Image Analysis

Algorithmics

This course covers basic and advanced foundations, problems and solutions of algorithmic computation. A first part offer an overview of the fundamental notions of algorithm analysis and recalls algorithmic solutions (and their complexity) for some basic problems like sorting and searching. The second part of the course will focus on advanced algorithms which are essential in some of the research fields relevant to the different curriculum of the Computer Decision and System Science track.

Network Theory

Course description: Basic of Graph Theory: degree, clustering, connectivity, assortativity, communities. Analysis of Complex Networks, datasets and software. Community Detection, Modularity, Spectral Properties. Fractals, Self-Organised Criticality, Scale Invariance. Random Graph, Barabasi Albert Model, Fitness model, Small world. HITS Algorithm and PageRank. Real instances of Complex Networks in Biology and Social Sciences. Board of Directors, Ownership Networks, measures of Centrality and Control. World Trade Web, Minimal Spanning Trees, Competition and Products spaces.

Machine Learning and Pattern Recognition

Basics of pattern recognition and machine learning and real world applications in imaging, internet, finance. Similarities and differences. Decision theory, ROC curves, Likelihood tests. Linear and quadratic discriminants. Template based recognition and feature detection/extraction. Supervised learning (Support vector machines, Logistic regression, Bayesian). Unsupervised learning (clustering methods, EM, PCA, ICA). Current trends in Machine Learning. Prerequisites: Probability and basic random processes, linear algebra, basic computer programming, numerical methods.

Advanced Topics of Complex Networks

This course will be organized as series of reading groups or specialized seminars by members or collaborators of the research unit on Natural Networks (Networks).

Theory and Numerics of Ordinary and Partial Differential Equations

The first lesson of the course will provide a primer on complex variables. Using this mathematical formalism, the focus of the remaining first part of the course will be to introduce linear ordinary and linear partial differential equations, and the "cheap" methods to solve them using Fourier and Laplace transforms. The ordinary and partial differential equations will be placed into a context of applied mathematics (e.g. classic deterministic and stochastic systems) saving the theoretical approach for advanced lectures.

Stochastic Processes and Stochastic Calculus

This course aims at introducing some important stochastic processes (Markov chains, martingales,
Poisson process, Wiener process) and Ito 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:

Statistics Lab.

- Brief introduction to R (http://www.r-project.org/)
- Creating random variables.
- Applications to the central limit theorem and the law of large numbers
- Descriptive statistics: (i) Representing probability and cumulative distribution functions in discrete and continuous cases; (ii) calculating mean, variance, concentration indexes, covariance and correlation coeff.
- Statistical inference: (i) Point estimation and properties; (ii) interval estimation and properties; (iii) hypothesis testing and properties.

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.