Computer Science and Systems Engineering

Applications of Stochastic Processes

This course offers an introduction to stochastic processes as a practical modelling tool for the quantitative analysis of systems. It covers the fundamentals of Markov chains, and presents algorithms and state-of-the-art software applications and libraries for their numerical solution and simulation. The class of Markov Population Processes is presented, with its most notable applications to as diverse disciplines as chemistry, ecology, systems biology, health care, computer networking, and electrical engineering.

Advanced Topics of Control Systems

This course will cover a selected advanced topic in control, identification, or dynamical optimization.

Prerequisites: Linear algebra and matrix computation, calculus and mathematical analysis, control systems, numerical optimization.

Advanced Topics of Computer Science

This course will be organized as series of reading groups or specialized seminars by members or collaborators of the research unit on System Modelling and Analisys (SysMA).

Advanced Topics of Computational Mechanics

The course is organized as a set of seminars and lectures delivered by IMT Professors and by invited recognized international experts. It covers advanced topics of computational mechanics.

Advanced Topics in Network Theory: Dynamical Processes of Networks

Mean field and master equations.
Percolation and epidemic models.
Contagion: the case of financial networks.
Applications of network theory.

Lecture 1: Master equations for network models
Lecture 2: Fitness and relevance models
Lecture 3: Epidemic processes in mean fiels
Lecture 4: Epidemics on networks
Lecture 5: Scaling and percolation on networks
Lecture 6: Contagion in financial network I
Lecture 7: Contagion in financial network II
Lecture 8: Game theory on networks
Lecture 9: Evolutionary network games

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

2.b Direct methods for sparse linear systems

Factorizations of banded matrices

Advanced Neuroimaging

Early 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.