Lefschetz Center for Dynamical Systems Seminar
Brown University Center for Statistical Sciences Seminar
Abstract: Exact, small-sample methods for categorical data are exact in term of using probability distributions that do not depend on unknown parameters. However, they are conservative inferentially, having actual error probabilities for tests and confidence intervals that are bounded above by the nominal level. We examine the conservatism for interval estimation and suggest ways of reducing it, illustrating for the binomial proportion, the difference between two proportions, and the odds ratio. We also summarize simple ways of adjusting standard large-sample confidence intervals to improve dramatically their small-sample performance. The standard intervals for proportions and their differences have poor performance, the actual confidence level often being much lower than the nominal level. Simple adjustments based on adding four pseudo observations, half of each type, perform well even for small samples with interval estimation of the proportion and the difference of independent or dependent proportions.
Center for Fluid Mechanics Seminar
Massachusetts Institute of Technology, Cambridge, MA | |
Abstract: The velocity profile of the planar jet was first obtained by Bickley, in 1937. Subsequent analysis revealed that the jet is unstable to two different modes, one symmetric and the other anti-symmetric about the jet centreline. This analysis, in combination with acoustic forcing experiments, resolved the issue of sensitive flames; a phenomenon first reported by LeComte, in 1858, and studied in ever more dramatic experiments by Lord Rayleigh.
With the advent of micro-technology it is now possible to perform a wealth of novel experiments in fluid dynamics. We here present the results of an experimental study in which MEMS micro-actuators were used to excite the instabilities of a planar jet. In contrast with earlier acoustic forcing experiments, we have been able to excite both the anti-symmetric and symmetric modes, and the results are compared with numerical stability calculations. As they progress downstream the modes are amplified, giving rise to large-scale vortices. These vortices entrain air into the jet and control the transfer of energy from large to small-scale motions, making them important considerations in combustion and mixing processes.
Brown Analysis Seminar
Applied Mathematics Colloquium
N.C. State University, Raleigh, N. C. 27695-8205, USA, e-mail: htbanks@eos.ncsu.edu | |
Abstract: In this lecture we will discuss a number of ways in which uncertainty arises in classes of inverse problems. Examples from biology and materials will be used to motivate a framework in which parameters to be estimated are treated as random variables. Detailed results from a project on modeling uncertainty in production delays in HIV pathways will be given to illustrate the ideas.
Scientific Computing Seminar
From Kinetic Theory to Fluid Mechanics | |
Abstract: Kinetic theory is based on the solution of the Boltzmann equation for the velocity distribution function of some physical system (energetic electrons, protons, atoms, etc.). The usual approach is to expand the distribution function in a product of spherical harmonics for the orientation of the velocity vector and in Laguerre polynomials in the particle energy. In the study of electron thermalization in atomic moderators, it was discovered that a new set of basis functions, "speed polynomials" dramatically increased the rate of convergence. These were subsequently used with considerable success in numerous applications.
In this talk, I will first discuss this historical aspect of the development of spectral methods with nonclassical basis functions. I will then present numerous applications of the use of nonclassical basis sets in the solution of a large class of problems in physics (Fokker-Planck equation, Poisson equation, Schroedinger equation, etc.) and in fluid mechanics.
PDE Seminar
Department of Mathematics Colloquium
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