After introducing the foundations of classical and quantum information theory, and quantum measurement, the course will address the theory and practice of digital quantum computing, covering fundamental and advanced topics such as recent quantum algorithms ...
We cover the theory and applications of sparse stochastic processes (SSP). SSP are solutions of differential equations driven by non-Gaussian innovations. They admit a parsimonious representation in a wavelet basis and are relevant to coding, compressed se ...
The course focuses on mathematical models based on PDEs with random parameters, and presents numerical techniques for forward uncertainty propagation, inverse uncertainty analysis in a Bayesian framework and optimal control under uncertainty. ...
Probabilistic proof system (eg PCPs and IPs) have had a tremendous impact on the theoretical computer science, and have also found practical uses. They underlie delegation of computation protocols and hardness of approximation. This course covers the found ...
The classical distinction between polynomial time solvable and NP-hard problems is often too coarse. This course covers techniques for proving more fine-grained lower and upper bounds on complexity of computational problems. ...
Statistical learning theory for supervised learning and generalization in PAC and online models (VC theory, MDL/SRM, covering numbers, Radamacher Averages, boosting, compression, stability and connection with strong convexity in Banch spaces); Computationa ...
The introduction to asymptotic analysis provides the basis for constructing many simplified analytical models in mechanics and for testing computations in limiting cases. ...