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 Events
Yale
Mon 3 May 2010, 4:00pm SPECIAL
Probability Seminar
MATH 104
Entropy ideas in high-dimensional convex geometry
MATH 104
Mon 3 May 2010, 4:00pm-5:00pm

Abstract

Our primary goal is to describe a strong quantitative form of the Shannon-McMillan-Breiman theorem for log-concave 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 Brunn-Minkowski inequality of V. Milman. This is joint work with Sergey Bobkov (Minnesota).
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Helmut Maurer
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 Bang-Bang and Singular Control Problems
WMAX 216
Tue 18 May 2010, 12:30pm-2:00am

Abstract

 We consider optimal control problems with control appearing linearly. The evaluation of the Pontryagin Minimum Principle shows that optimal controls are composed of bang-bang and singular arcs. Values of bang-bang 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 finite-dimensional optimization problem with respect to the switching times between bang-bang and singular arcs. The arc-parametrization is an efficient method for solving the induced optimization problems and allows to check second-order sufficient conditions (SSC). It can be shown that SSC for the induced optimization problem and a regularity property imply SSC for bang-bang 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 real-time control techniques. Several examples illustrate theory and numerics: optimal control of (1) a Van-der-Pol 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
One Time Event
Math 125
Graduation Reception for Class of 2010
Math 125
Mon 31 May 2010, 2:45pm-4:00pm

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, 4:00pm-5:15pm

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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