Probability and Statistics Seminar
Abstract: To understand how the brain processes information, it is often necessary to search for neural activity that exhibits certain patterns. This is in particular important for the study on the mechanisms of sleep. The problem can be formulated as detection of patterned clusters of points (``targets''). I will describe pattern detection for point processes, considering respectively short and long targets which require different probability models. The models give rise to many probability problems and I will present some results on large deviations. The application of pattern matching will be illustrated, including a phenomenon of sleep ``preplay'', besides the well-known phenomenon of sleep ``replay''.
Brown University --
Joint Materials/Solid Mechanics Seminar Series
Johns Hopkins University, Baltimore, MD 21218, USA | |
Abstract: Determining the regions where solids contact plays a central role in studies of adhesion, friction, lubrication and wear. For example, the adhesive and frictional forces between two solids arise from regions where their atoms are close enough to interact. The area and geometry of these contacts affects the stiffness and electrical and thermal conductivity of the interface, and is determined by elastic and plastic deformation that extends well below the surface. This deformation may lead to local heating and wear that limits the useful lifetime of sliding contacts. Not surprisingly, the practical importance of contact has motivated many theoretical studies. Recent advancements in computational methods and power permit to shine new light on the development of contact regions and associated deformation mechanisms.
After a brief historical review of previous work, starting from the original work of Hertz (1882), this presentation focuses on a finite-element analysis of contact between rough elasto-plastic solids. The roughness is modeled with a self-affine fractal surface. The calculations are conducted within an explicit dynamic Lagrangian framework. The elasto-plastic response of the material is described by a J_{2} isotropic plasticity law. Parametric studies are used to establish general relations between contact properties and key material parameters. Scaling laws are proposed. The results are contrasted with contact models for purely elastic solids. The "equalizing" effect of plastic deformation with respect to different rough surfaces is discussed.
Cognitive & Linguistic Sciences
Spring 2005 Colloquium & CG233 Speaker
Brown University -
Division of Biology and Medicine
Center for Statistical Sciences Seminar Series
Abstract: The analysis of dose response studies has long been divided according to two major strategies: multiple comparison procedures and model- based approaches. The model-based approach assumes a functional relationship between the response and the dose, taken as a quantitative factor. Such an approach provides flexibility and insight into the dose-response mechanism, but the validity of its conclusions will depend on the correct specification of the dose-response model. Within the regulated drug development environment, in which it is required that analysis methods be defined prior to data collection, this often poses a problem. Multiple comparison procedures, on the other hand, regard the dose as a qualitative factor and make very few, if any, assumptions about the underlying dose-response model. Such procedures are relatively robust to the underlying dose-response shape, but are not designed for extrapolation of information beyond the observed dose levels and provide little insight into the dose-response relationship.
This talk describes a unified strategy for the design and analysis of dose-response studies which combines multiple comparison and modeling techniques. A candidate set of possible dose-response models is identified and multiple comparison techniques used to choose the one that best represents the true underlying dose-response curve, provided it achieves statistical significance. The selected model, if any, is then used for dose selection, using modeling techniques. The methods will be illustrated with data from a phase II dose-finding study and simulation results.
Joint work with Frank Bretz and Michael Branson.
Stochastic Systems Seminar
Abstract: Classical occupancy problem centers on the distribution of empty urns after throwing $r$ balls into $n$ urns. In the large deviation regime, the interesting quantities can be the probability of having exceptional small number of urns empty, or having exceptional large number of urns empty. In this talk, refined large deviation asymptotics will be derived for these problems. Such asymptotics will be given in explicit formulas that provide more accuracy and are easy to compute. The results are established for a sequential filling experiment and an occupancy experiment. In the first case the random variable of interest is the number of balls required to fill a given fraction of the urns, while in the latter one, a fixed number of balls are thrown and random variable is the fraction of nonempty urns.
Probability & Statistics Seminar
Abstract: Suppose we have two random vectors $(X_{1}, . . . , X_{n})$ and $(Y_{1}, . . . , Y_{n})$, and a smooth function $f : R^{n} --> R$. Under what conditions can we say that $f(X_{1}, . . . , X_{n})$ and $f(Y_{1}, . . . , Y_{n})$ are close in distribution? The speaker will describe a general approach to handling such problems (including cases where the variables are not independent), based on an extension of Lindeberg's proof of the CLT. Specific applications to permutation statistics and random matrices will be worked out.
Special Colloquium
PLEASE NOTE SPECIAL DAY AND TIME FOR THIS WEEK ONLY! |
Brown University Center for Statistical Sciences Seminar
School of Public Health, University of Minnesota | |
Abstract: A recent biotechnology advance is the use of chromatin- immunoprecipitation (ChIP) microarray experiments to conduct genome-wide location analysis. Due to high noise and often a small number of replicates in a ChIP experiment, it is difficult to reliably detect all genuine binding sites of a transcription factor by analyzing DNA-protein binding data alone. An alternative is to take advantage of the existence of other sources of data in an integrative analysis. In our motivating example, a ChIP experiment was conducted to detect binding sites of a broad transcription regulator, leucine responsive regulatory protein (Lrp) in E. coli. In addition, a cDNA microarray dataset is available to compare gene expression of the wild type with that of a mutant with the Lrp gene deleted in E. coli. It is biologically reasonable to assume that genes with altered expression are more likely to be regulated by Lrp than genes with no expression changes. Hence there is information contained in the genes expression data for the binding sites of Lrp.
We propose a novel joint model of protein-DNA binding data and gene expression data that links the two sources of data together. We adapt a nonparametric empirical Bayes (EB) method to draw statistical inference in the joint model. We use simulated data to demonstrate the improved performance of the proposed joint modeling approach over that of other approaches, including using binding data or expression data alone, taking an intersection of the results from the two separate analysis, and a sequential Bayes method that inputs the results of analyzing expression data as priors for the subsequent analysis of binding data. Application to the Lrp data also shows better performance of the joint modeling than that of analyzing the binding data alone. This is joint work with Yang Xie of Biostatistics and Kyeong S. Jeong and Arkady Khodursky of Biochemistry of U of M.
Scientific Computing Seminar
Abstract: One of the main difficulties one comes across while solving nonlinear time-dependent PDEs numerically is the loss of smoothness -- the solution may develop discontinuities even if the initial data are smooth. For conservation laws, for instance, possible nonsmooth solutions are shocks, rarefaction waves, and contact discontinuities.
Most popular shock-capturing numerical methods are nonoscillatory high-order finite-volume methods. These methods provide a sharp resolution of shock waves and rarefaction corners, but typically smear contact discontinuities due to numerical diffusion. Such a smearing may be unacceptable in certain circumstances, especially when a system of conservation or balance laws is coupled with a nonlinear transport equation as, for instance, in numerical simulations of transport of a passive pollutant or compressible inviscid reacting gases. The presence of a numerical dissipation in finite-volume methods may not only seriously degrade the quality of computed the solution but also lead to nonphysical states, which in turn, may completely destroy the solution.
We introduce a new hybrid finite-volume-particle method whose core idea is to use a finite-volume method to numerically integrate a system of conservation (balance) laws and a particle method to solve transport equations coupled with the system. This way the specific advantages of each scheme are utilized at the right place. Particle methods applied to transort equations, can ameliorate most of the problems posed by the presence of numerical viscosity since particles provide a non-dissipative approximation of the convection. The proposed hybrid method has been tested on a series of one- and two- dimensional numerical examples. The results clearly demonstrate the enhanced resolution and improved quality of the computed solutions and thus establish a great potential of the method.
This is the joint work with Alexander Kurganov, Tulane University.
<--- 2005 Index