On the Effect of Random Alternating Perturbations on Hazard Rates

We consider a model for systems perturbed by dichotomous noise, in which the hazard rate function of a random lifetime is subject to additive time-alternating perturbations described by the telegraph process. This leads us to define a real-valued continuous-time stochastic process of alternating type expressed in terms of the integrated telegraph process for which we obtain the probability distribution, mean and variance. An application to survival analysis and reliability data sets based on confidence bands for estimated hazard rate functions is also provided.Comment: 14 pages, 6 figure

A multispecies birth-death-immigration process and its diffusion approximation

We consider an extended birth-death-immigration process defined on a lattice formed by the integers of $d$ semiaxes joined at the origin. When the process reaches the origin, then it may jumps toward any semiaxis with the same rate. The dynamics on each ray evolves according to a one-dimensional linear birth-death process with immigration. We investigate the transient and asymptotic behavior of the process via its probability generating function. The stationary distribution, when existing, is a zero-modified negative binomial distribution. We also study a diffusive approximation of the process, which involves a diffusion process with linear drift and infinitesimal variance on each ray. It possesses a gamma-type transient density admitting a stationary limit. As a byproduct of our study, we obtain a closed form of the number of permutations with a fixed number of components, and a new series form of the polylogarithm function expressed in terms of the Gauss hypergeometric function.Comment: 26 pages, 7 figure

A review on symmetry properties of birth-death processes

In this paper we review some results on time-homogeneous birth-death processes. Specifically, for truncated birth-death processes with two absorbing or two reflecting endpoints, we recall the necessary and sufficient conditions on the transition rates such that the transition probabilities satisfy a spatial symmetry relation. The latter leads to simple expressions for first-passage-time densities and avoiding transition probabilities. This approach is thus thoroughly extended to the case of bilateral birth-death processes, even in the presence of catastrophes, and to the case of a two-dimensional birth-death process with constant rates.Comment: 16 pages, 4 figure

A stochastic model for the stepwise motion in actomyosin dynamics

A jump-diffusion process is proposed to describe the displacements performed by single myosin heads along actin filaments during the rising phases. The process consists of the superposition of a Wiener and a jump process, with jumps originated by sequences of Poisson-distributed energy-supplying pulses. In a previous paper, the amplitude of the jumps was described by a mixture of two Gaussian distributions. To embody the effects of ATP hydrolysis, we now refine such a model by assuming that the jumps' amplitude is described by a mixture of three Gaussian distributions. This model has been inspired by the experimental data of T. Yanagida and his co-workers concerning observations at single molecule processes level.Comment: 9 pages, 4 figure

On a bilateral birth-death process with alternating rates

We consider a bilateral birth-death process characterized by a constant transition rate $\lambda$ from even states and a possibly different transition rate $\mu$ from odd states. We determine the probability generating functions of the even and odd states, the transition probabilities, mean and variance of the process for arbitrary initial state. Some features of the birth-death process confined to the non-negative integers by a reflecting boundary in the zero-state are also analyzed. In particular, making use of a Laplace transform approach we obtain a series form of the transition probability from state 1 to the zero-state.Comment: 13 pages, 3 figure

Compound Poisson process with a Poisson subordinator

A compound Poisson process whose randomized time is an independent Poisson process is called compound Poisson process with Poisson subordinator. We provide its probability distribution, which is expressed in terms of the Bell polynomials, and investigate in detail both the special cases in which the compound Poisson process has exponential jumps and normal jumps. Then for the iterated Poisson process we discuss some properties and provide convergence results to a Poisson process. The first-crossing-time problem for the iterated Poisson process is finally tackled in the cases of (i) a decreasing and constant boundary, where we provide some closed-form results, and (ii) a linearly increasing boundary, where we propose an iterative procedure to compute the first-crossing-time density and survival functions.Comment: 16 pages, 7 figure

Realizzazione di modelli 3-D in vitro per lo studio morfologico e funzionale della barriera epiteliale intestinale

Il miglioramento di modelli sperimentali in vivo ed in vitro per studi di ingegneria tissutale, farmacologia e studi metabolici è ampiamente richiesto. I sistemi di coltura in vitro vengono comunemente utilizzati per lo studio di fenomeni biologici come la crescita ed il differenziamento cellulare e per lo studio dei processi fisiopatologici. Questi metodi sono vantaggiosi per la loro disponibilità e la relativa economicità, per la facile standardizzazione e per riproducibilità sperimentale. I sistemi di coltura cellulare in vitro tradizionali sono però scarsamente rappresentativi della fisiologia animale o umana e per questo motivo, nella valutazione dei risultati, va considerata la notevole semplificazione di questi modelli sperimentali rispetto ai complessi meccanismi biologici di un organismo vivente. La progettazione di dispositivi e sistemi bioingegneristici che riproducano le caratteristiche degli organismi viventi è necessaria per il superamento di questi limiti. Lo scopo di questa tesi è lo sviluppo di un nuovo sistema in vitro in cui ricreare le caratteristiche morfologiche e funzionali della barriera intestinale e la valutazione del passaggio di sostanze attraverso questo epitelio. La prima parte dello studio è basata sull’utilizzo di colture cellulari in condizioni statiche e dinamiche, che prevedono l’utilizzo di bioreattori modulari multi-compartimentali (MCmB). I risultati ottenuti mediante l’uso di questi nuovi sistemi, sono stati confrontati con i dati ricavati da colture cellulari convenzionali. Durante il corso degli esperimenti, sono stati eseguite misure, saggi biochimici, esami immunocitochimici e la valutazione della vitalità e della funzionalità cellulare. La seconda parte dello studio riguarda la sperimentazione e la valutazione di nuovi materiali polimerici. Questa parte dello studio ha consentito di individuare la loro biocompatibilità ed il loro possibile futuro utilizzo per la progettazione di sistemi più evoluti, in grado di riprodurre le condizioni fisiologiche presenti nell’intestino umano

A Quantile-Based Probabilistic Mean Value Theorem

For non-negative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows us to construct new distributions with support (0, 1), and to obtain a new quantile-based version of the probabilistic generalization of Taylor's theorem. Similarly, for pairs of stochastically ordered random variables we come to a new quantile-based form of the probabilistic mean value theorem. The latter involves a distribution that generalizes the Lorenz curve. We investigate the special case of proportional quantile functions and apply the given results to various models based on classes of distributions and measures of risk theory. Motivated by some stochastic comparisons, we also introduce the “expected reversed proportional shortfall order”, and a new characterization of random lifetimes involving the reversed hazard rate function.The research of A.D.C. and B.M. has been performed under partial support by GNCS-INdAM and Regione Campania (Legge 5). J.M. was supported by project MTM2012-34023-FEDER, “Comparación y dependencia en modelos probabilísticos con aplicaciones en fiabilidad y riesgos”, from Universidad de Murcia

Financial Literacy among Buffalo State College Undergraduate Students

Financial literacy can be complex and difficult for college students to comprehend. Many students struggle to afford college and are faced with large amounts of student loan debt. Financial awareness needs to be addressed early on for students to make informed decisions about college costs, student debt, and financial aid. However, financial aid applications, terms and conditions, and eligibility requirements are difficult for many students to comprehend on their own. The purpose of this study is to access financial literacy among undergraduate students at Buffalo State College. A quantitative approach is used in this study by implementing a web-based cross-sectional survey via Qualtrics. All undergraduate students were invited to participate in the survey, which was designed to understand the knowledge and skills of students to manage financial resources efficiently. The study found that there is a need for financial literacy education and students are interested in increasing their financial knowledge