Preserving Co-Location Privacy in Geo-Social Networks

The number of people on social networks has grown exponentially. Users share very large volumes of personal informations and content every days. This content could be tagged with geo-spatial and temporal coordinates that may be considered sensitive for some users. While there is clearly a demand for users to share this information with each other, there is also substantial demand for greater control over the conditions under which their information is shared. Content published in a geo-aware social networks (GeoSN) often involves multiple users and it is often accessible to multiple users, without the publisher being aware of the privacy preferences of those users. This makes difficult for GeoSN users to control which information about them is available and to whom it is available. Thus, the lack of means to protect users privacy scares people bothered about privacy issues. This paper addresses a particular privacy threats that occur in GeoSNs: the Co-location privacy threat. It concerns the availability of information about the presence of multiple users in a same locations at given times, against their will. The challenge addressed is that of supporting privacy while still enabling useful services.Comment: 10 pages, 5 figure

Stationary Mean Field Games systems defined on networks

We consider a stationary Mean Field Games system defined on a network. In this framework, the transition conditions at the vertices play a crucial role: the ones here considered are based on the optimal control interpretation of the problem. We prove separately the well-posedness for each of the two equations composing the system. Finally, we prove existence and uniqueness of the solution of the Mean Field Games system

A numerical model for the simulation of a solitary wave in a coastal region

In this paper we propose a numerical model for the simulation of the tsunami wave propagation on coastal region. The model can simulate the wave transformation due to refraction, shoaling, diffraction and breaking phenomena that take place in the surf zone and can simulate the wet front progress on the mainland. The above mentioned model is based on the numerical integration of the Fully Non-linear Boussinesq Equations in the deep water region and of the Non-linear Shallow Water Equations in the surf zone. These equations are expressed in an integral contravariant formulation and are integrated on generalized curvilinear boundary conforming grid that can reproduce the complex morphology of the coast line. The numerical integration of the model equations is implemented by a high order Upwind WENO numerical scheme that involves an exact Riemann Solver. For the simulation of the wet front progress on the dry bed, the exact solution of the Riemann problem for the wet-dry front is used. The capacity of the proposed model to simulate the wet front progress velocity is tested by numerical reproducing the dam-break problem on a dry bed. The capacity of the proposed model to correctly simulate the tsunami wave evolution and propagation on the coastal region is tested by numerical reproducing a benchmark test case about the tsunami wave propagation on a conic island

Viscosity solutions of Eikonal equations on topological networks

In this paper we introduce a notion of viscosity solutions for Eikonal equations defined on topological networks. Existence of a solution for the Dirichlet problem is obtained via representation formulas involving a distance function associated to the Hamiltonian. A comparison theorem based on Ishii's classical argument yields the uniqueness of the solution

Memory effects in measure transport equations

Transport equations with a nonlocal velocity field have been introduced as a continuum model for interacting particle systems arising in physics, chemistry and biology. Fractional time derivatives, given by convolution integrals of the time-derivative with power-law kernels, are typical for memory effects in complex systems. In this paper we consider a nonlinear transport equation with a fractional time-derivative. We provide a well-posedness theory for weak measure solutions of the problem and an integral formula which generalizes the classical push-forward representation formula to this setting

A time-fractional mean field game

We consider a Mean Field Games model where the dynamics of the agents is subdiffusive. According to the optimal control interpretation of the problem, we get a system involving fractional time-derivatives for the Hamilton-Jacobi-Bellman and the Fokker-Planck equations. We discuss separately the well-posedness for each of the two equations and then we prove existence and uniqueness of the solution to the Mean Field Games syste

A model problem for Mean Field Games on networks

In [14], Gueant, Lasry and Lions considered the model problem ``What time does meeting start?'' as a prototype for a general class of optimization problems with a continuum of players, called Mean Field Games problems. In this paper we consider a similar model, but with the dynamics of the agents defined on a network. We discuss appropriate transition conditions at the vertices which give a well posed problem and we present some numerical results