A new technique is presented to create nosologic images of the brain based on magnetic resonance imaging (MRI) and magnetic resonance spectroscopic imaging (MRSI). A nosologic image summarizes the presence of different tissues and lesions in a single image by color coding each voxel or pixel according to the histopathological class it is assigned to. The proposed technique applies advanced methods from image processing as well as pattern recognition to segment and classify brain tumours. First, a registered brain atlas and a subject-specific abnormal tissue prior, obtained from MRSI data, are used for the segmentation. Next, the detected abnormal tissue is classified based on supervised pattern recognition methods. Class probabilities are also calculated for the segmented abnormal region. Compared to previous approaches, the new framework is more flexible and able to better exploit spatial information leading to improved nosologic images. The combined scheme offers a new way to produce high-resolution nosologic images, representing tumour heterogeneity and class probabilities, which may help clinicians in decision making.

The Generalized- ? -Space G? (p, m, w) contains many classical rearrangement invariant spaces. Here we shall study its associate space and we shall estimate its associate norm. In particular, we characterize all optimal functions u achieving the associate norm of Generalized ? -space G ? (p, m, w) when it is reflexive. For the purpose, we use the notion of relative rearrangement and new additional results on this concept. Moreover, we prove that the space G? (p, m, w) is reflexive under the conditions that m > 1 and p >= 2.

This work presents the results of a quantitative analysis of an interferometric SAR (InSAR) Digital Elevation Model (DEM), obtained by the Shuttle Radar Topography Mission (SRTM). The analysis aims to identify additional parameters to recognize areas in southern Italy with different tectonic activity and behaviour. The axial zone of the Campania-Lucania Apennine and the Sila Massif in Calabria, Italy, characterized by quite different evolutionary histories, have been chosen as test areas sufficiently wide to validate observations on a sub-regional scale at least. Geomorphological information on the shape of palaeosurfaces has been used to estimate uplift and/or erosion amounts and rates. Palaeosurfaces are identified on the DEM as regions with an altitude higher than 1000 m a.s.l. and sub-planar land surfaces dipping less than 6 degrees. Information about the shape of palaeosurfaces during the first stage of uplift and before the tectonic-induced block fragmentation has been extracted. A fragmentation index has been computed for these erosional surfaces. The first stage of this landscape evolution has been studied in terms of the geometric characteristics of fragmented blocks. The last erosional stage has been recognized both in terms of geometric characteristics and fragmentation index of the sub-horizontal land surfaces. Altitude and age of the palaeosurfaces, referred to ancient base-levels of the erosion, have been used to estimate the erosional rate.

We investigate the analytical behavior of the solution of the test equation and derive the qualitative and quantitative properties of the numerical solution. The numerical experiments show that the stability conditions obtained represent sufficient conditions for the stability of the numerical method applied to a more general equation.

A truly functional Bayesian method for detecting temporally differentially expressed genes between two experimental conditions is presented. The method distinguishes between two biologically different set ups, one in which the two samples are interchangeable, and one in which the second sample is a modification of the first, i.e. the two samples are non-interchangeable. This distinction leads to two different Bayesian models, which allow more flexibility in modeling gene expression profiles. The method allows one to identify differentially expressed genes, to rank them and to estimate their expression profiles. The proposed procedure successfully deals with various technical difficulties which arise in microarray time-course experiments, such as small number of observations, non-uniform sampling intervals and presence of missing data or repeated measurements. The procedure allows one to account for various types of error, thus offering a good compromise between nonparametric and normality assumption based techniques. In addition, all evaluations are carried out using analytic expressions, hence the entire procedure requires very little computational effort. The performance of the procedure is studied using simulated and real data. A truly functional Bayesian method for detecting temporally differentially expressed genes between two experimental conditions is presented. The method distinguishes between two biologically different set ups, one in which the two samples are interchangeable, and one in which the second sample is a modification of the first, i.e. the two samples are non-interchangeable. This distinction leads to two different Bayesian models, which allow more flexibility in modeling gene expression profiles. The method allows one to identify differentially expressed genes, to rank them and to estimate their expression profiles. The proposed procedure successfully deals with various technical difficulties which arise in microarray time-course experiments, such as small number of observations, non-uniform sampling intervals and presence of missing data or repeated measurements. The procedure allows one to account for various types of error, thus offering a good compromise between nonparametric and normality assumption based techniques. In addition, all evaluations are carried out using analytic expressions, hence the entire procedure requires very little computational effort. The performance of the procedure is studied using simulated and real data.

Most physical systems are described by time-dependent Hamiltonian systems with qualitative features that should be preserved by numerical integrators used for approximating their dynamics. The initial energy of the system together with the energy added or subtracted by the outside forces, represent a conserved quantity of the motion. For a class of time-dependent Hamiltonian systems this invariant can be defined by means of an auxiliary function whose dynamics has to be integrated simultaneously with the system's equations. We propose splitting procedures featured by a SB3A property that allows to construct composition methods with a reduced number of determining order equations and to provide the same high accuracy for both the dynamics and the preservation of the invariant quantity.

We consider splitting methods for the numerical integration of non-autonomous sep- arable differential equations. Splitting methods have been extensively used as geometric numerical integrators during the last years showing excellent performances (both qualitatively and quantita- tively) when applied on many problems. They are designed for autonomous separable systems and a substantial number of methods tailored for different structures of the equations have recently ap- peared. When these methods are used on non-autonomous problems, usually their performance diminishes considerably, and even they can lose the order of accuracy. Previous attempts to preserve such performance on non-autonomous problems required to modify, in a non-trivial way, the existing methods. In this paper, we present a simple alternative which, in many relevant cases, allows to retain the high performance of the splitting methods using the same schemes as for the autonomous problems. This technique is applied on different problems and its performance is illustrated on several numerical examples.

A partire da fenomeni reali viene esposto il percorso che, mediante il linguaggio della matematica, conduce all'astrazione ed alle teorie assiomatiche formali.

Capobianco, Criscuolo and Junghanns [2] have studied an integro differential equation of Prandtl type and a collocation method as well as a quadrature method for its approximate solution in weighted Sobolev spaces. Furthermore, collocation and collocation quadrature methods for the same integral equation have been studied in weighted spaces of continuous functions [3]. The aim of the present paper is to present an algorithm related to a numerical model for a hypersingular Integral equation arising in a solid circular plate problem, based on the collocation methods with quadrature methods on orthogonal polynomials as in [2, 3]. The optimal convergence rates is proved.

The analysis of the convergence and stability theory is carried out for a class of integrals accessible to Gauss quadrature as singular principal value integrals. Numerical examples confirming the theoretical results are also given.