Stochastic Models for Complex Systems

Project 2019-2023 by Italian MIUR

PRIN 2017

The research targets will be achieved through a collective effort among the scholars of the three units. In relationship with the previously described project targets, Lecce research unit will mainly develop the following specific sub-tasks:

WP1: It will develop suitable dependence measures for non-continuous random vectors, also by using suitable metrics recently introduced in the space of subcopulas. Moreover, it will quantify the impact of the presence of ties in the statistical analysis of dependence models, also by means of new methodologies relying on the notion of entropy.

WP2: In collaboration with Napoli and Salerno units, it will study suitable copula models and/or association measures to describe the behavior of stochastic reliability systems with complex interactions (e.g. shared components). Moreover, it will study suitable functional inequalities (for copulas and distortion of copulas) able to describe ageing property of a system.

WP6: First it aims to construct effective cost-functions for the maximum entropy approach by taking into account results on single neuron inspections by other units (e.g. suitable modification of integrate&fire neurons more biologically tolerated). Then, we will test the emerging properties of small clusters of these "improved neurons" (a so called "neural network"), namely properties that are present at the network level but get lost when reducing back to single neurons. This quests for a heavily usage of consolidated techniques in the statistical mechanics of disordered systems as the stochastic stability analysis or the cavity field/belief-propagation routes.

Salento Unit Components

Adriano Barra

Adriano Barra is Associate Professor at the Dipartimento di Matematica e Fisica “Ennio De Giorgi” within the University of Salento and member of the Istituto Nazionale di Fisica Nucleare (INFN) and Istituto Nazionale d'Alta Matematica (INdAM). His main interest of research is statistical mechanics of complex systems with principal applications to artificial intelligence and biological complexity.

Fabrizio Durante

Fabrizio Durante is Full Professor in Mathematical Methods of Economics, Finance and Actuarial Sciences at the Department of Economic Sciences of the University of Salento. His research interests focus on the fields of dependence and copula models, with particular emphasis on applications in quantitative risk management, reliability theory, environmental science and decision theory.

Claudio Ignazzi

Claudio Ignazzi is a PhD student the Dipartimento di Matematica & Fisica “Ennio De Giorgi” within the University of Salento. His research activities mainly concern Probability and Statistics, and focus on the fields of dependence, uniform distribution theory, copula models and risk measures, with computational applications.

Gianfausto Salvadori

Gianfausto Salvadori is Assistant Professor of Probability and Mathematical Statistics at the Department of Mathematics and Physics “Ennio De Giorgi” of the University of Salento. His research interests mainly lie in the multivariate statistical modelling of (extreme) environmental phenomena, both maritime, terrestrial and atmospheric. A particular attention is devoted to the assessment of the corresponding multivariate hazards, where the dependencies of the variables at play are modelled via Copulas.

Carlo Sempi

Carlo Sempi is honorary Full Professor in Probability and Mathematical Statistics at the Department of Mathematics and Physics “Ennio De Giorgi” of the University of Salento. His scientific activity is directed to Information theory and entropy functionals, Statistical Mechanics, Probabilistic metric spaces, Copula Theory. For more information about his academic life, see here.