Brown University Center for Statistical Sciences Seminar
Division of Biostatistics - School of Public Health, | |
Sponsored by the CV Starr Lectureship |
Abstract: There are usually two types of correlations in multivariate spatial data: correlations between variables measured at the same locations, and correlations of each variable across the locations. We hypothesize that these two types of correlations are caused by a common spatially correlated underlying factor. Under this hypothesis, we propose a generalized common spatial factor model. The parameters are estimated using Bayesian method and Markov chain Monte Carlo computing technique. Our main goals are to determine which observed variables share a common underlying spatial factor and also to predict the common spatial factor. The model is first applied to county level cancer mortality data in Minnesota to find whether there exists a common spatial factor underlying the cancer mortality throughout the state. The model is then applied to a binary soil pollution data set to indicate and map a possible common polluting source.
Brown University/ Joint Materials/Solid Mechanics Seminar Series
Abstract: Underwater pipelines and cables are protected by trenches in the seabed. One way of cutting the trenches rapidly and economically is to use a plow, and this talk describes the development of large subsea plows that make trenches 2 m and more deep. It involves some interesting large-deformation soil mechanics, and in sand there some unexpected speed effects related to rapid undrained deformation. The story takes in some excursions into nuts-and-bolts engineering, politics, the environment, business and engineering fashion.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Abstract: This talk looks at how spatio-temporal patterns are stored and recalled in the neocortex and thalamus. I will use the memory of melodies as a representative problem. Memory of melodies requires storage of long sequences of spatial patterns, representation of these sequences invariant of spatial location (i.e. invariant of frequency), recall of these sequences in novel context (e.g. a new musical key), and precise representation of pattern duration (rhythm) yet which is tolerant of tempo variation.
I will deduce logical/algorithmic structures required to implement these attributes of memory and then match these algorithms to cortical anatomy. I will propose several general principles of thalamo-cortical function derived in this manner. All would likely apply broadly throughout the neocortex.
Pop Code Seminar
PDE Seminar
Abstract: We describe a method for deriving and justifying a hierarchy of "reduced equations" for the dynamics of a scalar hyperbolic equation on thin elastic media, i.e. starting with a PDE defined on a three-dimensional domain, we will show that its solutions can be approximated by the solutions of equations defined on a two-dimensional domain, and, furthermore, there is a sequence of approximating equations, each of which afford a successively better approximation. The approach is based on ideas from Hamiltonian mechanics, and is related to Nekhoroshev theory. The work is joint with C. Eugene Wayne of Boston University.
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