In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction ratios for this model.

Bootstrap percolation is a well-known activation process in a graph, in which a node becomes active when it has at least r active neighbors. Such process, originally studied on regular structures, has been recently investigated also in the context of random graphs, where it can serve as a simple model for a wide variety of cascades, such as the spreading of ideas, trends, viral contents, etc. over large social networks. In particular, it has been shown that in G(n, p) the final active set can exhibit a phase transition for a sub-linear number of seeds.

We give a general Gaussian bound for the first chaos (or innovation) of point processes with stochastic intensity constructed by embedding in a bivariate Poisson process. We apply the general result to nonlinear Hawkes processes, providing quantitative central limit theorems.

The precession of a test gyroscope along unbound equatorial plane geodesic orbits around a Kerr black hole is analyzed with respect to a static reference frame whose axes point towards the "fixed stars." The accumulated precession angle after a complete scattering process is evaluated and compared with the corresponding change in the orbital angle. Limiting results for the nonrotating Schwarzschild black hole case are also discussed.

A malicious alteration of system-provided timeline can negatively affect the reliability of computer forensics. Indeed, detecting such changes and possibly reconstructing the correct timeline of events is of paramount importance for court admissibility and logical coherence of collected evidence. However, reconstructing the correct timeline for a set of network nodes can be difficult since an adversary has a wealth of opportunities to disrupt the timeline and to generate a fake one.

The precession of a test gyroscope along stable bound equatorial plane orbits around a Kerr black hole is analyzed, and the precession angular velocity of the gyro's parallel transported spin vector and the increment in the precession angle after one orbital period is evaluated. The parallel transported Marck frame which enters this discussion is shown to have an elegant geometrical explanation in terms of the electric and magnetic parts of the Killing-Yano 2-form and a Wigner rotation effect.

Global Navigation Satellite System (GNSS) tomography provides 3-D reconstructions of atmosphere wet refractivity, related to water vapor. A simulated analysis of the integration of Global Positioning System and future Galileo data is presented. Atmospheric refractivity is derived from radiosonde data acquired over the Lisbon area. The impact of Galileo data on the tomographic reconstruction is assessed.