Special Seminar
Mathematical/Computational Biology
Abstract: Knots and links in things as diverse as the slime eel to the very molecule that codes for life: DNA. Why are knots so important in DNA? And what role can mathematicians play in undertanding them?
Today I will partially answer these questions by giving an example where knot theory, when properly translated, has helped answer a question in molecular biology. In particular, I'll illustrate how an action of a particular protein can be translated into the 3-manifold notion of Dehn Surgery. Using a combination of biochemical and topological techniques, we can infer the local geometry of the DNA when bound, and shed light on the ensuing pathway.
(No prior knowledge of molecular biology required)
Lefschetz Center for Dynamical Systems Seminar
Abstract: The study of many-body coupled systems is a problem of common interest to fluid dynamics, plasma physics, and statistical mechanics. Some examples include vortices in two-dimensional fluids, mutually interacting charged particles, and spin systems. The dynamics of these systems is self-consistent in the sense that the evolution of each member of the ensemble is determined by the collective effects of all the other members in the ensemble. In this talk we discuss a mean-field, self-consistent model that describes the weakly nonlinear dynamics of marginally stable fluids and plasmas. The model also describes globally coupled oscillators. With the model we study the role of self-consistent Hamiltonian chaos in the formation of coherent structures, and the problem of chaotic vorticity mixing in dynamically consistent fields.
Brown University Center for Statistical Sciences Seminar
Department of Epidemiology and Public Health, Yale University School of Medicine | |
* Refreshments following seminar at 167 Angell St., 2nd floor conference room. |
Abstract: Coupled with environmental factors, genes contribute to numerous human diseases and traits. While there are many epidemiological methods to assess the familial clustering of traits, few are flexible enough to accommodate interactions between covariates and familial factors. In this paper, we propose and develop a frailty model that establishes an integrated framework to evaluate familial transmission of a disease by controlling for covariate effects and conveniently testing the interactions between covariates and familial factors. We also present a peeling algorithm that dramatically reduces the computational burden. This frailty model is employed to examine the familial transmission of major subtypes of alcoholism, namely, alcohol abuse and dependence. We conclude that alcohol dependence is strongly familial whereas alcohol abuse expresses a marginally significant pattern of familial transmission. Moreover, females manifest alcoholism at a lower threshold, and there is no sex-specific familial transmission of alcoholism after adjustment for the threshold effect.
This is a joint work with Kathleen Merikangas.
Brown University
Joint Solid Mechanics/Materials Science Seminar Series
***PLEASE NOTE CHANGE IN DAY, TIME AND LOCATION - THIS WEEK ONLY
***PLEASE NOTE CHANGE IN DAY, TIME AND LOCATION - THIS WEEK ONLY |
Abstract: Anisotropic elasticity calculations were performed to estimate the intrinsic strength of dislocation reactions in both Groups VB, -VIB transition metals, and Iron. A dislocation phase space desciption is used to systematically categorize both repulsive and attractive interactions for dislocations on {110}, {112}, and {123} slip planes: reducing the number of unique interactions from 1176 to<= 24. The phase space description extends previous work on dislocation junction formation reactions to encompass more general interactions including glide and climb. The theory of ``rational'' dislocation elements, (simultaneously proposed by both Eshelby and Indenbom) is used as a framework to evaluate the elastic interaction energy, including self-energies, of individual "elements" of the dislocation network. Pair-wise phase space interaction diagrams form a basis for evaluating collective dislocation behavior in a statistical manner (similar to network models in polymer physics). As expected, the regions of phase space where isolated dislocations are strongly attractive coincide with the previously determined junction formation regions. Examination of the diagrams reveals that certain dislocation configurations are relatively "transparent" to each other while others are much more "opaque", forming junctions. The calculations form a critical link between microscale phenomena of dislocation interaction and the formulation of stochastic models of crystal plasticity by establishing a taxonomy of dislocation interactions. The resulting catalog provides estimates of the strength of dislocation reactions, imposes certain symmetry restrictions for physics-based hardening models, and suggests specific latent hardening experiments to measure the influence of dislocation interactions on the work hardening of BCC metals.
This work is performed under the auspices of the U.S. Department of Energy and Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.
Center for Fluid Mechanics Seminar
Abstract: Direct numerical simulations have recently emerged as a viable tool to understand finite Reynolds number multiphase flows. The approach parallels direct numerical simulations of turbulent flows, but the unsteady motion of a deforming phase boundary add considerable complexity. Here, studies of flows containing many bubbles are presented. The Navier-Stokes equations are solved by a finite difference/front tracking technique that allows the inclusion of fully deformable interfaces and surface tension, in addition to inertial and viscous effects. A parallel version of the method makes it possible to use large grids and resolve flows containing a few hundred bubbles. Simulations of the motion of two- and three- dimensional finite Reynolds number buoyant bubbles in a periodic domain have shown, for example, that finite Reynolds number effects are important even at 0(1) Reynolds numbers, how the small scale structure changes as the Reynolds number is increased, and how the large scale evolution can be affected by a relatively small increase in the deformability of the bubbles. The extension of the methodology to problems involving the effects of thermal and electric fields, solidification and boiling will also be discussed.
Special Seminar
Mathematical/Computational Biology
Abstract: Understanding how the brain constructs movements remains a fundamental challenge in neuroscience. The brain may control complex movements through flexible combination of basis functions, where each basis is an element of computation in the sensorimotor map that transforms desired limb trajectories into motor commands. I will present theoretical and computational work revealing how basis functions can shape performance. Controllers that rely upon wide and sparse bases to estimate environmental forces generalize information across movement space and are therefore computationally efficient. These wide bases, however, limit the ability of th controllers to learn complex environments and to closely follow desired trajectories; wide bases also make controllers more sensitive to perturbations in training. Human subjects display all three of these limitations. Humans also produce errors that closely correlate with errors of simulated controllers that rely on wide bases; these correlations indicate that people may indeed use wide basis functions as building blocks to estimate environmental forces. Recent primate neurophysiological recordings suggest a brain region that could represent individual basis functions and another region that could represent the adaptive sum of bases; in between these regions could reside the locus of learning novel dynamic environments.
Brown Analysis Seminar
PDE Seminar
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