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We present significant improvements to our previous work on noise reduction in {\sl Herschel} observation maps by defining sparse filtering tools capable of handling, in a unified formalism, a significantly improved noise reduction as well as a deconvolution in order to reduce effects introduced by the limited instrumental response (beam). We implement greater flexibility by allowing a wider choice of parsimonious priors in the noise-reduction process. More precisely, we introduce a sparse filtering and deconvolution approach approach of type $l^2$-$l^p$, with $p > 0$ variable and apply it to a larger set of molecular clouds using {\sl Herschel} 250 $\mu $m data in order to demonstrate their wide range of application. In the {\sl Herschel} data, we are able to use this approach to highlight extremely fine filamentary structures and obtain singularity spectra that tend to show a significantly less $\log$-normal behavior and a filamentary nature in the less dense regions. We also use high-resolution adaptive magneto-hydrodynamic simulation data to assess the quality of deconvolution in such a simulated beaming framework., Comment: 24 pages, 32 figures, official acceptance date on 16/05/2024 (Astronomy & Astrophysics)

In the present paper, we study transport properties of coherent vortices. These structures are formed by tubes of fluid parcels that complete similar material rotation. Here, we demonstrate that time $t_0$ positions of such physical structures can be identified from the angular momentum along their trajectories. We identify and extract these Lagrangian vortices as material domain in which fluid elements complete similar Lagrangian angular momentum around the same axis and over the same finite time duration. The present method shows high vortices' monitoring capacity by identifying automatically all coherent clockwise and counterclockwise vortices. The performance of the proposed method is illustrated over different two- and three-dimensional flows.

Principal Component Analysis (PCA) and other multi-variate models are often used in the analysis of "omics" data. These models contain much information which is currently neither easily accessible nor interpretable. Here we present an algorithmic method which has been developed to integrate this information with existing databases of background knowledge, stored in the form of known sets (for instance genesets or pathways). To make this accessible we have produced a Graphical User Interface (GUI) in Matlab which allows the overlay of known set information onto the loadings plot and thus improves the interpretability of the multi-variate model. For each known set the optimal convex hull, covering a subset of elements from the known set, is found through a search algorithm and displayed. In this paper we discuss two main topics; the details of the search algorithm for the optimal convex hull for this problem and the GUI interface which is freely available for download for academic use.