PhD in Modeling and Data Science

• Stochastic processes: construction, simulation and Bayesian inference (Scientific director: Matteo Ruggiero)

Abstract: The research under my supervision could concern one of the following: the construction of stochastic dynamics through interacting particle systems, typically to obtain multidimensional diffusions after appropriate scaling limits; the construction of finite-dimensional stochastic models through transformation of other processes; the elaboration of simulation and inferential strategies for estimating the trajectories and the parameters of these processes in a hidden Markov model setting. Typical models of interest in my area of expertise find application in population dynamics, mathematical finance and Bayesian inference in a temporal framework.

• Stochastic and/or physics techniques for HPC problems (Scientific directors: Laura Sacerdote, Marco Maggiora)

Abstract (stochastic): The project will involve the study of statistical and stochastic techniques devoted to improve the use of computers. For example, the study will deal with the impact of the cache state on the execution time of tasks and the effect of the deployment of the tasks on different cores.

Abstract (physics):The project will involve the development and test of a general purpose library to perform within an HPC infrastructure the tracking and reconstruction of the secondary vertices of short living particles. The research activity will be performed within the BESIII and BELLE II Collaborations, exploiting as well existing code from the ALICE Collaboration, in close collaboration with the similar activities performed within our PNRR projects.

• Modeling emerging human behavior towards a sustainable and pro-environment urban life (Scientific directors: Rossano Schifanella)
• Confidential Data Science: Federated Learning in Trusted Execution Environments (Scientific directors: Marco Aldinucci)
• Investigation with multi-agent system models, within the framework of the H2020 Green Cities pillar, of urban permeability to lepidoptera motion and of their diffusion in mixed urban areas (buildings and green spaces)(Scientific directors: Marco Maggiora)
   

Abstract: Experimental data recently collected on butterflies motion in Turin could be exploited, profiting as well of data available from different sources on buildings, green areas, water sources and traffic, in order to develop Multi Agents Systems that could later provide predictions and optimisation tools to design location, type and size of new green areas in European Cities. A research group composed of Biologists and Physicists aims in fact to develop those tools needed to design cities in order to, within the framework of the H2020 Green Cities pillar, allow for and optimise the permeability of urban ecosystem to butterflies and other insects needed to sustain pollination for most of vegetables in urban environment.

1. Stochastic processes with applications (Scientific director: Laura Sacerdote)

The acceptable topics in this framework are: 

• Approximations of first passage time distribution

Referent: Elvira Di Nardo

Abstract: The first-passage-time (FPT) phenomenon arises in many applications in which a stochastic process evolves in the presence of a threshold. The mathematical problem of the FPT consists in finding its probability density function (pdf), although closed form expressions are available only in a few cases. There are several strategies to approach this problem, whose effectiveness depends on the formulation of a suitable model for the stochastic process and on its properties. But when a sample of FPTs is analyzed without any prior information on the stochastic dynamics generating the data, the identification of a model could be difficult to implement. The aim of this project is to investigate model-independent methods involving orthogonal series approximations of the pdf and to check their numericalperfomances in fitting data and in estimating the parameters.

• Interacting particle systems as microscopic stochastic representation of partial differential equations

Referent: Elena Issoglio

Abstract: Interacting particle systems are mathematical models that describe the motion of interacting particles at the microscopic level. They find applications in many fields, such as biology (herds), sociology (herding behaviour), energy markets (price formation), etc. Most often these systems are random, hence the equations are stochastic equations. It is known that under suitable conditions the system will converge (as the number of particle goes to infinity) to an equation describing the "typical" particle motion together with the density of the cloud of particles, hence describing the system at the macroscopic level. This PhD project will focus on the study of stochastic interacting particle systems with singular coefficients, for example when the drift of the each particle dynamics is highly non smooth. Singular coefficients would account for the singular nature of the dynamics of each particle, that could be due to exogenous factors (the environment) or endogenous ones (the particles themselves).

• Stochastic modelling of anomalous diffusion

Referent: Bruno Toaldo

Abstract: In the latest years, anomalous diffusions started to play a central role in modelling, as more and more physical systems are shown to have non-diffusive behaviours. Among anomalous diffusions, subdiffusions are widely used, for instance, in thermo-and visco-elasticity and to model particles moving in porous media, hence subject to trapping phenomena. Despite such a variety of applications, the knowledge about subdiffusions is still limited. The proposed project focuses on the study of subdiffusions whose behaviour is connected with nonlocal operators, that arise from the afore mentioned applications. In particular, attention is devoted to modelling the stochastic behaviour of the particles involved in such physical phenomena, whose “ensemble behaviour” exhibit the required nonlocal/subdiffusive behaviour.

• Optimal detection of anomalies with metrological applications

Referent: Cristina Zucca

Abstract: Study of stochastic processes  for the optimal detection of anomalies with metrological applications. These problems involve the analysis of diffusion processes constrained by one or more boundaries. Study of exact simulation algorithms for the first exit time.

2. Open science cloud: marketplace users data analysis models (Scientific director: Enrico Pasini)

Abstract: Open science cloud services (e.g. EOSC) make use of a MarketPlace platform through which various categories of users, in different capacities, make use of data, add data, produce data with their behavior. Information of this requires appropriate modeling and analysis, the development of which is the project object. The project is a joint enterprise of the Modeling and Data Science PhD program and the Italian Research Council, that will provide joint scientific support.