Computer Science and Systems Engineering

Advanced Topics in Network Theory: Algorithms and Applications

Centrality metrics and spectral properties of graphs.
Community detection.
Bipartite and multilayer networks.
Applications: Worls Trade Web
Lecture 1: Centrality metrics
Lecture 2: Spectral properties
Lecture 3: Ranklings and reputation on graphs
Lecture 4: Community detection in networks I
Lecture 5: Community detection in networks II
Lecture 6: Bipartite networks
Lecture 7: Multilayer networks
Lecture 8: World Trade Web
Lecture 9: Infrastructural network I
Lecture 10: Infrastructural network II 

Advanced Numerical Analysis

1. General considerations on matrices
Matrices:definitions and properties; norm of matrices
The condition number of a matrix
Sparse matrices and sparse formats (sparsity, structure, functionals)
The role of the PDE discretization (e.g., parameter dependence)

2.a Direct methods for general linear systems
Factorizations: definitions and properties
Factorization algorithms
Cost and numerical stability

Advanced Neuroimaging

xEarly brain functional studies, based on MRI, PET or EEG, focused on univariate analyses, in which the activity of each region is processed independently from each other. Nowadays, multivariate machine learning techniques have been developed to model complex, sparse neuronal populations. This course will provide an introduction to new methods and cutting-edge machine-learning techniques in the neuroimaging field by exploring multivariate statistical modeling of brain-activity data and computational modeling of brain information processing.

Stochastic Processes and Stochastic Calculus

This course aims at introducing some important stochastic processes and Ito stochastic calculus. Some proofs are sketched or omitted in order to have more time for examples, applications and exercises.

In particular, the course deals with the following topics:

- Markov chains (definitions and basic properties, classification of states, invariant measure, stationary distribution, some convergence results and applications, passage problems, random walks, urn models, introduction to the Markov chain Monte Carlo method),

Probabilistic and Stochastic Model Checking

Model checking is an automated formal verification technique whose main idea is to formally specify both the system specification and its properties (typically, by means of temporal logic) and automatically verify that such properties are satisfied (or to which extent they are). This course aims at presenting the fundamentals of model checking techniques for the verification of distributed and concurrent systems. Different classes of temporal logics will be introduced that rely on the use of semantic models to provide a logical framework for the analysis and verification of complex systems.

Principles of Concurrent and Distributed Programming

The course objective is to introduce the basics of concurrent programming problems through an illustration of the concepts and techniques related to modeling systems in which there are more components that are simultaneously active and need to coordinate and compete for the use of shared resources. At the end of the course the student will have a good understanding of the constructs for concurrent programming and be able to use them to write and analyze concurrent programs.

Optimal Control

Discrete-time optimal control: dynamic programming for finite/infinite horizon and deterministic/stochastic optimization problems. LQ and LQG problems, Riccati equations, Kalman filter. Deterministic continuous-time optimal control: the Hamilton-Jacobi-Bellman equation and the Pontryagin?s principle. Examples of optimal control problems in economics.