Randomness and variability of the neuronal activity described by the Ornstein-Uhlenbeck model

Network: Computation in Neural Systems

Volumn 18, Issue 1, 2007, Pages 63-75

  Kostal, Lubomir ^a   Lansky, Petr ^a   Zucca, Cristina ^b  

^a INSTITUTE OF PHYSIOLOGY   (Czech Republic)

^b UNIVERSITY OF TURIN   (Italy)

Author keywords

Entropy; Ornstein Uhlenbeck model; Randomness; Variability

Indexed keywords

ACTION POTENTIAL; ANIMAL; ARTICLE; BIOLOGICAL MODEL; CLASSIFICATION; ENTROPY; NERVE CELL; PHYSIOLOGY; STATISTICAL MODEL; TIME;

ACTION POTENTIALS; ANIMALS; ENTROPY; MODELS, NEUROLOGICAL; MODELS, STATISTICAL; NEURONS; TIME FACTORS;

EID: 34047238964     PISSN: 0954898X     EISSN: 13616536     Source Type: Journal    
DOI: 10.1080/09548980701243134     Document Type: Article

References (37)

1. Abramowitz M, Stegun IA. 1972. Handbook of mathematical functions. New York: Dover.
2. Beirlant J, Dudewicz EJ, Gyorfi L, van der Meulen EC, 1997, Nonparametric entropy estimation: An overview. Int J Math Stat Sci 6:17-39.
3. Buonocore A, Nobile AG, Ricciardi LM. 1987. A new integral equation for the evaluation of FPT probability densities. Adv Appl Prob 19:784-800.
4. Burkitt AN. 2006. A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biol Cybern 95:1-19.
5. Chacron MJ, Longtin A, Maler L. 2001. Negative interspike interval correlations increase the neuronal capacity for encoding time-dependent stimuli. J Neurosci 21:5328-5343.
6. Chacron MJ, Longtin A, Maler L. 2003. The effects of spontaneous activity, background noise, and the stimulus ensemble on information transfer in neurons. Network: Comput Neural Syst 14:803-824.
7. Chhikhara RS, Folks JL. 1989. The inverse Gaussian distribution: Theory, methodology and applications. New York: Marcel Dekker, Inc.
8. Cover TM, Thomas JA. 1991. Elements of information theory. New York: John Wiley & Sons, Inc.
9. DeWeese MR, Meister M. 1999. How to measure the information gained from one symbol. Network: Comput Neural Syst 10:325-340.
10. Ditlevsen S, Lansky P. 2005. Estimation of the input parameters in the Ornstein-Uhlenbeck neuronal model. Phys Rev E 71:011907.
11. Gerstner W, Kistler WM. 2002. Spiking neuron models: Single neurons, populations, plasticity. Cambridge: Cambridge University Press.
12. Han YMY, Chan YS, Lo KS, Wong TM. 1998. Spontaneous activity and barosensitivity of the barosensin've neurons in the rostral ventrolateral medulla of hypertensive rats induced by transection of aortic depressor nerves. Brain Res 813:262-267.
13. Hanson FB, Tuckwell HC. 1983. Diffusion Approximation for neuronal activity including reversal potentials. J Theor Neurobiol 2:127-153.
14. Inoue J, Sato S, Ricciardi LM. 1995. 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 73:209-221.
15. Johnson DH, Gruner CM, Baggerly K, Seshagiri C. 2001. Information-theoretic analysis of the neural code. J Comput Neurosci 10:47-69.
16. Kandel ER, Schwartz JH. 1985. Principles of neural science. 2nd ed. New York: Elsevier.
17. Keilson J, Ross HF. 1975. Passage time distributions for Gaussian Markov (Ornstein-Uhlenbeck) statistical processes. Selected Tables in Mathematical Statistics 3:233-328.
18. Kostal L, Lansky P. 2006a. Similarity of interspike interval distributions and information gain in a stationary neuronal firing. Biol Cybern 94:157-167.
19. Kostal L, Lansky P. 2006b. Classification of stationary neuronal activity according to its information rate. Network: Comput Neural Sys 17:193-210.
20. Kostal L, Lansky P. 2007. Variability and randomness in stationary neuronal activity, Biosystems, doi: 10.1016/j.biosystems.2006.05.010 (in press).
21. La Camera G, Rauch A, Luscher HR, Senn W, Fusi S. 2004. Minimal models of adapted neuronal response to in vivo-like input currents. Neural Comput 16:2101-2124.
22. Lansky P, Rospars J-P. 1995. Ornstein-Uhlenbeck neuronal model revisited. Biol Cybern 72:397-406.
23. Lansky P, Sacerdote L. 2001. The Ornstein-Uhlenbeck neuronal model with the signal-dependent noise. Phys Lett A 285:132-140.
24. Laughlin SB, 2001. Energy as a constraint on the coding and processing of sensory information. Curr Opin Neurobio 11:475480.
25. Lewis CD, Gebber GL, Larsen PD, Barman SM. 2001. Long-term correlations in the spike trains of medullary sympathetic neurons. J Neurophysiol 85:1614-1622.
26. Lindner B, Schimansky-Geier L, Longtin A. 2002. Maximizing spike train coherence or incoherence in the leaky integrate-and-fire neuron. Phys Rev E 66:031916 - 2.
27. Perkel DH, Bullock TH. 1968. Neural coding: A report based on a NRP work session. Neurosci Res Program Bull 6:221-248.
28. Ricciardi LM, Di Crescenzo A, Giorno V, Nobile AG. 1999. An outline of theoretical and algorithmic approaches to first passage time problems with applications to biological modeling. Math Jap 50:247-322.
29. Ruskin DN, Bergstrom DA, Walters JR. 2002. Nigrostriatal lesion and dopamine agonists affect firing patterns of rodent entopeduncular nucleus neurons. J Neurophysiol 88:487-496.
30. Siegert AJF. 1951. On the first passage time probability problem. Phys Rev 81:617-623.
31. Shinomoto S, Yutaka S, Hiroshi O. 2002. Recording site dependence of the neuronal spiking statistics. Biosystems 67:259-263.
32. Softky WR, Koch C. 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSP's. J Neurosci 13:334-530.
33. Stevens C, Zador A. 1998. Novel integrate-andfire -like model of repetitive firing in cortical neurons. In: Proceeding of the 5th Joint Symposium on Neural Computation 8:172-177.
34. Tsybakov AB, van der Meulen EC. 1996. Root-n consistent estimators of entropy for densities with unbounded support. Scand J Statist 23:75-83.
35. Tuckwell HC. 1988. Introduction to theoretical neurobiology. Cambridge: Cambridge University Press.
36. Tuckwell HC, Cope DK. 1980. Accuracy of neuronal interspike times calculated from a diffusion approximation. J Theor Biol 83:377-87.
37. Tuckwell HC, Richter W. 1978. Neuronal interspike time distributions and the estimation of neurophysiological and neuroanatomical parameters. J Theor Biol 71:167-183.