The optimal Orlicz target space and the optimal rearrangement- invariant target space are exhibited for embeddings of fractional-order Orlicz- Sobolev spaces W^{s,A}(R^n). Related Hardy type inequalities are proposed as well. Versions for fractional Orlicz-Sobolev seminorms of the Bourgain-Brezis-Mironescu theorem on the limit as s->1^- and of the Maz'ya-Shaposhnikova theorem on the limit as s ->0^+ are established. This is a joint work with Andrea Cianchi, Lubos Pick and Lenka Slavikova.

The optimal Orlicz target space and the optimal rearrangement-invariant tar- get space are exhibited for embeddings of fractional-order Orlicz-Sobolev spaces W^{s,A}(R^n). Related Hardy type inequalities are proposed as well. Versions for frac- tional Orlicz-Sobolev seminorms of the Bourgain-Brezis-Mironescu theorem on the limit as s->1^- and of the Maz'ya-Shaposhnikova theorem on the limit as s ->0^+ are established. This is a joint work with Andrea Cianchi, Lubos Pick and Lenka Slavikova.

In this paper, we consider the problem of estimating multiple Gaussian Graphical Models from high-dimensional datasets. We assume that these datasets are sampled from different distributions with the same conditional independence structure, but not the same precision matrix. We propose jewel, a joint data estimation method that uses a node-wise penalized regression approach. In particular, jewel uses a group Lasso penalty to simultaneously guarantee the resulting adjacency matrix's symmetry and the graphs' joint learning.

Extended versions of the Bourgain-Brezis-Mironescu theorems on the limit as s->1^- of the Gagliardo-Slobodeckij fractional seminorm are established in the Orlicz space setting. The results hold for fractional Orlicz-Sobolev spaces built upon general Young functions, as well. The case of Young functions with an asymptotic linear growth is also considered in connection with the space of functions of bounded variation. An extended version of the Maz'ya-Shaposhnikova theorem on the limit as s->0^+ of the Gagliardo-Slobodeckij fractional seminorm is established in the Orlicz space setting.

A prey-predator system with logistic growth of prey and hunting cooperation of predators is studied. The introduction of fractional time derivatives and the related persistent memory strongly characterize the model behavior, as many dynamical systems in the applied sciences are well described by such fractional-order models. Mathematical analysis and numerical simulations are performed to highlight the characteristics of the proposed model.

The recent COVID-19 pandemic came alongside with an "infodemic", with online social media flooded by often unreliable information associating the medical emergency with popular subjects of disinformation. In Italy, one of the first European countries suffering a rise in new cases and dealing with a total lockdown, controversial topics such as migrant flows and the 5G technology were often associated online with the origin and diffusion of the virus.

Systems medicine (SM) has emerged as a powerful tool for studying the human body at the systems level with the aim of improving our understanding, prevention and treatment of complex diseases. Being able to automatically extract relevant features needed for a given task from high-dimensional, heterogeneous data, deep learning (DL) holds great promise in this endeavour. This review paper addresses the main developments of DL algorithms and a set of general topics where DL is decisive, namely, within the SM landscape.

A reaction-diffusion system governing the prey-predator interaction with Allee effect on the predators, already introduced by the authors in a previous work is reconsidered with the aim of showing destabilization mechanisms of the biologically meaning equilibrium and detecting some aspects for the eventual oscillatory pattern formation. Extensive numerical simulations, depicting such complex dynamics, are shown. In order to complete the stability analysis of the coexistence equilibrium, a nonlinear stability result is shown.

Investigation about the mechanisms involved in the onset of type 2 diabetes in absence of familiarity is the focus of a research project which has led to the development of a computational model that recapitulates the aetiology of the disease. The model simulates the metabolic and immunological alterations related to type-2 diabetes associated to several clinical, physiological and behavioural characteristics of representative virtual patients.

We prove that on a smooth bounded set, the positive least energy solution of the Lane-Emden equation with sublinear power is isolated. As a corollary, we obtain that the first (Formula presented.) eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the (Formula presented.) spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.