42nd cycle

The course will focus on medical processes, with a particular emphasis on their representation and management. Various representation models for clinical guidelines, clinical trials, and medical workflows will be examined, alongside key aspects concerning data acquisition and/or data mining, representation, and utilization (e.g., simulation and decision support). Finally, the treatment of patients with comorbidities will be considered as a prototype of a complex context where multiple models must be reconciled.

Students will acquire knowledge of the primary types of models for medical processes, as well as the operational tools to acquire, represent, and utilize them. The course will provide foundational knowledge on these topics, along with insights into advanced research and the most recent hot topics in the field.

Course Duration: 18 hours

Data Science with Python

This course introduces the core concepts of data science using key Python libraries such as Scikit-learn, Pandas, NumPy, and others. The use of Python is of particular relevance given its widespread popularity within the data science community. The course explores the nature of data science and analytics, focusing on both the underlying workflow and the outcomes that can be achieved. Key features of Python are covered, including a brief introduction to the programming language itself. Students will apply fundamental principles of machine learning, pattern recognition, and artificial intelligence, which underpin the algorithms and implementations used throughout the examples. Regression analysis with Python, clustering techniques, and classification algorithms are covered in the final phase of the course. Hierarchical clustering, decision trees, and ensemble methods are also explored, alongside dimensionality reduction techniques and recommendation systems. The Support Vector Machine algorithm and the "kernel trick" are discussed as time permits.

Course Duration: 12 hours

Network Science & Computational Social Science

This advanced course bridges the gap between data-driven computational methods and social theory. Students will explore how network science can decipher complex social systems, tracking everything from information diffusion and pandemic spread to political polarization and algorithmic bias. The course balances theoretical mathematical foundations with hands-on computational workflows, introducing students to state-of-the-art research trends in the field.

This course aims to equip doctoral candidates with the theoretical foundations and practical competencies necessary to analyze and model complex human behaviors through the lens of network science and computational social science. 

Course Duration: 24 hours

Mathematics of Artificial Intelligence

This course explores the mathematical structures underlying artificial intelligence from a rigorous perspective. It covers AI methods and algorithms, providing in-depth insights into their connections with statistical physics, alongside the development of dedicated mathematical frameworks.

Course Duration: 24 hours

Quantum Computing

This is an advanced course that lays the foundations of quantum programming. It aims to provide computer science students with a new perspective and physics students with a more programming-oriented approach.

Course Duration: 24 hours

Artificial Intelligence in Physics

This course explores the application of artificial intelligence to physics, ranging from the study of elementary particles (utilizing data from CERN and other experimental platforms) to string theory. It also covers multi-agent computing techniques.

Course Duration: 24 hours

Introduction to Functional Data Analysis

The course offers an introduction to functional data analysis, i.e., the study of samples in which each observation is represented by a function defined on a continuous domain, such as curves or surfaces. Both theoretical and operational tools will be presented, with a focus on exploratory and predictive analysis methods. Among these, scalar-on-function regression models and functional response regression models will be introduced.

Course Duration: 10 hours

Multivariate Stochastic Processes and Social/Economic Applications

The course offers a theoretical and applied overview of a class of multivariate mean-reverting stochastic processes (multivariate Lévy-driven Ornstein–Uhlenbeck processes). These models are particularly relevant in the study of dynamic economic and social phenomena characterized by complexity, interdependence, and uncertainty. The main theoretical aspects of the models will be presented, along with numerical simulation methodologies, parameter estimation techniques for multivariate time series, and applications to economic and production networks. The course will also include computational implementations in Python.

Course Duration: 8 hours

Numerical Methods for Stochastic Gradient Estimation  

The course provides an introduction to numerical techniques for estimating derivatives in stochastic systems, particularly the gradient estimation of functions defined through statistical sampling and/or simulation of random variables (e.g., expected values, probabilities, and quantiles). The theoretical application and limitations of classical methodologies such as the finite difference method and infinitesimal perturbation analysis will be discussed. Subsequently, alternative methods for correctly estimating the gradient will be introduced in cases where classical approaches are inapplicable or ineffective, including the Likelihood Ratio method and its generalizations. The course will conclude with applications to reinforcement learning problems. The course will also include computational implementations in Python.

Course Duration: 8 hours

Introduction to Probability  

The course introduces the fundamentals of probability, starting with the formal definition of probability spaces and the concept of probability measures. Independence between events, conditional probability, and Bayes' theorem are then discussed.

Discrete and continuous random variables are studied, along with their main properties, expected value, and extensions to the multivariate case. Transformations of random variables and notions of convergence are also explored. Finally, the course introduces asymptotic results such as the laws of large numbers and the central limit theorem, and a first introduction to stochastic processes.

Course Duration: 10 hours

Introduction to Bayesian Models and Inference  

The course introduces the Bayesian approach to statistical inference, developing its methodology, theoretical foundations, and computational techniques, using R software, for the practical implementation of models. Single- and multi-parameter models, linear and generalized regression models in the Bayesian framework, as well as methods for model evaluation and selection, will be covered. Particular attention will be paid to Monte Carlo techniques for approximating posterior distributions, using MCMC algorithms such as Gibbs sampler and Metropolis–Hastings.

Course Duration: 10 hours

Simplicial Data

The course focuses on the statistical analysis of simplicial data, i.e., vectors of non-negative values ​​constrained to sum to a constant, typically one (e.g., microbiome data, proportions in social phenomena, etc.). Two main methodological approaches will be presented: the "stay-in-the-simplex" approach, based on parametric models defined directly on the simplex (e.g., the Dirichlet distribution and its recent extensions), and the "log-ratio" approach introduced by Aitchison, based on appropriate transformations and the geometry of the simplex. Particular attention will be paid to regression models with response and/or compositional covariates. The course will also address the problem of values ​​on the simplex boundary, with reference to the presence of zeros and ones in the observed data.

Course Duration: 8 hours

Game-theoretic foundations for AI and Finance  

The course introduces the foundations of Algorithmic Game Theory (AGT), a field that studies the strategic interactions between rational agents from a computational perspective, at the intersection of economics, mathematics, and theoretical computer science. Topics covered range from noncooperative and cooperative game theory to learning in strategic environments, with applications to financial and insurance risk management, market microstructure, and artificial intelligence systems. In particular, the concepts of equilibrium and cooperative allocation find direct application in risk sharing between counterparties, the allocation of economic capital between risk units, and the measurement of systemic risk. The connection with AI emerges across the board: from the alignment of autonomous agents to the design of mechanisms for complex systems, and the interpretability of machine learning models through the Shapley value.

Course Duration: 10 hours

Computational Finance and Risk Modeling