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

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

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

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

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 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

Finding “A Self to Speak Of”: Affective Enactments of the Self in Black and White Victorian Women’s Elegies

This thesis explores the genre of sentimental elegy within Antebellum Victorian America, drawing on affect studies, American religious history, and Black critical theory in order to contextualize the particular socio-political and religious influences that shaped the medium of the sentimental elegy and its role within Victorian America. This is punctuated by a close reading of six personal elegies written by Black and white women in the years 1855-1865. By attending to the differential application of sentimental norms about human bodies and their capacities for thought and feeling, this paper identifies the personal sentimental elegy as a technology of the self that was uniquely accessible to middle- and upper-class Victorian Americans, especially women, through which they mediated and navigated changing ideas about Christian cosmology, embodiment, and sentiment alongside their own personal and existential griefs. Although sentimental elegy is often reduced to one single and comprehensive genre, this project’s comparison of the different themes and motives that undergird elegies written by Black and white Victorian women complicates this tendentious categorization and encourages a re-examination of the medium

On a Symmetric, Nonlinear Birth-Death Process with Bimodal Transition Probabilities

We consider a bilateral birth-death process having sigmoidal-type rates. A thorough discussion on its transient behaviour is given, which includes studying symmetry properties of the transition probabilities, finding conditions leading to their bimodality, determining mean and variance of the process, and analyzing absorption problems in the presence of 1 or 2 boundaries. In particular, thanks to the symmetry properties we obtain the avoiding transition probabilities in the presence of a pair of absorbing boundaries, expressed as a series