The protection, preservation and restoration of aquatic ecosystems and their functions are of global importance. For European states it became legally binding mainly through the EUWater Framework Directive (WFD). In order to assess the ecological status of a given water body, aquatic biodiversity data are obtained and compared to a reference water body. The quantified mismatch obtained determines the extent of potential management actions. The current approach to biodiversity assessment is based on morpho-taxonomy. This approach has many drawbacks such as being time consuming, limited in temporal and spatial resolution, and error-prone due to the varying individual taxonomic expertise of the analysts. Novel genomic tools can overcome many of the aforementioned problems and could complement or even replace traditional bioassessment. Yet, a plethora of approaches are independently developed in different institutions, thereby hampering any concerted routine application. The goal of this Action is to nucleate a group of researchers across disciplines with the task to identify gold-standard genomic tools and novel ecogenomic indices for routine application in biodiversity assessments of European fresh- and marine water bodies. Furthermore, DNAqua-Net will provide a platform for training of the next generation of European researchers preparing them for the new technologies. Jointly with water managers, politicians, and other stakeholders, the group will develop a DNAqua-Net: Developing new genetic tools for bioassessment and monitoring ... 3 conceptual framework for the standard application of eco-genomic tools as part of legally binding assessments.

In this paper we study extensions between Cohen–Macaulay modules for algebras arising in the categorifications of Grassmannian cluster algebras. We prove that rank 1 modules are periodic, and we give explicit formulas for the computation of the period based solely on the rim of the rank 1 module in question. We determine Exti(LI,LJ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{Ext}^i(L_I, L_J)$$\end{document} for arbitrary rank 1 modules LI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_I$$\end{document} and LJ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_J$$\end{document}. An explicit combinatorial algorithm is given for the computation of Exti(LI,LJ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{Ext}^i(L_I, L_J)$$\end{document} when i is odd, and when i even, we show that Exti(LI,LJ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{Ext}^i(L_I, L_J)$$\end{document} is cyclic over the centre, and we give an explicit formula for its computation. At the end of the paper we give a vanishing condition of Exti(LI,LJ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{Ext}^i(L_I, L_J)$$\end{document} for any i>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i>0$$\end{document}.

I revisit a set of pseudo-observables (PO) in Higgs decays that parameterise, in great generality, possible beyond the Standard Model effects. PO are defined from the decomposition of onshell decay amplitudes around the physical poles. On the one hand, PO can be determined from experimental data, providing a systematic generalisation of the ”κ-framework” so far adopted by the LHC experiments. On the other hand, PO can be computed in large set of new physics (NP) models and, in particular, in any Effective Field Theory (EFT) approach to Higgs physics. The PO framework allows for a systematic inclusion of higher-order QED/QCD corrections. These features single out PO as a correct formalism for general interpretation of the upcoming precision measurements in Higgs physics.