We present a mathematical model describing the evolution of sea ice and meltwater during summer. The system is described by two coupled partial differential equations for the ice thickness h(x,t) and pond depth w(x,t) fields. The model is similar, in principle, to the one put forward by Luthije et al. (2006), but it features i) a modified melting term, ii) a non-uniform seepage rate of meltwater through the porous ice medium and a minimal coupling with the atmosphere via a surface wind shear term, ?s (Scagliarini et al. 2020).

Given a random sample drawn from a Multivariate Bernoulli Variable (MBV), we consider the problem of estimating the structure of the undirected graph for which the distribution is pairwise Markov and the parameters' vector of its exponential form. We propose a simple method that provides a closed form estimator of the parameters' vector and through its support also provides an estimate of the undirected graph associated with the MBV distribution. The estimator is proved to be asymptotically consistent but it is feasible only in low-dimensional regimes.

This contribution outlines current research aimed at developing models for personalized type 2 diabetes mellitus (T2D) prevention in the framework of the European project PRAESIIDIUM (Physics Informed Machine Learn-ing-Based Prediction and Reversion of Impaired Fasting Glucose Management) aimed at building a digital twin for preventing T2D in patients at risk.

Real-world facility planning problems often require to tackle simultaneously network connectivity and zonal requirements, in order to guarantee an equitable provision of services and an efficient flow of goods, people and information among the facilities. Nonetheless, such challenges have not been addressed jointly so far. In this paper we explore the introduction of advanced network connectivity features and spatial-related requirements within Covering Location Problems.