Brown University Graduate School Dissertation Defense
Brown University, Division of Applied Mathematics | |
Lattice Differential Equations: Generic Properties and Higher Codimension Phenomena | |
Brown University Graduate School Dissertation Defense
Defense Location Will Be University of North Carolina
Brown University, Division of Applied Mathematics | |
One and Several Space Dimensions | |
Time Arranged Locally |
Lefschetz Center for Dynamical Systems Seminar
Tufts University | |
in Dynamical Systems | |
Abstract: We describe a variational principle for locating periodic orbits of first-order dynamical systems. We introduce a quantity that is a functional of the phase-space orbit and a function of the period, both unknowns, and we demand that its variation with respect to both of these dependencies vanish. The Euler-Lagrange equations corresponding to this variational principle lead to a second-order nonlinear integrodifferential equation that must be satisfied along any periodic orbit. We demonstrate that this variational principle may be used as the basis of a numerical algorithm for locating periodic orbits. We begin by applying the method to a simple model problem possessing an unstable limit cycle. We next apply the method to find unstable periodic orbits of the Lorenz equations. Finally, we show how the method can be adapted to find unstable periodic orbits of the driven, incompressible Navier-Stokes equations of viscous hydrodynamics.
Center for Statistical Sciences
Brown University
Statistics Seminar
Department of Population Health Sciences and Industrial Engineering, University of Wisconsin Medical School | |
Years from Longitudinal Cohort Data: Some Results; Some Problems | |
Abstract: A community cohort of 1430 older adults (mean initial age 64.1 years) in Beaver Dam, Wisconsin, is used here to estimate the expected number of quality-adjusted life years that a person of given sex, initial age, and initial self-rated health will accrue in the next 10 years. Members of this cohort completed the SF-36 health status questionnaire at four time points over a 10 year span; the SF-36 data were converted to SF-6D health-related quality of life utility scores for analysis. The cohort was continuously monitored for mortality over the same time period. Bayesian methods are used to simultaneously estimate parameters for a Weibull survival model and a time series of quality of life weights; these are integrated and parameter uncertainty averaged out to obtain predictive distributions for quality-adjusted life expectancy in the 10 year observation period conditioned on initial age, sex, and categorical self-rated health. The resulting model is a prototype for longitudinal determination of quality-adjusted life expectancy.
Sponsored by the Charles K. Colson Lectureship and Publication Fund
Co-Sponsored by the Bruce M. Bigelow Class of 1955 Lecture Series
Center for Computational Molecular Biology Seminar
Information Retrieval for Biomedical Text Mining | |
Refreshments will be served at 10:45 am |
Abstract: Current advances in high-throughput biology are accompanied by a tremendous increase in the number of related publications. Much biomedical information is reported in the abundant literature. The ability to rapidly and effectively survey the literature can support both the design and the interpretation of large-scale experiments, and the curation of structured biomedical knowledge in public databases. In an effort to meet these goals, a variety of text-mining methods are being applied to the biomedical literature.
This talk will briefly survey such methods, and will focus on two applications in which we use information retrieval, in non-traditional ways, to directly support biomedical discovery.
Host: Professor Sorin Istrail
Participating Departments:
Applied Mathematics, Computer Science, Ecology and
Evolutionary Biology,
Molecular Biology, Cell Biology and Biochemistry,
and Molecular Pharmacology,
Physiology and Biotechnology
Brown University,
Mathematics Department - Analysis Seminar
Biomedical Engineering Lecture Series
Associate Professor of Biomedical Engineering | |
Abstract: In recent years, the interface between blood and the vascular endothelium in microvessels has drawn considerable attention as evidence is uncovered that a macromolecular endothelial surface layer (ESL), strategically located at this interface, may serve several important functional roles in vascular physiology and pathophysiology. Direct evidence revealing the full extent of the structure in vivo was made possible using a dye-exclusion method in skeletal muscle capillaries (which is limited to microvessels less than ~15 µm in diameter), and more recently, through a method we have developed for microvessels greater than ~20 µm in diameter, which combines a detailed analysis of near-wall microfluidics in arterioles and venules with intravital fluorescent micro-particle image velocimetry (µ-PIV). From µ-PIV data of the instantaneous speeds and radial positions of fluorescently labeled microspheres (0.5 µm diameter) in an optical section through the median plane of the vessel, fluid-particle translational speeds can be inferred from a detailed three-dimensional analysis of the local microfluidics in the vicinity of the vessel wall. This velocity profile can then be used to estimate the effective hydrodynamic thickness of the ESL in vivo.
In addition to our in vivo studies, we have also applied our methods in vitro to interrogate the ESL on a confluent endothelial-cell monolayer. In light of the myriad studies that have been undertaken using endothelial cells in culture, which are intended to elucidate mechanisms of endothelial- cell function, it is essential to determine if a physiologically typical ESL can be grown and maintained on cultured endothelial cells and what the precise conditions are under which this does and does not occur. In order to make this determination, we used fluorescent µ-PIV in cylindrical collagen tubes (120 to 160 µm in diameter) steadily perfused with cell culture media and lined on their luminal surface with a confluent monolayer of human umbilical-cord vascular endothelial cells (HUVECs). Contrary to our in vivo studies, results in HUVEC-lined collagen tubes show that there is no hydrodynamically relevant ESL present within this culture system when maintained under standard cell-culture conditions. This finding broadly impacts disciplines ranging from inflammation and cell adhesion to vascular permeability and endothelial-cell mechanotransduction, where conclusions derived from studies in cultured endothelial cells, which lack the cell surface chemistry that we know to exist in vivo, must now be reconsidered.
Lefschetz Center for Dynamical Systems
Lefschetz Center Conference on
Partial Differential Equations and Fluids
April 20 -- April 23, 2006
Brown University
Joint Materials/Solid Mechanics Seminar Series
Department of Mathematical Science, Carnegie-Mellon University | |
Abstract: This talk considers finite plasticity based on the decomposition F=FeFp of the deformation gradient F into elastic and plastic distortions Fe and Fp and begins by discussing a basic misconception concerning the placement of the undistorted lattice: does it belong in the reference configuration or the relaxed configuration, or both? It is shown that the macroscopic Burgers vector may be characterized by the tensor field G=Fp Curl Fp. A natural convected rate for G associated with the evolution of Fp is introduced; the importance of this rate is that temporal changes in G --- as characterized by its convected time derivative --- may be decomposed into temporal changes in distributions of screw and edge dislocations on the individual slip systems. (This result is purely kinematical.) A discussion of defect energies dependent on the densities of these distributions is given; interestingly, corresponding thermodynamic forces are macroscopic counterparts of classical Peach-Koehler forces.
Note: There will be a dinner following the seminar.
Please contact Ms. Pat Capece at x3-1501 if you plan to attend.
Center for Computation and Visualization Seminar
Center for Computation and Technology, Louisiana State University | |
Abstract: Historically, technology and computer architecture have evolved together, mutually complementing each others advances. Underlying these developments have been transitions in execution models, the set of abstract principles that govern the structure, semantics, and operation from programming languages and compilers through runtime and operating systems, to system and micro-architectures. But over the last decade and a half we have been fixed in the dominant model, Communicating Sequential Processes or message passing even as technology has improved by at least two orders of magnitude over the same period. Most recently, power and complexities issues have forced the vendor industry to deploy multi-core components, chips with more than one processor. Severe challenges face continued growth of effective computing with system scale. This presentation will discuss the challenges to sustainable high performance computer design and describe a new class of system architectures, Long Bow, in combination with ParalleX, a new execution model providing a governing discipline to guide is structure and logical operation. Long Bow is a heterogeneous architecture with components optimized for different regimes of computational temporal locality. ParalleX address such challenges as latency, overhead, contention, and starvation within the computing framework by means of a model based on message-driven split-phase transactions coordinated by local in-memory synchronization constructs. Statistical parametric studies will be described that demonstrate that one to two orders of magnitude improved performance could be achieved by means of conventional technologies through a new class of parallel architectures and execution model.
Distinguished Lectures in Mathematics
Center for Computational Molecular Biology,
Distinguished Lecture Series
University of Southern California, Professor of Biological, Mathematical and Computer Sciences | |
Abstract: As innovative new technology, optical mapping, is used to infer the genome map of the location of short sequence patterns called restriction sites. The technology, developed by David Schwartz, allows the visualization of the maps of randomly located single molecules around a million base pairs in length. The genome map is constructed from overlapping these shorter maps. The mathematical and computational challenges come from modeling the measurement errors and from the process of map assembly.
Research Interests:: I have been using computational approaches to study molecular sequence data. With the era of genome sequencing and large-scale datasets such as from microarrays, the importance of computational methods and bioinformatics to molecular biology is certainly growing proportionally. My work concentrates on the creation and application of mathematics, statistics and computer science to molecular biology, particularly to DNA, RNA, and protein sequence data. I am the co-developer of the Smith-Waterman algorithm for sequence comparison and of the Lander-Waterman formulas for physical mapping and sequencing. I am a founding editor of Journal of Computational Biology, am on the editorial board of seven journals, and am author of the first text in this area: Introduction to Computational Biology: Maps, Sequences and Genomes.
Dr. Waterman is a Professor of Biological, Mathematical and Computer Sciences at the University of Southern California. He is a Member of the National Academy of Sciences and a Member of the French Academy of Sciences.
Distinguished Lectures in Mathematics
<--- 2006 Index