Abstract not found

Cortical neurons of behaving animals generate irregular spike sequences. Recently, there has been a heated discussion about the origin of this irregularity. Softky and Koch (1993) pointed out the inability of standard single neuron models to reproduce the irregularity of the observed spike sequences when the model parameters are chosen within a certain range which they consider to be plausible. Shadlen and Newsome (1994), on the other hand, demonstrated that a standard leaky integrator model can reproduce the irregularity if the inhibition is balanced with the excitation. Motivated by this discussion, we attempted to determine whether the Ornstein-Uhlenbeck process, which is naturally derived from the leaky integration assumption, can in fact reproduce higher order statistics of biological data. For this purpose, we consider actual neuronal spike sequences recorded from the monkey prefrontal cortex to calculate the higher order statistics of the inter-spike intervals. Consistency of th...

In this paper we consider the classical Erlang loss model, i.e., the M/M/c/0 system with Poisson arrival process, exponential service times, c servers and no extra waiting space, where blocked calls are lost. We let the individual service rate be 1 and the arrival rate (which coincides with the offered load) be a. We show how to compute several transient characteristics by numerical transform inversion. Transience arises by considering arbitrary fixed initial states.

The effect of a random initial value is examined in several stochastic integrate-and-fire neural models with a constant threshold and a constant input. The three models considered are approximations of Stein's model, namely: (1) a leaky integrator with deterministic trajectories, (2) a Wiener process with drift, and (3) an Ornstein Uhlenbeck process. For model (1) different distributions for the initial value lead to commonly observed interspike interval distributions. For model (2) a discrete and a uniform distribution for the initial value are examined along with some parameter estimation procedures. For model (3) with a truncated normal distribution for the initial value, the coefficient of variation is shown to be greater than one and as the threshold becomes large, the first passage time distribution approaches an exponential distribution. The relationship among the models and to previous models is also discussed, along with the robustness of the model assumptions and methods of their verification. The effects of a random initial value are found to be most pronounced at high firing rates.

a stochastic model for circulatory transport

Abstract not found

asv # u. This holds if Cov(Y s ,Y t ) is continuous over R R . Note that this is a statement about distributions, not sample paths. Having dispensed with preliminaries, we turn to the central topic. A stochastic process {X t : t # 0} is an Ornstein-Uhlenbeck process or a Gauss-Markov 0 Copyright c # 2004 by Steven R. Finch. All rights reserved. process if it is stationary, Gaussian, Markovian, and continuous in probability [1, 2]. A fundamental theorem, due to Doob [3, 4, 5], ensures that {X t : t # 0} necessarily satisfies the following linear stochastic di#erential equation: dX t = -#(X t - )dt + #dW t where {W t : t # 0} is Brownian motion with unit variance parameter and , #, # are constants. We have moments E(X t )=, Cov(X s ,X t )= in the unconditional (strictly stationary) case and E(X t | X 0 = c)= +(c - )e Cov(X s ,X t | X 0 = c)= - e -#(s+t) in the conditional (asymptotically stationary) case, where X 0 is initially constant. The latter case encom