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Cross nearest-spike interval based method to measure synchrony dynamics
Estimating nonstationary inputs from a single spike train based on a neuron model with adaptation
1. | NTT Service Evolution Laboratories, NTT Corporation, Yokosuka-shi, Kanagawa, 239-0847, Japan |
2. | Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan |
References:
[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.
doi: 10.1152/jn.00240.2010. |
[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.
doi: 10.2307/1427102. |
[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.
doi: 10.1103/PhysRevE.71.011907. |
[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.
doi: 10.1103/PhysRevE.79.021905. |
[7] |
M. J. Higley and D. Contreras, Balanced excitation and inhibition determine spike timing during frequency adaptation, J. Neurosci., 26 (2006), 448-457.
doi: 10.1523/JNEUROSCI.3506-05.2006. |
[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.
doi: 10.1007/BF00201423. |
[9] |
S. Iyengar and Q. Liao, Modeling neural activity using the generalized inverse Gaussian distribution, Biol. Cybern., 77 (1997), 289-295.
doi: 10.1007/s004220050390. |
[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.
doi: 10.1103/PhysRevE.86.051903. |
[12] |
P. Lánský and V. Lánská, Diffusion approximation of the neuronal model with synaptic reversal potentials, Biol. Cybern., 56 (1987), 19-26.
doi: 10.1007/BF00333064. |
[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] |
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.
doi: 10.1016/j.jtbi.2004.08.030. |
[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.
doi: 10.1007/s10827-007-0047-5. |
[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.
doi: 10.1016/j.neucom.2006.10.101. |
[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.
doi: 10.1162/0899766042321797. |
[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.
doi: 10.1007/s10827-007-0042-x. |
[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.
doi: 10.2307/3214232. |
[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.
doi: 10.1016/S0893-6080(99)00053-2. |
[27] |
T. Shimokawa and S. Shinomoto, Estimating instantaneous irregularity of neuronal firing, Neural Comput., 21 (2009), 1931-1951.
doi: 10.1162/neco.2009.08-08-841. |
[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.
doi: 10.1162/089976699300016511. |
[29] |
A. Smith and E. Brown, Estimating a state-space model from point process observations, Neural Comput., 15 (2003), 965-991.
doi: 10.1162/089976603765202622. |
[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.
doi: 10.1038/nature01616. |
[32] |
C. F. Stevens and A. M. Zador, Input synchrony and the irregular firing of cortical neurons, Nat. Neurosci., 1 (1998), 210-217.
doi: 10.1038/659. |
[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.
doi: 10.1162/neco.1997.9.5.971. |
[34] |
H. C. Tuckwell, "Introduction to Theoretical Neurobiology," Cambridge Studies in Mathematical Biology, No. 8, Cambridge University Press, Cambridge, 1988.
doi: 10.1017/CBO9780511623271. |
[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.
doi: 10.1016/j.jtbi.2008.11.004. |
[36] |
M. Wehr and A. M. Zador, Balanced inhibition underlies tuning and sharpens spike timing in auditory cortex, Nature, 426 (2003), 442-446.
doi: 10.1038/nature02116. |
[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.
doi: 10.1162/neco.2009.06-08-807. |
show all references
References:
[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.
doi: 10.1152/jn.00240.2010. |
[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.
doi: 10.2307/1427102. |
[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.
doi: 10.1103/PhysRevE.71.011907. |
[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.
doi: 10.1103/PhysRevE.79.021905. |
[7] |
M. J. Higley and D. Contreras, Balanced excitation and inhibition determine spike timing during frequency adaptation, J. Neurosci., 26 (2006), 448-457.
doi: 10.1523/JNEUROSCI.3506-05.2006. |
[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.
doi: 10.1007/BF00201423. |
[9] |
S. Iyengar and Q. Liao, Modeling neural activity using the generalized inverse Gaussian distribution, Biol. Cybern., 77 (1997), 289-295.
doi: 10.1007/s004220050390. |
[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.
doi: 10.1103/PhysRevE.86.051903. |
[12] |
P. Lánský and V. Lánská, Diffusion approximation of the neuronal model with synaptic reversal potentials, Biol. Cybern., 56 (1987), 19-26.
doi: 10.1007/BF00333064. |
[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] |
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.
doi: 10.1016/j.jtbi.2004.08.030. |
[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.
doi: 10.1007/s10827-007-0047-5. |
[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.
doi: 10.1016/j.neucom.2006.10.101. |
[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.
doi: 10.1162/0899766042321797. |
[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.
doi: 10.1007/s10827-007-0042-x. |
[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.
doi: 10.2307/3214232. |
[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.
doi: 10.1016/S0893-6080(99)00053-2. |
[27] |
T. Shimokawa and S. Shinomoto, Estimating instantaneous irregularity of neuronal firing, Neural Comput., 21 (2009), 1931-1951.
doi: 10.1162/neco.2009.08-08-841. |
[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.
doi: 10.1162/089976699300016511. |
[29] |
A. Smith and E. Brown, Estimating a state-space model from point process observations, Neural Comput., 15 (2003), 965-991.
doi: 10.1162/089976603765202622. |
[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.
doi: 10.1038/nature01616. |
[32] |
C. F. Stevens and A. M. Zador, Input synchrony and the irregular firing of cortical neurons, Nat. Neurosci., 1 (1998), 210-217.
doi: 10.1038/659. |
[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.
doi: 10.1162/neco.1997.9.5.971. |
[34] |
H. C. Tuckwell, "Introduction to Theoretical Neurobiology," Cambridge Studies in Mathematical Biology, No. 8, Cambridge University Press, Cambridge, 1988.
doi: 10.1017/CBO9780511623271. |
[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.
doi: 10.1016/j.jtbi.2008.11.004. |
[36] |
M. Wehr and A. M. Zador, Balanced inhibition underlies tuning and sharpens spike timing in auditory cortex, Nature, 426 (2003), 442-446.
doi: 10.1038/nature02116. |
[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.
doi: 10.1162/neco.2009.06-08-807. |
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