It is well known that given a single time series, or image, it might not be possible to utilize various statistical techniques that for their implementation require more than a single observation at a fixed point in time/space. If the researcher has repeated measurements in form of functions/images, than wavelets can be successfully employed in a functional-type data analysis. In the first part of this paper we focus on wavelet based functional ANOVA procedure in which the noise is separated from the signal for different treatments, and at the same time the treatment responses are additionally split on the mean response and the treatment effect, in the spirit of traditional ANOVA. The key properties utilized are abilities of wavelets to decorrelate and regularize the inputs. Different strategies for (multivariate) shrinkage separation of treatment effects and significance testing in the wavelet domain are discussed. In the second part of this we propose a method for wavelet-filtering of noisy images when prior information about their L 2 -energy is available but the researcher has only a single measurement. Assuming the independence model, according to which the wavelet coefficients are treated individually, we propose a level dependent shrinkage rule that turns out to be the ?-minimax rule for a suitable class, say ?, of realistic priors on the wavelet coefficients. Both methods are illustrated and evaluated on test-functions and images with controlled signal-to-noise ratios

The need for anti-HIV-1 vaccines is universally recognized. Although several potential vaccine formulations are being tested in clinical trials, the complexity of the viral system and the length of the experimentation required and its costs makes the goal of obtaining such a vaccine still elusive. We have built a mathematical model for the simulation of HIV-1 infection spreading into the body, which allows us study in silico the effect of hypothetical anti-HIV-1 vaccines having different properties. In particular, vaccines eliciting a cytolytic T-cell response, a humoral response, or both can be simulated. The vaccines considered can be envisaged either as preventive or therapeutic and can have different strength. The kinetic parameters used for solving the model are those of HIV-1 infection obtained from experimental and clinical observations. The vaccines are instead characterized by parameters that can be varied in order to mimic different behaviors: the rate of killing of the single effector cell and the rate of neutralization of the single antibody molecule; and the level of the immune response raised. The model allows us to predict which characteristics of immunogenicity a preventive or therapeutic vaccine should possess to be efficacious, and which are the key factors that most likely will affect its ability to control the spread of the infection. We discuss here the conclusions that can be drawn from a such a model and some of its limitations.

The authors develop an algorithm for the numerical evaluation of Cauchy principal value integrals of oscillatory functions. The method is based on an interpolatory procedure at the zeros of the orthogonal polynomials with respect to a Jacobi weight. A numerically stable procedure is obtained and the corresponding algorithm can be implemented in a fast way yielding satisfactory numerical results. Bounds of the error and of the amplification factor are also proved.

A method for the numerical inversion of the Laplace transform of a continuous positive function $f(t)$ is proposed. Random matrices distributed according to a Gibbs law whose energy $V(x)$ is a function of $f(t)$ are considered as well as random polynomials orthogonal with respect to $w(x)=e^{-V(x)}$. The equation relating $w(x)$ to the reproducing kernel and to the condensed density of the roots of the random orthogonal polynomials is exploited. Basic results from the theories of orthogonal polynomials, random matrices and random polynomials are revisited in order to provide a unified and almost self--contained context. The qualitative behavior of the solutions provided by the proposed method is illustrated by numerical examples and discussed by using logarithmic potentials with external fields that give insight into the asymptotic behavior of the condensed density when the number of data points goes to infinity.

Space-born measuring devices require an accurate determination of the satellite rest frame. This frame consists of a clock and a triad of orthonormal axes which provide a local Cartesian reference system. The aim of this paper is to find the mathematical representation of this triad in two cases which may correspond to actual satellite attitudes. First we construct a Fermi frame which can be operationally fixed by a set of three mutually orthogonal gyroscopes, then we find a frame which corresponds to the expected attitude of the satellite GAIA which was ESA approved to fly not later than 2012. In the latter case, we were able to find an analytical solution accurate to (v/c)3. In order to exploit this solution in the treatment of GAIA's astrometrical observations, we illustrate all the steps needed to deduce the components of this triad of vectors.

Relativistic astrometry has recently become an active field of research owing to new observational technologies which allow for accuracies of a microarcsecond. To assure this accuracy in data analysis, one has to perform ray tracing in a general relativistic framework including terms of the order of (v/c)3 in the weak field treatment of Einstein equations applied to the solar system. Basic to the solution of a ray tracing problem are the boundary conditions that one has to fix from the observational data. In this paper we solve this problem to (v/c)3 in a fully analytical way

We study the motion of test particles and electromagnetic waves in the Kerr–Newman–Taub–NUT spacetime in order to elucidate some of the effects associated with the gravitomagnetic monopole moment of the source. In particular, we determine in the linear approximation the contribution of this monopole to the gravitational time delay and the rotation of the plane of the polarization of electromagnetic waves. Moreover, we consider 'spherical' orbits of uncharged test particles in the Kerr–Taub–NUT spacetime and discuss the modification of the Wilkins orbits due to the presence of the gravitomagnetic monopole

Test particle geodesic motion is analysed in detail for the background spacetimes of the degenerate Ferrari–Ibañez colliding gravitational wave solutions. Killing vectors have been used to reduce the equations of motion to a first-order system of differential equations which have been integrated numerically. The associated constants of motion have also been used to match the geodesics as they cross over the boundary between the single plane wave and interaction zones

Accelerated circular orbits in the equatorial plane of the Taub-NUT spacetime are analyzed to investigate the effects of its gravitomagnetic monopole source. The effect of a small gravitomagnetic monopole on these orbits is compared to the corresponding orbits pushed slightly off the equatorial plane in the absense of the monopole.

The de Rham Laplacian $\Delta_{\rm (dR)}$ for differential forms is a geometric generalization of the usual covariant Laplacian $\Delta$, and it may be extended naturally to tensor-valued $p$-forms using the exterior covariant derivative associated with a metric connection. Using it the wave equation satisfied by the curvature tensors in general relativity takes its most compact form. This wave equation leads to the Teukolsky equations describing integral spin perturbations of black hole spacetimes.

The behaviour of a massless Dirac field on a general spacetime background representing two colliding gravitational plane waves is discussed in the Newman-Penrose formalism. The geometrical properties of the neutrino current are analysed and explicit results are given for the special Ferrari-Iba\~nez solution.