Abstract:
Over the past 15 years, DNA vaccines have gone from a scientific curiosity to one of the most dynamic research field and may offer new alternatives for the control of parasitic diseases such as leishmaniasis and Chagas disease. We review here some of the advances and challenges for the development of DNA vaccines against these diseases. Many studies have validated the concept of using DNA vaccines for both protection and therapy against these protozoan parasites in a variety of mouse models. The challenge now is to translate what has been achieved in these models into veterinary or human vaccines of comparable efficacy. Also, genome-mining and new antigen discovery strategies may provide new tools for a more rational search of novel vaccine candidates.

Abstract:
chagas' disease, caused by the protozoan parasite trypanosoma cruzi, represents a major public health problem in most of the american continent. as transmission of the parasite is being interrupted in most of south america, the disease remains endemic in various areas of mexico. we review here some of the information gathered in recent years. seroprevalence of t. cruzi infection in humans remains relatively high in some areas, and there has been a general increase in the number of chronic cases reported to health authorities in recent years. in fact, chronic chagasic cardiomyopathy appears to be affecting a large number of patients with heart disease, but many cases may be misreported because of the unspecific nature of the clinical symptoms. epidemiological monitoring of vector and reservoir populations, as well as of human cases is helping focus on endemic areas, but a better coordination and development of these efforts is still needed. recent studies of parasite biology are in agreement with previous work showing the great diversity of parasite characteristics, and support the need for a regional approach to this zoonosis. strong and continuing support from health and academic authorities is thus still needed to further improve our understanding of chagas' disease in mexico and implement efficient control programs.

Abstract:
Chagas' disease, caused by the protozoan parasite Trypanosoma cruzi, represents a major public health problem in most of the American continent. As transmission of the parasite is being interrupted in most of South America, the disease remains endemic in various areas of Mexico. We review here some of the information gathered in recent years. Seroprevalence of T. cruzi infection in humans remains relatively high in some areas, and there has been a general increase in the number of chronic cases reported to health authorities in recent years. In fact, chronic chagasic cardiomyopathy appears to be affecting a large number of patients with heart disease, but many cases may be misreported because of the unspecific nature of the clinical symptoms. Epidemiological monitoring of vector and reservoir populations, as well as of human cases is helping focus on endemic areas, but a better coordination and development of these efforts is still needed. Recent studies of parasite biology are in agreement with previous work showing the great diversity of parasite characteristics, and support the need for a regional approach to this zoonosis. Strong and continuing support from health and academic authorities is thus still needed to further improve our understanding of Chagas' disease in Mexico and implement efficient control programs.

Abstract:
Many physical observables can be represented as a particle spending some random time within a given domain. For a broad class of transport-dominated processes, we detail how it is possible to express the moments of the number of particle collisions in an arbitrary volume in terms of repeated convolutions of the ensemble equilibrium distribution. This approach is shown to generalize the celebrated Kac formula for the moments of residence times, which is recovered in the diffusion limit. Some practical applications are illustrated for bounded, unbounded and absorbing domains.

Abstract:
Many random transport phenomena, such as radiation propagation, chemical/biological species migration, or electron motion, can be described in terms of particles performing {\em exponential flights}. For such processes, we sketch a general approach (based on the Feynman-Kac formalism) that is amenable to explicit expressions for the moments of the number of collisions and the residence time that the walker spends in a given volume as a function of the particle equilibrium distribution. We then illustrate the proposed method in the case of the so-called {\em rod problem} (a 1d system), and discuss the relevance of the obtained results in the context of Monte Carlo estimators.

Abstract:
Branching random walks are key to the description of several physical and biological systems, such as neutron multiplication, genetics and population dynamics. For a broad class of such processes, in this Letter we derive the discrete Feynman-Kac equations for the probability and the moments of the number of visits $n_V$ of the walker to a given region $V$ in the phase space. Feynman-Kac formulas for the residence times of Markovian processes are recovered in the diffusion limit.

Abstract:
In this paper we analyze some aspects of {\em exponential flights}, a stochastic process that governs the evolution of many random transport phenomena, such as neutron propagation, chemical/biological species migration, or electron motion. We introduce a general framework for $d$-dimensional setups, and emphasize that exponential flights represent a deceivingly simple system, where in most cases closed-form formulas can hardly be obtained. We derive a number of novel exact (where possible) or asymptotic results, among which the stationary probability density for 2d systems, a long-standing issue in Physics, and the mean residence time in a given volume. Bounded or unbounded, as well as scattering or absorbing domains are examined, and Monte Carlo simulations are performed so as to support our findings.

Abstract:
For a broad class of random walks with anisotropic scattering kernel and absorption, we derive explicit formulas that allow expressing the moments of the collision number $n_V$ performed in a volume $V$ as a function of the particle equilibrium distribution. Our results apply to arbitrary domains $V$ and boundary conditions, and allow assessing the hitting statistics for systems where the typical displacements are comparable to the domain size, so that the diffusion limit is possibly not attained. An example is discussed for one-dimensional (1d) random flights with exponential displacements, where analytical calculations can be carried out.

Abstract:
By building upon a Feynman-Kac formalism, we assess the distribution of the number of hits in a given region for a broad class of discrete-time random walks with scattering and absorption. We derive the evolution equation for the generating function of the number of hits, and complete our analysis by examining the moments of the distribution, and their relation to the walker equilibrium density. Some significant applications are discussed in detail: in particular, we revisit the gambler's ruin problem and generalize to random walks with absorption the arcsine law for the number of hits on the half-line.

Abstract:
Branching random flights are key to describing the evolution of many physical and biological systems, ranging from neutron multiplication to gene mutations. When their paths evolve in bounded regions, we establish a relation between the properties of trajectories starting on the boundary and those starting inside the domain. Within this context, we show that the total length travelled by the walker and the number of performed collisions in bounded volumes can be assessed by resorting to the Feynman-Kac formalism. Other physical observables related to the branching trajectories, such as the survival and escape probability, are derived as well.