We consider a random walk on the support of an ergodic simple point process on R, d ≥ 2, furnished with independent energy marks. The jump rates of the random walk decay exponentially in the jump length and depend on the energy marks via a Boltzmann–type factor. This is an effective model for the phonon–induced hopping of electrons in disordered solids in the regime of strong Anderson localizat...

In network topology discovery, it is often necessary to collect measurements between network elements without injecting large amounts of traffic into the network. A possible solution to this problem is to actively query the network for some measurements and use these to infer the remaining ones. We frame this as a particular version of the Noisy Matrix Completion problem where the entries refle...

Many modern block ciphers use maximum distance separable (MDS) matrices as the main part of their diffusion layers. In this paper, we propose a new class of diffusion layers constructed from several rounds of Feistel-like structures whose round functions are linear. We investigate the requirements of the underlying linear functions to achieve the maximal branch number for the proposed 4×4 words...

In this paper we extend recent results on the existence and uniqueness of solutions of ODEs with non-smooth vector fields to the case of martingale solutions, in the StroockVaradhan sense, of SDEs with non-smooth coefficients. In the first part we develop a general theory, which roughly speaking allows to deduce existence, uniqueness and stability of martingale solutions for L-almost every init...

We study electrical current in two-dimensional periodic Lorentz gas in the presence of a weak homogeneous electric field. When the horizon is finite, i.e. the free flights between collisions are bounded, the resulting current J is proportional to the voltage difference E, i.e. J = 1 2 D∗E + o(‖E‖), where D∗ is the diffusion matrix of the Lorentz particle moving freely without electrical field (...

We present phase-space techniques for the modelling of spontaneous emission in two-level bosonic atoms. The positive-P representation is shown to give a full and complete description within the limits of our model. The Wigner representation, even when truncated at second order, is shown to need a doubling of the phase-space to allow for a positive-definite diffusion matrix in the appropriate Fo...

Finite-volume methods for problems involving second-order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality condition. This discrete gradient is shown to satisfy a strong convergence property for the interpolation of regular functions, and a weak one for functions b...

In general, block ciphers consist of one top-level structural model into which the round function F is plugged into. The study focuses on Extended-FeistelNetwork (EFN) that is a generalization of a Feistel Network (FN). This structure is employed in several ciphers that were developed for Advanced Encryption Standard such as CAST-256, MARS and RC6. The problem with EFN is that it requires many ...

A flow composed of two populations of pedestrians moving in different directions is modeled by a two-dimensional system of convection-diffusion equations. An efficient simulation of the two-dimensional model is obtained by a finite-volume scheme combined with a fully adaptive multiresolution strategy. Numerical tests show the flow behavior in various settings of initial and boundary conditions,...

We here establish an a priori Hölder estimate of Krylov and Safonov type for the viscosity solutions of a degenerate quasilinear elliptic PDE of non-divergence form. The diffusion matrix may degenerate when the norm of the gradient of the solution is small: the exhibited Hölder exponent and Hölder constant only depend on the growth of the source term and on the bounds of the spectrum of the dif...