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.

Reputation systems are nowadays widely used to support decision making in networked systems. Parties in such systems rate each other and use shared ratings to compute reputation scores that drive their interactions. The existence of reputation systems with remarkable differences calls for formal approaches to their analysis. We present a verification methodology for reputation systems that is based on the use of the coordination language Klaim and related analysis tools.

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.

Introduction: Network and systems medicine has rapidly evolved over the past decade, thanks to computational and integrative tools, which stem in part from systems biology. However, major challenges and hurdles are still present regarding validation and translation into clinical application and decision making for precision medicine.

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.

A novel approach for extracting gauge-invariant information about spin-orbit coupling in gravitationally interacting binary systems is introduced. This approach is based on the "scattering holonomy", i.e. the integration (from the infinite past to the infinite future) of the differential spin evolution along the two worldlines of a binary system in hyperboliclike motion. We apply this approach to the computation, at the first post-Minkowskian approximation (i.e.