11 - 16 of 16 results for: CS161

Over the years, many powerful algorithms have been built via tools such as linear programming relaxations, spectral properties of graphs, and others, that all bridge the discrete and continuous worlds. This course will cover another such tool recently gaining popularity: polynomials, their roots, and their analytic properties, collectively known as geometry of polynomials. The course will cover fundamental properties of polynomials that are useful in designing algorithms, and then will showcase applications in several areas of algorithm design: combinatorial optimization, graph sparsification, high-dimensional expanders, analysis of random walks on combinatorial objects, and counting algorithms. Prerequisites: CS161 or equivalent. Basic knowledge of probability, linear algebra, and calculus.

This course will cover various algorithm design techniques for two intimately connected class of problems: sampling from complex probability distributions and counting combinatorial structures. A large part of the course will cover Markov Chain Monte Carlo techniques: coupling, stationary times, canonical paths, Poincare and log-Sobolev inequalities. Other topics include correlation decay in spin systems, variational techniques, holographic algorithms, and polynomial interpolation-based counting. Prerequisites: CS161 or equivalent, STAT116 or equivalent.

Techniques for design and analysis of efficient geometric algorithms for objects in 2-, 3-, and higher dimensions. Topics: convexity, triangulations and simplicial complexes, sweeping, partitioning, and point location. Voronoi/Delaunay diagrams and their properties. Arrangements of curves and surfaces. Intersection and visibility problems. Geometric searching and optimization. Random sampling methods. Range searching. Impact of numerical issues in geometric computation. Example applications to robotic motion planning, visibility preprocessing and rendering in graphics, and model-based recognition in computer vision. Prerequisite: discrete algorithms at the level of CS161. Recommended: CS164.

Many 21st-century computer science applications require the design of software or systems that interact with multiple self-interested participants. This course will provide students with the vocabulary and modeling tools to reason about such design problems. Emphasis will be on understanding basic economic and game theoretic concepts that are relevant across many application domains, and on case studies that demonstrate how to apply these concepts to real-world design problems. Topics include auction and contest design, equilibrium analysis, cryptocurrencies, design of networks and network protocols, reputation systems, social choice, and social network analysis. Case studies include BGP routing, Bitcoin, eBay's reputation system, Facebook's advertising mechanism, Mechanical Turk, and dynamic pricing in Uber/Lyft. Prerequisites: CS106B/X and CS161, or permission from the instructor.

Introduction to the major underpinnings of systems immunology: first principles of development of computational approaches to immunological questions and research; details of the algorithms and statistical principles underlying commonly used tools; aspects of study design and analysis of data sets. Prerequisites: CS106a and CS161 strongly recommended.