Modeling neuronal firing in the presence of refractoriness

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2686, Issue , 2003, Pages 1-8

  Ricciardi, L M ^a   Esposito, G ^a   Giorno, V ^b   Valerio, C ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b UNIVERSITY OF SALERNO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

NEURONS;

DIFFUSION MODEL; EXACT FORMULAS; MATHEMATICAL CHARACTERIZATION; MEMBRANE POTENTIALS; NEURONAL FIRINGS; SINGLE NEURON; STATISTICAL FEATURES; VARIABLE MODEL;

NEURAL NETWORKS;

EID: 26444580099     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44868-3_1     Document Type: Article

References (15)

1. Buonocore, A., Giorno, V., Nobile, A.G., Ricciardi, L.M.: Towards modeling refractoriness for single neuron's activity. In Cybernetics and Systems 2002 Vol. 1 (Trappl, R., ed.). Austrian Society for Cybernetics Studies, Vienna. (2002) 319-324
2. Buonocore, A., Giorno, V., Nobile, A.G., Ricciardi, L.M.: A neuronal modeling paradigm in the presence of refractoriness. BioSystems 67 (2002) 35-43.
3. Feller, W.: The parabolic differential equations and the associated semi-groups of transformations. Ann. Math. 55 (1952) 468-518.
4. Gerstein, G.L., Mandelbrot, B.: Random walk models for the spike activity of a single neuron. Biophys. J. 4 (1964) 41-68.
5. Giorno, V., Lánský, P., Nobile, A.G., Ricciardi, L.M.: Diffusion approximation and first-passage-time problem for a model neuron. III. A birth-and-death process approach. Biol. Cybern. 58 (1988) 387-404.
6. Giorno, V., Nobile, A.G., Ricciardi, L.M.: On the asymptotic behavior of first-passage-time densities for one-dimensional diffusion processes and varying boundaries. Adv. Appl. Prob. 22 (1990) 883-514.
7. Giorno, V., Nobile, A.G., Ricciardi, L.M.: Instantaneous return process and neuronal firings. In Cybernetics and Systems Research 1992 (Trappl, R., ed.). World Scientific (1992) 829-836.
8. Giorno, V., Nobile, A.G., Ricciardi, L.M.: On asymptotic behaviors of stochastic models for single neuron's activity. In Cybernetics and System 1996 (Trappl, R., ed.). Austrian Society for Cybernetic Studies (1996) 524-529.
9. Lánský, P., Smith, C.E.: The effect of a random initial value in neuronal first-passage-time models. Math. Biosci. 93 (1989) 191-215.
10. Ricciardi, L.M., Esposito, F.: On some distribution functions for non-linear switching elements with finite dead time. Kybernetik 3 (1966) 148-152.
11. Ricciardi, L.M., Di Crescenzo, A., Giorno, V., Nobile, A.G.: On the instantaneous return process for neuronal diffusion models. In Structure: from Physics to General Systems (Marinaro, M., Scarpetta, G., eds.). World Scientific (1992) 78-94.
12. Ricciardi, L.M., Di Crescenzo, A., Giorno, V., Nobile, A.G.: An outline of theoretical and algorithmic approaches to first passage time problems with applications to biological modeling. Math. Japonica 50 No. 2 (1999) 247-322.
13. Ricciardi, L.M., Lánský, P.: Diffusion models of neuron activity. In The Handbook of Brain Theory and Neural Networks (Arbib, M.A., ed.). The MIT Press, Cambridge (2002) 343-348.
14. Siegert, A.J.F.: On the first passage time probability problem. Phys. Rev. 81 (1951) 617-623.
15. Teich, M.C., Matin, L., Cantor, B.I.: Refractoriness in the maintained discharge of the cats retinal ganglion cell. J. Opt. Soc. Am. 68(3) (1978) 386-402.