Parsimonious Time Series Clustering

We introduce a parsimonious model-based framework for clustering time course data. In these applications the computational burden becomes often an issue due to the number of available observations. The measured time series can also be very noisy and sparse and a suitable model describing them can be hard to define. We propose to model the observed measurements by using P-spline smoothers and to cluster the functional objects as summarized by the optimal spline coefficients. In principle, this idea can be adopted within all the most common clustering frameworks. In this work we discuss applications based on a k-means algorithm. We evaluate the accuracy and the efficiency of our proposal by simulations and by dealing with drosophila melanogaster gene expression data

On the maximum principle for elliptic operators in weighted spaces

We establish a maximum principle for subsolutions of second order elliptic equations. In particular, we consider some linear operators with leading coefficients locally VMO, while the other coefficients and the boundary conditions involve a suitable weight function

Some Remarks on Spaces of Morrey Type

We deepen the study of some Morrey type spaces, denoted byMp,λ(Ω), defined on an unbounded open subsetΩofℝn. In particular, we construct decompositions for functions belonging to two different subspaces ofMp,λ(Ω), which allow us to prove a compactness result for an operator in Sobolev spaces. We also introduce a weighted Morrey type space, settled between the above-mentioned subspaces

Weighted a priori bounds for elliptic operators of Cordes type

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Analysis of web visit histories, part I: Distance-based visualization of sequence rules

This paper constitutes Part I of the contribution to the analysis of web visit histories through a new methodological framework. Firstly, web usage and web structure mining are considered as an unique mining process to detect the latent structure of the web navigation across the web sections of a single portal. We extend association rules theory to web data defining new concepts of web (patterns) association and preference matrices, as well as of (indirect and direct) sequence rules. We identify the most significant rules, according to a multiple testing procedure. In the literature, web usage patterns can be visualized in no-distance-based graphs describing the navigation behavior across web pages with sequential arrows. In the following, we introduce a geometrical visualization of sequence rules at any click of the web navigation. In particular, we provide two distance-based visualization methods for the static analysis of all data tout court and the dynamic analysis to discover the most significant web paths click by click. A real world case study is considered throughout the methodological description

Heart transplantation in patients with dystrophinopathic cardiomyopathy: Review of the literature and personal series

Cardiomyopathy associated with dystrophinopathies [Duchenne muscular dystrophy (DMD), Becker muscular dystrophy (BMD), X-linked dilated cardiomyopathy (XL-dCM) and cardiomyopathy of Duchenne/Becker (DMD/BMD) carriers] is an increasing recognized manifestation of these neuromuscular disorders and notably contributes to their morbidity and mortality. Dystrophinopathic cardiomyopathy (DCM) is the result of the dystrophin protein deficiency at the myocardium level, parallel to the deficiency occurring at the skeletal muscle level. It begins as a "presymptomatic" stage in the first decade of life and evolves in a stepwise manner toward pictures of overt cardiomyopathy (hypertrophic stage, arrhythmogenic stage and dilated cardiomyopathy). The final stage caused by the extensive loss of cardiomyocytes results in an irreversible cardiac failure, characterized by frequent episodes of acute congestive heart failure (CHF), despite a correct pharmacological treatment. The picture of a severe dilated cardiomyopathy with intractable heart failure is typical of BMD, XL-dCM and cardiomyopathy of DMD/BMD carriers, while it is less frequently observed in patients with DMD. Heart transplantation (HT) is the only curative therapy for patients with dystrophinopathic end-stage heart failure who remain symptomatic despite an optimal medical therapy. However, no definitive figures exist in literature concerning the number of patients with DCM transplanted, and their outcome. This overview is to summarize the clinical outcomes so far published on the topic, to report the personal series of dystrophinopathic patients receiving heart transplantation and finally to provide evidence that heart transplantation is a safe and effective treatment for selected patients with end-stage DCM