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Background and Aims: Severe hypoglycemia is not rare in diabetes and markedly impacts on health resource use. We aimed to describe the characteristics of patients attending emergency departments (EDs) following a severe episode of hypoglycemia, the factors associated with the management of events and the final outcome., Methods and Results: We carried out a retrospective analysis of cases attending 46 Italian EDs for hypoglycemia from January 2011 to June 2012. A total of 3753 records were retrieved from the databases of the participating centers, part of a network repeatedly involved in collaborative studies; 3516 episodes occurred in subjects with diabetes (median age, 76 years; range, 1-102). Comorbidities were recorded in 2320 (65.9%) diabetes cases; association with trauma or road accidents in 287 (8.2%) and 47 (1.3%), respectively. Patients were treated with insulin (49.8%), oral agents (31.4%), or combination treatment (15.1%). The event required assistance by the out-of-hospital Emergency services in 1821 cases (51.8%). Following the ED visit, admission to hospital departments was deemed necessary in 1161 cases (33.1%). Diabetes treatment (oral agents: OR, 1.63; 95% confidence interval (CI), 1.37-1.94), increasing age (OR, 1.39; 95% CI, 1.31-1.48) and the number of comorbidities (OR, 1.51; 95% CI, 1.38-1.66) were the main drivers of admission. The in-hospital death rate was 10%, associated with the number of comorbidities (OR, 1.28; 95%CI, 1.01-1.63)., Conclusion: Severe hypoglycemia requiring referral to EDs is associated with a significant work-up of the Emergency services and a remarkable in-hospital death rate in frail individuals with diabetes., (Copyright © 2014 Elsevier B.V. All rights reserved.)

The leaky integrate-and-fire neuronal model proposed in Stevens and Zador (1998), in which time constant and resting potential are postulated to be time dependent, is revisited within a stochastic framework in which the membrane potential is mathematically described as a gauss-diffusion process. The first-passage-time probability density, miming in such a context the firing probability density, is evaluated by either the Volterra integral equation of Buonocore, Nobile, and Ricciardi ( 1987 ) or, when possible, by the asymptotics of Giorno, Nobile, and Ricciardi (1990). The model examined here represents an extension of the classic leaky integrate-and-fire one based on the Ornstein-Uhlenbeck process in that it is in principle compatible with the inclusion of some other physiological characteristics such as relative refractoriness. It also allows finer tuning possibilities in view of its accounting for certain qualitative as well as quantitative features, such as the behavior of the time course of the membrane potential prior to firings and the computation of experimentally measurable statistical descriptors of the firing time: mean, median, coefficient of variation, and skewness. Finally, implementations of this model are provided in connection with certain experimental evidence discussed in the literature.

As a model of Brownian motor we consider the jump diffusion motion of a particle in the presence of an asymmetric periodic potential with a unique minimum and subject to half-period space shifts at the instants of occurrence of two Poisson processes. The relevant quantities, i.e., probability current, effective driving force, stall force, power and efficiency of the motor are explicitly calculated as averages of certain functions of the random variable representing the particle position.

We address the controversial hot question concerning the validity of the loose coupling versus the lever-arm theories in the actomyosin dynamics by re-interpreting and extending the phenomenological washboard potential model proposed by some of us in a previous paper. In this new model a Brownian motion harnessing thermal energy is assumed to co-exist with the deterministic swing of the lever-arm, to yield an excellent fit of the set of data obtained by some of us on the sliding of Myosin II heads on immobilized actin filaments under various load conditions. Our theoretical arguments are complemented by accurate numerical simulations, and the robustness of the model is tested via different choices of parameters and potential profiles.

With reference to the experimental observations by Yanagida and his co-workers on actomyosin interaction, a Brownian motor of fluctuating ratchet kind is designed with the aim to describe the interaction between a Myosin II head and a neighboring actin filament. Our motor combines the dynamics of the myosin head with a chemical external system related to the ATP cycle, whose role is to provide the energy supply necessary to bias the motion. Analytical expressions for the duration of the ATP cycle, for the Gibbs free energy and for the net displacement of the myosin head are obtained. Finally, by exploiting a method due to Sekimoto [J. Phys. Soc. Jpn. 66 (1997) 1234], a formula is worked out for the amount of energy consumed during the ATP cycle.

With reference to the experimental observations by Yanagida and his co-workers concerning actomyosin interaction during muscle contraction processes, we propose a phenomenological model for the sliding of the myosin head on the actin filament, in which the myosin head is viewed as an active Brownian particle in a periodic, elastic-type potential subject to tilting. The sample paths thus obtained are qualitatively alike to those experimentally recorded. Furthermore, our model is proved to be susceptible of a consistent parameters regulation yielding step frequencies, mean step dwell time and dwell time distribution in excellent agreement with the experimental evidence.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.