Wednesday, May 24, 2006

Bright lights


Alumni in tha house
I've noticed a number of potentially fun talks scheduled for this week, that is, they're closely related to things I'm currently interested in. I went to one last week that was potentially interesting and yet just somehow not magical enough, hence I'm attending none of this week's.

What does it say that I go to lectures to be entertained...when so many other people are at "work."

I've stubbornly insisted on being thrilled at school, and have often been. in love.
with a book.
with a class, so much that I couldn't wait to see my Prof. again.
with the "story" of a field: what it's useful for, or the context in which it was developed by people, how it answers a question that i've had, how it opens my eyes to something new, or to a new trick in thinking.

The lecture announcements:
DATE: May 24 (Wednesday)
and May 26 (Friday)
TIME: 12:00--1:00PM
LOCATION: 110 Steele
Pablo A. Parrilo
EE & CS, Massachusetts Institute of Technology
SOS-based computational methods for polynomial games

In the last few years, techniques based on sum of squares (SOS) decompositions of multivariate polynomials, semidefinite programming (SDP), and results from real algebraic geometry have proved extremely useful in the formulation of hierarchies of convex relaxations for difficult polynomial optimization problems. In this talk we show how these can be extended to a game theoretic setting.
In particular, we discuss a class of zero-sum two-person games with an infinite number of pure strategies, where the payoff function is a polynomial expression of the actions of the players. We show that the value of the game, and the corresponding optimal strategies, can be computed by solving a single semidefinite program, thus providing a natural generalization of the well-known LP characterization of finite games. We also discuss the possible extensions to correlated equilibria, and to the nonzero sum case. In addition, we show how the results can be applied, with suitable modifications, to a general class of semialgebraic games and problems with two quantifiers.

Wednesday's lecture will be more introductory in nature, and discuss the basic setup of separable games and SOS/SDP methods. On Friday, we will put these basic elements together and discuss some further extensions.

BIO:Pablo A. Parrilo received an Electronics Engineering undergraduate degree from the University of Buenos Aires, and a Ph.D. in Control and Dynamical Systems from the California Institute of Technology in 1995 and 2000, respectively. He has held short-term visiting appointments at the University of California at Santa Barbara (Physics), Lund Institute of Technology (Automatic Control), and UC Berkeley (Mathematics). From October 2001 through September 2004, he was Assistant Professor of Analysis and Control Systems at the Automatic Control Laboratory of the Swiss Federal Institute of Technology (ETH Zurich). He is currently an Associate Professor at the Department of Electrical Engineering and Computer Science of the Massachusetts Institute of Technology, where he is affiliated with the Laboratory for Information and Decision Systems (LIDS) and the Operations Research Center (ORC).

Prof. Parrilo is the recipient of the 2005 Donald P. Eckman Award of the American Automatic Control Council, as well as the triennial SIAM Activity Group on Control and Systems Theory (SIAG/CST) Prize. He was also a finalist for the Tucker Prize of the Mathematical Programming Society for the years 2000-2003.

His research interests include optimization methods for engineering applications, control and identification of uncertain complex systems, robustness analysis and synthesis, and the development and application of computational tools based on convex optimization and algorithmic algebra to practically relevant engineering problems.


2. CDS Seminar: Wednesday, May 24, 2006
Time: 2pm-3pm
Location: 070 Moore
Distributed Coordination and Consensus algorithms with boundary:from flocking and synchronization to geographic routing in adhoc networks

Ali Jadbabaie
University of Pennsylvania

In this talk we provide a unified view of several distributed coordination and consensus algorithms which have appeared in various disciplines such as distributed systems, statistical physics, biology, computer graphics, robotics, and control theory over the past 2 decades. These algorithms have been proposed as a mechanism for demonstrating emergence of a global collective behavior (such as social aggregation in animals, schooling, flocking and synchronization) using purely local interactions. Utilizing tools from spectral graph theory and control and dynamical systems theory, we provide an analysis of these algorithms.
Furthermore, we show that by imposing fixed boundary conditions (e.g., designating a leader in a swarm) , one can obtain algorithms for a wide range of applications, from leader-follower swarms to synchronization in oscillator networks, and from shortest path routing to geographic routing without location information.
Finally, we describe a one-parameter family of distributed consensus algorithms with boundary conditions, which at one extreme, recovers the well-known Bellman-Ford Algorithm for shortest-path routing, and at the other, results in a routing scheme based on diffusion, and mean-first passage times. Connections between these algorithms and harmonic functions, electric networks, and discrete Dirichlet problems are also discussed.

Ali Jadbabaie got his BS from Sharif University of Technology in in 1995. He received a Masters degree in Electrical and Computer Engineering from the University of New Mexico, Albuquerque in 1997 and a Ph.D. degree in Control and Dynamical Systems from California Institute of Technology (Caltech) in June 2001. From July 2001-July 2002 he was a postdoctoral associate at the department of Electrical Engineering at Yale University. Since July 2002 he has been an assistant professor in the department of Electrical and Systems Engineering at the University of Pennsylvania. He is a recipient of an NSF Career Award, an ONR Young Investigator award, and the George S. Axelby Outstanding Paper Award of the IEEE Control Systems Society.


Francois Lekien
Mechanical and Aerospace Engineering
Princeton University

May 25, 12 noon
114 Steele (CDS Library)

In autonomous and time-periodic dynamical systems, transport and mixing can be studied using the stable and unstable manifolds of hyperbolic fixed points and periodic orbits. Numerous experiments have revealed the presence of similar coherent structures in aperiodic systems. These mixing templates are usually invisible to the naked eye but can be extracted, for example, by computing finite-time Lyapunov exponents or finite-time hyperbolic invariant manifolds. These structures indicate alleyways and barriers to transport and provide a geometric description of the mixing processes in the system. In recent years, there has been much effort in applying this methodology to the study of mixing in fluids and geophysical flows. Indeed, these systems are strongly aperiodic and do not have, in general, fixed points or periodic orbits.

In this talk, I will describe fluid transport in Monterey Bay. High-frequency radar stations provide current measurements in real-time for the bay and permit the computation of dynamical barriers and alleyways in this complex system. The coherent structures reveal the existence of optimal release windows in which contaminants can be efficiently advected away from the coast, reducing their negative impact on the marine environment. In addition, the alleyways can be used to optimize the deployment of drifters and the routes of underwater vehicles to maximize coverage of an area. Transport and mixing near a coastline can also be studied in terms of separation and re-attachment profiles attached to the boundary. I will discuss how to obtain exact criteria to detect and control separation points and related separation profiles in Monterey Bay. Jet-actuated systems can control their separation points to a desired location and fine-tune the lift on an airfoil, or transport fuel efficiently along separation profiles. For drifters and underwater vehicles in the ocean, weak actuators, such as a rudder or a deformable rogue, can be used to control the effective separation points seen by the vehicle. Such controllers do not "fight the currents". They take advantage of the strong hyperbolic structures that are present in the ocean, require less energy, and increase the time that the vehicle spends at sea.

I'm skipping the talks and going outside to browse a too-advanced math book. The book ends in a historical sketch of the field written by the the author. (anticipation. yay.)
I may also find and interact with humans in an exciting way.

On Love and Marriage
Movies you should watch, if you care to:
Houseboat and Friends with Money
These movies have very little acting, that is to say, the performances in them are very good: mature, natural, smooth, untheatrical.

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