Mathematical Biosciences and Engineering (MBE)

Successive spike times predicted by a stochastic neuronal model with a variable input signal
Pages: 495 - 507, Issue 3, June 2016

doi:10.3934/mbe.2016003      Abstract        References        Full text (2329.8K)           Related Articles

Giuseppe D'Onofrio - Dipartimento di Matematica e Applicazioni, Università degli studi di Napoli, FEDERICO II, Via Cinthia, Monte S.Angelo, Napoli, 80126, Italy (email)
Enrica Pirozzi - Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli, Italy (email)

1 A. N. Burkitt, A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input, Biological Cybernetics, 95 (2006), 1-19.       
2 A. Buonocore, L. Caputo, E. Pirozzi and L. M. Ricciardi, The first passage time problem for Gauss-diffusion processes: Algorithmic approaches and applications to LIF neuronal model, Methodol. Comput. Appl. Prob., 13 (2011), 29-57.       
3 A. Buonocore, L. Caputo, E. Pirozzi and L. M. Ricciardi, On a stochastic leaky integrate-and-fire neuronal model, Neural Computation, 22 (2010), 2558-2585.       
4 A. Buonocore, L. Caputo, E. Pirozzi and M. F. Carfora, Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons, Math. Biosci. Eng., 11 (2014), 189-201.       
5 A. Buonocore, L. Caputo, A. G. Nobile and E. Pirozzi, Gauss-Markov processes in the presence of a reflecting boundary and applications in neuronal models, Applied Mathematics and Computation, 232 (2014), 799-809.       
6 A. Buonocore, L. Caputo, A. G. Nobile and E. Pirozzi, Restricted Ornstein-Uhlenbeck process and applications in neuronal models with periodic input signals, Journal of Computational and Applied Mathematics, 285 (2015), 59-71.       
7 A. Buonocore, L. Caputo, A. G. Nobile and E. Pirozzi, Gauss-markov processes for neuronal models including reversal potentials, Advances in Cognitive Neurodynamics (IV), 11 (2015), 299-305.
8 M. J. Chacron, K. Pakdaman and A. Longtin, Interspike interval correlations, memory, adaptation, and refractoriness in a leaky integrate-and-fire neuron with threshold fatigue. Neural Computation, 15 (2003), 253-276.
9 E. Di Nardo, A. G. Nobile, E. Pirozzi and L. M. Ricciardi, A computational approach to first passage-time problems for Gauss-Markov processes, Adv. Appl. Prob., 33 (2001), 453-482.       
10 J. M. Fellous, P. H. Tiesinga, P. J. Thomas and T. J. Sejnowski, Discovering spike patterns in neuronal responses, The Journal of Neuroscience, 24 (2004), 2989-3001.
11 V. Giorno and S. Spina, On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model, Math. Bios. Eng., 11 (2014), 285-302.       
12 H. Kim and S. Shinomoto, Estimating nonstationary inputs from a single spike train based on a neuron model with adaptation, Math. Bios. Eng., 11 (2014), 49-62.       
13 P. Lánský and S. Ditlevsen, A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models, Biol. Cybern., 99 (2008), 253-262.       
14 P. Lánský, Sources of periodical force in noisy integrate-and-fire models of neuronal dynamics, Physical Review E, 55 (1997), 2040-2043.
15 B. Lindner, Interspike interval statistics for neurons driven by colored noise, Physical Review E, 69 (2004), 022901-1-022901-4.
16 L. M. Ricciardi and L. Sacerdote, The Ornstein-Uhlenbeck process as a model for neuronal activity, Biological Cybernetics, 35 (1979), 1-9.
17 L. M. Ricciardi, A. Di Crescenzo, V. Giorno and A. G. Nobile, An outline of theoretical and algorithmic approaches to first passage time problems with applications to biological modeling, Mathematica Japonica, 50 (1999), 247-322.       
18 T. Schwalger, F. Droste and B. Lindner, Statistical structure of neural spiking under non-Poissonian or other non-white stimulation, Journal of Computational Neuroscience, 39 (2015), 29-51.       
19 M. Shaked and J. G. Shanthikumar, Stochastic Orders and Their Applications, Academic Press, Boston (USA), 1994.       
20 S. Shinomoto, Y. Sakai and S. Funahashi, The Ornstein-Uhlenbeck process does not reproduce spiking statistics of cortical neurons, Neural Computation, 11 (1997), 935-951.
21 T. Taillefumier and M. 0. Magnasco, A phase transition in the first passage of a Brownian process through a fluctuating boundary: Implications for neural coding, PNAS, 110 (2013), E1438-E1443.
22 T. Taillefumier and M. Magnasco, A transition to sharp timing in stochastic leaky integrate-and-fire neurons driven by frozen noisy input, Neural Computation, 26 (2014), 819-859.       
23 T. Taillefumier and M. Magnasco, A fast algorithm for the first-passage times of Gauss-Markov processes with Holder continuous boundaries, J. Stat. Phys., 140 (2010), 1130-1156.       
24 P. J. Thomas, A lower bound for the first passage time density of the suprathreshold Ornstein-Uhlenbeck process, J. Appl. Probab., 48 (2011), 420-434.       
25 J. V. Toups, J. M. Fellous, P. J. Thomas, T. J. Sejnowski and P. H. Tiesinga, Multiple spike time patterns occur at bifurcation points of membrane potential dynamics, PLoS Comput. Biol., 8 (2012), e1002615, 1-19.       
26 H. C. Tuckwell, Stochastic Processes in the Neurosciences, SIAM, 1989.       
27 E. Urdapilleta, Series solution to the first-passage-time problem of a Brownian motion with an exponential time-dependent drift, J. Stat. Phys., 140 (2010), 1130-1156.

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