On the time to reach a critical number of infections in epidemic models with infective and susceptible immigrants.

In this paper we examine the time T to reach a critical number K0 of infections during an outbreak in an epidemic model with infective and susceptible immigrants. The underlying process X, which was first introduced by Ridler-Rowe (1967), is related to recurrent diseases and it appears to be analytically intractable. We present an approximating model inspired from the use of extreme values, and we derive formulae for the Laplace-Stieltjes transform of T and its moments, which are evaluated by using an iterative procedure. Numerical examples are presented to illustrate the effects of the contact and removal rates on the expected values of T and the threshold K0, when the initial time instant corresponds to an invasion time. We also study the exact reproduction number Rexact,0 and the population transmission number Rp, which are random versions of the basic reproduction number R0.

Stochastic descriptors to study the fate and potential of naive T cell clonotypes in the periphery

The population of naive T cells in the periphery is best described by determining both its T cell receptor diversity, or number of clonotypes, and the sizes of its clonal subsets. In this paper, we make use of a previously introduced mathematical model of naive T cell homeostasis, to study the fate and potential of naive T cell clonotypes in the periphery. This is achieved by the introduction of several new stochastic descriptors for a given naive T cell clonotype, such as its maximum clonal size, the time to reach this maximum, the number of proliferation events required to reach this maximum, the rate of contraction of the clonotype during its way to extinction, as well as the time to a given number of proliferation events. Our results show that two fates can be identified for the dynamics of the clonotype: extinction in the short-term if the clonotype experiences too hostile a peripheral environment, or establishment in the periphery in the long-term. In this second case the probability mass function for the maximum clonal size is bimodal, with one mode near one and the other mode far away from it. Our model also indicates that the fate of a recent thymic emigrant (RTE) during its journey in the periphery has a clear stochastic component, where the probability of extinction cannot be neglected, even in a friendly but competitive environment. On the other hand, a greater deterministic behaviour can be expected in the potential size of the clonotype seeded by the RTE in the long-term, once it escapes extinction.

A Hardware Implementation of a Run-Time Scheduler for Reconfigurable Systems

New generation embedded systems demand high performance, efficiency and flexibility. Reconfigurable hardware can provide all these features. However the costly reconfiguration process and the lack of management support have prevented a broader use of these resources. To solve these issues we have developed a scheduler that deals with task-graphs at run-time, steering its execution in the reconfigurable resources while carrying out both prefetch and replacement techniques that cooperate to hide most of the reconfiguration delays. In our scheduling environment task-graphs are analyzed at design-time to extract useful information. This information is used at run-time to obtain near-optimal schedules, escaping from local-optimum decisions, while only carrying out simple computations. Moreover, we have developed a hardware implementation of the scheduler that applies all the optimization techniques while introducing a delay of only a few clock cycles. In the experiments our scheduler clearly outperforms conventional run-time schedulers based on As-Soon-As-Possible techniques. In addition, our replacement policy, specially designed for reconfigurable systems, achieves almost optimal results both regarding reuse and performance.