Yale

Mon 3 May 2010, 4:00pm
SPECIAL
Probability Seminar
MATH 104

Entropy ideas in highdimensional convex geometry

MATH 104
Mon 3 May 2010, 4:00pm5:00pm
Abstract
Our primary goal is to describe a strong quantitative form of the ShannonMcMillanBreiman theorem for logconcave probability measures on linear spaces, even in the absence of stationarity. The main technical result is a concentration of measure inequality for the “information content” of certain random vectors. We will also discuss other related work. For instance, by combining this concentration result with ideas from information theory and convex geometry, we obtain a reverse entropy power inequality for convex measures that generalizes the reverse BrunnMinkowski inequality of V. Milman. This is joint work with Sergey Bobkov (Minnesota).
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Universitaet Muenster, Institut fuer Numerische und Angewandte Mathematik

Tue 18 May 2010, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
WMAX 216

Theory and Applications of BangBang and Singular Control Problems

WMAX 216
Tue 18 May 2010, 12:30pm2:00am
Abstract
We consider optimal control problems with control appearing linearly. The evaluation of the Pontryagin Minimum Principle shows that optimal controls are composed of bangbang and singular arcs. Values of bangbang controls switch discontinuously between their upper and lower bounds, whereas singular controls can take values in the interior of the control region. The optimal control problem induces a finitedimensional optimization problem with respect to the switching times between bangbang and singular arcs. The arcparametrization is an efficient method for solving the induced optimization problems and allows to check secondorder sufficient conditions (SSC). It can be shown that SSC for the induced optimization problem and a regularity property imply SSC for bangbang control problem. SSC for singular control problems require stronger conditions which are currently under investigation. SSC constitute the basis for a parametric sensitivity analysis and the development of realtime control techniques. Several examples illustrate theory and numerics: optimal control of (1) a VanderPol oscillator, (2) a semiconductor laser, (3) a batch fermentation process and (4) chemotherapy of HIV.
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Mon 31 May 2010, 2:45pm
SPECIAL
Math 125

Graduation Reception for Class of 2010

Math 125
Mon 31 May 2010, 2:45pm4:00pm
Details
Special Undergraduate Awards will be presented at the beginning of the reception and refreshments will be served. This will be followed by the Niven lecture at 4:00 pm in MATX 1100.
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Stanford University

Mon 31 May 2010, 4:00pm
SPECIAL
PIMS Seminars and PDF Colloquiums
MATH ANNEX 1100

2010 Niven Lecture: The Search for Randomness

MATH ANNEX 1100
Mon 31 May 2010, 4:00pm5:15pm
Abstract
I will examine some of our most primitive images of random phenomenon: tossing coins, spinning a roulette wheel and shuffling cards. In each case, practical experiments, combined with a bit of mathematics shows that while randomness is possible, usually we are lazy and things are quite far from random. Connections problems with large scale modelling are developed.
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Seminar Information Pages
