We study the Perspective Shape from Shading problem from the numerical point of view pre- senting a simple algorithm to compute its solution. The scheme is based on a semi-Lagrangian approximation of the first order Hamilton-Jacobi equation related to the problem. The scheme is converging to the weak solution (in the viscosity sense) of the equation and allows to compute accurately regular as well as non regular solutions. Since the partial differential equation must be complemented with boundary conditions on the silhouette, we analyse the effect of various types of boundary conditions on the numerical solution. Some tests on synthetic and real images are presented.

We propose a mathematical model for the dynamics of spread of a viral infection in the organism which incorporates a continuously distributed intracellular delay. The model, consisting of a set of second type Volterra integral equations, can account for viruses having different mechanisms of propagation. We perform the analysis of the qualitative behavior of the solution by proving its positivity and boundedness and by explicitely giving its limiting values.

We consider a system of ordinary differential equations representing a large class of mathematical models concerning the dynamics of an infection in an organism or in a population and we show that the study of the linearized stability leads to some conditions on the basic reproduction number which are sufficient, not only for the local asymptotic stability of a stationary point, but also for its global asymptotic stability. For a more restricted class of problems also the necessity is proved and the limiting behaviour of the model is described.

Agent-based modeling allows the description of very complex systems. To run large scale simulations of agent-based models in a reasonable time, it is crucial to carefully design data structures and algorithms. We describe the main computational features of agent-based models and report about the solutions we adopted in two applications: The simulation of the immune system response and the simulation of the stock market dynamics.

We present a systematic approach to search for an effective vaccination schedule using mathematical computerized models. Our study is based on our previous model that simulates the cancer vs immune system competition activated by tumor vaccine. This model accurately reproduces in-vivo experiments results on HER-2/neu mice treated with the immuno-prevention cancer vaccine (Triplex) for mammary carcinoma. In vivo experiments have shown the effectiveness of Triplex vaccine in protection of mice from mammary carcinoma. The full protection was conferred using chronic (prophylactic) vaccination protocol while therapeutic vaccination was less effcient. In the present paper we use the computer simulations to systematically search for a vaccination schedule which prevents solid tumor formation. The strategy we used for defining a successful vaccination schedule is to control the number of cancer cells with vaccination cycles. We found that, applying the vaccination scheme used in in-vivo experiments, the number of vaccine injections can be reduced roughly by 30%.

Network firewalls filter traffic by comparing all arriving packets to a set of rules, typically in a sequential manner. This activity requires a high amount of processing time and introduces a significantly delay to the traffic. As a result, a packet filter can become a bottleneck for the connection [3] [5]. For this reason, speed requirement is a fundamental feature for a network firewall. In this paper, we analyse the results of a firewall performance testing, in which we compare the packet processing time of two popular Open Source O.S., Linux and OpenBSD, with their related packet filter tools, Iptables and PF (Packet Filter). Our goals are to evaluate the packet forwarding speed of tested environment and to determine how different conditions can affect performances; therefore tests are made under a variety of conditions and configurations. Linux or OpenBSD based firewalls are often used as routing-firewalls, but they both also have the ability to act as bridging-firewalls, so we tested and compared them in that configuration too.

We consider a generalized version of the small Lebesgue spaces, introduced by Fiorenza, as the associate spaces of the grand Lebesgue spaces. We find a simplified expression for the norm, prove relevant properties, compute the fundamental function and discuss the comparison with the Orlicz spaces.

Sharp exponential estimates for solutions to homogeneous Neumann problems for nonlinear elliptic equations in open subsets ! of Rn are established, with data from limiting Lebesgue spaces, or, more generally, Lorentz spaces.

Collective communication performance is critical in a number of MPI applications. In this paper we focus on two widely used primitives, broadcast and reduce, and present experimental results obtained on a cluster of PC connected by Myrinet. We compare the performance of the MPICH primitives with our implementation based on alpha-trees. Our tests show that the MPICH implementation can be improved.

We consider the problem of estimating the baseline signal from repeated noisy measurements taken on some object or individual of interest whose response is not fixed. We devise some wavelet shrinkage schemes to efficiently address the baseline signal estimation problem, adapting some well-known wavelet shrinkage procedures from the standard nonparametric regression literature. These schemes are based on the empirical wavelet coefficients of the observed data. Wavelet decompositions allow one to characterise different types of smoothness conditions assumed on the response function by means of its wavelet coefficients for a wide range of function classes. Furthermore, synthetic data sets, appropriate for baseline signal estimation, are introduced and used to examine the finite sample performance of the various baseline signal estimators. Insight into the performance of the various baseline signal estimators is obtained from numerical tables and graphical outputs. Two real-life data sets, arising from oxygen tension in rats experiments and from human event-related potentials experiments, are also considered as an illustration of the competing baseline signal estimators.

Within the framework of generic programming, we implement an abstract algorithm for solution of an integral equation of the second kind with the resolvent kernels method. Then, as an application of the idempotent analysis analog of resolvent kernels developed in \cite{MR2002d:49038}, we apply the algorithm to the numerical solution of an optimal control problem with stopping time.

This paper deals with the construction of effective heuristic methods for investigating the effect of corrosion on the inaccesible side of a thin metallic plate. In particular, we derive explicit formulas for the Thin Plate Approximation of the positive functions $\gamma$ and $\theta$ that, in our model, describe energy dispersion and material loss respectively.

A priori estimates for solutions to homogeneous Neumann problems for uniformly elliptic equa- tions in open subsets \Omega­ of IR^n are established when the datum on right-hand side is in the limiting space L^{n/2}(\Omega), or, more generally, in the Lorentz spaces L^{n/2, q}(\Omega). These estimates are optimal as far as either constants or norms are concerned.

The biclustering method can be a very useful analysis tool when some genes have multiple functions and experimental conditions are diverse in gene expression measurement. This is because the biclustering approach, in contrast to the conventional clustering techniques, focuses on finding a subset of the genes and a subset of the experimental conditions that together exhibit coherent behavior. However, the biclustering problem is inherently intractable, and it is often computationally costly to find biclusters with high levels of coherence. In this work, we propose a novel biclustering algorithm that exploits the zero-suppressed binary decision diagrams(ZBDDs) data structure to cope with the computational challenges. Our method can find all biclusters that satisfy specific input conditions, and it is scalable to practical gene expression data. We also present experimental results confirming the effectiveness of our approach.