Ann. Appl. Statist. 8 (2014) 674-702.
    • (2014) Ann. Appl. Statist. , vol.8 , pp. 674-702
    • Ditlevsen, S.1    Samson, A.2
  • 19
    • 84938635586 scopus 로고    scopus 로고
    • Statistical estimation of a growthfragmentation model observed on a genealogical tree
    • M. Doumic, M. Hoffmann, N. Krell and L. Robert, Statistical estimation of a growthfragmentation model observed on a genealogical tree, Bernoulli 21 (2015) 1760-1799.
    • (2015) Bernoulli , vol.21 , pp. 1760-1799
    • Doumic, M.1    Hoffmann, M.2    Krell, N.3    Robert, L.4
  • 20
    • 0001446567 scopus 로고
    • A cluster process representation of a self-exciting process
    • A. G. Hawkes and D. Oakes, A cluster process representation of a self-exciting process, J. Appl. Probab. 11 (1974) 493-503.
    • (1974) J. Appl. Probab. , vol.11 , pp. 493-503
    • Hawkes, A.G.1    Oakes, D.2
  • 21
    • 83055179797 scopus 로고    scopus 로고
    • Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process
    • P. Jahn, R. W. Berg, J. Hounsgaard and S. Ditlevsen, Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process, J. Comput. Neurosci. 31 (2011) 563-579.
    • (2011) J. Comput. Neurosci. , vol.31 , pp. 563-579
    • Jahn, P.1    Berg, R.W.2    Hounsgaard, J.3    Ditlevsen, S.4
  • 23
    • 33745639826 scopus 로고
    • An example of Wold's point processes with Markov-dependent intervals
    • C. D. Lai, An example of Wold's point processes with Markov-dependent intervals, J. Appl. Probab. 15 (1978) 748-758.
    • (1978) J. Appl. Probab. , vol.15 , pp. 748-758
    • Lai, C.D.1
  • 24
    • 0018519083 scopus 로고
    • Simulation of nonhomogeneous Poisson processes by thinning
    • P. A. W. Lewis and G. S. Shedler, Simulation of nonhomogeneous Poisson processes by thinning, Naval Res. Logistics Quart. 26 (1979) 403-413.
    • (1979) Naval Res. Logistics Quart. , vol.26 , pp. 403-413
    • Lewis, P.A.W.1    Shedler, G.S.2
  • 25
    • 85036133906 scopus 로고    scopus 로고
    • Population dynamics of interacting spiking neurons
    • M. Mattia and P. Del Giudice, Population dynamics of interacting spiking neurons, Phys. Rev. E 66 (2002) 051917.
    • (2002) Phys. Rev. e , vol.66 , pp. 051917
    • Mattia, M.1    Del Giudice, P.2
  • 27
    • 27144475437 scopus 로고    scopus 로고
    • Perfect simulation of Hawkes processes
    • J. Møller and J. G. Rasmussen, Perfect simulation of Hawkes processes, Adv. Appl. Probab. 37 (2005) 629-646.
    • (2005) Adv. Appl. Probab. , vol.37 , pp. 629-646
    • Møller, J.1    Rasmussen, J.G.2
  • 28
    • 0019396823 scopus 로고
    • On Lewis' simulation method for point processes
    • Y. Ogata, On Lewis' simulation method for point processes, IEEE Trans. Inform. Theory 27 (1981) 23-31.
    • (1981) IEEE Trans. Inform. Theory , vol.27 , pp. 23-31
    • Ogata, Y.1
  • 29
    • 0034083940 scopus 로고    scopus 로고
    • On the simulation of large populations of neurons
    • A. Omurtag, B. W. Knight and L. Sirovich, On the simulation of large populations of neurons, J. Comp. Neurosci. 8 (2000) 51-63.
    • (2000) J. Comp. Neurosci. , vol.8 , pp. 51-63
    • Omurtag, A.1    Knight, B.W.2    Sirovich, L.3
  • 30
    • 76149134681 scopus 로고    scopus 로고
    • Dynamics of a structured neuron population
    • K. Pakdaman, B. Perthame and D. Salort, Dynamics of a structured neuron population, Nonlinearity 23 (2010) 55-75.
    • (2010) Nonlinearity , vol.23 , pp. 55-75
    • Pakdaman, K.1    Perthame, B.2    Salort, D.3
  • 31
    • 84884136684 scopus 로고    scopus 로고
    • Relaxation and self-sustained oscillations in the time elapsed neuron network model
    • K. Pakdaman, B. Perthame and D. Salort, Relaxation and self-sustained oscillations in the time elapsed neuron network model, SIAM J. Appl. Math. 73 (2013) 1260-1279.
    • (2013) SIAM J. Appl. Math. , vol.73 , pp. 1260-1279
    • Pakdaman, K.1    Perthame, B.2    Salort, D.3
  • 32
    • 84944278383 scopus 로고    scopus 로고
    • Adaptation and fatigue model for neuron networks and large time asymptotics in a nonlinear fragmentation equation
    • K. Pakdaman, B. Perthame and D. Salort, Adaptation and fatigue model for neuron networks and large time asymptotics in a nonlinear fragmentation equation, J. Math. Neurosci. 4 (2014) 1-26.
    • (2014) J. Math. Neurosci. , vol.4 , pp. 1-26
    • Pakdaman, K.1    Perthame, B.2    Salort, D.3
  • 34
    • 0032053324 scopus 로고    scopus 로고
    • Activity in sparsely connected excitatory neural networks: Effect of connectivity
    • J. Pham, K. Pakdaman, J. Champagnat and J.-F. Vibert, Activity in sparsely connected excitatory neural networks: Effect of connectivity, Neural Netw. 11 (1998) 415-434.
    • (1998) Neural Netw. , vol.11 , pp. 415-434
    • Pham, J.1    Pakdaman, K.2    Champagnat, J.3    Vibert, J.-F.4
  • 36
    • 84877817715 scopus 로고    scopus 로고
    • Impact of spike train autostructure on probability distribution of joint spike events
    • G. Pipa, S. Grün and C. van Vreeswijk, Impact of spike train autostructure on probability distribution of joint spike events, Neural Comput. 25 (2013) 1123-1163.
    • (2013) Neural Comput. , vol.25 , pp. 1123-1163
    • Pipa, G.1    Grün, S.2    Van Vreeswijk, C.3
  • 37
    • 67349278162 scopus 로고    scopus 로고
    • Automatic spike train analysis and report generation. An implementation with R R2HTML and
    • C. Pouzat and A. Chaffiol, Automatic spike train analysis and report generation. An implementation with R, R2HTML and STAR, J. Neurosci. Methods 181 (2009) 119-144.
    • (2009) STAR, J. Neurosci. Methods , vol.181 , pp. 119-144
    • Pouzat, C.1    Chaffiol, A.2
  • 38
    • 3142740626 scopus 로고    scopus 로고
    • Mean-field theory of irregularly spiking neuronal populations and working memory in recurrent cortical networks
    • ed. J. Feng ( Chapman & Hall/CRC
    • A. Renart, N. Brunel and X.-J. Wang, Mean-field theory of irregularly spiking neuronal populations and working memory in recurrent cortical networks, in Computational Neuroscience: A Comprehensive Approach, ed. J. Feng (Chapman & Hall/CRC, 2004).
    • (2004) Computational Neuroscience: A Comprehensive Approach
    • Renart, A.1    Brunel, N.2    Wang, X.-J.3
  • 39
    • 84899459301 scopus 로고    scopus 로고
    • Goodnessof-fit tests and nonparametric adaptive estimation for spike train analysis
    • P. Reynaud-Bouret, V. Rivoirard, F. Grammont and C. Tuleau-Malot, Goodnessof-fit tests and nonparametric adaptive estimation for spike train analysis, J. Math. Neurosci. 4 (2014) 1-41.
    • (2014) J. Math. Neurosci. , vol.4 , pp. 1-41
    • Reynaud-Bouret, P.1    Rivoirard, V.2    Grammont, F.3    Tuleau-Malot, C.4
  • 42
    • 0346490012 scopus 로고    scopus 로고
    • Statistical analysis of temporal evolution in single-neuron firing rates
    • V. Ventura, R. Carta, R. E. Kass, S. N. Gettner and C. R. Olson, Statistical analysis of temporal evolution in single-neuron firing rates, Biostatistics 3 (2002) 1-20.
    • (2002) Biostatistics , vol.3 , pp. 1-20
    • Ventura, V.1    Carta, R.2    Kass, R.E.3    Gettner, S.N.4    Olson, C.R.5


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.