We analyze a variational problem for the recovery of vector valued functions and compute its numerical solution. The data of the problem are a small set of complete samples of the vector valued function and some significant incomplete information where the former are missing. The incomplete information is assumed as the result of a distortion, with values in a lower dimensional manifold. For the recovery of the function we minimize a functional which is formed by the discrepancy with respect to the data and total variation regularization constraints. We show the existence of minimizers in the space of vector valued bounded variation functions. For the computation of minimizers we provide a stable and efficient method. First, we approximate the functional by coercive functionals on W-1,W-2 in terms of Gamma- convergence. Then we realize approximations of minimizers of the latter functionals by an iterative procedure to solve the PDE system of the corresponding Euler-Lagrange equations. The numerical implementation comes naturally by finite element discretization. We apply the algorithm to the restoration of color images from limited color information and gray levels where the colors are missing. The numerical experiments show that this scheme is very fast and robust. The reconstruction capabilities of the model are shown, also from very limited ( randomly distributed) color data. Several examples are included from the real restoration problem of A. Mantegna's art frescoes in Italy.

We describe the methods employed for the generation of possible scenarios for term structure evolution. The problem originated as a request from the Italian Ministry of Economy and Finance to find an optimal strategy for the issuance of Public Debt securities. The basic idea is to split the evolution of each rate into two parts. The first component is driven by the evolution of the official rate (the European Central Bank official rate in the present case). The second component of each rate is represented by the fluctuations having null correlation with the ECB rate.

Motivation: Highly Active AntiRetroviral Therapies (HAART) can pro- long life significantly to people infected by HIV since, although unable to eradicate the virus, they are quite effective in maintaining control of the infection. However, since HAART have several undesirable side effects, it is considered useful to suspend the therapy according to a suitable schedule of Structured Therapeutic Interruptions (STI). In the present paper we describe an application of genetic algo- rithms (GA) aimed at finding the optimal schedule for a HAART simulated with an agent-based model (ABM) of the immune system that reproduces the most significant features of the response of an organism to the HIV-1 infection. Results: The genetic algorithm helps in finding an optimal therapeu- tic schedule that maximizes immune restoration, minimizes the viral count and, through appropriate interruptions of the therapy, minimizes the dose of drug administered to the simulated patient. To validate the efficacy of the therapy that the genetic algorithm indicates as optimal, we ran simulations of oppor tunistic diseases and found that the selected therapy shows the best survival curve among the different simulated control groups.

We show that the condition is not necessary, though sufficient, for the asymptotic stability of . We prove the existence of a class of Volterra difference equations (VDEs) that violate this condition but whose zero solutions are asymptotically stable.

We consider the heat equation for director fields, with values in the unit sphere. A variational approach is used to construct axially symmetric traveling wave solutions defined in an infinitely long cylinder. The traveling waves have a point singularity of topological degree 0 or 1. The construction of solutions with degree 0 is based on minimization of a relaxed energy.

: In this article we present the implementation of an environment supporting Levy's optimal reduction for the X-calculus on parallel (or distributed) computing systems. In a similar approach to Lamping's, we base our work on a graph reduction technique, known as directed virtual reduction, which is actually a restriction of Danos-Regnier virtual reduction. The environment, which we refer to as PELCR (parallel environment for optimal lambdacalculus reduction), relies on a strategy for directed virtual reduction, namely half combustion. While developing PELCR we adopted both a message aggregation technique, allowing reduction of the communication overhead, and a fair policy for distributing dynamically originated load among processors. We also present an experimental study demonstrating the ability of PELCR to definitely exploit the parallelism intrinsic to lambda-terms while performing the reduction. We show how PELCR allows achieving up to 70-80% of the ideal speedup on last generation multiprocessor computing systems. As a last note, the software modules have been developed with. the C language and using a standard interface for message passing, that is, MPI, thus making PELCR itself a highly portable software package.

We prove that if the exponent function p((.)) satisfies log-Holder continuity conditions locally and at infinity, then the fractional maximal operator M(alpha), 0 < alpha < n, maps L(p(.)) to L(q(.)), where 1/p(x) - 1/q(x) = alpha/n. We also prove a weak-type inequality corresponding to the weak (1, n/(n - a)) inequality for M(alpha). We build upon earlier work on the Hardy-Littlewood maximal operator by Cruz-Uribe, Fiorenza and Neugebauer [3]. As a consequence of these results for M(alpha), we show that the fractional integral operator I(alpha) satisfies the same norm inequalities. These in turn yield a generalization of the Sobolev embedding theorem to variable L(p) spaces.

The objective of the present paper is to develop a truly functional Bayesian method specifically designed for time series microarray data. The method allows one to identify differentially expressed genes in a time-course microarray experiment, to rank them and to estimate their expression profiles. Each gene expression profile is modeled as an expansion over some orthonormal basis, where the coefficients and the number of basis functions are estimated from the data. The proposed procedure deals successfully with various technical difficulties that arise in typical microarray experiments such as a small number of observations, non-uniform sampling intervals and missing or replicated data. The procedure allows one to account for various types of errors and offers a good compromise between nonparametric techniques and techniques based on normality assumptions. In addition, all evaluations are performed using analytic expressions, so the entire procedure requires very small computational effort. The procedure is studied using both simulated and real data, and is compared with competitive recent approaches. Finally, the procedure is applied to a case study of a human breast cancer cell line stimulated with estrogen. We succeeded in finding new significant genes that were not marked in an earlier work on the same dataset.

Precise knowledge of X-ray diffraction profile shape is crucial in the investigation of the properties of matter in crystals powder. Line-broadening analysis is the fourth pre-processing step in most of the full powder pattern fitting softwares. The final result of line-broadening analysis strongly depends on three further steps: noise filtering, removal of background signal, and peak fitting. In this work a new model independent procedure for two of the aforementioned steps (background suppression and peak fitting) is presented. The former is dealt with by using morphological mathematics, while the latter relies on the Hankel–Lanczos singular value decomposition technique. Real X-ray powder diffraction (XRPD) intensity profiles of Ceria samples are used to test the performance of the proposed procedure. Results show the robustness of this approach and its capability of efficiently improving the disentangling of instrumental broadening. These features make the proposed approach an interesting and user-friendly tool for the pre-processing of XRPD data.

Spatial distributions of heavy particles suspended in an incompressible isotropic and homogeneous turbulent flow are investigated by means of high resolution direct numerical simulations. In the dissipative range, it is shown that particles form fractal clusters with properties independent of the Reynolds number. Clustering is there optimal when the particle response time is of the order of the Kolmogorov time scale tau(eta). In the inertial range, the particle distribution is no longer scale invariant. It is, however, shown that deviations from uniformity depend on a rescaled contraction rate, which is different from the local Stokes number given by dimensional analysis. Particle distribution is characterized by voids spanning all scales of the turbulent flow; their signature in the coarse-grained mass probability distribution is an algebraic behavior at small densities.

Uno degli interventi proposti dal protocollo di Kyoto per la stabilizzazione delle concentrazionidi gas serra si riferisce alla necessità di determinare la localizzazione delle sorgenti e delle fonti ditali gas. Il metodo del bilancio di massa, implementato a partire da misure rilevate da piattaforma aerea,presenta la potenzialità di poter quantificare gli scambi gassosi superficiali su aree di diversi chilometriquadrati, permettendo una stima anche in condizioni di eterogeneità superficiale, contrariamente ai metoditradizionali. In questo studio il metodo è stato applicato ad un sito nei pressi di Forlì utilizzando dati telerilevatiad alta frequenza nello strato limite planetario. La scarsa risoluzione verticale ottenuta in fase dirilevamento dati è stata risolta attraverso un metodo di regressione non parametrico. I campi di concentrazionedel gas e del vento in corrispondenza dell'altezza dello strato limite planetario sono determinaticon un modello additivo non parametrico. Risulta che la superficie del territorio esaminato emette un flussodi anidride carbonica di 13±0.3 ?moli/m2/s, a causa della presenza di un centro industriale all'internodell'area esaminata.