We present the first analytical computation of the (conservative) gravitational self-force correction to the periastron advance around a spinning black hole. Our result is accurate to the second order in the rotational parameter and through the 9.5 post-Newtonian level. It has been obtained as the circular limit of the correction to the gyroscope precession invariant along slightly eccentric equatorial orbits in the Kerr spacetime. The latter result is also new and we anticipate here the first few terms only of the corresponding post-Newtonian expansion.

Magnetoencephalography (MEG) aims at reconstructing the unknown neuroelectric activity in the brain from non-invasive measurements of the magnetic field induced by neural sources. The solution of this ill-posed, ill-conditioned inverse problem is usually dealt with using regularization techniques that are often time-consuming, and computationally and memory storage demanding. In this paper we analyze how a slimmer procedure, random sampling, affects the estimation of the brain activity generated by both synthetic and real sources.

We propose an approach to the numerical simulation of thin-film flows based on the lattice Boltzmann method. We outline the basic features of the method, show in which limits the expected thin-film equations are recovered, and perform validation tests. The numerical scheme is applied to the viscous Rayleigh-Taylor instability of a thin film and to the spreading of a sessile drop toward its equilibrium contact angle configuration. We show that the Cox-Voinov law is satisfied and that the effect of a tunable slip length on the substrate is correctly captured.

The societal impact of traffic is a long-standing and complex problem. We focus on the estimation of ground-level ozone production due to vehicular traffic. We propose a comprehensive computational approach combining four consecutive modules: a traffic simulation module, an emission module, a module for the main chemical reactions leading to ozone production, and a module for the diffusion of gases in the atmosphere. The traffic module is based on a second-order traffic flow model, obtained by choosing a special velocity function for the Collapsed Generalized Aw-Rascle-Zhang model.

Network-based ranking methods (e.g. centrality analysis) have found extensive use in systems medicine for the prediction of essential proteins, for the prioritization of drug targets candidates in the treatment of several pathologies and in biomarker discovery, and for human disease genes identification. Here we propose to use critical nodes as defined by the Critical Node Problem for the analysis of key physiological and pathophysiological signaling pathways, as target candidates for treatment and management of several cancer types, neurologic and inflammatory dysfunctions, among others.

Competition between biological species in marine environments is affected by the motion of the surrounding fluid. An effective 2D compressibility can arise, for example, from the convergence and divergence of water masses at the depth at which passively traveling photosynthetic organisms are restricted to live. In this report, we seek to quantitatively study genetics under flow. To this end, we couple an off-lattice agent-based simulation of two populations in 1D to a weakly compressible velocity field--first a sine wave and then a shell model of turbulence.

In recent years, a number of functional inequalities have been derived for Poisson random measures, with a wide range of applications. In this paper, we prove that such inequalities can be extended to the setting of marked temporal point processes, under mild assumptions on their Papangelou conditional intensity. First, we derive a Poincare inequality. Second, we prove two transportation cost inequalities. The first one refers to functionals of marked point processes with a Papangelou conditional intensity and is new even in the setting of Poisson random measures.

Marine species reproduce and compete while being advected by turbulent flows. It is largely unknown, both theoretically and experimentally, how population dynamics and genetics are changed by the presence of fluid flows. Discrete agent-based simulations in continuous space allow for accurate treatment of advection and number fluctuations, but can be computationally expensive for even modest organism densities. In this report, we propose an algorithm to overcome some of these challenges. We first provide a thorough validation of the algorithm in one and two dimensions without flow.