A single master equation is given describing spin s <~ 2 test fields that are gauge- and tetrad-invariant perturbations of the Kerr-Taub-NUT (Newman-Unti-Tamburino) spacetime representing a source with a mass M, gravitomagnetic monopole moment -l, and gravitomagnetic dipole moment (angular momentum) per unit mass a. This equation can be separated into its radial and angular parts. The behavior of the radial functions at infinity and near the horizon is studied and used to examine the influence of l on the phenomenon of superradiance, while the angular equation leads to spin-weighted spheroidal harmonic solutions generalizing those of the Kerr spacetime. Finally, the coupling between the spin of the perturbing field and the gravitomagnetic monopole moment is discussed.

Segmentation (tissue classification) of medical images obtained from a magnetic resonance (MR) system is a primary step in most applications of medical image post-processing. This paper describes nonparametric discriminant analysis methods to segment multispectral MR images of the brain. Starting from routinely available spin-lattice relaxation time, spin-spin relaxation time, and proton density weighted images (T1w, T2w, PDw) the proposed family of statistical methods is based on: i) a transform of the images into components that are statistically independent from each other; ii) a nonparametric estimate of probability density functions of each tissue starting from a training set; iii) a classic Bayes 0-1 classification rule. Experiments based on a computer built brain phantom (brainweb) and eight real patient data set are shown. A comparison with parametric discriminant analysis is also reported. The capability of nonparametric discriminant analysis in improving brain tissue classification of parametric methods is demonstrated. Finally, an assessment of the role of multispectrality in classifying brain tissues is discussed.

The historical origins of Fermi-Walker transport and Fermi coordinates and the construction of Fermi-Walker transported frames in black hole spacetimes are reviewed. For geodesics this transport reduces to parallel transport and these frames can be explicitly constructed using a Killing-Yano tensor as shown by Marck. For accelerated or geodesic circular orbits in such spacetimes, both parallel and Fermi-Walker transported frames can be given, and allow one to study circular holonomy and related clock and spin transport effects. In particular the total angle of rotation that a spin vector undergoes around a closed loop can be expressed in a factored form, where each factor is due to a different relativistic effect, in contrast with the usual sum of terms decomposition. Finally the Thomas precession frequency is shown to be a special case of the simple relationship between the parallel transport and Fermi-Walker transport frequencies for stationary circular orbits.

We introduce a nonparametric method for discriminant analysis based on the search of independent components in a signal (ICDA). Keypoints of the method are reformulation of the classification problem in terms of transform matrices; use of Independent Component Analysis (ICA) to choose a transform matrix so that transformed components are as independent as possible; nonparametric estimation of the density function for each independent component; application of a Bayes rule for class assignment. Convergence of the method is proved and its performance is illustrated on simulated and real data examples.

We show that a nonparametric estimator of a regression function, obtained as solution of a specific regularization problem is the bestlinear unbiased predictor in some nonparametric mixed effect model. Since this estimator is intractable from a numerical point of view, we propose a tight approximation of it easy and fast to implement. This second estimator achieves the usual optimal rate of convergence of the mean integrated squared error over a Sobolev class both for equispaced and non equispaced design. Numerical experiments are presented both on simulated and ERP real data.

The conceptual framework for modeling the inertial subrange is strongly influenced by the Kolmogorov cascade phenomena, which is now the subject of significant reinterpretation. It has been argued that the effects of boundary conditions influence large-scale motion and direct interaction between large and small scales is possible by means other than passing sequentially through the full cascade. Using longitudinal (u) and vertical (w) velocity and temperature (T) time series measurements collected in the atmospheric surface layer (ASL), we evaluate whether the inertial subrange multifractral function (f(alpha)) of all three flow variables is influenced byatmospheric stability (xi), which is a bulk measure of the effect of boundary conditions on large scale flow properties for ASL turbulence. This study is the first to demonstrate that xi significantly influences f(alpha) for all three flow variables. Here, statistical significance is evaluated using a novel wavelet-based Functional Analysis of Variance (FANOVA) approach that explicitly considers different classes of xi, the flow variable type, and possible interactions between xi and the three flow variables.

In the field of resource constrained scheduling, the papers in the literature are mainly focused on minimizing the maximum completion time of a set of tasks to be carried out, paying attention to respecting the maximum simultaneous availability of each resource type in the system. This work, instead, considers the issues of balancing the resource usage and minimizing the peak of the resources allocated each time in the schedule, while keeping the makespan low. To this aim we propose a local search algorithm which acts as a multi start greedy heuristic. Extensive experiments on various randomly generated test instances are provided. Furthermore, we present a comparison with lower bounds and known heuristics.

In this paper an on-line algorithm for the Rectangle Packing Problem is presented. The method is designed to be able to accept or reject incoming boxes to maximize efficiency. We provide a wide computational analysis showing the behavior of the proposed algorithm as well as a comparison with existing off-line heuristics.

In this work we study a finite dynamical system for the description of the bifurcation pattern of the convection flow of a fluid between two parallel horizontal planes which undergoes a {\em horizontal} gradient of temperature ({\em horizontal} convection flow). Although in the two-dimensional case developed here,literature reports as well a long list of analytical and numerical solutions to this problem, the peculiar aim of this work makes it worthwhile. Actually we develop the route that Saltzman (1962) \cite{Sal62} and Lorenz (1963) \cite{Lor63} proposed for the {\em vertical} convection flow that started successfully the approach to finite dynamical systems. We obtain steady-to-steady and steady-to-periodic bifurcations in qualitative agreement with already published results. At first we adopt the non-dimensional scheme used by Saltzman and Lorenz; as it admits also physically meaningless solutions, we introduce a different set of reference quantities so overcoming this drawback.

The existence of global smooth solutions to the multi-dimensional hydrodynamic model for plasmas of electrons and positively charged ions is shown under the assumption that the initial densities are close to a constant. The model consists of the conservation laws for the particle densities and the current densities, coupled to the Poisson equation for the electrostatic potential. Furthermore, it is proved that the particle densities converge exponentially fast to the (constant) steady state. The proof uses a higher-order energy method inspired from extended thermodynamics.

We derive an asymptotic equation that describes the propagation of weakly nonlinear surface waves on a tangential discontinuity in incompressible magnetohydrodynamics. The equation is similar to, but simpler than, previously derived asymptotic equations for weakly nonlinear Rayleigh waves in elasticity. The most interesting feature of the surface waves is that their nonlinear self-interaction is nonlocal.

In refined network analysis, a compact network model is combined with distributed models for semiconductor devices in a multiphysics approach. For linear RLC networks containing diodes as distributed devices, we construct a mathematical model that combines the differential-algebraic network equations of the circuit with elliptic boundary value problems modeling the diodes. For this mixed initial-boundary value problem of partial differential-algebraic equations a first existence result is given.

The global existence of smooth solutions of the Cauchy problem for the $N$-dimensional Euler-Poisson model for semiconductors is established, under the assumption that the initial data is a perturbation of a stationary solution of the drift-diffusion equations with zero electron velocity, which is proved to be unique. The resulting evolutionary solutions converge asymptotically in time to the unperturbed state. The singular relaxation limit is also discussed.

We perform a multiple time scale, single space scale analysis of a compressible fluid in a time-dependent domain, when the time variations of the boundary are small with respect to the acoustic velocity. We introduce an average operator with respect to the fast time. The averaged leading order variables satisfy modified incompressible equations, which are coupled to linear acoustic equations with respect to the fast time. We discuss possible initial-boundary data for the asymptotic equations inherited from the initial-boundary data for the compressible equations.

We consider the Cauchy problem for a general one dimensional $n\times n$ hyperbolic symmetrizable system of balance laws. It is well known that, in many physical examples, for instance for the isentropic Euler system with damping, the dissipation due to the source term may prevent the shock formation, at least for smooth and small initial data. Our main goal is to find a set of general and realistic sufficient conditions to guarantee the global existence of smooth solutions, and possibly to investigate their asymptotic behavior. For systems which are entropy dissipative, a quite natural generalization of the Kawashima condition for hyperbolic-parabolic systems can be given. In this paper, we first propose a general framework to set this kind of problems, by using the so-called entropy variables. Therefore, we pass to prove some general statements about the global existence of smooth solutions, under different sets of conditions. In particular, the present approach is suitable for dealing with most of the physical examples of systems with a relaxation extension. Our main tools will be some refined energy estimates and the use of a suitable version of the Kawashima condition.

We study the deterministic counterpart of a backward-forward stochastic differential utility, which has recently been characterized as the solution to the Cauchy problem related to a PDE of degenerate parabolic type in two spatial variables, with a rank-1 diffusion and a conservative first order term. We first establish a local existence result for strong solutions and a continuation principle, and we produce a counterexample showing that, in general, strong solutions fail to be globally.

We introduce a differential model to study damage accumulation processes in presence of chemical reactions. The influence of micro-structure leads to a nonlinear parabolic system characterized by the presence of a characteristic length. Here, we first present an analytical description of the qualitative behavior of solutions which blow-up in finite time. Numerical simulations are given to describe the shape of solutions near the rupture time and the influence of the chemical reagents. Like in the non reactive model, the failure of the material occurs in a region of positive measure, due to the diffusive effects of the micro-structure, although some localization phenomena are observed. Moreover, if we increase the chemical concentration beyond a given threshold, which depends on the specific conditions of the material, we observe a strong acceleration in the damage process.