Lefschetz Center for Dynamical Systems Seminar
Abstract: We ask whether a given steady state is stable or not. The three physical systems are a collisionless plasma, a semiconducting material and a surface water wave. Each system is modeled by a hyperbolic equation with or without dissipation.
Brown University
Center for Statistical Sciences Lecture Series<
Seattle, Washington | |
Do Combination Tests Improve Detection? | |
Abstract: In early detection of disease, panels of biomarkers promise improved discrimination over tests based on single markers. For example, in prostate cancer screening, additional markers, such as percent free PSA and complexed PSA, have been proposed to improve the specificity of the standard PSA-based test. Similarly in predicting disease recurrence after a prostate cancer diagnosis, additional biomarkers are being sought to improve the performance of available nomograms.
When considering a panel of biomarkers, and-or combinations of conditions on each biomarker, called logic rules, provide an intuitive and meaningful way to construct tests for use in clinical practice. For example, tests combining PSA, which increases in men with cancer, and percent free PSA, which falls in men with cancer, have generally been of the form: IF (PSA>c1 OR (PSA>c2 AND percent free PSA < d )), then test positive. We refer to tests of this type as logic rules.
In this seminar, we present a statistical framework for identifying logic rules that are likely to perform well, and evaluating their performance. Our methods extend classical measures of diagnostic accuracy, like Receiver Operating Characteristic (ROC) curves and the areas under these curves, to logic combinations of markers. The resulting ROC framework allows us to compare tests and identify covariates associated with test performance.
We use this framework to analyze data on free, complexed and total PSA among 429 prostate cancer cases and 1,640 controls who participated in the Physicians' Health Study. Although the different tests (total PSA, complexed PSA, and the logic rule combining total and percent free PSA) show similar overall diagnostic performance, the ROC curves indicate that there exist combination tests with both lower false-positive and higher true-positive rates than the standard PSA-based test. Given the wide prevalence of PSA testing in the population, we conclude that use of the combination test could translate into a practically important reduction in unnecessary biopsies without sacrificing cancers detected.
This is joint work with Margaret Pepe, Charles Kooperberg, Seth Falcon, Peter Gann and Meier Stampfer
**Sponsored by the Charles P. Sisson II Memorial Lectureship
***Co Sponsored by The Marshall Woods Lectureships Foundation of
Fine Arts
Brown University
Joint Materials/Solid Mechanics Seminar Series
And Consulting Professor, Stanford University | |
Abstract: Stroh, in 1958 and 1962, developed an elegant and powerful formalism for treating two-dimensional problems involving dislocations, line forces and steady state waves in anisotropic elastic solids. The formalism is well known in the physics and materials science community but (until the last six years or so) is rarely employed by the mechanics community. There is a wide spread and justifiable misconception among the mechanics community that (i) one must know theory of isotropic elasticity before studying anisotropic elasticity and (ii) the analysis of problems in anisotropic elasticity is much more difficult and complicated than those in isotropic elasticity. Nothing could be further from the truth if one employs the Stroh formalism. The analysis of two-dimensional deformations for anisotropic elastic solid is simpler than that for isotropic elastic solid because isotropic elastic solid is, mathematically, a {\it degenerate} material. A mathematically degenerate problem usually requires {\it more} effort in obtaining the solution. Besides its elegance, the Stroh formalism allows one to convert a complex-form solution to a real form. As a result, many interesting and physically puzzling phenomena that have been shrouded in complex-form solutions have been discovered. Some of the results are unexpected even for isotropic elastic solids. Examples that will be presented are: invariance of certain aspects of the solutions; image singularities of Green's function; singularity-free anisotropic elastic solids; one-component surface waves; solutions that have only one displacement component; uncoupling of inplane and antiplane stresses but not inplane and antiplane displacements, and vice versa; and no bounds for Poisson ratios in anisotropic elastic solids. As it turns out, isotropic elastic material in {\it not} the most degenerate material of all anisotropic elastic materials.
Center for Fluid Mechanics Seminar
Virginia Polytechnic Institute and State University, Blacksburg, VA | |
Abstract: Near wall measurements are notoriously challenging and complicated. Understanding the structure of the flow near the wall is of paramount importance for a number of applications ranging from viscous drag to the regulation of the endothelial cell function on the arterial walls. Our understanding of the physical mechanisms associated with the wall shear stresses is hampered by the lack of accurate non-invasive measurement techniques with high spatiotemporal resolution. Moreover, the need for such measurements extends beyond the laboratory environment to full scale experiments.
This talk will be divided in two parts. First we will demonstrate the accuracy of resolving near wall turbulence and performing skin friction measurements non-invasively using Time Resolved Digital Partical Image Velocimetry with kHz sampling rates. A novel scheme for the indirect estimation of the wall shear stresses from the measured velocities will be presented. The analysis provides a framework for non-invasive measurements of skin friction using TRDPIV. The newly developed scheme improves accuracy over an extended range of length scales. The method is demonstrated through turbulent boundary layer experiments and experiments employing active flow control for viscous drag reduction.
The second part of the talk will address the development of a new class of a mini/micro sensor for direct wall shear stress fluctuation measurements. This sensor provides a unique combination of features. It can be operated in air and water or multi-phase flow environments, it is non-invasive and flush mountable, immune to vibration and pressure effects and more importantly delivers high sensitivity, high frequency response and fluctuating wall shear measurement accuracy better than 4%. Calibration issues, accuracy and application of the sensor to turbulent boundary layer flow will be presented.
Stochastic Systems Seminar
Brown Applied Mathematics Pattern Theory and Vision Seminar
Brown Analysis Seminar
Brown University Center for Statistical Sciences Seminar
Conference Room 106 (Coffee at 3:50 p.m.) |
Abstract: In many prospective studies, participants are evaluated for the occurrence of an absorbing event of interest (e.g., HIV seroconversion) at baseline and a common set of pre-specified visit times after enrollment. Since participants often miss scheduled visits, the underlying visit of first detection may be interval censored, or more generally, coarsened. Interval-censored data are usually analyzed assuming non-informative censoring, a special case of coarsening at random (CAR).
We posit a class of models for the event-time distribution that loosen the CAR assumption and use the EM algorithm for estimation. To perform inference on the estimated survivor functions, we propose an extension of the logrank test utilizing the EM-based estimates. We extend this methodology to estimate regression parameters for a discrete-time proportional hazards model with a low-dimensional covariate. Since CAR is usually not testable and often scientifically implausible, estimation is performed by incorporating elicited expert opinion about the relationship between event times and visit compliance into the model. The procedures are illustrated using data from the AIDS Link to the Intravenous Experience (ALIVE) study, an observational study of HIV infection among injection drug users in Baltimore, Maryland. Performance of our method is assessed via simulation studies.
Geometry and Topology Special Seminar
Abstract: In joint work with Scott Sheffield and Andrei Okounkov, we study a simple 2D statistical mechanical model, the dimer model, which can be used to model crystal surfaces. The exact solution involves computing the spectrum of a certain discrete operator, the Kasteleyn operator, on an underlying planar graph. The phase space of the system turns out to be the "amoeba" of an associated two-variabele polynomial.
Center of Computational Molecular Biology
Fall 2004 Lecture Series
Please Note Change in Place, Day and Time for this Week Only |
Abstract: The exciting results emerging from comparative analyses of whole genomes have highlighted the need for rapid and accurate multiple alignment techniques. Although there is a history of research on multiple alignment algorithms, the scale of current problems are beyond the reach of many methods. We will review some recent approaches to whole genome multiple alignment, and discuss some methods we have developed. In particular we will focus on a new approach for parametric alignment that can be used to test the robustness of alignments to parameter changes.
Participating Departments:
Applied Mathematics
Computer Science
Ecology and Evolutionary Biology
Molecular Biology, Cell Biology and Biochemistry
Molecular Pharmacology, Physiology and Biotechnology
PDE Seminar
Department of Mathematics Colloquium
Abstract: This is joint work with Andrei Okounkov. We consider a natural family of models of crystalline surfaces in R^3 arising in the planar dimer model (random domino tiling model). For fixed boundary conditions, the law of large numbers leads to a PDE for the limit shape (when the lattice spacing tends to zero) of the surfaces. This PDE is a variant of the complex Burger's equation and can be ``solved'' analytically. This is surprising since the surfaces generically have both smooth parts and facets. The interplay between analytic (even algebraic) functions and facet formation in the surfaces leads to some interesting questions in real algebraic geometry.
<--- 2004 Index