The large H2020 project ECOPOTENTIAL (2015-2019, 47 partners, contributing to GEO and GEOSS http://www.ecopotential-project.eu/) is devoted to making best use of remote sensing and in situ data to improve future ecosystem benefits, adopting the view of ecosystems as one physical system with their environment, focusing on geosphere-biosphere interactions, Earth Critical Zone dynamics, Macrosystem Ecology and cross-scale interactions, the effect of extreme events and using Essential (Climate, Biodiversity and Ocean) Variables as descriptors of change.

Protected Areas are subject to long-term modifications associated with climate and environmental change, enhancing the risk of ecosystem collapse, tipping points and unexpected responses to droughts, fires, floods and other individual events.

This paper investigates the problem of quantifying the impact of unex- pected deviations of mortality trend on a longevity indexed life annuity in a Solvency II perspective. Solvency II quantitative requirements regulate the margins required to offset the insurance risk in a one year risk horizon. Indeed, the idea of deepening the expected changes of future mortality rates over a single year is gaining. In the following the authors propose a com- putational tractable approach to assess the technical provisions by means of an internal model, in line with Solvency II directives.

Given a N-function A and a continuous function h satisfying certain assumptions, we derive the inequality [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], with constants [C.sub.1], [C.sub.2] independent of f, where f [greater than or equal to] 0 belongs locally to the Sobolev space [W.sup.2,1] (R), f' has compact support, p 1 is smaller than the lower Boyd index of A, [T.sub.h,p] (*) is certain nonlinear transform depending of h but not of A and M denotes the Hardy-Littlewood maximal function. Moreover, we show that when h [equivalent to] 1, then Mf" can be improved by f".

We propose novel positive numerical integrators for approximating predator-prey models. The schemes are based on suitable symplectic procedures applied to the dynamical system written in terms of the log transformation of the original variables. Even if this approach is not new when dealing with Hamiltonian systems, it is of particular interest in population dynamics since the positivity of the approximation is ensured without any restriction on the temporal step size. When applied to separable M-systems, the resulting schemes are proved to be explicit, positive, Poisson maps.

By applying Helmholtz decomposition, the unknowns of a linearized Euler system can be recast as solutions of uncoupled linearwave equations. Accordingly, the Kirchhoff expression of the exact solutions is recast as a time-marching, Lax-Wendroff type, numerical scheme for which consistency with one-dimensional upwinding is checked. This discretization, involving spherical means, is set up on a 2D uniform Cartesian grid, so that the resulting numerical fluxes can be shown to be conservative.

Well-balanced schemes, nowadays mostly developed for both hyperbolic and kinetic equations, are extended in order to handle linear parabolic equations, too. By considering the variational solution of the resulting stationary boundary-value problem, a simple criterion of uniqueness is singled out: the C1 regularity at all knots of the computational grid. Being easy to convert into a finite-difference scheme, a well-balanced discretization is deduced by defining the discrete time-derivative as the defect of C1 regularity at each node.

Given a population of N elements with their geographical positions and the genetic (or lexical) distances between couples of elements (inferred, for example, from lexical differences between dialects which are spoken in different towns or from genetic differences between animal populations living in different faunal areas) a very interesting problem is to reconstruct the geographical positions of individuals using only genetic/lexical distances.