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Gauss-diffusion processes for modeling the dynamics of a couple of interacting neurons
1. | Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università di Napoli Federico II, Via Cintia, 80126 Napoli |
2. | Istituto per le Appplicazioni del Calcolo "Mauro Picone", Consiglio Nazionale delle Ricerche, Via Pietro Castellino, Napoli |
References:
[1] |
K. Amemori and S. Ishii, Gaussian process approach to spiking neurons for inhomogeneous Poisson inputs, Neural Comp., 13 (2001), 2763-2797.
doi: 10.1162/089976601317098529. |
[2] |
A. Buonocore, A. G. Nobile and L. M. Ricciardi, A new integral equation for evaluation of first-passage-time probability densities, Advances in Applied Probability, 19 (1987), 784-990.
doi: 10.2307/1427102. |
[3] |
A. Buonocore, L. Caputo, E. Pirozzi and L. M. Ricciardi, On a stochastic leaky integrate-and-fire neuronal model, Neural Comput., 22 (2010), 2558-2585.
doi: 10.1162/NECO_a_00023. |
[4] |
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. Probab., 13 (2011), 29-57.
doi: 10.1007/s11009-009-9132-8. |
[5] |
A. N. Burkitt, A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input, Biol. Cybern., 95 (2006), 1-19.
doi: 10.1007/s00422-006-0068-6. |
[6] |
A. Di Crescenzo, B. Martinucci and E. Pirozzi, Feedback effects in simulated Stein's coupled neurons, in Computer Aided Systems Theory – EUROCAST 2005, Lecture Notes in Computer Science, 3643, Springer, Berlin-Heidelberg, 2005, 436-446.
doi: 10.1007/11556985_57. |
[7] |
A. Di Crescenzo, B. Martinucci and E. Pirozzi, On the dynamics of a pair of coupled neurons subject to alternating input rates, BioSystems, 79 (2005), 109-116.
doi: 10.1016/j.biosystems.2004.09.020. |
[8] |
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. |
[9] |
Y. Dong, F. Mihalas and E. Niebur, Improved integral equation solution for the first passage time of leaky integrate-and-fire neurons, Neural Computation, 23 (2011), 421-434.
doi: 10.1162/NECO_a_00078. |
[10] |
V. Giorno, A. G. Nobile and L. M. Ricciardi, On the asymptotic behaviour of first-passage-time densities for one-dimensional diffusion processes and varying boundaries, Adv. Appl. Prob., 22 (1990), 883-914.
doi: 10.2307/1427567. |
[11] |
D. Golomb and G. B. Ermentrout, Bistability in pulse propagation in networks of excitatory and inhibitory populations, Phys. Rev. Lett., 68 (2001), 4179-4182.
doi: 10.1103/PhysRevLett.86.4179. |
[12] |
A. G. Nobile, E. Pirozzi and L. M. Ricciardi, On the estimation of first-passage time densities for a class of Gauss-Markov processes, in Computer Aided Systems Theory – EUROCAST 2007, Lecture Notes in Computer Science, 4739, Springer, Berlin-Heidelberg, 2007, 146-153.
doi: 10.1007/978-3-540-75867-9_19. |
[13] |
A. G. Nobile, E. Pirozzi and L. M. Ricciardi., Asymptotics and evaluations of fpt densities through varying boundaries for Gauss-Markov processes, Scientiae Mathematicae Japonicae, 67 (2008), 241-266. Available from: http://www.jams.or.jp/scm/contents/e-2008-2/2008-12.pdf. |
[14] |
A. Politi and S. Luccioli, Dynamics of networks of leaky-integrate-and-fire neurons, in Network Science, Springer, London, 2010, 217-242.
doi: 10.1007/978-1-84996-396-1_11. |
[15] |
L. Sacerdote, M. Tamborrino and C. Zucca, Detecting dependencies between spike trains of pairs of neurons through copulas, Brain Research, 1434 (2012), 243-256.
doi: 10.1016/j.brainres.2011.08.064. |
[16] |
H. Sakaguchi, Oscillatory phase transition and pulse propagation in noisy integrate-and-fire neurons, Phys. Rev. E., 70 (2004), 1-4.
doi: 10.1103/PhysRevE.70.022901. |
[17] |
H. Sakaguchi and S. Tobiishi, Synchronization and spindle oscillation in noisy integrate-and-fire-or-burst neurons with inhibitory coupling, Progress of Theoretical Physics, 114 (2005), 1-18.
doi: 10.1143/PTP.114.539. |
[18] |
R. Sirovich, L. Sacerdote and A. E. P. Villa, Effect of increasing inhibitory inputs on information processing within a small network of spiking neurons, in Computational and Ambient Intelligence, Lecture Notes in Computer Science, 4507, Springer, Berlin-Heidelberg, 2007, 23-30.
doi: 10.1007/978-3-540-73007-1_4. |
[19] |
H. Soula and C. C. Chow, Stochastic dynamics of a finite-size spiking neural network, Neural Comput., 19 (2007), 3262-3292.
doi: 10.1162/neco.2007.19.12.3262. |
show all references
References:
[1] |
K. Amemori and S. Ishii, Gaussian process approach to spiking neurons for inhomogeneous Poisson inputs, Neural Comp., 13 (2001), 2763-2797.
doi: 10.1162/089976601317098529. |
[2] |
A. Buonocore, A. G. Nobile and L. M. Ricciardi, A new integral equation for evaluation of first-passage-time probability densities, Advances in Applied Probability, 19 (1987), 784-990.
doi: 10.2307/1427102. |
[3] |
A. Buonocore, L. Caputo, E. Pirozzi and L. M. Ricciardi, On a stochastic leaky integrate-and-fire neuronal model, Neural Comput., 22 (2010), 2558-2585.
doi: 10.1162/NECO_a_00023. |
[4] |
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. Probab., 13 (2011), 29-57.
doi: 10.1007/s11009-009-9132-8. |
[5] |
A. N. Burkitt, A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input, Biol. Cybern., 95 (2006), 1-19.
doi: 10.1007/s00422-006-0068-6. |
[6] |
A. Di Crescenzo, B. Martinucci and E. Pirozzi, Feedback effects in simulated Stein's coupled neurons, in Computer Aided Systems Theory – EUROCAST 2005, Lecture Notes in Computer Science, 3643, Springer, Berlin-Heidelberg, 2005, 436-446.
doi: 10.1007/11556985_57. |
[7] |
A. Di Crescenzo, B. Martinucci and E. Pirozzi, On the dynamics of a pair of coupled neurons subject to alternating input rates, BioSystems, 79 (2005), 109-116.
doi: 10.1016/j.biosystems.2004.09.020. |
[8] |
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. |
[9] |
Y. Dong, F. Mihalas and E. Niebur, Improved integral equation solution for the first passage time of leaky integrate-and-fire neurons, Neural Computation, 23 (2011), 421-434.
doi: 10.1162/NECO_a_00078. |
[10] |
V. Giorno, A. G. Nobile and L. M. Ricciardi, On the asymptotic behaviour of first-passage-time densities for one-dimensional diffusion processes and varying boundaries, Adv. Appl. Prob., 22 (1990), 883-914.
doi: 10.2307/1427567. |
[11] |
D. Golomb and G. B. Ermentrout, Bistability in pulse propagation in networks of excitatory and inhibitory populations, Phys. Rev. Lett., 68 (2001), 4179-4182.
doi: 10.1103/PhysRevLett.86.4179. |
[12] |
A. G. Nobile, E. Pirozzi and L. M. Ricciardi, On the estimation of first-passage time densities for a class of Gauss-Markov processes, in Computer Aided Systems Theory – EUROCAST 2007, Lecture Notes in Computer Science, 4739, Springer, Berlin-Heidelberg, 2007, 146-153.
doi: 10.1007/978-3-540-75867-9_19. |
[13] |
A. G. Nobile, E. Pirozzi and L. M. Ricciardi., Asymptotics and evaluations of fpt densities through varying boundaries for Gauss-Markov processes, Scientiae Mathematicae Japonicae, 67 (2008), 241-266. Available from: http://www.jams.or.jp/scm/contents/e-2008-2/2008-12.pdf. |
[14] |
A. Politi and S. Luccioli, Dynamics of networks of leaky-integrate-and-fire neurons, in Network Science, Springer, London, 2010, 217-242.
doi: 10.1007/978-1-84996-396-1_11. |
[15] |
L. Sacerdote, M. Tamborrino and C. Zucca, Detecting dependencies between spike trains of pairs of neurons through copulas, Brain Research, 1434 (2012), 243-256.
doi: 10.1016/j.brainres.2011.08.064. |
[16] |
H. Sakaguchi, Oscillatory phase transition and pulse propagation in noisy integrate-and-fire neurons, Phys. Rev. E., 70 (2004), 1-4.
doi: 10.1103/PhysRevE.70.022901. |
[17] |
H. Sakaguchi and S. Tobiishi, Synchronization and spindle oscillation in noisy integrate-and-fire-or-burst neurons with inhibitory coupling, Progress of Theoretical Physics, 114 (2005), 1-18.
doi: 10.1143/PTP.114.539. |
[18] |
R. Sirovich, L. Sacerdote and A. E. P. Villa, Effect of increasing inhibitory inputs on information processing within a small network of spiking neurons, in Computational and Ambient Intelligence, Lecture Notes in Computer Science, 4507, Springer, Berlin-Heidelberg, 2007, 23-30.
doi: 10.1007/978-3-540-73007-1_4. |
[19] |
H. Soula and C. C. Chow, Stochastic dynamics of a finite-size spiking neural network, Neural Comput., 19 (2007), 3262-3292.
doi: 10.1162/neco.2007.19.12.3262. |
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