The results of some numerical computations are discussed to shed some light on the input-output behavior of a formal neuron whose dynamics is modeled by a diffusion process of Ornstein-Uhlenbeck type.Expand

The idea is to collect the existing methods and the available analytical results for the most common one dimensional stochastic Integrate and Fire models to make them available for studies on networks.Expand

The transition p.d.f. for a one-dimensional Rayleigh process in the presence of an absorption condition or a zero-flux condition in the origin is obtained in closed form. The first-passage-time… Expand

Three different definitions of firing frequency are compared in an effort to contribute to a better understanding of the input-output properties of a neuron.Expand

Use of one-parameter group transformations is made to obtain the transition p.d.f. of a Feller process confined between the origin and a hyperbolic-type boundary. Such a procedure, previously used by… Expand

A new, non–parametric and binless estimator for the mutual information of a d–dimensional random vector that is unbiased even for larger dimensions and smaller sample sizes while the other tested estimators show a bias in these cases.Expand

The inverse first-passage problem for a Wiener process $(W_t)_{t\ge0}$ seeks to determine a function $b{}:{}\mathbb{R}_+\to\mathbb{R}$ such that \[\tau=\inf\{t>0| W_t\ge b(t)\}\] has a given law. In… Expand

The series expansion for the solution of the integral equation for the first-passage-time probability density function, obtained by resorting to the fixed point theorem, is used to achieve… Expand

It is shown that the presence of a firing threshold brings a systematic error to the estimation procedure of stochastic (leaky) integrate-and-fire neuronal models, and the effect of the bias has to be taken into account in experimental studies.Expand