We raise the analytical knowledge of the eccentricity expansion of the Detweiler-Barack-Sago redshift invariant in a Schwarzschild spacetime up to the 9.5th post-Newtonian order (included) for the e(2) and e(4) contributions, and up to the 4th post-Newtonian order for the higher eccentricity contributions through e(20). We convert this information into an analytical knowledge of the effective-one-body radial potentials (d) over bar (u), p(u) and q(u) through the 9.5th post-Newtonian order. We find that our analytical results are compatible with current corresponding numerical self-force data.

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.

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 scattering of massive particles by a Schwarzschild black hole also undergoing a drag force is considered. The latter is modeled as a viscous force acting on the orbital plane, with components proportional to the associated particle 4-velocity components. The energy and angular momentum losses as well as the dependence of the hyperbolic scattering angle on the strength of the drag are investigated in situations where strong field effects cause large deflections.

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.

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.

In general relativity, relativistic gravity gradiometry involves the measurement of the relativistic tidal matrix, which is theoretically obtained from the projection of the Riemann curvature tensor onto the orthonormal tetrad frame of an observer. The observer's 4-velocity vector defines its local temporal axis and its local spatial frame is defined by a set of three orthonormal nonrotating gyro directions. The general tidal matrix for the timelike geodesics of Kerr spacetime has been calculated by Marck [Proc. R. Soc. A 385, 431 (1983)].

A new methodology for the mapping of intertidal terrain morphology is presented. It is based on the use of synthetic aperture radar (SAR) images and the temporal correlation between the SAR backscatter intensity and the water level on the intertidal zone. The proposed methodology does not require manual editing, providing a set of geolocated pixels that can be used to generate a digital elevation model of the intertidal zone. The methodology is validated using TerraSAR-X SAR images acquired over Tagus estuary.