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Generation of slow phase-locked oscillation and variability of the interspike intervals in globally coupled neuronal oscillators
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Non-Markovian spiking statistics of a neuron with delayed feedback in presence of refractoriness
Fano factor estimation
1. | Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlarska 2a, 611 37 Brno, Czech Republic |
2. | Institute of Physiology, Academy of Sciences of the Czech Republic, Videnska 1083, 142 20 Prague |
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] |
M. J. Chacron, A. Longtin and L. Maler, Negative interspike interval correlations increase the neuronal capacity for encoding time-dependent stimuli, J. Neurosci., 21 (2001), 5328-5343. |
[3] |
M. H. Chang, K. M. Armstrong and T. Moore, Dissociation of response variability from firing rate effects in frontal eye field neurons during visual stimulation, working memory, and attention, J. Neurosci. Methods, 32 (2012), 2204-2216.
doi: 10.1523/JNEUROSCI.2967-11.2012. |
[4] |
M. M. Churchland, B. M. Yu, J. P. Cunningham, L. P. Sugrue, M. R. Cohen, G. S. Corrado, W. T. Newsome, A. M. Clark, P. Hosseini, B. B. Scott, D. C. Bradley, M. A. Smith, A. Kohn, J. A. Movshon, K. M. Armstrong, T. Moore, S. W. Chang, L. H. Snyder, S. G. Lisberger, N. J. Priebe, I. M. Finn, D. Ferster, S. I. Ryu, G. Santhanam, M. Sahani and K. V. Shenoy, Stimulus onset quenches neural variability: A widespread cortical phenomenon, Nat. Neurosci., 13 (2010), 369-378.
doi: 10.1038/nn.2501. |
[5] |
D. R. Cox, "Renewal Theory," Methuen & Co., Ltd., London; John Wiley & Sons, Inc., New York, 1962. |
[6] |
O. Darbin, J. Soares and T. Wichmann, Nonlinear analysis of discharge patterns in monkey basal ganglia, Brain Res., 1118 (2006), 84-93.
doi: 10.1016/j.brainres.2006.08.027. |
[7] |
M. Deger, M. Helias, C. Boucsein and S. Rotter, Statistical properties of superimposed stationary spike trains, J. Comput. Neurosci., 32 (2012), 443-463.
doi: 10.1007/s10827-011-0362-8. |
[8] |
S. Ditlevsen and P. Lansky, Firing variability is higher than deduced from the empirical coefficient of variation, Neural. Comput., 23 (2011), 1944-1966.
doi: 10.1162/NECO_a_00157. |
[9] |
U. T. Eden and M. A. Kramer, Drawing inferences from fano factor calculations, J. Neurosci. Methods, 190 (2010), 149-152.
doi: 10.1016/j.jneumeth.2010.04.012. |
[10] |
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. |
[11] |
W. Gerstner and W. M. Kistler, "Spiking Neuron Models. Single Neurons, Populations, Plasticity," Cambridge University Press, Cambridge, 2002. |
[12] |
C. Hussar and T. Pasternak, Trial-to-trial variability of the prefrontal neurons reveals the nature of their engagement in a motion discrimination task, P. Natl. Acad. Sci. USA, 107 (2010), 21842-21847.
doi: 10.1073/pnas.1009956107. |
[13] |
W. S. Jewell, The properties of recurrent-event processes, Oper. Res., 8 (1960), 446-472.
doi: 10.1287/opre.8.4.446. |
[14] |
L. Kostal, P. Lansky and O. Pokora, Variability measures of positive random variables, PLOS ONE, 6 (2011), e21998.
doi: 10.1371/journal.pone.0021998. |
[15] |
S. Koyama and S. Shinomoto, Inference of intrinsic spiking irregularity based on the Kullback-Leibler information, BioSystems, 89 (2007), 69-73.
doi: 10.1016/j.biosystems.2006.05.012. |
[16] |
A. M. Mood, F. A. Graybill and D. C. Boes, "Introduction to the Theory of Statistics," McGraw-Hill, Inc., 1974. |
[17] |
M. P. Nawrot, Analysis and interpretation of interval and count variability in neural spike trains, in "Analysis of Parallel Spike Trains," Springer, Inc., New York, (2010), 37-58. |
[18] |
M. P. Nawrot, C. Boucsein, V. R. Molina, A. Riehle, A. Aertsen and S. Rotter, Measurement of variability dynamics in cortical spike trains, J. Neurosci. Methods, 169 (2008), 374-390.
doi: 10.1016/j.jneumeth.2007.10.013. |
[19] |
T. Omi and S. Shinomoto, Optimizing time histograms for non-Poissonian spike trains, Neural. Comput., 23 (2011), 3125-3144.
doi: 10.1162/NECO_a_00213. |
[20] |
Z. Pawlas, L. B. Klebanov, M. Prokop and P. Lansky, Parameters of spike trains observed in a short time window, Neural. Comput., 20 (2008), 1325-1343.
doi: 10.1162/neco.2007.01-07-442. |
[21] |
B. V. D. Pol and H. Bremmer, "Operational Calculus Based on the Two-Sided Laplace Integral," Cambridge University Press, Cambridge, 1950. |
[22] |
A. Ponce-Alvarez, B. E. Kilavik and A. Riehle, Comparison of local measures of spike time irregularity and relating variability to firing rate in motor cortical neurons, J. Comput. Neurosci., 29 (2010), 351-365.
doi: 10.1007/s10827-009-0158-2. |
[23] |
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. |
[24] |
S. Shinomoto, K. Miura and S. Koyama, A measure of local variation of inter-spike intervals, BioSystems, 79 (2005), 67-72.
doi: 10.1016/j.biosystems.2004.09.023. |
[25] |
M. C. Teich, D. H. Johnson, A. R. Kumar and R. G. Turcott, Rate fluctuations and fractional power-law noise recorded from cells in the lower auditory pathway of the cat, Hearing Res., 46 (1990), 41-52.
doi: 10.1016/0378-5955(90)90138-F. |
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] |
M. J. Chacron, A. Longtin and L. Maler, Negative interspike interval correlations increase the neuronal capacity for encoding time-dependent stimuli, J. Neurosci., 21 (2001), 5328-5343. |
[3] |
M. H. Chang, K. M. Armstrong and T. Moore, Dissociation of response variability from firing rate effects in frontal eye field neurons during visual stimulation, working memory, and attention, J. Neurosci. Methods, 32 (2012), 2204-2216.
doi: 10.1523/JNEUROSCI.2967-11.2012. |
[4] |
M. M. Churchland, B. M. Yu, J. P. Cunningham, L. P. Sugrue, M. R. Cohen, G. S. Corrado, W. T. Newsome, A. M. Clark, P. Hosseini, B. B. Scott, D. C. Bradley, M. A. Smith, A. Kohn, J. A. Movshon, K. M. Armstrong, T. Moore, S. W. Chang, L. H. Snyder, S. G. Lisberger, N. J. Priebe, I. M. Finn, D. Ferster, S. I. Ryu, G. Santhanam, M. Sahani and K. V. Shenoy, Stimulus onset quenches neural variability: A widespread cortical phenomenon, Nat. Neurosci., 13 (2010), 369-378.
doi: 10.1038/nn.2501. |
[5] |
D. R. Cox, "Renewal Theory," Methuen & Co., Ltd., London; John Wiley & Sons, Inc., New York, 1962. |
[6] |
O. Darbin, J. Soares and T. Wichmann, Nonlinear analysis of discharge patterns in monkey basal ganglia, Brain Res., 1118 (2006), 84-93.
doi: 10.1016/j.brainres.2006.08.027. |
[7] |
M. Deger, M. Helias, C. Boucsein and S. Rotter, Statistical properties of superimposed stationary spike trains, J. Comput. Neurosci., 32 (2012), 443-463.
doi: 10.1007/s10827-011-0362-8. |
[8] |
S. Ditlevsen and P. Lansky, Firing variability is higher than deduced from the empirical coefficient of variation, Neural. Comput., 23 (2011), 1944-1966.
doi: 10.1162/NECO_a_00157. |
[9] |
U. T. Eden and M. A. Kramer, Drawing inferences from fano factor calculations, J. Neurosci. Methods, 190 (2010), 149-152.
doi: 10.1016/j.jneumeth.2010.04.012. |
[10] |
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. |
[11] |
W. Gerstner and W. M. Kistler, "Spiking Neuron Models. Single Neurons, Populations, Plasticity," Cambridge University Press, Cambridge, 2002. |
[12] |
C. Hussar and T. Pasternak, Trial-to-trial variability of the prefrontal neurons reveals the nature of their engagement in a motion discrimination task, P. Natl. Acad. Sci. USA, 107 (2010), 21842-21847.
doi: 10.1073/pnas.1009956107. |
[13] |
W. S. Jewell, The properties of recurrent-event processes, Oper. Res., 8 (1960), 446-472.
doi: 10.1287/opre.8.4.446. |
[14] |
L. Kostal, P. Lansky and O. Pokora, Variability measures of positive random variables, PLOS ONE, 6 (2011), e21998.
doi: 10.1371/journal.pone.0021998. |
[15] |
S. Koyama and S. Shinomoto, Inference of intrinsic spiking irregularity based on the Kullback-Leibler information, BioSystems, 89 (2007), 69-73.
doi: 10.1016/j.biosystems.2006.05.012. |
[16] |
A. M. Mood, F. A. Graybill and D. C. Boes, "Introduction to the Theory of Statistics," McGraw-Hill, Inc., 1974. |
[17] |
M. P. Nawrot, Analysis and interpretation of interval and count variability in neural spike trains, in "Analysis of Parallel Spike Trains," Springer, Inc., New York, (2010), 37-58. |
[18] |
M. P. Nawrot, C. Boucsein, V. R. Molina, A. Riehle, A. Aertsen and S. Rotter, Measurement of variability dynamics in cortical spike trains, J. Neurosci. Methods, 169 (2008), 374-390.
doi: 10.1016/j.jneumeth.2007.10.013. |
[19] |
T. Omi and S. Shinomoto, Optimizing time histograms for non-Poissonian spike trains, Neural. Comput., 23 (2011), 3125-3144.
doi: 10.1162/NECO_a_00213. |
[20] |
Z. Pawlas, L. B. Klebanov, M. Prokop and P. Lansky, Parameters of spike trains observed in a short time window, Neural. Comput., 20 (2008), 1325-1343.
doi: 10.1162/neco.2007.01-07-442. |
[21] |
B. V. D. Pol and H. Bremmer, "Operational Calculus Based on the Two-Sided Laplace Integral," Cambridge University Press, Cambridge, 1950. |
[22] |
A. Ponce-Alvarez, B. E. Kilavik and A. Riehle, Comparison of local measures of spike time irregularity and relating variability to firing rate in motor cortical neurons, J. Comput. Neurosci., 29 (2010), 351-365.
doi: 10.1007/s10827-009-0158-2. |
[23] |
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. |
[24] |
S. Shinomoto, K. Miura and S. Koyama, A measure of local variation of inter-spike intervals, BioSystems, 79 (2005), 67-72.
doi: 10.1016/j.biosystems.2004.09.023. |
[25] |
M. C. Teich, D. H. Johnson, A. R. Kumar and R. G. Turcott, Rate fluctuations and fractional power-law noise recorded from cells in the lower auditory pathway of the cat, Hearing Res., 46 (1990), 41-52.
doi: 10.1016/0378-5955(90)90138-F. |
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