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The clock errors are modeled by stochastic differential equations (SDE) and the relationships between the diffusion coefficients used in SDE and the Allan variance, a typical tool used to estimate clock noise, are derived. This relationship is fundamental when a mathematical clock model is used, for example in Kalman filter, noise estimation, and clock(More)
Normalized entropy as a measure of randomness is explored. It is employed to characterize those properties of neuronal firing that cannot be described by the first two statistical moments. We analyze randomness of firing of the Ornstein-Uhlenbeck (OU) neuronal model with respect either to the variability of interspike intervals (coefficient of variation) or(More)
The dynamics of a neuron are influenced by the connections with the network where it lies. Recorded spike trains exhibit patterns due to the interactions between neurons. However, the structure of the network is not known. A challenging task is to investigate it from the analysis of simultaneously recorded spike trains. We develop a non-parametric method(More)
We present a computational algorithm aimed to classify single unit spike trains on the basis of observed interspikes intervals (ISI). The neuronal activity is modeled with a stochastic leaky integrate and fire model and the inverse first passage time method is extended to the Ornstein-Uhlenbeck (OU) process. Differences between spike trains are detected in(More)
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A first passage problem for a bivariate diffusion process: numerical solution with an application to neuroscience. Abstract We consider a bivariate diffusion process and we study the first passage time of one component through a boundary. We prove that its probability density is the unique solution of a new integral equation and we propose a numerical(More)
An optimum signal in the Ornstein-Uhlenbeck neuronal model is determined on the basis of interspike interval data. Two criteria are proposed for this purpose. The first, the classical one, is based on searching for maxima of the slope of the frequency transfer function. The second one uses maximum of the Fisher information, which is, under certain(More)
Motivated by a neuronal modeling problem, a bivariate Wiener process with two independent components is considered. Each component evolves independently until one of them reaches a threshold value. If the first component crosses the threshold value, it is reset while the dynamics of the other component remains unchanged. But, if this happens to the second(More)