For G open bounded subset of R^2 with C^1 boundary, we study the regularity of the variational solution u in H^1_0(G) to the quasilinear elliptic equation of Leray-Lions type: -div A(x,Du)=f , when f belongs to the Zygmund space L(log L)^{\delta}, \delta>0. As an interpolation between known results for \delta=1/2 and \delta=1 of [Stampacchia] and [Alberico-Ferone], we prove that |Du| belongs to the Lorentz space L^{2, 1/\delta}(G) for \delta in [1/2, 1].

We consider the problem of short-time extrapolation of blue chips' stocks indexes in the context of wavelet subspaces following the theory proposed by X.-G. Xia and co-workers in a series of papers \cite{XLK,XKZ,LK,LXK}. The idea is first to approximate the oscillations of the corresponding stock index at some scale by means of the scaling function which is part of a given multi-resolution analysis of $L^2(\Re)$. Then, since oscillations at a finer scale are discarded, it becomes possible to extend such a signal up to a certain time in the future; the finer the approximation, the shorter this extrapolation interval. At the numerical level, a so--called Generalized Gerchberg-Papoulis (GGP) algorithm is set up which is shown to converge toward the minimum $L^2$ norm solution of the extrapolation problem. When it comes to implementation, an acceleration by means of a Conjugate Gradient (CG) routine is necessary in order to obtain quickly a satisfying accuracy. Several examples are investigated with different international stock market indexes.

An analytical solution for solving the transient drug diffusion in adjoining porous wall layers faced with a drug-eluting stent is presented. The endothelium, intima, internal elastic lamina and media are all treated as homogeneous porous media and the drug transfer through them is modelled by a set of coupled partial differential equations. The classical separation of variables method for a multi-layer configuration is used. The model addresses the concept of penetration depth for multi-layer solids that is useful to treat the wall thickness by estimating a physical bound for mass diffusion. Drug concentration level and mass profiles in each layer at various times are given and discussed.

We consider a rather simple algorithm to address the fascinating field of numerical extrapolation of (analytic) band-limited functions. It relies on two main elements: namely, the lower frequencies are treated by projecting the known part of the signal to be extended onto the space generated by ``Prolate Spheroidal Wave Functions" (PSWF, as originally proposed by Slepian), whereas the higher ones can be handled by the recent so--called ``Compressive Sampling" (CS, proposed by Cand\`es) algorithms which are independent of the largeness of the bandwidth. Slepian functions are recalled and their numerical computation is explained in full detail whereas $\ell^1$ regularization techniques are summarized together with a recent iterative algorithm which has been proved to work efficiently on so--called ``compressible signals" which appear to match rather well the class of smooth bandlimited functions. Numerical results are displayed for both numerical techniques and the accuracy of the process consisting in putting them altogether is studied for some test-signals showing a quite fast Fourier decay.

We present a study of Eulerian and Lagrangian statistics from a high-resolution numerical simulation of isotropic and homogeneous turbulence using the FLASH code, with an estimated Taylor microscale Reynolds number of around 600. Statistics are evaluated over a data set with 18563 spatial grid points and with 2563 = 16.8 million particles, followed for about one large-scale eddy turnover time. We present data for the Eulerian and Lagrangian structure functions up to the tenth order. We analyze the local scaling properties in the inertial range. The Eulerian velocity field results show good agreement with previous data and confirm the puzzling differences previously found between the scaling of the transverse and the longitudinal structure functions. On the other hand, accurate measurements of sixth-and-higher- order Lagrangian structure functions allow us to highlight some discrepancies from earlier experimental and numerical results. We interpret this result in terms of a possible contamination from the viscous scale, which may have affected estimates of the scaling properties in previous studies. We show that a simple bridge relation based on a multifractal theory is able to connect scaling properties of both Eulerian and Lagrangian observables, provided that the small differences between intermittency of transverse and longitudinal Eulerian structure functions are properly considered.

We present the results of a high resolution numerical study of two-dimensional (2D) Rayleigh-Taylor turbulence using a recently proposed thermal lattice Boltzmann method The goal of our study is both methodological and physical We assess merits and limitations concerning small- and large-scale resolution/accuracy of the adopted integration scheme We discuss quantitatively the requirements needed to keep the method stable and precise enough to simulate stratified and unstratified flows driven by thermal active fluctuations at high Rayleigh and high Reynolds numbers We present data with spatial resolution up to 4096 x 10 000 grid points and Rayleigh number up to Ra similar to 10(11) The statistical quality of the data allows us to investigate velocity and temperature fluctuations, scale-by-scale, over roughly four decades We present a detailed quantitative analysis of scaling laws in the viscous, inertial, and integral range, supporting the existence of a Bolgiano-like inertial scaling, as expected in 2D systems We also discuss the presence of small/large intermittent deviations to the scaling of velocity/temperature fluctuations and the Rayleigh dependency of gradients flatness.

Human blood flow is a multiscale problem: in first approximation, blood is a dense suspension of plasma and deformable red cells. Physiological vessel diameters range from about one to thousands of cell radii. Current computational models either involve a homogeneous fluid and cannot track particulate effects or describe a relatively small number of cells with high resolution but are incapable to reach relevant time and length scales. Our approach is to simplify much further than existing particulate models. We combine well-established methods from other areas of physics in order to find the essential ingredients for a minimalist description that still recovers hemorheology. These ingredients are a lattice Boltzmann method describing rigid particle suspensions to account for hydrodynamic long-range interactions and-in order to describe the more complex short-range behavior of cells-anisotropic model potentials known from molecular-dynamics simulations. Paying detailedness, we achieve an efficient and scalable implementation which is crucial for our ultimate goal: establishing a link between the collective behavior of millions of cells and the macroscopic properties of blood in realistic flow situations. In this paper we present our model and demonstrate its applicability to conditions typical for the microvasculature.

We present the results of our numerical simulations of the Rayleigh-Taylor turbulence, performed using a recently proposed (Sbragaglia et al 2009 J. Fluid Mech. 628 299, Scagliarini et al 2010 Phys. Fluids 22 055101) lattice Boltzmann method that can describe consistently a thermal compressible flow subjected to an external forcing. The method allowed us to study the system in both the nearly Boussinesq regime and the strongly compressible regime. Moreover, we show that when the stratification is important, the presence of the adiabatic gradient causes the arrest of the mixing process.

Two T helper (Th) cell subsets, namely Th1 and Th2 cells, play an important role in inflammatory diseases. The two subsets are thought to counter-regulate each other, and alterations in their balance result in different diseases. This paradigm has been challenged by recent clinical and experimental data. Because of the large number of genes involved in regulating Th1 and Th2 cells, assessment of this paradigm by modeling or experiments is difficult. Novel algorithms based on formal methods now permit the analysis of large gene regulatory networks. By combining these algorithms with in silico knockouts and gene expression microarray data from human T cells, we examined if the results were compatible with a counterregulatory role of Th1 and Th2 cells. We constructed a directed network model of genes regulating Th1 and Th2 cells through text mining and manual curation. We identified four attractors in the network, three of which included genes that corresponded to Th0, Th1 and Th2 cells. The fourth attractor contained a mixture of Th1 and Th2 genes. We found that neither in silico knockouts of the Th1 and Th2 attractor genes nor gene expression microarray data from patients with immunological disorders and healthy subjects supported a counter-regulatory role of Th1 and Th2 cells. By combining network modeling with transcriptomic data analysis and in silico knockouts, we have devised a practical way to help unravel complex regulatory network topology and to increase our understanding of how network actions may differ in health and disease.

We state some pointwise estimates for the rate of weighted approximation of a continuous function on the semiaxis by polynomials. Furthermore we derive matching converse results and estimates involving the derivatives of the approximating polynomials. Using special weighted moduli of continuity, we bridge the gap between an old result by V.M. Fedorov based on the ordinary modulus of smoothness, and the recent norm estimates implicating the Ditzian-Toytik modulus of continuity.

Background: Pathological angiogenesis represents a critical issue in the progression of many diseases. Down syndrome is postulated to be a systemic anti-angiogenesis disease model, possibly due to increased expression of anti-angiogenic regulators on chromosome 21. The aim of our study was to elucidate some features of circulating endothelial progenitor cells in the context of this syndrome. Methods: Circulating endothelial progenitors of Down syndrome affected individuals were isolated, in vitro cultured and analyzed by confocal and transmission electron microscopy. ELISA was performed to measure SDF-1 alpha plasma levels in Down syndrome and euploid individuals. Moreover, qRT-PCR was used to quantify expression levels of CXCL12 gene and of its receptor in progenitor cells. The functional impairment of Down progenitors was evaluated through their susceptibility to hydroperoxide-induced oxidative stress with BODIPY assay and the major vulnerability to the infection with human pathogens. The differential expression of crucial genes in Down progenitor cells was evaluated by microarray analysis. Results: We detected a marked decrease of progenitors' number in young Down individuals compared to euploid, cell size increase and some major detrimental morphological changes. Moreover, Down syndrome patients also exhibited decreased SDF-1 alpha plasma levels and their progenitors had a reduced expression of SDF-1 alpha encoding gene and of its membrane receptor. We further demonstrated that their progenitor cells are more susceptible to hydroperoxide-induced oxidative stress and infection with Bartonella henselae. Further, we observed that most of the differentially expressed genes belong to angiogenesis, immune response and inflammation pathways, and that infected progenitors with trisomy 21 have a more pronounced perturbation of immune response genes than infected euploid cells. Conclusions: Our data provide evidences for a reduced number and altered morphology of endothelial progenitor cells in Down syndrome, also showing the higher susceptibility to oxidative stress and to pathogen infection compared to euploid cells, thereby confirming the angiogenesis and immune response deficit observed in Down syndrome individuals.

In recent years, the introduction of massively parallel sequencing platforms for Next Generation Sequencing (NGS) protocols, able to simultaneously sequence hundred thousand DNA fragments, dramatically changed the landscape of the genetics studies. RNA-Seq for transcriptome studies, Chip-Seq for DNA-proteins interaction, CNV-Seq for large genome nucleotide variations are only some of the intriguing new applications supported by these innovative platforms. Among them RNA-Seq is perhaps the most complex NGS application. Expression levels of specific genes, differential splicing, allele-specific expression of transcripts can be accurately determined by RNA-Seq experiments to address many biological-related issues. All these attributes are not readily achievable from previously widespread hybridization-based or tag sequence-based approaches. However, the unprecedented level of sensitivity and the large amount of available data produced by NGS platforms provide clear advantages as well as new challenges and issues. This technology brings the great power to make several new biological observations and discoveries, it also requires a considerable effort in the development of new bioinformatics tools to deal with these massive data files. The paper aims to give a survey of the RNA-Seq methodology, particularly focusing on the challenges that this application presents both from a biological and a bioinformatics point of view.

A mathematical model of the galvanic iron corrosion is, here, presented. The iron(III)-hydroxide formation is considered together with the redox reaction. The PDE system, assembled on the basis of the fundamental holding electro-chemistry laws, is numerically solved by a locally refined FD method. For verification purpose we have assembled an experimental galvanic cell; in the present work, we report two tests cases, with acidic and neutral electrolitical solution, where the computed electric potential compares well with the measured experimental one

Here we give mathematical support to the choice of the Helmholtz versus the Laplace equation for the formulation of an inverse problem in infrared thermography. Such a choice accounts for the values of physical parameters like the thermal conductivity and the Biot number. We check the effectiveness of the corresponding boundary value problems and compare the condition numbers. The Helmholtz choice is confirmed to be usually better, but there are cases in which Laplace (less expensive) works well.

A thin conducting plate has an inaccessible side in contact with aggressive external agents. On the other side, we are able to heat the plate and take temperature maps in laboratory conditions. Detecting and evaluating damages on the inaccessible side from thermal data requires the solution of a nonlinear inverse problem for the heat equation in presence of suitable boundary conditions for heat equation. We carry on this task using domain derivative and integral formulation of the corresponding boundary value problem. Under non restrictive hypothesis, we find explicit regularized schemes for Fourier reconstruction of damages.