In this paper, we study linear parabolic equations on a finite oriented star-shaped network; the equations are coupled by transmission conditions set at the inner node, which do not impose continuity on the unknown.

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 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.

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.

The paper deals with a special filtered approximation method, which originates interpolation polynomials at Chebyshev zeros by using de la Vallée Poussin filters. In order to get an optimal approximation in spaces of locally continuous functions equipped with weighted uniform norms, the related Lebesgue constants have to be uniformly bounded. In previous works this has already been proved under different sufficient conditions. Here, we complete the study by stating also the necessary conditions to get it.