Biomedical subjects

L M Ricciardi

Publications and source records attributed to L M Ricciardi.

At least 19 recordsLinked to original sources

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↗

PubMed1995

On the parameter estimation for diffusion models of single neuron's activities. I. Application to spontaneous activities of mesencephalic reticular formation cells in sleep and waking states.

For the Ornstein-Uhlenbeck neuronal model a quantitative method is proposed for the estimation of the two parameters characterizing the unknown input process, namely the neuron's mean input per unit time mu and the infinitesimal standard deviation per unit time sigma. This method is based on the experimentally observed first- and second-order moments of interspike intervals. The dependence of the estimates mu and ŝigma on the moments of the observed interspike intervals and on the neuronal parameters is clarified, and a comparison is made between the estimates based on the classical Wiener model and those yielded by the Ornstein-Uhlenbeck model. Comprehensive tables are included in which the displayed values of mu and ŝigma have been calculated in terms of physiologically realistic pairs of first- and second-order moments. Our method is finally applied to interspike interval data recorded from neurons in the mesencephalic reticular formation of the cat during hypothetical sleep, slow-wave sleep stage, and wake stage.

Animals↗

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↗

PubMed1979

On a conjecture concerning population growth in random environment.

Discrete stochastic models are constructed and their limit diffusion processes are derived to shed light on a controversial conjecture regarding the effects of environmental variance on the asymptotic behavior of a population subject to logistic growth in random environment.

Environment↗

PubMed1979

The Ornstein-Uhlenbeck process as a model for neuronal activity. I. Mean and variance of the firing time.

Mean and variance of the first passage time through a constant boundary for the Ornstein-Uhlenbeck process are determined by a straight-forward differentiation of the Laplace transform of the first passage time probability density function. 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.

Dendrites↗

PubMed1976