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• W343552405 abstract "A description of the sequence of interspike intervals and of the subsequent firing times for single neurons is performed by means of an instantaneous return pro- cess in the presence of refractoriness. Every interspike interval consists of an absolute refractory period of fixed duration followed by a period of relative refractoriness whose duration is described by the first-passage time of the modeling diffusion process through a generally time-dependent threshold. In the cases of Wiener and Ornstein-Uhlenbeck processes, the interspike probability density functions and some of its statistical fea- tures are explicitly obtained for special monotonically non-increasing thresholds. 1 Introduction Stochastic models for neuronal firing in the presence of refractoriness have been the object of various investigations. The first attempt to study the effect of refractoriness in a point process is made in (22) and in (25) in which the authors consider the role played by the dead time in determining the distribution of the output when the input obeys a given distribution. Successively, an instantaneous return process, constructed on a diffusion, has been considered aiming to a quantitative description of neuron's membrane potential behavior. Within such a context, the presence of refractoriness has been included in two different ways. The first way assumes that the firing threshold acts as an elastic barrier that is partially transparent, i.e. such that its behavior is intermediate between total absorption and total reflection (cf. (3), (4), (5), (20)). Alternatively, the return process paradigm for the description of the time course of the membrane potential is analyzed by assuming that the neuronal refractoriness period is a random variable with a pre-assigned probability density (cf. (1), (10), (11), (15), (23)). Recently, in (2) and (16), the Wiener neuronal model in the presence of constant and of exponentially distributed refractoriness has been considered, and expressions for output distributions and for interspike interval densities have been obtained in closed form. Customarily, the firing threshold has been viewed in the literature as a constant which may not be appropriate, especially for rapidly firing cells (cf. (7), (13), (14), (26)). Indeed, when a neuron releases an action potential, it becomes temporarily incapable of responding to further input signals. In fact, for a period of time, of the order of one or two milliseconds, the neuron is unable to respond to any stimuli (absolute refractory period). After that, for several successive milliseconds its sensitivity to the incoming stimuli is normally reduced, in some cases increasing successively. This type of after-firing behavior (after potentials) may last up to about 100 msec. In the present context we focus our attention on a constant absolute refractory period followed by a period of relative refractoriness that we model as a random variable. Hence, after a spike release, we assume that the neuron is unable to fire again during the absolute refractory period, while the firing threshold is assumed to decrease progressively as the inhibitory effect of the previous spike fades away." @default.
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• W343552405 date "2008-03-01" @default.
• W343552405 modified "2023-09-23" @default.
• W343552405 title "MODELING REFRACTORINESS FOR STOCHASTICALLY DRIVEN SINGLE NEURONS" @default.
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• W343552405 doi "https://doi.org/10.32219/isms.67.2_173" @default.
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