Approximations for time-dependent distributions in Markovian fluid models

In this paper we study the distribution of the level at time $\theta$ of Markovian fluid queues and Markovian continuous time random walks, the maximum (and minimum) level over $[0,\theta]$, and their joint distributions. We approximate $\theta$ by a random variable $T$ with Erlang distribution and we use an alternative way, with respect to the usual Laplace transform approach, to compute the distributions. We present probabilistic interpretation of the equations and provide a numerical illustration

Perturbation analysis of Markov modulated fluid models

We consider perturbations of positive recurrent Markov modulated fluid models. In addition to the infinitesimal generator of the phases, we also perturb the rate matrix, and analyze the effect of those perturbations on the matrix of first return probabilities to the initial level. Our main contribution is the construction of a substitute for the matrix of first return probabilities, which enables us to analyze the effect of the perturbation under consideration

Voter engagement, electoral inequality and first time compulsory voting

This paper reviews the problem of declining turnout and proposes as a solution a system whereby each elector would be legally obliged to vote in the first election for which they were eligible. Popular attitudes toward first-time compulsory voting are measured and probed by means of UK data. The main findings of the paper are that first-time compulsory voting is a politically and administratively feasible proposal that appears tentatively to command popular support and has the potential to help address a number of the problems associated with declining turnout, and in particularly low rates of electoral participation among younger citizens

Poisson's equation for discrete-time quasi-birth-and-death processes

We consider Poisson's equation for quasi-birth-and-death processes (QBDs) and we exploit the special transition structure of QBDs to obtain its solutions in two different forms. One is based on a decomposition through first passage times to lower levels, the other is based on a recursive expression for the deviation matrix. We revisit the link between a solution of Poisson's equation and perturbation analysis and we show that it applies to QBDs. We conclude with the PH/M/1 queue as an illustrative example, and we measure the sensitivity of the expected queue size to the initial value

General solution of the Poisson equation for Quasi-Birth-and-Death processes

We consider the Poisson equation $(I-P)\boldsymbol{u}=\boldsymbol{g}$, where $P$ is the transition matrix of a Quasi-Birth-and-Death (QBD) process with infinitely many levels, $\bm g$ is a given infinite dimensional vector and $\bm u$ is the unknown. Our main result is to provide the general solution of this equation. To this purpose we use the block tridiagonal and block Toeplitz structure of the matrix $P$ to obtain a set of matrix difference equations, which are solved by constructing suitable resolvent triples

Leadership Curriculum Evaluation: Final Report DFE- RR639

Evaluation report of the National College for Teaching and Leadership's Leadership Curriculum commissioned by Department for Education (2013-2016

Sensitive plant (Mimosa pudica) hiding time depends on individual and state.

The decisions animals make to adjust their antipredator behavior to rapidly changing conditions have been well studied. Inducible defenses in plants are an antipredator behavior that acts on a longer time scale, but sensitive plants, Mimosa pudica, have a much more rapid antipredator response; they temporarily close their leaves when touched. The time they remain closed is defined as hiding time. We studied hiding time in sensitive plants and found that individual plants differed significantly in their hiding times. We then showed that the effect of individual explained substantial variation in hiding time on a short time scale. Finally, on a longer time scale, individuality persisted but the amount of variation attributed to individual decreased. We hypothesized that variation in plant condition might explain this change. We therefore manipulated sunlight availability and quantified hiding time. When deprived of light for 6 h, sensitive plants significantly shortened their hiding times. But when only half a plant was deprived of light, hiding times on the deprived half and light exposed half were not significantly different. This suggests that overall condition best explains variation in sensitive plant antipredator behavior. Just like in animals, sensitive plant antipredator behavior is condition dependent, and, just like in animals, a substantial amount of the remaining variation is explained by individual differences between plants. Thus, models designed to predict plasticity in animal behavior may be successfully applied to understand behavior in other organisms, including plants

Implementing Pasteur's vision for rabies elimination: the evidence base and the needed policy actions

It has been 129 years since Louis Pasteur's experimental protocol saved the life of a child mauled by a rabid dog, despite incomplete understanding of the etiology or mechanisms by which the miracle cure worked (1). The disease has since been well understood, and highly effective vaccines are available, yet Pasteur's vision for ridding the world of rabies has not been realized. Rabies remains a threat to half the world's population and kills more than 69,000 people each year, most of them children (2). We discuss the basis for this neglect and present evidence supporting the feasibility of eliminating canine-mediated rabies and the required policy actions