Questa presentazione descrive le conclusioni finali del progetto ECOPOTENTIAL riguardo al coinvolgimento degli stakeholder delle aree protette nel definire e condurre le attività di ricerca a fianco dei ricercatori, illustrando punti di forza e di debolezza, come risultati da un questionario sottoposto ai gestori delle Aree Protette.

For the finite weighted Hilbert transform we consider two different product integration rules, the VP rule and the L-rule, based on the same nodes and obtained by approximating the density function with filtered de la Vallée Poussin and classical Lagrange interpolation polynomials, respectively. The L-rule is well known and widely studied.

The aim of this talk is to show how classical approximation tools such as Lagrange interpolation and more generally de la Vallée Poussin type interpolation, both of them based on Chebyshev zeros of first kind, can be fruitfully applied for resizing an arbitrary digital image. By means of such operators, we get image scaling methods running for any scale factor or desired size, in both downscaling and upscaling. The performance of such interpolation methods is discussed by several numerical experiments and some theoretical estimates of the mean squared error.

According to the European Charter for Researchers «all researchers should ensure [...] that the results of their research are disseminated and exploited, e.g. communicated, transferred into other research settings or, if appropriate, commercialised ...». Therefore, it's part of the researchers' mission to raise the general public awareness with respect to science. This need is further emphasized by a survey of Eurobarometer 2010: society is strongly interested in science but, at the same time, is often scared by the risks connected with new technologies.

The present paper concerns filtered de la Vallée Poussin (VP) interpolation at the Chebyshev nodes of the four kinds. This approximation model is interesting for applications because it combines the advantages of the classical Lagrange polynomial approximation (interpolation and polynomial preserving) with the ones of filtered approximation (uniform boundedness of the Lebesgue constants and reduction of the Gibbs phenomenon). Here we focus on some additional features that are useful in the applications of filtered VP interpolation.

Aggregating transcriptomics data across hospitals can increase sensitivity and robustness of differential expression analyses, yielding deeper clinical insights. As data exchange is often restricted by privacy legislation, meta-analyses are frequently employed to pool local results. However, the accuracy might drop if class labels are inhomogeneously distributed among cohorts. Flimma (https://exbio.wzw.tum.de/flimma/) addresses this issue by implementing the state-of-the-art workflow limma voom in a federated manner, i.e., patient data never leaves its source site.