A color quantization algorithm is presented, which is based on the reduction of the spatial resolution of the input image. The maximum number of colors nf desired for the output image is used to fix the proper spatial resolution reduction factor. This is used to build a lower resolution version of the input image with size nf. Colors found in the lower resolution image constitute the palette for the output image. The three components of each color of the palette are interpreted as the coordinates of a voxel in the 3D discrete space. The Voronoi Diagram of the set of voxels corresponding to the colors of the palette is computed and is used for color mapping of the input image.

Efficient recovery of smooth functions which are s-sparse with respect to the basis of so-called prolate spheroidal wave functions from a small number of random sampling points is considered. The main ingredient in the design of both the algorithms we propose here consists in establishing a uniform L? bound on the measurement ensembles which constitute the columns of the sensingmatrix. Such a bound provides us with the restricted isometry property for this rectangular random matrix, which leads to either the exact recovery property or the "best s-term approximation" of the original signal by means of the 1 minimization program. The first algorithm considers only a restricted number of columns for which the L? holds as a consequence of the fact that eigenvalues of the Bergman's restriction operator are close to 1 whereas the second one allows for a wider system of PSWF by taking advantage of a preconditioning technique. Numerical examples are spread throughout the text to illustrate the results.

The ability of Well-Balanced (WB) schemes to capture very accurately steady-state regimes of non-resonant hyperbolic systems of balance laws has been thoroughly illustrated since its introduction by Greenberg and LeRoux (1996) [15] (see also the anterior WB Glimm scheme in E, 1992 [8]). This paper aims at showing, by means of rigorous C0 t (L1x ) estimates, that these schemes deliver an increased accuracy in transient regimes too. Namely, after explaining that for the vast majority of non-resonant scalar balance laws, the C0 t (L1x ) error of conventional fractional-step (Tang and Teng, 1995 [45]) numerical approximations grows exponentially in time like exp(max(g )t) ? x (as a consequence of the use of Gronwall's lemma), it is shown that WB schemes involving an exact Riemann solver suffer from a much smaller error amplification: thanks to strict hyperbolicity, their error grows at most only linearly in time (see also Layton, 1984 [30]). Numerical results on several testcases of increasing difficulty (including the classical LeVeque-Yee's benchmark problem (LeVeque and Yee, 1990 [34]) in the non-stiff case) confirm the analysis.

Indefinite symmetric matrices occur in many applications, such as optimization, least squares problems, partial differential equations, and variational problems. In these applications one is often interested in computing a factorization of the indefinite matrix that puts into evidence the inertia of the matrix or possibly provides an estimate of its eigenvalues. In this paper we propose an algorithm that provides this information for any symmetric indefinite matrix by transforming it to a block antitriangular form using orthogonal similarity transformations. We also show that the algorithm is backward stable and has a complexity that is comparable to existing matrix decompositions for dense indefinite matrices.

We present a lattice Boltzmann (LB) model for the simulation of hemodynamic flows in the presence of compliant walls. The new scheme is based on the use of a continuous bounce-back boundary condition, as combined with a dynamic constitutive relation between the flow pressure at the wall and the resulting wall deformation. The method is demonstrated for the case of two-dimensional (axisymmetric) pulsatile flows, showing clear evidence of elastic wave propagation of the wall perturbation in response to the fluid pressure. The extension of the present two-dimensional axisymmetric formulation to more general three-dimensional geometries is currently under investigation. © World Scientific Publishing Company.

We consider a communication system in which a given digital content has to be delivered sequentially at constant rate to a set of users who asynchronously request it according to a Poisson process. Users can retrieve data: 1) from one or more sources that statically store the entire content; and 2) from users who have previously requested the content, and contribute (for limited time) a random amount of upload bandwidth to the system. We propose a stochastic fluid framework that allows characterizing the aggregate streaming rate necessary at the sources to satisfy all active requests. In particular, we establish the conditions under which the system becomes asymptotically scalable as the number of users grows. Our theoretical results apply to increasingly popular video-on-demand systems exploiting users' cooperation.

A system of nonlinear hyperbolic partial differential equations is derived using mixture theory to model the formation of biofilms. In contrast with most of the existing models, our equations have a finite speed of propagation, without using artificial free boundary conditions. Adapted numerical scheme will be described in detail and several simulations will be presented in one and more space dimensions in the particular case of cyanobacteria biofilms. Besides, the numerical scheme we present is able to deal in a natural and effective way with regions where one of the phases is vanishing.

In this paper we design and analyse a physiologically based model representing the accumulation of protein p53 in the nucleus after triggering of ATM by DNA damage. The p53 protein is known to have a central role in the response of the cell to cytotoxic or radiotoxic insults resulting in DNA damage. A reasonable requirement for a model describing intracellular signalling pathways is taking into account the basic feature of eukaryotic cells: the distinction between nucleus and cytoplasm. Our aim is to show, on a simple reaction network describing p53 dynamics, how this basic distinction provides a framework which is able to yield expected oscillatory dynamics without introducing either positive feedbacks or delays in the reactions. Furthermore we prove that oscillations appear only if some spatial constraints are respected, e.g. if the diffusion coefficients correspond to known biological values. Finally we analyse how the spatial features of a cell influence the dynamic response of the p53 network to DNA damage, pointing out that the protein oscillatory dynamics is indeed a response that is robust towards changes with respect to cellular environments. Even if we change the cell shape or its volume or better its ribosomal distribution, we observe that DNA damage yields sustained oscillations of p53.

Indefinite symmetric matrices occur in many applications, such as optimization, least squares problems, partial differential equations and variational problems. In these applications one is often interested in computing a factorization of the indefinite matrix that puts into evidence the inertia of the matrix or possibly provides an estimate of its eigenvalues. In this paper we propose an algorithm that provides this information for any symmetric indefinite matrix by transforming it to a block anti-triangular form using orthogonal similarity transformations. We also show that the algorithm is backward stable and has a complexity that is comparable to existing matrix decompositions for dense indefinite matrices.