Mathematical Biosciences and Engineering (MBE)

Fluctuation scaling in neural spike trains
Pages: 537 - 550, Issue 3, June 2016

doi:10.3934/mbe.2016006      Abstract        References        Full text (515.0K)           Related Articles

Shinsuke Koyama - Department of Statistical Modeling, The Institute of Statistical Mathematics, 10-3 Midoricho, Tachikawa, Tokyo, Japan (email)
Ryota Kobayashi - Principles of Informatics Research Division, National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo, Japan (email)

1 M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965.
2 R. M. Anderson and R. M. May, Epidemiological parameters of HIV transmission, Nature, 333 (1988), 514-519.
3 B. B. Averbeck, Poisson or not Poisson: Differences in spike train statistics between parietal cortical areas, Neuron, 62 (2009), 310-311.
4 P. Bremaud, Point Processes and Queues, Springer, New York, 1981.       
5 A. N. Burkitt, Balanced neurons: Analysis of leaky integrate-and-fire neurons with reversal potentials, Biol. Cybern., 85 (2001), 247-255.
6 A. N. Burkitt, A review of the integrate-and-fire neuron model, I: Homogeneous synaptic input, Biol. Cybern., 95 (2006), 1-19.       
7 M. M. Churchland, et al., Stimulus onset quenches neural variability: A widespread cortical phenomenon, Nat. Neurosci., 13 (2010), 369-378.
8 A. K. Churchland, et al., Variance as a signature of neural computations during decision making, Neuron, 69 (2011), 818-831.
9 M. M. Churchland and L. F. Abbott, Two layers of neural variability, Nat. Neurosci., 15 (2012), 1472-1474.
10 D. R. Cox, Renewal Theory, Chapman and Hall, London, 1962.       
11 D. R. Cox and P. A. W. Lewis, The Statistical Analysis of Series of Events, Chapman and Hall, London, 1966.       
12 D. J. Daley and D. Vere-Jones, An Introduction to the Theory of Point Processes, Springer Series in Statistics, Springer-Verlag, New York, 1988.       
13 M. A. de Menezes and A. L. Barabasi, Fluctuations in network dynamics, Phys. Rev. Lett., 92 (2004), 028701.
14 A. Destexhe, Z. Mainen and T. J. Sejnowski, Kinetic models of synaptic transmission, in Methods in Neuronal Modeling (eds. C. Koch and I. Segev), MIT Press, Cambridge, MA, 1998, 1-26.
15 S. Ditlevsen and P. Lansky, Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model, Phys. Rev. E., 71 (2005), 011907, 9pp.       
16 Z. Eisler, I. Bartos and J. Kertesz, Fluctuation scaling in complex systems: Taylor's law and beyond, Adv. Phys., 57 (2008), 89-142.
17 A. Fronczak and P. Fronczak, Origins of Taylor's power law for fluctuation scaling in complex systems, Phys. Rev. E, 81 (2010), 066112.
18 J. Inoue, S. Sato and L. M. Ricciardi, On the parameter estimation for diffusion models of single neuron's activities. I. Application to spontaneous activities of mesencephalic reticular formation cells in sleep and waking states, Biol. Cybern., 73 (1995), 209-221.
19 D. H. Johnson, Point process models of single-neuron discharges, J. Comput. Neurosci., 3 (1996), 275-299.
20 J. Keilson and H. F. Ross, Passage time distribution for Gaussian Markov (Ornstein-Uhlenbeck) statistical processes, in Selected Tables in Mathematical Statistics, 3, American Mathematical Society, 1975, 233-327.       
21 W. S. Kendal and P. Frost, Experimental metastasis: A novel application of the variance-to-mean power function, J. Natl. Cancer Inst., 79 (1987), 1113-1115.
22 W. S. Kendal, A scale invariant clustering of genes on human chromosome 7, BMC Evol. Biol., 4 (2004), p3.
23 P. Lansky and V. Lanska, Diffusion approximation of the neuronal model with synaptic reversal potentials, Biol. Cybern., 56 (1987), 19-26.       
24 A. Lerchner, et al., Response variability in balanced cortical networks, Neural Comput., 18 (2006), 634-659.       
25 B. Lindner and A. Longtin, Comment on "Characterization of Subthreshold Voltage Fluctuations in Neuronal Membranes," by M. Rudolph and A. Destexhe, Neural Comput., 18 (2006), 1896-1931.
26 A. G. Nobile, L. M. Ricciardi and L. Sacerdote, Exponential trends of Ornstein-Uhlenbeck first-passage-time densities, J. Appl. Probab., 22 (1985), 360-369.       
27 Y. Ogata, Statistical models for earthquake occurrences and residual analysis for point processes, J. Amer. Statist. Assoc., 83 (1988), 9-27.
28 L. M. Ricciardi and S. Sato, First-passage-time density and moments of the Ornstein-Uhlenbeck process, J. Appl. Probab., 25 (1988), 43-57.       
29 M. J. Richardson and W. Gerstner, Synaptic shot noise and conductance fluctuations affect the membrane voltage with equal significance, Neural Comput., 17 (2005), 923-947.       
30 B. K. Roy and D. R. Smith, Analysis of the exponential decay model of the neuron showing frequency threshold effects, Bull. Math. Biophys., 31 (1969), 341-357.
31 N. M. Shadlen and W. T. Newsome, The variable discharge of cortical neurons: Implications for connectivity, computation, and information coding, J. Neurosci., 18 (1998), 3870-3896.
32 A. J. F. Siegert, On the first passage time probability problem, Phys. Rev., 81 (1951), 617-623.       
33 D. L. Snyder, Random Point Processes, John Wiley & Sons, Inc., New York, 1975.       
34 L. R. Taylor, Aggregation, variance and the mean, Nature, 189 (1961), 732-735.
35 D. J. Tolhurst, J. A. Movshon and I. D. Thompson, The dependence of response amplitude and variance of cat visual cortical neurones on stimulus contrast, Exp. Brain Res., 41 (1981), 414-419.
36 J. B. Troy and J. G. Robson, Steady discharges of X and Y retinal ganglion cells of cat under photopic illuminance, Vis. Neurosci., 9 (1992), 535-553.
37 H. C. Tuckwell, Introduction to Theoretical Neurobiology, Cambridge University Press, New York, 1988.       
38 N. G. van Kampen, Stochastic Processes in Physics and Chemistry, 2nd edition, North-Holland, Amsterdam, 1992.
39 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.       
40 F. Y. M. Wan and H. C. Tuckwell, Neuronal firing and input variability, J. Theoret. Neurobiol., 1 (1982), 197-218.

Go to top