Firing variability is higher than deduced from the empirical coefficient of variation

Neural Computation

Volumn 23, Issue 8, 2011, Pages 1944-1966

  Ditlevsen, Susanne ^a   Lansky, Petr ^b  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

^b INSTITUTE OF PHYSIOLOGY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ANIMAL; BIOLOGICAL MODEL; LETTER; NERVE CELL; PHYSIOLOGY; RAT; THEORETICAL MODEL;

ALGORITHMS; ANIMALS; MODELS, NEUROLOGICAL; MODELS, THEORETICAL; NEURONS; RATS;

EID: 79959644027     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/NECO_a_00157     Document Type: Letter

References (51)

1. Abrahamowitz, M., & Stegun, I. (1972). Handbook of mathematical functions. New York: Dover.
2. Barry, B., Pascoe, M., Jesunathadas, M.,&Enoka, R. (2007). Rate coding is compressed but variability is unaltered for motor units in a hand muscle of old adults. J. Neurophysiol., 97, 3206-3218.
3. Berger, D., Pribram, K., Wild, H., & Bridges, C. (1990). An analysis of neural spiketrain distributions: Determinants of the response of visual-cortex neurons to changes in orientation and spatial-frequence. Experimental Brain Research, 80, 129-134.
4. Bhumbra, G., & Dyball, R. (2004). Measuring spike coding in the rat supraoptic nucleus. J. Phys.-London, 555, 281-296.
5. Breunig, R. (2001). An almost unbiased estimator of the coefficient of variation. Economics Letters, 70, 15-19.
6. Cecchi, G., Sigman, M., Alonso, J.,Martinez, L., Chialvo, D., &Magnasco, M. (2000). Noise in neurons is message dependent. PNAS, 97, 5557-5561.
7. Chhikara, R., & Folks, J. (1989). The inverse gaussian distribution: Theory, methodology, and applications. New York: Marcel Dekker.
8. Christodoulou, C.,&Bugmann, G. (2001). Coefficient of variation vs. mean interspike interval curves: What do they tell us about the brain? Neurocomput., 38, 1141-1149.
9. Cox, D., & Miller, H. (1965). The theory of stochastic processes. London: Methuen.
10. Davies, R., Gerstein, G., & Baker, S. (2006). Measurement of time-dependent changes in the irregularity of neural spiking. J. Neurophysiol., 96, 906-918.
11. Ditlevsen, S., & Lansky, P. (2007). Parameters of stochastic diffusion processes estimated from observations of first hitting-times: Application to the leaky integrateand-fire neuronal model. Phys. Rev. E, 76, 041906.
12. Dorval, A. D. (2008). Probability distributions of the logarithm of inter-spike intervals yield accurate entropy estimates from small datasets. J. Neurosci. Meth., 173, 129-139.
13. Duchamp-Viret, P., Kostal, L., Chaput, M., Lansky, P., & Rospars, J. (2005). Patterns of spontaneous activity in single rat olfactory receptor neurons are different in normally breathing and tracheotomized animals. J. Neurobiol., 65, 97-114.
14. Farkhooi, F., Strube, M., & Nawrot, M. P. (2009). Serial correlation in neural spike trains: Experimental evidence, stochasticmodeling, and single neuron variability. Physical Review E, 79, 021905.
15. Fujiwara, K., Fujiwara, H., Tsukada, M., & Aihara, K. (2007). Reproducing bursting interspike interval statistics of the gustatory cortex. Biosystems, 90(2), 442-448.
16. Gerstein, G., & Mandelbrot, B. (1964). Random walk models for spike activity of a single neuron. Biophys. J., 4, 41-68.
17. Gutkin, B., & Ermentrout, G. (1998). Dynamics of membrane excitability determine interspike interval variability: A link between spike generation mechanisms and cortical spike train statistics. Neural Comput., 10, 1047-1065.
18. Hentall, I. (2000). Interactions between brainstem and trigeminal neurons detected by cross-spectral analysis. Neuroscience, 96, 601-610.
19. Inoue, J., & Doi, S. (2007). Sensitive dependence of the coefficient of variation of interspike intervals on the lower boundary of membrane potential for the leaky integrate-and-fire neuron model. BioSystems, 87, 49-57.
20. Iyengar, S., & Liao, Q. (1997). Modeling neural activity using the generalized inverse gaussian distribution. Biol. Cybern., 77, 289-295.
21. Jackson, B. (2004). Including long-range dependence in integrate-and-fire models of the high interspike-interval variability of cortical neurons. Neural Comput., 16, 2125-2195.
22. Johnson, N., Kotz, S., & Balakrishnan, N. (1994). Continuous univariate distributions (2nd ed.). Hoboken, NJ:Wiley.
23. Jones, K. (2005).Motor unit firing statistics and the Fuglevand model. J. Neurophysiol., 94, 2255-2256.
24. Kang, K., & Amari, S. (2008). Discrimination with spike times and ISI distributions. Neural Comput., 20, 1411-1426.
25. Kostal, L., & Lansky, P. (2006). Similarity of interspike interval distributions and information gain in a stationary neuronal firing. Biol. Cybern., 94, 157-167.
26. Lansky, P., Rodriguez, R., & Sacerdote, L. (2004). Mean instantaneous firing frequency is always higher than the firing rate. Neural Comput., 16, 477-489.
27. Lansky, P., & Sacerdote, L. (2001). The Ornstein-Uhlenbeck neuronal model with signal-dependent noise. Physics Letters A, 285(3-4), 132-140.
28. Levine, M. (1991). The distribution of the intervals between neural impulses in the maintained discharges of retinol ganglion-cells. Biol. Cybern., 65, 459-467.
29. Lindner, B., Longtin, A., & Bulsara, A. (2003). Analytic expressions for rate and CV of a type I neuron driven by white gaussian noise. Neural Comput., 15, 1761-1788.
30. Ly, C., & Tranchina, D. (2009). Spike train statistics and dynamics with synaptic input fromany renewal process: A population density approach. Neural Comput., 21, 360-396.
31. Mandl, G. (1993). Coding for stimulus velocity by temporal patterning of spike discharges in visual cells of cat superior colliculus. Vision Research, 33(11), 1451-1475.
32. McKeegan, D. (2002). Spontaneous and odour evoked activity in single avian olfactory bulb neurones. Brain Research, 929(1), 48-58.
33. Miura, K., Okada, M., & Amari, S.-I. (2006). Estimating spiking irregularities under changing environments. Neural Comput., 18, 2359-2386.
34. Musila,M., & Lansky, P. (1994). On the interspike intervals calculated from diffusion approximations of Stein's neuronal model with reversal potentials. J. Theo. Biol., 171, 225-232.
35. Nawrot, M., Boucsein, C., Molina, V., Riehle, A., Aertsen, A., & Rotter, S. (2008). Measurement of variability dynamics in cortical spike trains. J. Neurosci. Meth., 169, 374-390.
36. Panzeri, S., Brunel, N., Logothetis, N. K., & Kayser, C. (2010). Sensory neural codes using multiplexed temporal scales. Trends in Neurosciences, 33, 111-120.
37. Pawlas, Z., Klebanov, L., Prokop, M., & Lansky, P. (2008). Parameters of spike trains observed in a short time window. Neural Comput., 20, 1325-1343.
38. Perkel, D., & Bullock, T. (1968). Neural coding. Neurosci. Res. Prog. Sum., 3, 405-527.
39. Ponce-Alvarez, A., Kilavik, B. E., & Riehle, A. (2009). Comparison of local measures of spike time irregularity and relating variability to firing rate in motor cortical neurons. J. Comput. Neurosci., 29, 351-365.
40. R Development Core Team. (2009). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing.
41. Rieke, F., Warland, D., de Ruyter van Steveninck, R., & Bialek, W. (1997). Spikes: Exploring the neural code. Cambridge, MA: MIT Press.
42. Segev, R., Benveniste, M., Hulata, E., Cohen, N., Palevski, A., Kapon, E., et al. (2002). Long term behavior of lithographically prepared in vitro neuronal networks. Phys. Rev. Letters, 88, 118102.
43. Shimokawa, T., Koyama, S., & Shinomoto, S. (2010). A characterization of the timerescaled gamma process as a model for spike trains. J. Comput. Neurosci., 29, 183-191.
44. Shimokawa, T., & Shinomoto, S. (2009). Estimating instantaneous irregularity of neuronal firing. Neural Comput., 21, 1931-1951.
45. Shinomoto, S., Kim, H., Shimokawa, T., Matsuno, N., Funahashi, S., Shima, K., et al. (2009). Relating neuronal firing patterns to functional differentiation of cerebral cortex. PLoS Comput. Biol., 5(7), e1000433.
46. Shinomoto, S., Miura, K., & Koyama, S. (2005). A measure of local variation of interspike intervals. BioSystems, 79(1-3), 67-72.
47. Shinomoto, S., Shima, K., & Tanji, J. (2003). Differences in spiking patterns among cortical neurons. Neural Comput., 15, 2823-2842.
48. Stein, R., Gossen, E., & Jones, K. (2005). Neuronal variability: Noise or part of the signal? Nature Rev. Neurosci., 6(5), 389-397.
49. Theunissen, F.,&Miller, J. (1995). Temporal encoding in nervous systems:Arigorous definition. J. Comput. Neurosci., 2, 149-162.
50. Vilela, R., & Lindner, B. (2009). Are the input parameters of white noise driven integrate and fire neurons uniquely determined by rate and CV? J. Theo. Biol., 257(1), 90-99.
51. Wiener,M. C. (2003). An adjustment of the time-rescaling method for application to short-trial spike train data. Neural Comput., 15, 2565-2576.