We present and make available novel implementations of the two-dimensional Ising model that is used as a benchmark to show the computational capabilities of modern Graphic Processing Units (GPUs). The rich programming environment now available on GPUs and flexible hardware capabilities allowed us to quickly experiment with several implementation ideas: a simple stencil-based algorithm, recasting the stencil operations into matrix multiplies to take advantage of Tensor Cores available on NVIDIA GPUs, and a highly optimized multi-spin coding approach.

Bandelt and Mulder's structural characterization of bipartite distance hereditary graphs 16 asserts that such graphs can be built inductively starting from a single vertex and by re- 17 peatedly adding either pendant vertices or twins (i.e., vertices with the same neighborhood 18 as an existing one). Dirac and Duffin's structural characterization of 2-connected series- 19 parallel graphs asserts that such graphs can be built inductively starting from a single edge 20 by adding either edges in series or in parallel.

We consider a mathematical model describing population dynamics of normal and abnormal cell densities with contact inhibition of cell growth from a theoretical point of view. In the first part of this paper, we discuss the global existence of a solution satisfying the segregation property in one space dimension for general initial data. Here, the term segregation property means that the different types of cells keep spatially segregated when the initial densities are segregated.

We introduce non-local dynamics on directed networks through the construction of a fractional version of a non-symmetric Laplacian for weighted directed graphs. Furthermore, we provide an analytic treatment of fractional dynamics for both directed and undirected graphs, showing the possibility of exploring the network employing random walks with jumps of arbitrary length. We also provide some examples of the applicability of the proposed dynamics, including consensus over multi-agent systems described by directed networks.

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.

This paper introduces a dominance test that allows to determine whether or not a financial institution can be classified as being more systemically important than another in a multivariate framework. The dominance test relies on a new risk measure, the NetCoVaR that is specifically tailored to capture the joint extreme co-movements between institutions belonging to a network. The asymptotic theory for the statistical test is provided under mild regularity conditions concerning the joint distribution of asset returns which is assumed to be elliptically contoured.

This article is concerned with the analysis of the one-dimensional compressible Euler equations with a singular pressure law, the so-called hard sphere equation of state. The result is twofold. First, we establish the existence of bounded weak solutions by means of a viscous regularization and refined compensated compactness arguments. Second, we investigate the smooth setting by providing a de- tailed description of the impact of the singular pressure on the breakdown of the solutions.

Extended versions of the Bourgain-Brezis-Mironescu theorems on the limit as s->1^- of the Gagliardo-Slobodeckij fractional seminorm are established in the Orlicz space setting. Our results hold for fractional Orlicz-Sobolev spaces built upon general Young functions, and complement those of [13], where Young functions satisfying the $\Delta_2$ and the $\nabla_2$ conditions are dealt with. The case of Young functions with an asymptotic linear growth is also considered in connection with the space of functions of bounded variation.

This paper deals with the solution of an inverse problem for the heat equation aimed at nondestructive evaluation of fractures, emerging on the accessible surface of a slab, by means of Active Thermography. In real life, this surface is heated with a laser and its temperature is measured for a time interval by means of an infrared camera. A fundamental step in iterative inversion methods is the numerical solution of the underlying direct mathematical model.

We consider an empirical Bayes approach to standard nonparametric regression estimation using a nonlinear wavelet methodology. Instead of specifying a single prior distribution on the parameter space of wavelet coefficients, which is usually the case in the existing literature, we elicit the epsilon-contamination class of prior distributions that is particularly attractive to work with when one seeks robust priors in Bayesian analysis.