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On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model
1. | Dipartimento di Studi e Ricerche Aziendali (Management &Information Technology), Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy |
2. | Dipartimento di Matematica, Università degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano (SA), Italy |
References:
[1] |
A. Buonocore, A. G. Nobile and L. M. Ricciardi, A new integral equation for the evaluation of first-passage-time probability densities, Adv. Appl. Prob., 19 (1987), 784-800.
doi: 10.2307/1427102. |
[2] |
A. Buonocore, L. Caputo and E. Pirozzi, On the evaluation of firing densities for periodically driven neuron models, Math. Biosci., 214 (2008), 122-133.
doi: 10.1016/j.mbs.2008.02.003. |
[3] |
R. M. Capocelli and L. M. Ricciardi, Diffusion approximation and first passage time problem for a model neuron, Kybernetik (Berlin), 8 (1971), 214-223.
doi: 10.1007/BF00288750. |
[4] |
S. Ditlevsen and P. Lansky, Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model, Phys. Rev. E (3), 71 (2005), 011907, 9 pp.
doi: 10.1103/PhysRevE.71.011907. |
[5] |
S. Ditlevsen and P. Lansky, Comparison of statistical methods for estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model from first-passage times data, in Collective Dynamics: Topics on Competition and Cooperation in the Biosciences (eds. L. M. Ricciardi, A. Buonocore and E. Pirozzi), AIP Conf. Proc., 1028, Amer. Inst. Phys., Melville, NY, 2008, 171-185.
doi: 10.1063/1.2965085. |
[6] |
G, Esposito, V. Giorno, A. G. Nobile, L. M. Ricciardi and C. Valerio, Neuronal modeling in the presence of random refractoriness, Sci. Math. Jpn., 64 (2006), 1-36. |
[7] |
G. L. Gerstein and B. Mandelbrot, Random walk models for the spike activity of a single neuron, Biophys. J., 4 (1964), 41-68.
doi: 10.1016/S0006-3495(64)86768-0. |
[8] |
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. in Appl. Probab., 22 (1990), 883-914.
doi: 10.2307/1427567. |
[9] |
M. T. Giraudo and L. Sacerdote, Jump-diffusion processes as models for neuronal activity, BioSystems, 40 (1997), 75-82.
doi: 10.1016/0303-2647(96)01632-2. |
[10] |
P. Lansky and L. Sacerdote, The Ornstein-Uhlenbeck neuronal model with signal-dependent noise, Physics Letters A, 285 (2001), 132-140.
doi: 10.1016/S0375-9601(01)00340-1. |
[11] |
P. Lansky, P. Sanda and J. He, The parameters of the stochastic leaky integrate-and-fire neuronal model, J. Comput. Neurosci., 21 (2006), 211-223.
doi: 10.1007/s10827-006-8527-6. |
[12] |
L. M. Ricciardi and F. Esposito, On some distribution functions for non-linear switching elements with finite dead time, Kybernetik, 3 (1966), 148-152.
doi: 10.1007/BF00288925. |
[13] |
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, Math. Japon., 50 (1999), 247-322. |
[14] |
L. M. Ricciardi and L. Sacerdote, The Ornstein-Uhlenbeck process as a model for neuronal activity, Biol. Cyb., 35 (1979), 1-9.
doi: 10.1007/BF01845839. |
[15] |
M. C. Teich, L. Matin and B. I. Cantor, Refractoriness in the maintained discharge of the cat's retinal ganglion cell, J. Opt. Soc. Am., 68 (1978), 386-402.
doi: 10.1364/JOSA.68.000386. |
show all references
References:
[1] |
A. Buonocore, A. G. Nobile and L. M. Ricciardi, A new integral equation for the evaluation of first-passage-time probability densities, Adv. Appl. Prob., 19 (1987), 784-800.
doi: 10.2307/1427102. |
[2] |
A. Buonocore, L. Caputo and E. Pirozzi, On the evaluation of firing densities for periodically driven neuron models, Math. Biosci., 214 (2008), 122-133.
doi: 10.1016/j.mbs.2008.02.003. |
[3] |
R. M. Capocelli and L. M. Ricciardi, Diffusion approximation and first passage time problem for a model neuron, Kybernetik (Berlin), 8 (1971), 214-223.
doi: 10.1007/BF00288750. |
[4] |
S. Ditlevsen and P. Lansky, Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model, Phys. Rev. E (3), 71 (2005), 011907, 9 pp.
doi: 10.1103/PhysRevE.71.011907. |
[5] |
S. Ditlevsen and P. Lansky, Comparison of statistical methods for estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model from first-passage times data, in Collective Dynamics: Topics on Competition and Cooperation in the Biosciences (eds. L. M. Ricciardi, A. Buonocore and E. Pirozzi), AIP Conf. Proc., 1028, Amer. Inst. Phys., Melville, NY, 2008, 171-185.
doi: 10.1063/1.2965085. |
[6] |
G, Esposito, V. Giorno, A. G. Nobile, L. M. Ricciardi and C. Valerio, Neuronal modeling in the presence of random refractoriness, Sci. Math. Jpn., 64 (2006), 1-36. |
[7] |
G. L. Gerstein and B. Mandelbrot, Random walk models for the spike activity of a single neuron, Biophys. J., 4 (1964), 41-68.
doi: 10.1016/S0006-3495(64)86768-0. |
[8] |
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. in Appl. Probab., 22 (1990), 883-914.
doi: 10.2307/1427567. |
[9] |
M. T. Giraudo and L. Sacerdote, Jump-diffusion processes as models for neuronal activity, BioSystems, 40 (1997), 75-82.
doi: 10.1016/0303-2647(96)01632-2. |
[10] |
P. Lansky and L. Sacerdote, The Ornstein-Uhlenbeck neuronal model with signal-dependent noise, Physics Letters A, 285 (2001), 132-140.
doi: 10.1016/S0375-9601(01)00340-1. |
[11] |
P. Lansky, P. Sanda and J. He, The parameters of the stochastic leaky integrate-and-fire neuronal model, J. Comput. Neurosci., 21 (2006), 211-223.
doi: 10.1007/s10827-006-8527-6. |
[12] |
L. M. Ricciardi and F. Esposito, On some distribution functions for non-linear switching elements with finite dead time, Kybernetik, 3 (1966), 148-152.
doi: 10.1007/BF00288925. |
[13] |
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, Math. Japon., 50 (1999), 247-322. |
[14] |
L. M. Ricciardi and L. Sacerdote, The Ornstein-Uhlenbeck process as a model for neuronal activity, Biol. Cyb., 35 (1979), 1-9.
doi: 10.1007/BF01845839. |
[15] |
M. C. Teich, L. Matin and B. I. Cantor, Refractoriness in the maintained discharge of the cat's retinal ganglion cell, J. Opt. Soc. Am., 68 (1978), 386-402.
doi: 10.1364/JOSA.68.000386. |
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