Computer Science

In this course we will venture to go through some of the most advanced control schemes whose development has been motivated by problems in process control and economics. The course's main objective will be to bring students in touch with the state of the art in MPC theory and explore various research opportunities that emerge. We will see how the mature concept of model predictive control (MPC) can be combined with process economics to yield a unifying framework -- known as economic model predictive control (EMPC) -- for simultaneous control and process optimization.

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).

Principles of imaging modalities (optical microscopy, spectroscopy, CT, MRI, PET, SPECT) and their applications in natural and life sciences (Dharmakumar); Basics of image analysis (filtering, segmentation, detection) and basics of statistical mining; Designing robust image analysis methods; Large-scale analysis; Integration with databases and knowledge sharing platforms; Error testing and precision bound repetition studies for longitudonal and group studies (phenotyping); High performance computing for imaging (computer vision); Scientific and data visualization; Prerequisites: Probability an

The course aims at giving a modern and thorough treatment of algorithms for solving convex, large-scale and nonsmooth optimization problems. Applications of convex optimization. Convex sets, functions and optimization problems. Optimality conditions. Basic algorithms for unconstrained optimization (gradient, fast gradient and Newton methods). Basic algorithms for constrained optimization (Interior point and active set methods). Subdifferential and conjugate of convex functions. Duality. Proximal mappings. Proximal minimization algorithm. Augmented Lagrangian Method.

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.

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.

Methods and approach to problem solving. Problem analysis; analysis of complex systems (related to cultural heritage, such as a city of art organization, promotion, etc.). The course will include practical simulations. The course will be linked to a seminar on specific Case studies.

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.

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).

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.