Mathematical Biosciences and Engineering (MBE)

Estimating nonstationary inputs from a single spike train based on a neuron model with adaptation
Pages: 49 - 62, Issue 1, February 2014

doi:10.3934/mbe.2014.11.49      Abstract        References        Full text (753.6K)           Related Articles

Hideaki Kim - NTT Service Evolution Laboratories, NTT Corporation, Yokosuka-shi, Kanagawa, 239-0847, Japan (email)
Shigeru Shinomoto - Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan (email)

1 O. Avila-Akerberg and M. J. Chacron, Nonrenewal spike train statistics: Causes and functional consequences on neural coding, Exp. Brain Res., 210 (2011), 353-371.
2 J. Benda, L. Maler and A. Longtin, Linear versus nonlinear signal transmission in neuron models with adaptation currents or dynamic thresholds, J. Neurophysiol., 104 (2010), 2806-2820.
3 A. Buonocore, A. G. Nobile and L. M. Ricciardi, A new integral equation for the evaluation of first-passage-time probability densities, Adv. Appl. Probab., 19 (1987), 784-800.       
4 D. R. Cox and P. A. W. Lewis, "The Statistical Analysis of Series of Events," Methuen & Co., Ltd., London; John Wiley & Sons, Inc., New York, 1966.       
5 S. Ditlevsen and P. Lansky, Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model, Phys. Rev. E, 71 (2005), 011907, 9 pp.       
6 F. Farkhooi, M. F. Strube-Bloss and M. P. Nawrot, Serial correlation in neural spike trains: Experimental evidence, stochastic modeling, and single neuron variability, Phys. Rev. E, 79 (2009), 021905.
7 M. J. Higley and D. Contreras, Balanced excitation and inhibition determine spike timing during frequency adaptation, J. Neurosci., 26 (2006), 448-457.
8 J. Inoue, S. Sato and L. M. Ricciardi, On the parameter estimation for diffusion models of single neuron's activities, Biol. Cybern., 73 (1995), 209-221.
9 S. Iyengar and Q. Liao, Modeling neural activity using the generalized inverse Gaussian distribution, Biol. Cybern., 77 (1997), 289-295.
10 J. Keilson and H. F. Ross, Passage time distributions for Gaussian Markov (Ornstein-Uhlenbeck) statistical processes, in "Selected tables in mathematical statistics, Vol. III," Amer. Math. Soc., Providence, RI, (1975), 233-327.       
11 H. Kim and S. Shinomoto, Estimating nonstationary input signals from a single neuronal spike train, Phys. Rev. E, 86 (2012), 051903.
12 P. Lánský and V. Lánská, Diffusion approximation of the neuronal model with synaptic reversal potentials, Biol. Cybern., 56 (1987), 19-26.       
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 N. N. Lebedev, "Special Functions and Their Applications," Revised edition, Dover Publications, Inc., New York, 1972.       
15 B. Lindner and A. Longtin, Effect of an exponentially decaying threshold on the firing statistics of a stochastic integrate-and-fire neuron, J. Theor. Biol., 232 (2005), 505-521.       
16 Y.-H. Liu and X.-J. Wang, Spike-frequency adaptation of a generalized leaky integrate-and-fire model neuron, J. Comput. Neurosci., 10 (2001), 25-45.
17 A. Mason and A. Larkman, Correlations between morphology and electrophysiology of pyramidal neurons in slices of rat visual cortex. II. Electrophysiology, J. Neurosci., 10 (1990), 1415-1428.
18 A. Mason, A. Nicoll and K. Stratford, Synaptic transmission between individual pyramidal neurons of the rat visual cortex in vitro, J. Neurosci., 11 (1991), 72-84.
19 D. A. McCormick, B. W. Connors, J. W. Lighthall and D. A. Prince, Comparative electrophysiology of pyramidal and sparsely spiny stellate neurons of the neocortex, J. Neurophysiol., 54 (1985), 782-806.
20 P. Mullowney and S. Iyengar, Parameter estimation for a leaky integrate-and-fire neuronal model from ISI data, J. Comput. Neurosci., 24 (2008), 179-194.       
21 M. P. Nawrot, C. Boucsein, V. Rodriguez-Molina, A. Aertsen, S. Grün and S. Rotter, Serial interval statistics of spontaneous activity in cortical neurons in vivo and in vitro, Neurocomput., 70 (2007), 1717-1722.
22 L. Paninski, J. W. Pillow and E. P. Simoncelli, Maximum likelihood estimation of a stochastic integrate-and-fire neural encoding model, Neural Comput., 16 (2004), 2533-2561.
23 L. Paninski, A. Haith and G. Szirtes, Integral equation methods for computing likelihoods and their derivatives in the stochastic integrate-and-fire model, J. Comput. Neurosci., 24 (2008), 69-79.       
24 W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery, "Numerical Recipes in C: The Art of Scientific Computing," $2^{nd}$ edition, Cambridge University Press, Cambridge, 1992.       
25 L. M. Ricciardi and S. Sato, First-passage-time density and moments of the Ornstein-Uhlenbeck process, J. Appl. Prob., 25 (1988), 43-57.       
26 Y. Sakai, S. Funahashi and S. Shinomoto, Temporally correlated inputs to leaky integrate-and-fire models can reproduce spiking statistics of cortical neurons, Neural Netw., 12 (1999), 1181-1190.
27 T. Shimokawa and S. Shinomoto, Estimating instantaneous irregularity of neuronal firing, Neural Comput., 21 (2009), 1931-1951.       
28 S. Shinomoto, Y. Sakai and S. Funahashi, The Ornstein-Uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex, Neural Comput., 11 (1999), 935-951.
29 A. Smith and E. Brown, Estimating a state-space model from point process observations, Neural Comput., 15 (2003), 965-991.
30 W. R. Softky and C. Koch, The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs, J. Neurosci., 13 (1993), 334-350.
31 Y. Shu, A. Hasenstaub and D. A. McCormick, Turning on and off recurrent balanced cortical activity, Nature, 423 (2003), 288-293.
32 C. F. Stevens and A. M. Zador, Input synchrony and the irregular firing of cortical neurons, Nat. Neurosci., 1 (1998), 210-217.
33 T. W. Troyer and K. D. Miller, Physiological gain leads to high ISI variability in a simple model of a cortical regular spiking cell, Neural Comput., 9 (1997), 971-983.
34 H. C. Tuckwell, "Introduction to Theoretical Neurobiology," Cambridge Studies in Mathematical Biology, No. 8, Cambridge University Press, Cambridge, 1988.
35 R. D. Vilela and B. Lindner, Are the input parameters of white noise driven integrate and fire neurons uniquely determined by rate and CV?, J. Theor. Biol., 257 (2009), 90-99.       
36 M. Wehr and A. M. Zador, Balanced inhibition underlies tuning and sharpens spike timing in auditory cortex, Nature, 426 (2003), 442-446.
37 X. Zhang, G. You, T. Chen and J. Feng, Maximum likelihood decoding of neuronal inputs from an interspike interval distribution, Neural Comput., 21 (2009), 3079-3105.       

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