Observational data from the European Space Agency astrometric mission Gaia determining the positions of celestial objects within an accuracy of a few microarcseconds will be soon fully available. Other satellite-based space missions are currently planned to significantly improve such precision in the next years. The data reduction process needs high-precision general relativistic models, allowing one to solve the inverse ray-tracing problem in the gravitational field of the Solar System up to the requested level of accuracy and leading then to the estimate of astrometric parameters.

The literature on k-splittable flows, see Baier et al. (2002) Baier et al. (2005), provides evidence on how controlling the number of used paths enables practical applications of flows optimization in many real-world contexts. Such a modeling feature has never been integrated so far in Quickest Flows, a class of optimization problems suitable to cope with situations such as emergency evacuations, transportation planning and telecommunication systems, where one aims to minimize the makespan, i.e. the overall time needed to complete all the operations, see Pascoal et al. (2006) Pascoal et al.

We focus on interacting neurons organized in a block-layered network devoted to the information processing from the sensory system to the brain. Specifically, we consider the firing activity of olfactory sensory neurons, periglomerular, granule and mitral cells in the context of the neuronal activity of the olfactory bulb. We propose and investigate a stochastic model of a layered and modular network to describe the dynamic behavior of each prototypical neuron, taking into account both its role (excitatory/inhibitory) and its location within the network.

This paper is concerned with diffusive approximations of some numerical schemes for several linear (or weakly nonlinear) kinetic models which are motivated by wide-range applications, including radiative transfer or neutron transport, run-and-tumble models of chemotaxis dynamics, and Vlasov-Fokker-Planck plasma modeling. The well-balanced method applied to such kinetic equations leads to time-marching schemes involving a ``{\it scattering $S$-matrix}'', itself derived from a normal modes decomposition of the stationary solution.

The protozoan parasite Trypanosoma cruz causes the Chagas disease, which final outcome can be morbidity or death. The complexity of this infection is due to the many kinds of players involved in the immune response and to the variety of host cells targeted by the parasite. We built an ordinary differential equation model which includes aspects of innate and adaptive immune response to study the T. cruzi infection. The model also includes cardiomyocytes to represent how the infection affects the heart.

Localization phenomena (sometimes called ``{\it flea on the elephant}'') for the operator $L^\varepsilon=-\varepsilon^2 \Delta u + p(\xx) u$, $p(\xx)$ being an asymmetric double-well potential, are studied both analytically and numerically, mostly in two space dimensions within a perturbative framework. Starting from a classical harmonic potential, the effects of various perturbations are retrieved, especially in the case of two asymmetric potential wells.

Standard reaction-diffusion systems are characterized by infinite velocities and no persistence in the movement of individuals, two conditions that are violated when considering living organisms. Here we consider a discrete particle model in which individuals move following a persistent random walk with finite speed and grow with logistic dynamics. We show that, when the number of individuals is very large, the individual-based model is well described by the continuous reactive Cattaneo equation (RCE), but for smaller values of the carrying capacity important finite-population effects arise.

Infection by Leishmania can cause diseases ranging from self-healing cutaneous to visceral dissemination that can lead to death if untreated. In order to explore the early phase of the infection and the role of macrophages, we implement a system of differential equations involving the major players in the innate immune response to leishmaniasis (i.e., parasites in the intracellular and free form, infected and uninfected macrophages, and NO/ROS). The model was adjusted and validated using data from C57BL/6, KO and SCID mice published in the literature.

A binary mixture saturating a horizontal porous layer, with large pores and uniformly heated from below, is considered. The instability of a vertical uid motion (throughflow) when the layer is salted by one salt (either from above or from below) is analyzed. Ultimately boundedness of solutions is proved, via the existence of positively invariant and attractive sets (i.e. absorbing sets). The critical Rayleigh numbers at which steady or oscillatory instability occurs, are recovered.