An extended version of the Maz'ya-Shaposhnikova theorem on the limit as s -> 0+ of the Gagliardo-Slobodeckij fractional seminorm is established in the Orlicz space setting. Our result holds in fractional Orlicz-Sobolev spaces associated with Young functions satisfying the \Delta2-condition, and, as shown by counterexamples, it may fail if this condition is dropped.

The aim of this paper is to solve an inverse problem which regards a mass moving in a bounded domain. We assume that the mass moves following an unknown velocity field and that the evolution of the mass density can be described by a partial differential equation, which is also unknown. The input data of the problems are given by some snapshots of the mass distribution at certain times, while the sought output is the velocity field that drives the mass along its displacement.

We complete our previous derivation, at the sixth post-Newtonian (6PN) accuracy, of the local-in-time dynamics of a gravitationally interacting two-body system by giving two gauge-invariant characterizations of its complementary nonlocal-in-time dynamics. On the one hand, we compute the nonlocal part of the scattering angle for hyberboliclike motions; and, on the other hand, we compute the nonlocal part of the averaged (Delaunay) Hamiltonian for ellipticlike motions.

Let P and (P) over tilde be the laws of two discrete-time stochastic processes defined on the sequence space S-N,where S is a finite set of points. In this paper we derive a bound on the total variation distance d(TV)(P, (P) over tilde) in terms of the cylindrical projections of P and (P) over tilde. We apply the result to Markov chains with finite state space and random walks on Z with not necessarily independent increments, and we consider several examples.

An Ermakov-Pinney-like equation associated with the scalar wave equation in curved space-time is here studied. The example of Schwarzschild space-time considered in the present work shows that this equation can be viewed more as a "model equation," with interesting applications in black hole physics. Other applications studied involve cosmological space-times (de Sitter) and pulse of plane gravitational waves: in all these cases the evolution of the Ermakov-Pinney field seems to be consistent with a rapid blow-up, unlike the Schwarzschild case where spatially damped oscillations are allowed.

A new class of multiscale scheme is presented for micro-hydrodynamic problems based on a dual representation of the fluid observables. The hybrid model is first tested against the classical flow between two parallel plates and then applied to a plug flow within a micrometer-sized striction and a shear flow within a microcavity.

The idea that individuals tend to choose a romantic partner following similarities on personality traits has always attracted much attention in the psychological literature, although results were controversial. We conducted a new data analysis approach to personality traits of 235 newlywed couples. Univariate analysis revealed that a neurotic husband is usually paired with a lesser extrovert and open wife.

Systems medicine (SM) has emerged as a powerful tool for studying the human body at the systems level with the aim of improving our understanding, prevention and treatment of complex diseases. Being able to automatically extract relevant features needed for a given task from high-dimensional, heterogeneous data, deep learning (DL) holds great promise in this endeavour. This review paper addresses the main developments of DL algorithms and a set of general topics where DL is decisive, namely, within the SM landscape.

A limitation of current modeling studies in waterborne diseases (one of the leading causes of death worldwide) is that the intrinsic dynamics of the pathogens is poorly addressed, leading to incomplete, and often, inadequate understanding of the pathogen evolution and its impact on disease transmission and spread. To overcome these limitations, in this paper, we consider an ODEs model with bacterial growth inducing Allee effect. We adopt an adequate functional response to significantly express the shape of indirect transmission.