Modeling Neuronal Firing in the Presence of Refractoriness

A mathematical characterization of the membrane potential as an instantaneous return process in the presence of refractoriness is investigated for diffusion models of single neuron’s activity. The statistical features of the random variable modeling the number of neuronal firings is analyzed by including the additional assumption of the existence of neuronal refractoriness. Asymptotic exact formulas for the multiple firing probabilities and for the expected number of produced firings are finally given.

[1]  Virginia Giorno,et al.  Towards Modeling Refractoriness for Single Neuron's Activity , 2002 .

[2]  Virginia Giorno,et al.  Instantaneous return process and neuronal firings , 1992 .

[3]  L. M. Ricciardi,et al.  Diffusion approximation and first-passage-time problem for a model neuron , 2004, Kybernetik.

[4]  W. Feller.  THE PARABOLIC DIFFERENTIAL EQUATIONS AND THE ASSOCIATED SEMI-GROUPS OF TRANSFORMATIONS , 1952 .

[5]  A. Siegert.  On the First Passage Time Probability Problem , 1951 .

[6]  Virginia Giorno,et al.  AN OUTLINE OF THEORETICAL AND ALGORITHMIC APPROACHES TO FIRST PASSAGE TIME PROBLEMS WITH APPLICATIONS TO BIOLOGICAL MODELING , 1999 .

[7]  R. Capocelli,et al.  Diffusion approximation and first passage time problem for a model neuron , 1971, Biological cybernetics.

[8]  Virginia Giorno,et al.  On asymptotic behaviors of stochastic models for single neuron's activity , 1996 .

[9]  Virginia Giorno,et al.  ON THE ASYMPTOTIC BEHAVIOUR OF FIRST- PASSAGE-TIME DENSITIES FOR ONE-DIMENSIONAL DIFFUSION PROCESSES AND VARYING BOUNDARIES , 1990 .

[10]  黄晓军,et al.  CD , 2003 .

[11]  B. Mandelbrot,et al.  RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. , 1964, Biophysical journal.

[12]  A. G. Nobile,et al.  A neuronal modeling paradigm in the presence of refractoriness. , 2002, Bio Systems.

[13]  P Lánský,et al.  The effect of a random initial value in neural first-passage-time models. , 1989, Mathematical biosciences.

[14]  Luigi M. Ricciardi,et al.  On some distribution functions for non-linear switching elements with finite dead time , 1966, Kybernetik.

[15]  Luigi M. Ricciardi,et al.  Diffusion models of neuron activity , 1998 .

[16]  Michael A. Arbib,et al.  The handbook of brain theory and neural networks , 1995, A Bradford book.

[17]  Virginia Giorno,et al.  On the instantaneous return process for neuronal diffusion models , 1992 .

[18]  M C Teich,et al.  Refractoriness in the maintained discharge of the cat's retinal ganglion cell. , 1978, Journal of the Optical Society of America.