This course introduces slow/fast systems and the mathematical tools used to derive effective equations governing their behaviour. Students will learn core concepts and techniques for rigorously analysing complex stochastic multi-scale systems. ...
The students gain an in-depth knowledge of several current and emerging areas of theoretical computer science. The course familiarizes them with advanced techniques, and develops an understanding of fundamental questions that underlie some of the key probl ...
Machine learning and data analysis are becoming increasingly central in sciences including physics. In this course, fundamental principles and methods of machine learning will be introduced and practised. ...
The students understand tools from the statistical physics of disordered systems, and apply them to study computational and statistical problems in graph theory, discrete optimisation, inference and machine learning. ...
A first graduate course in algorithms, this course assumes minimal background, but moves rapidly. The objective is to learn the main techniques of algorithm analysis and design, while building a repertory of basic algorithmic solutions to problems in many ...
The class covers topics related to statistical inference and algorithms on graphs: basic random graphs concepts, thresholds, subgraph containment (planted clique), connectivity, broadcasting on trees, stochastic block models and perceptron models. Requirem ...
The 'probabilistic method' is a fundamental tool in combinatorics. The basic idea is as follows: to prove that an object (for example, graph) with certain properties exists, it suffices to prove that if the object is chosen at random, then it has the desir ...
The class will cover statistical models and statistical learning problems involving discrete structures. It starts with an overview of basic random graphs and discrete probability results. It then covers topics such as reconstruction on trees, stochastic b ...