Distinguished Lectures in Mathematics
First Talk of Three Lectures on Algebra and Dynamics
Lefschetz Center for Dynamical Systems Seminar
Abstract: A relatively new technology (HF Radar) is now providing us with near-surface velocity data in littoral areas. Dynamical systems tools can be used to identify Lagrangian coherent structures which have significant influence on mixing kinematics in these littorals. we compare and apply a variety of these tools to HF radar of Monterey Bay to data from both Auguest 1997 and August 2000: those which locate a hyperbolic trajectory associated with a partical stagnation point (e.g. SP-DHT) and then grow associated manifolds, and those which use a computable criteria to immediately identify manifolds (e.g. direct Lyaponov exponent). Although HF radar offers a valuable data source, there can be a significant amount of measurement error and gaps in the data. We discuss methods for defining our dynamical system as an incomplete data set: projecting the available data onto subsets of the function space spanned by select eigenfunction and how to optimize the amplitude choice in order to minimize the error in the Lagrangian coherent structures. We will discuss some practical uses of such technology in littoral areas, such as distribution of sensor arrays and optimal release of contaminants.
Joint Pattern Theory/Statistics Seminar
Abstract: The fields of statistics and genetics share a long history of mutual benefit that has recently been reaffirmed through advances in molecular genetics, genomics, and bioinformatics. Resulting from this resurgence are cooperative connections between the fields of mathematics, statistics, computer science, and biology that are fueled by technological advances and are leading to interdisciplinary approaches to biological questions. The general complexity of the questions being asked, and magnitude of the data being generated by genetic and genomic experiments present new and challenging problems to statisticians working in this arena. Details of statistical issues and methods applied to a range of agricultural genetic/genomic experiments will be discussed as examples of the important role statistics plays in the future of biological studies.
Distinguished Lectures in Mathematics
Second Talk of Three Lectures on Algebra and Dynamics
Center for Fluid Mechanics Seminar
Abstract: An overview of ongoing research in fluid mechanics at the department of Mechanics, KTH (Stockholm) will be given as an introduction. In the past the research has been focused on basic studies of transition and turbulence, but recently more applied projects related to electro-chemistry, materials processing and paper technology have gotten more attention. More details will be given on some experimental projects dealing with fluid mechanics in paper manufacturing.
The quality of paper is strongly dependent on the flow characteristics, and one key component in the paper machine is the hydraulic headbox. Ideally the headbox should break up fiber flocs, distribute the fiber suspension uniformly over the width of the paper machine and also produce a stable two-dimensional jet. However, jet instabilities are believed to be a source for non-uniformities in the final paper. Another issue which has been considered is the possibility of re-laminarization of the strongly accelerated boundary layers in the headbox, and whether this can lead to coherent structures with a negative influence on the paper.
Brown University
Joint Solid Mechanics/Materials Science Seminar Series
Massachusetts Institute of Technology, http://web.mit.edu/~kobrinsm/www/ | |
Abstract: A distinctive characteristic of FCC metallic structures with reduced dimensionality, such as thin films and lines, is their thickness-dependent strength, which can exceed that of the counterpart bulk metal by an order of magnitude or more. The need for a thorough understanding of the mechanical behavior of these metallic structures is twofold: high levels of stress affect the reliability of current devices based on them, and the development of a new generationof applications demands controlling their strength.
To investiigate the inelastic mechanisms that determine the mechanical behavior of films and lines, and to explore the relations between strength and characteristic length scales, we performed experiments on submicron-thick Ag and Cu films on silicon substrates, as well as submicron-width Cu interconnects (lines) on substrates.
We identifited the relevant inelastic mechanisms that dictate the mechanical behavior of FCC metallic thin films and lines: diffusional creep and dislocation-mediated plasticity controlled by the thermally-activated glide of dislocations through forest dislocation obstacles. Diffusional creep was found to be dominant at high temperatures, typically above a third of the melting temperature, while dislocatin plasticity was found to be dominant at low temperatures. The activation energy for the diffusional inelastic mechanism was found to be 0.6 eV for the case of Ag films. For the dislocation-mediated inelastic mechanism, individual ``jerky-type'' dislocation-motion events were found to occur over distances on the order of 50--100 nm, which define the characteristic length scale for dislocation plasticity. The magnitude of the characteristic length scale determines the stress that the material can sustain, and reveals the true origin of the high strength of FCC metallic thin films at low temperatures. In addition, the effects that grain size and film thickness have on the characteristic length scale of dislocation plasticity were investigated to identify the origin of the thickness dependence of the strength. The derivation of a physically based constitutive equation based on the low-temperature dislocation placticity mechanism will be discussed.
Distinguished Lectures in Mathematics
Third Talk of Three Lectures on Algebra and Dynamics
Brown University Graduate School Dissertation Defense Information
Brown University Graduate School Dissertation Defense Information
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: The role of information theory in probability limit theorems and mathematical statistics is reviewed. In probability theory, I review three themes to the use of information theory. The first concerns use of a simple chain rule to identify and characterize limits of Markov chains, martingales, and information projections and associated Pythagorean inequalities for convex sets of distributions. The second concerns characterization of large deviation exponents for sample averages and empirical distributions and its relationship to conditional limit theorems in which measures of information and their derivatives provide natural proofs of convergence to the normal distribution. The thread binding these areas of probability is the use of increments of information to establish convergence and characterize the limit.
Information theory and, in particular, data compression theory provide equally important tools for mathematical statistics. Efficiency, minimax rates, Bayes asymptotics, and model selection criteria are some of the statistical topics fruitfully addressed from this perspective. We briefly discuss some results for exponential families and recent results for mixture model estimation made possible by examining increments of information. In particular, each new component in a mixture sufficiently increases the likelihood (and decreases th information divergence from a target density) to provide information divergence of order 1/K using a K component mixture.
Brown University Department of Computer Science Seminar
Refreshments will be served at 11:45 a.m. |
Abstract: Many problems in the real world which are modeled as combinatorial optimization problems are stochastic in nature, i.e. the parameters defining the problem are random variables. This fact is traditionally neglected when a combinatorial model is built. It is demonstrated with an example of the traveling salesman, that the minimal solution computed on a single (training) instance of a random problem can perform suboptimally on a second (test) instance. I present empirical evidence that certain Markov Chain Monte Carlo algorithms provide solutions which are more robust than the optimal training solution. Learning is performed by sampling a typical permutation matrix or by suitably averaging over TSP solutions.
In the second half of the talk I will derive a large deviation bound in the spirit of statistical learning theory for a class of random search algorithms demonstrating that a controlled approximation to the optimal solution of the training instance yields enhanced robustness on test instances.
(This talk summarizes joint work with Mikio L. Braun.)
The Computer Science Department is located at 115 Waterman Street
Host: Professor Franco Preparata
Scientific Computing Seminar
Abstract: I will discuss our recent progress towards creating an accurate, flexible, robust and easily adopted numerical method based on high order, nodal, unstructured, finite-element discretization. I will demonstrate the characteristics of these methods with theoretical and numerical results for the simulation of conservation laws, with particular emphasis on the solution of Maxwell's equations. Further, I will introduce a new Matlab toolkit, based on this work, which can be used for both educational and research/development purposes.
PDE Seminar
Abstract: We consider a collisionless plasma modeled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge, which is independent of time and space, is assumed. The situation in which mobile negative ions balance the positive charge as |x| tends to infinity is considered. Hence the total positive charge and the total negative charge are infinite. A local (in time) existence result will be described. Particular consideration will be given to the main difficulty that arises, which is to show that the net spatial charge density decays sufficiently rapidly as |x| tends to infinity.
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