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A leaky integrate-and-fire model with adaptation for the generation of a spike train
Successive spike times predicted by a stochastic neuronal model with a variable input signal
1. | Dipartimento di Matematica e Applicazioni, Università degli studi di Napoli, FEDERICO II, Via Cinthia, Monte S.Angelo, Napoli, 80126, Italy |
2. | Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli |
References:
[1] |
A. N. Burkitt, A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input, Biological Cybernetics, 95 (2006), 1-19.
doi: 10.1007/s00422-006-0068-6. |
[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.
doi: 10.1007/s11009-009-9132-8. |
[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.
doi: 10.1162/NECO_a_00023. |
[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.
doi: 10.1016/j.amc.2014.01.143. |
[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.
doi: 10.1016/j.cam.2015.01.042. |
[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.
doi: 10.1007/978-94-017-9548-7_42. |
[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.
doi: 10.1239/aap/999188324. |
[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.
doi: 10.1523/JNEUROSCI.4649-03.2004. |
[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.
doi: 10.1007/s00422-008-0237-x. |
[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.
doi: 10.1103/PhysRevE.69.022901. |
[16] |
L. M. Ricciardi and L. Sacerdote, The Ornstein-Uhlenbeck process as a model for neuronal activity, Biological Cybernetics, 35 (1979), 1-9.
doi: 10.1007/BF01845839. |
[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.
doi: 10.1007/s10827-015-0560-x. |
[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.
doi: 10.1073/pnas.1212479110. |
[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.
doi: 10.1162/NECO_a_00577. |
[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.
doi: 10.1007/s10955-010-0033-6. |
[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.
doi: 10.1239/jap/1308662636. |
[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.
doi: 10.1371/journal.pcbi.1002615. |
[26] |
H. C. Tuckwell, Stochastic Processes in the Neurosciences, SIAM, 1989.
doi: 10.1137/1.9781611970159. |
[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.
doi: 10.1088/1751-8113/45/18/185001. |
show all references
References:
[1] |
A. N. Burkitt, A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input, Biological Cybernetics, 95 (2006), 1-19.
doi: 10.1007/s00422-006-0068-6. |
[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.
doi: 10.1007/s11009-009-9132-8. |
[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.
doi: 10.1162/NECO_a_00023. |
[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.
doi: 10.1016/j.amc.2014.01.143. |
[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.
doi: 10.1016/j.cam.2015.01.042. |
[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.
doi: 10.1007/978-94-017-9548-7_42. |
[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.
doi: 10.1239/aap/999188324. |
[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.
doi: 10.1523/JNEUROSCI.4649-03.2004. |
[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.
doi: 10.1007/s00422-008-0237-x. |
[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.
doi: 10.1103/PhysRevE.69.022901. |
[16] |
L. M. Ricciardi and L. Sacerdote, The Ornstein-Uhlenbeck process as a model for neuronal activity, Biological Cybernetics, 35 (1979), 1-9.
doi: 10.1007/BF01845839. |
[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.
doi: 10.1007/s10827-015-0560-x. |
[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.
doi: 10.1073/pnas.1212479110. |
[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.
doi: 10.1162/NECO_a_00577. |
[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.
doi: 10.1007/s10955-010-0033-6. |
[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.
doi: 10.1239/jap/1308662636. |
[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.
doi: 10.1371/journal.pcbi.1002615. |
[26] |
H. C. Tuckwell, Stochastic Processes in the Neurosciences, SIAM, 1989.
doi: 10.1137/1.9781611970159. |
[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.
doi: 10.1088/1751-8113/45/18/185001. |
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