Computer Science and Systems Engineering

Numerical Methods for the Solution of Partial Differential Equations

The course introduces numerical methods for the approximate solution of initial and boundary value problems governed by linear partial differential equations (PDEs) ubiquitous in physics, engineering, and quantitative finance. The fundamentals of the finite difference method and of the finite element method are introduced step-by-step in reference to exemplary model problems related to heat conduction, linear elasticity, and pricing of stock options in finance. Notions on numerical differentiation, numerical integration, interpolation, and time integration schemes are provided.

Networks

The course is structured into three modules: the first one will cover advanced topics in complex network theory, whereas, the second one will focus on economic and financial networks, dealing with both theory and applications.

Module 1: Advanced Theory of Complex Networks
Lecture 1 Models of Evolving Networks
Lecture 2 Fitness & Relevance models
Lecture 3 The Master Equations approach
Lecture 4 Percolation
Lecture 5 Epidemic Models on Networks
Lecture 6 Advanced Topological Properties
Lecture 7 Complex Networks Randomization

Modelling and Verification of Reactive Systems

Computing systems are becoming increasingly sophisticated and control key aspects of our lives. In light of the increasing complexity of such computing devices, one of the key scientific challenges in computer science is to design and develop computing systems that do what they were expected to do, and do so reliably. The aim of this course is to introduce models for the formal description of computing systems, with emphasis on parallel, reactive and possibly real-time systems, and the techniques for system verification and validation that accompany them.

Model Predictive Control

Quick review of linear dynamical systems in state-space form, stability, state-feedback control and observer design, linear quadratic regulation and Kalman filtering. Basic model predictive control (MPC) algorithm and the receding horizon principle. Linear MPC: formulation, quadratic programming, stability properties. Multiparametric programming and explicit MPC. MPC of hybrid dynamical systems subject to linear and logical constraints. Stochastic MPC. Selected applications of MPC to automotive and aerospace systems, supply chains, financial engineering.

Micromechanics

The course covers the fundamentals on modelling heterogeneous materials with periodic, quasi-periodic or non-ordered microstructures. Metamaterials, auxetic materials, chiral and anti-chiral microstructures belong to this class and their design and optimization requires a deep knowledge of their mechanical behaviour.

Machine Learning and Pattern Recognition

Basics of pattern recognition and machine learning and real world applications in imaging, internet, finance. Similarities and differences. Supervised vs unsupervised learning. Linear regression in many ways. The logistic regression. Support vector machines for classification and regression. Random Forests for classification. Linear and quadratic discriminant analysis. Unsupervised learning (k-means, c-means, kernel k-means, spectral clustering, EM). Feature extraction and selection (PCA, ICA, kernel PCA, and manifold learning). Current trends in Machine Learning.

Identification, Analysis and Control of Dynamical Systems

The course provides an introduction to dynamical systems, with emphasis on linear systems. After introducing the basic concepts of stability, controllability and observability, the course covers the main techniques for the synthesis of stabilizing controllers (state-feedback controllers and linear quadratic regulators) and of state estimators (Luenberger observer and Kalman filter). The course also covers data-driven approaches of parametric identification to obtain models of dynamical systems from a set of data, with emphasis on the analysis of the robustness of the estimated models w.r.t.

Game Theory

Mechanism Design. Revelation principle, Dominance and Nash Implementation. Strategic and Axiomatic Bargaining. Asymmetric Information and Optimal Contracts. Moral Hazard and Adverse Selection models. Signaling and Screening Models. Applications. Static games of complete information: definition of a game; normal form representation; strongly and weakly dominated strategies; Nash Equilibrium (NE); mixed strategy equilibrium. Applications of NE and introduction to market competition; Cournot competition; Bertrand competition; externalities; public goods.

Foundations of Probability and Statistical Inference

This course aims at introducing, from an advanced point of view, the fundamental concepts of probability and statistical inference.
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:

? probability space, random variable, expectation, variance, cumulative distribution function, discrete and absolutely continuous distributions, random vector, joint and marginal distributions, joint cumulative distribution function, covariance,

Finance

This course introduces students to the basic concepts used in quantitative finance, which forms the basis for many applications such as derivatives pricing, financial engineering and asset pricing. Anyone interested in these areas will have to acquire a good grasp of the topics in this course.