We propose a new class of hypertopologies, called here weak$^{\ast }$ hypertopologies, on the dual space $\mathcal{X}^{\ast }$ of a real or complex topological vector space $\mathcal{X}$. The most well-studied and well-known ...

In this Ph.D. thesis, we give some contributions to the theory of singularities, as well as to the theory of characteristic classes of singular spaces. The first part of this thesis is devoted to the theory of singularities ...

Stochastic resetting, a diffusive process whose amplitude is reset to the origin at random times, is a vividly studied strategy to optimize encounter dynamics, e.g., in chemical reactions. Here we generalize the resetting ...

Cellular contacts modify the way cells migrate in a cohesive group with respect to a free single cell. The resulting motion is persistent and correlated, with cells’ velocities self-aligning in time. The presence of a dense ...

We study the extremal properties of a stochastic process $x_t$ defined by the Langevin equation ${\dot {x}}_{t}=\sqrt{2{D}_{t}}\enspace {\xi }_{t}$, in which $\xi_t$ is a Gaussian white noise with zero mean and $D_t$ is a ...

We study Markovian continuous-time random walk models for Lévy flights and we show an example in which the convergence to stable densities is not guaranteed when jumps follow a bi-modal power-law distribution that is equal ...

We study the extremal properties of a stochastic process $x_t$ defined by a Langevin equation $\dot{x}= \sqrt{2D_o V (B_t )} \xi_t$, where $\xi$ is a Gaussian white noise with zero mean, $D_0$ is a constant scale factor, ...

In order to calibrate the model parameters, Sensitivity Analysis routines are mandatory to rank the parameters by their relevance and fix to nominal values the least influential factors. Despite the high number of works ...

We prove that the G\"{a}rtner--Ellis generating function of probability distributions associated with KMS states of weakly interacting fermions on the lattice can be written as the limit of logarithms of Gaussian Berezin ...

We study the macroscopic dynamics of fermion and quantum-spin systems with long-range, or mean-field, interactions, which turns out to be equivalent to an intricate combination of classical and short-range quantum dynamics. ...