In the Cultural Heritage area it is of fundamental importance to characterize and classify the conservation state of the materials constituting ancient monuments, in order to study and monitor their decay. Generally the decay diagnosis is provided by “naked eye” analysis done by expert scientists “walking around” the artifact and recording the conservation state of each individual element they observe. In this paper, a color image segmentation approach, based on histogram threshold and edge detection techniques is presented, to extract degradation regions, characterized by holes or cavities, from color images of stone-materials. The goal is to provide an aid to the decay diagnosis by segmenting degraded regions from color images, computing quantitative data, such as the area and perimeter of the extracted zones, and processing qualitative information, such as various levels of depth detected into the same zones. Since color is a powerful tool in the distinction between objects, a segmentation technique based on color, instead of intensity only, has been used to provide an clearer discrimination between regions. The study case concerns the impressive remains of the Roman Theatre in the city of Aosta (Italy). In particular we have processed and analyzed some color images of the Theatre puddingstones, acquired by a camera.

Using computer simulations, the finite sample performance of a number of classical and Bayesian wavelet shrinkage estimators for Poisson counts is examined. For the purpose of comparison, a variety of intensity functions, background intensity levels, sample sizes, primary resolution levels, wavelet filters and performance criteria are employed. A demonstration is given of the use of some of the estimators to analyse a data set arising in high-energy astrophysics. Following the philosophy of reproducible research, the Matlab programs and real-life data example used in this study are made freely available.

We consider the Cauchy problem for the 2 x 2 nonstrictly hyperbolic system [...] For possiblylarge, discontinuous and resonant data, the generalized solution to the Riemann problem is introduced, interaction estimates are carried out using an original change of variables and the convergence of Godunov approximations is shown. Uniqueness is addressed relying on a suitable extension of Kruz?kov's techniques

We present a computational approach for the WKB approximation of the wave function of an electron moving in a periodic one-dimensional crystal lattice. We derive a nonstrictly hyperbolic system for the phase and the intensity where the flux functions originate from the Bloch spectrum of the Schrodinger operator. Relying on the framework of the multibranch entropy solutions introduced by Brenier and Corrias, we compute efficiently multiphase solutions using well adapted and simple numerical schemes. In this first part we present computational results for vanishing exterior potentials which demonstrate the effectiveness of the proposed method.

We are concerned with efficient numerical simulation of the radiative transfer equations. To this end, we follow theWell-Balanced approach's canvas and reformulate the relaxation term as a nonconservative product regularized by steady-state curves while keeping the velocity variable continuous. These steady-state equations are of Fredholm type. The resulting upwind schemes are proved to be stable under a reasonable parabolic CFL condition of the type Dt <= O(Dx^2) among other desirable properties. Some numerical results demonstrate the realizability and the efficiency of this process.

We review some ideas about the physics of small-scale turbulent statistics, focusing on the scaling behavior of anisotropic fluctuations. We present results from direct numerical simulations of three-dimensional homogeneous, anisotropically forced, turbulent systems: the Rayleigh–Bénard system, the random-Kolmogorov-flow, and a third flow with constant anisotropic energy spectrum at low wave numbers. A comparison of the anisotropic scaling properties displays good similarity among these very different flows. Our findings support the conclusion that scaling exponents of anisotropic fluctuations are universal, i.e., independent of the forcing mechanism sustaining turbulence.

We present a computational approach for the WKB approximation of the wavefunction of an electron moving in a periodic one-dimensional crystal lattice by means of a nonstrictly hyperbolic system whose flux function stems from the Bloch spectrum of the Schrodinger operator. This second part focuses on the handling of the source terms which originate from adding a slowly varying exterior potential. Physically, relevant examples are the occurrence of Bloch oscillations in case it is linear, a quadratic one modelling a confining field and the harmonic Coulomb term resulting from the inclusion of a ''donor impurity'' inside an otherwise perfectly homogeneous lattice.

We consider an hyperbolic singular perturbation of the incompressible Navier Stokes equations in two space dimensions. The approximating system under consideration, arises as a diffusive rescaled version of a standard relaxation approximation for the incompressible Euler equations. The aim of this work is to give a rigorous justification of its asymptotic limit toward the Navier Stokes equations using the modulated energy method.

We study the numerical approximation of viscosity solutions for Parabolic Integro-Differential Equations (PIDE). Similar models arise in option pricing, to generalize the Black-Scholes equation, when the processes which generate the underlying stock returns may contain both a continuous part and jumps. Due to the non-local nature of the integral term, unconditionally stable implicit difference scheme are not practically feasible. Here we propose to use Implicit-Explicit (IMEX) Runge-Kutta methods for the time integration to solve the integral term explicitly, giving higher order accuracy schemes under weak stability time-step restrictions. Numerical tests are presented to show the computational efficiency of the approximation.

We design numerical schemes for nonlinear degenerate parabolic systems with possibly dominant convection. These schemes are based on discrete BGK models where both characteristic velocities and the source-term depend singularly on the relaxation parameter. General stability conditions are derived, and convergence is proved to the entropy solutions for scalar equations.

We consider a coperative control approach to address safety and optimality issues for simple model of a car-like robot. The approach makes use of optimal syntheses and Krasovskii solutions to discontinuous ODEs.

We provide a general approach to deal with entropy solutions to scalar conservation laws presenting nonclassical shocks.

This paper presents a generalization of Kokaram's model for scratch lines detection on digital film materials. It is based on the assumption that scratch is not purely additive on a given image but shows also a destroying effect. This result allows us to design a more efficacious scratch detector which performs on a hierarchical representation of a degraded image, i.e., on its cross section local extrema. Thanks to Weber's law, the proposed detector even works well on slight scratches resulting completely automatic, except for the scratch color (black or white). The experimental results show that the proposed detector works better in terms of good detection and false alarms rejection with a lower computing time.