A new fast and accurate tissue typing technique has recently been successfully applied to prostate MR spectroscopic imaging (MRSI) data. This technique is based on canonical correlation analysis (CCA), a statistical method able to simultaneously exploit the spectral and spatial information characterizing the MRSI data. Here, the performance of CCA is further investigated by using brain data obtained by two-dimensional turbo spectroscopic imaging (2DTSI) from patients affected by glioblastoma. The purpose of this study is to investigate the applicability of CCA when typing tissues of heterogeneous tumors. The performance of CCA is also compared with that of ordinary correlation analysis on simulated as well as in vivo data. The results show that CCA outperforms ordinary correlation analysis in terms of robustness and accuracy.

We present results of a numerical simulation of the thermal convection in the subsurface mushy ice layer of Europa, one of the Jupiter's moons. Beside fluid dynamics and heat transfer within such a layer, heat conduction in the solid crustal surface and heat exchange between the two phases - mushy ice and solid crust - are included in our model in order to follow also the evolution of the phase front. Since the images of Europa's crust taken by the spacecrafts Voyager and Galileo got to be known, planetary scientists stimulated this kind of investigations with the aim of studying the origin of such a topographic aspect. Actually the chaotic lineaments and splotches, clearly visible, solicited the conjecture of the existence of an internal ocean of water that is also supported by the most recent Galileo magnetic field data. The presence of water would make life possible on the jovian satellite. However, in the recent literature, just few numerical simulations describing the overall scenario and including either heat transfer and convection flow have been proposed. Here we adopt the stream-function/vorticity formulation of the Navier-Stokes equations for the flow of the mushy ice and a Stefan condition combined with a front-fixing technique for the front evolution. Our numerical discretization is based upon an ENO scheme. Mathematical model and numerical procedure have been thoroughly tested and have the advantage of yielding accurate numerical solutions via relatively coarse space discretization grids. For applications in this field the present one is the first attempt, at our knowledge, to solve a complete Stefan condition with convection flow, obtaining a good match with other numerical solutions in the literature.

Numericalmethods for Volterra integral equations with discontinuous kernel need to be tuned to their peculiar form. Here we propose a version of the trapezoidal direct quadrature method adapted to such a type of equations. In order to delineate its stability properties, we first investigate about the behavior of the solution of a suitable (basic) test equation and then we find out under which hypotheses the trapezoidal direct quadrature method provides numerical solutions which inherit the properties of the continuous problem.

Background: Gene expression levels in a given cell can be influenced by different factors, namely pharmacological or medical treatments. The response to a given stimulus is usually different for different genes and may depend on time. One of the goals of modern molecular biology is the high-throughput identification of genes associated with a particular treatment or a biological process of interest. From methodological and computational point of view, analyzing high-dimensional time course microarray data requires very specific set of tools which are usually not included in standard software packages. Recently, the authors of this paper developed a fully Bayesian approach which allows one to identify differentially expressed genes in a 'one-sample' time-course microarray experiment, to rank them and to estimate their expression profiles. The method is based on explicit expressions for calculations and, hence, very computationally efficient. Results: The software package BATS (Bayesian Analysis of Time Series) presented here implements the methodology described above. It allows an user to automatically identify and rank differentially expressed genes and to estimate their expression profiles when at least 5-6 time points are available. The package has a user-friendly interface. BATS successfully manages various technical difficulties which arise in time-course microarray experiments, such as a small number of observations, non-uniform sampling intervals and replicated or missing data. Conclusion: BATS is a free user-friendly software for the analysis of both simulated and real microarray time course experiments. The software, the user manual and a brief illustrative example are freely available online at the BATS website: http://www.na.iac.cnr.it/bats webcite

We are concerned with the discretization of optimal control problems when a Runge-Kutta scheme is selected for the related Hamiltonian system. It is known that Lagrangian's first order conditions on the discrete model, require a symplectic partitioned Runge-Kutta scheme for state-costate equations. In the present paper this result is extended to growth models, widely used in Economics studies, where the system is described by a current Hamiltonian.