Biomedical subjects

A G Nobile

Publications and source records attributed to A G Nobile.

7 recordsLinked to original sources

PubMed2001

Stochastic population models with interacting species.

A stochastic model concerning the evolution of a multi-species population is presented assuming species competition for a habitat. The model takes into account colonization, death and replacement for all individuals. Two cases are treated: (i) colonizations follow the hierarchic rule by which species of lower rank are always outcompeted by those of higher rank and (ii) there are no privileged species. In both cases, under suitable assumptions, a thorough description of the evolution of the population is obtained. The two models are finally compared and the corresponding evolutionary behaviors of the populations are discussed.

Animals↗

PubMed1997

Single neuron's activity: on certain problems of modeling and interpretation.

With reference to the Ornstein-Uhlenbeck model for single neuron activity, computational results and theoretical arguments are provided to discuss the accuracy and the appropriateness of analytical approximations to first-passage-time densities and its moments. A gamma approximation is initially discussed, use of which is successively made to construct a probability density of a new form that appears to be particularly suitable to approximate the as yet unknown firing probability density function.

Diffusion↗

PubMed1988

Diffusion approximation and first-passage-time problem for a model neuron. III. A birth-and-death process approach.

A stochastic model for single neuron's activity is constructed as the continuous limit of a birth-and-death process in the presence of a reversal hyperpolarization potential. The resulting process is a one dimensional diffusion with linear drift and infinitesimal variance, somewhat different from that proposed by Lánský and Lánská in a previous paper. A detailed study is performed for both the discrete process and its continuous approximation. In particular, the neuronal firing time problem is discussed and the moments of the firing time are explicitly obtained. Use of a new computation method is then made to obtain the firing p.d.f. The behaviour of mean, variance and coefficient of variation of the firing time and of its p.d.f. is analysed to pinpoint the role played by the parameters of the model. A mathematical description of the return process for this neuronal diffusion model is finally provided to obtain closed form expressions for the asymptotic moments and steady state p.d.f. of the neuron's membrane potential.

Membrane Potentials↗

PubMed1984

Growth with regulation in fluctuating environments. II. Intrinsic lower bounds to population size.

Population growth is modelled by means of diffusion processes originating from fluctuation equations of a new type. These equations are obtained in the customary way by inserting random fluctuations into first order non linear differential equations. However, differently from the cases so far considered in the literature, equations possessing two non trivial fixed points are taken into account. The underlying deterministic models depict the regulated growth of a population whose size cannot decrease below some preassigned lower threshold naturally acting as an absorbing boundary. A fairly comprehensive mathematical description of these models is provided.

Humans↗

PubMedDate not supplied

On some computational results for single neurons' activity modeling.

The classical Ornstein-Uhlenbeck diffusion neuronal model is generalized by inclusion of a time-dependent input whose strength exponentially decreases in time. The behavior of the membrane potential is consequently seen to be modeled by a process whose mean and covariance classify, it as Gaussian-Markov. The effect of the input on the neuron's firing characteristics is investigated by comparing the firing probability densities and distributions for such a process with the corresponding ones of the Ornstein-Uhlenbeck model. All numerical results are obtained by implementation of a recently developed computational method.

Computational Biology↗

PubMedDate not supplied

A neuronal modeling paradigm 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, assuming that the firing threshold acts as an elastic barrier. Steady-state probability densities and asymptotic moments of the neuronal membrane potential are explicitly obtained in a form that is suitable for quantitative evaluations. For the Ornstein-Uhlenbeck (OU) and Feller neuronal models, closed form expression are obtained for asymptotic mean and variance of the neuronal membrane potential and an analysis of the different features exhibited by the above mentioned models is performed.

Models, Neurological↗

PubMedDate not supplied

On a non-Markov neuronal model and its approximations.

Single neuron's activity modeling is considered with reference to some earlier contributions in which a non-Markov Gaussian process is assumed to describe the time course of the neuron's membrane potential. After re-formulating the problem in a rigorous framework and pinpointing the limits of validity of such a model, the available results on the firing probability density are compared with those obtained by us by means of an ad hoc numerical algorithm implemented for the leaky integrator diffusion firing model and with some data constructed by a simulation procedure of non-Markov Gaussian processes with pre-assigned covariances. Throughout this paper, the notion of 'correlation time' plays a fundamental role for the neuronal coding process modeling.

Markov Chains↗