We consider an empirical Bayes approach to standard nonparametric regression estimation using a nonlinear wavelet methodology. Instead of specifying a single prior distribution on the parameter space of wavelet coefficients, which is usually the case in the existing literature, we elicit the epsilon-contamination class of prior distributions that is particularly attractive to work with when one seeks robust priors in Bayesian analysis. The type II maximum likelihood approach to prior selection is used by maximizing the predictive distribution for the data in the wavelet domain over a suitable subclass of the epsilon-contamination class of prior distributions. For the prior selected, the posterior mean yields a thresholding procedure which depends on one free prior parameter and it is level- and amplitude-dependent, thus allowing better adaptation in function estimation. We consider an automatic choice of the free prior parameter, guided by considerations on an exact risk analysis and on the shape of the thresholding rule, enabling the resulting estimator to be fully automated in practice. We also compute pointwise Bayesian credible intervals for the resulting function estimate using a simulation-based approach. We use several simulated examples to illustrate the performance of the proposed empirical Bayes term-by-term wavelet scheme, and we make comparisons with other classical and empirical Bayes term-by-term wavelet schemes. As a practical illustration, we present an application to a real-life data set that was collected in an atomic force microscopy study.

Particular solutions of a class of higher order ordinary differential equations, with non-constant coefficients, are determined by using the properties of the Laguerre exponentials functions introduced by G. Dattoli and P. E. Ricci in [4]. © 2004, Heldermann Verlag. All rights reserved.

Clustering has been one of the most popular methods to discover useful biological insights from DNA microarray. An interesting paradigm is simultaneous clustering of both genes and experiments. This "biclustering "paradigm aims at discovering clusters that consist of a subset of the genes showing a coherent expression pattern over a subset of conditions. The pClustering approach is a technique that belongs to this paradigm. Despite many theoretical advantages, this technique has been rarely applied to actual gene expression data analysis. Possible reasons include the worst-case complexity of the clustering algorithm and the difficulty in interpreting clustering results. In this paper, we propose an enhanced framework for performing pClustering on actual gene expression analysis. Our new framework includes an effective data preparation method, highly scalable clustering strategies, and an intuitive result interpretation scheme. The experimental result confirms the effectiveness of our approach.

In this paper we examine the impact of graph theory and more particularly the scale-free topology on Immune Network models. In the case of a simple but not trivial model we analyze network performances as long term selectivity properties, its computational capabilities as memory capacity, and relation with Neural Networks. A more advanced Immune Network model is conceptualized and it is developed a scaffold for further mathematical investigation.

We consider the construction and the properties of the Riemann solver for the hyperbolic system \begin{equation}\label{E:hyp0} u_t + f(u)_x = 0, \end{equation} assuming only that $Df$ is strictly hyperbolic. In the first part we prove a general regularity theorem on the admissible curves $T_i$ of the $i$-family, depending on the number of inflection points of $f$: namely, if there is only one inflection point, $T_i$ is $C^{1,1}$. If the $i$-th eigenvalue of $Df$ is genuinely nonlinear, by it is well known that $T_i$ is $C^{2,1}$. However, we give an example of an admissible curve $T_i$ which is only Lipschitz continuous if $f$ has two inflection points. In the second part, we show a general method for constructing the curves $T_i$, and we prove a stability result for the solution to the Riemann problem. In particular we prove the uniqueness of the admissible curves for \eqref{E:hyp0}. Finally we apply the construction to various approximations to \eqref{E:hyp0}: vanishing viscosity, relaxation schemes and the semidiscrete upwind scheme. In particular, when the system is in conservation form, we obtain the existence of smooth travelling profiles for all small admissible jumps of \eqref{E:hyp0}.

A variant of the lattice Boltzmann scheme is presented as a mesoscopic model of glassy behavior. A hierarchical density-dependent interaction potential is introduced, which allows the coexistence and competition of multiple density minima. We find that this competition allows to model geometrical frustration which produces disordered patterns with sharp density contrasts and no phase-separation. A way of modeling mechanical arrest of real glasses is also proposed and discussed.