We propose and analyze a generalized two dimensional XY model, whose interaction potential has n weighted wells, describing corresponding symmetries of the system. As the lattice spacing vanishes, we derive by -convergence the discrete-to-continuum limit of this model. In the energy regime we deal with, the asymptotic ground states exhibit fractional vortices, connected by string defects. The -limit takes into account both contributions, through a renormalized energy, depending on the configuration of fractional vortices, and a surface energy, proportional to the length of the strings.

The phase separation of a two-dimensional active binary mixture is studied under the action of an applied shear through numerical simulations. It is highlighted how the strength of the external flow modifies the initial shape of growing domains. The activity is responsible for the formation of isolated droplets which affect both the coarsening dynamics and the morphology of the system. The characteristic dimensions of domains along the flow and the shear direction are modulated in time by oscillations whose amplitudes are reduced when the activity increases.

The selective entrapment of mutually annihilating species within a phase-changing carrier fluid is explored by both analytical and numerical means. The model takes full account of the dynamic heterogeneity which arises as a result of the coupling between hydrodynamic transport, dynamic phase-transitions and chemical reactions between the participating species, in the presence of a selective droplet interface. Special attention is paid to the dynamic symmetry breaking between the mass of the two species entrapped within the expanding droplet as a function of time.

Space exploration is revealing the abundance of other solar systems, but at the same time is showing the uniqueness of our Planet. Using sophisticated Earth Observation technologies such as the European "Sentinels", belonging to the greatest Earth Observation programme ever realised, Copernicus, we are now getting plenty of information at unprecedented high spatial and temporal resolution.

Unattended Wireless Sensor Networks (UWSNs), characterized by the intermittent presence of the sink, are exposed to attacks aiming at tampering with the sensors and the data they store. In order to prevent an adversary from erasing any sensed data before the sink collects them, it is common practice to rely on data replication. However, identifying the most suitable replication rate is challenging: data should be redundant enough to avoid data loss, but not so much as to pose an excessive burden on the limited resources of the sensors.

The challenge of exascale requires rethinking numerical algorithms and mathematical software for efficient exploitation of heterogeneous massively parallel supercomputers. In this talk, we present some activities aimed at developing highly scalable and robust sparse linear solvers for solving scientific and engineering applications with a huge number of degrees of freedom (dof)[1].

Terrestrial and marine ecosystems provide essential goods and services to human societies. In the last decades, however, anthropogenic pressure has produced a loss of ecosystem services that can seriously affect human wellbeing and climate processes at local and regional scale.

We prove the existence of weak solutions to the homogeneous wave equation on a suitable class of time-dependent domains. Using the approach suggested by De Giorgi and developed by Serra and Tilli, such solutions are approximated by minimizers of suitable functionals in space-time.

Supervised link prediction aims at finding missing links in a network by learning directly from the data suitable criteria for classifying link types into existent or non-existent. Recently, along this line, subgraph-based methods learning a function that maps subgraph patterns to link existence have witnessed great successes. However, these approaches still have drawbacks. First, the construction of the subgraph relies on an arbitrary nodes selection, often ineffective.

We discuss the well-posedness of the "transient eddy current" magneto-quasi-static approximation of Maxwell's initial value problem with bounded and measurable conductivity, with sources, on a domain. We prove the existence and uniqueness of weak solutions, and we provide global Hölder estimates for the magnetic part.