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).

We derive bounds on the Kolmogorov distance between the dis- tribution of a random functional of a {0, 1}-valued random sequence and the normal distribution. Our approach, which relies on the general framework of stochastic analysis for discrete-time normal martingales, extends existing results obtained for independent Bernoulli (or Rademacher) sequences. In particular, we obtain Kolmogorov distance bounds for the sum of normalized random sequences without any independence assumption.

Surface and vegetation monitoring is a key activity in analyzing and understanding how climate change is impacting natural resources. Moreover, identifying vegetation stress using remote-sensed data has proven to be essential in assessing said understanding, as well as in the effort to prevent or act upon extreme phenomena, such as premature land and forest dryness due to summer heatwaves in the Mediterranean area.

In a subsoil bioremediation intervention air or oxygen is injected in the polluted region and then a model for unsaturated porous media it is required, based on the theory of the dynamics of multiphase fluids in porous media. In order to optmize the costs of the intervention it is useful to consider the gas as compressible and this fact introduces nonlinearity in the mathematical model. The physical problem is described by a system of equations and the unknowns are: pollutant; bacteria concentration; oxygen saturation and oxygen pressure.

We analyze the bootstrap percolation process on the stochastic block model (SBM), a natural extension of the Erd?s-Rényi random graph that incorporates the community structure observed in many real systems. In the SBM, nodes are partitioned into two subsets, which represent different communities, and pairs of nodes are independently connected with a probability that depends on the communities they belong to.

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.

In recent years there has been a growing interest in frame based de-noising procedures. The advantage of frames with respect to classical orthonor- mal bases (e.g. wavelet, Fourier, polynomial) is that they can furnish an efficient representation of a more broad class of signals. For example, signals which have fast oscillating behavior as sonar, radar, EEG, stock market, audio and speech are much more well represented by a frame (with similar oscillating characteristic) than by a classical wavelet basis, although the frame representation for such kind of signals can be not properly sparse.

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.