Brown University --
Division of Biology and Medicine
Center for Statistical Sciences Seminar Series
Assistant Professor of Biostatistics, University of Minnesota | |
Refreshments Following Lecture |
Abstract: With accessibility to geo-coded locations where scientific data are collected through Geographical Information Systems (GIS), investigators are increasingly turning to spatial process models for carrying out statistical inference. Over the last decade hierarchical models implemented through Markov Chain Monte Carlo (MCMC) methods have become especially popular for spatial and spatiotemporal modeling, given their flexibility and capability to estimate models (and hence answer scientific questions) that would be infeasible with classical methods. However, fitting hierarchical spatial models often involves expensive matrix decompositions whose computational complexity increases exponentially with the number of spatial locations. This renders them infeasible for large spatiotemporal data sets. This commputational burden is exacerbated in multivariate settings with several spatially dependent response variables.
In this talk I will discuss approaches to multivariate spatial modeling focusing upon a predictive process formulation to handle large data sets. A predictive process is derived from the original spatial process that projects process realizations to a lower-dimensional subspace thereby reducing the computational burden. In particular, I will discuss attractive features of the predictive processs and how it seamlessly adapts to diverse modeling scenarios. A computationally feasible template that encompasses these diverse settings will also be presented.
Brown University --
Department of Physics Colloquium
Abstract: In the next decade, the abundance and spatial distribution of galaxy clusters will play a significant role in constraining cosmological parameters. To motivate why this is possible, I'll discuss a number of rather different descriptions of cluster abundances which all give the same answer: a coagulation-fragmentation model, a branching process model based on combinatorial trees, and one based on Brownian motion random walks.
Center for Fluid Mechanics Seminar
And
The Fluids, Thermal And Chemical Processes Group
Of
The Division of Engineering
Seminar Series
Emory University, Atlanta, Georgia | |
Abstract: Inspired by Purcell's fundamental investigations of swimming in viscous fluids we built a robotic granular swimmer with two rotating paddles. We investigate two types of repetitive swimming strategies, which have either one or two degrees of freedom. The strategy with one degree of freedom consists of two steps and mimics the opening and closing of Purcell's scallop. We observe that the robot using the two-step scallop stroking sequence can propel itself, which shows that unlike viscous fluids, quasi-static flows in granular media are not time reversible. The strategy with two degrees of freedom has four steps, where the rotation alternates between each paddle. The displacements using Purcell's four-step strategy are remarkably similar for granular and viscous swimming. Moreover, four-step strategies are far more effective than two-step strategies.
Brown University,
Mathematics Department,
Analysis Seminar
Abstract: #160 Let X_1, ..., X_M be independent identically distributed random variables taking values i [0,1). We discuss the analogue of the Central Limit Theorem for sums modulo 1, deriving a necessary and sufficient condition for X_1 + ... + X_M modulo 1 to converge to the uniform distribution in L1. Similar results have been shown to hold for n-fold convolutions of regular probability measures on compact Hausdorff groups, with the uniform distribution replaced by Haar measure. Our proof follows from analyzing the related Fejer series. An application is in detecting digit bias of products (Benford's Law), which can indicate whether or not certain data sets have been fabricated.
Scientific Computing Seminar
Abstract: This work concerns with numerical solutions to `Initial Boundary Value Problems' in complex multi-dimensional domains with evolving boundaries. And the main goal is to discuss the prospect of implementing the`embedded finite-difference' method to such problems.
The `embedded finite-difference' is a method, which had been applied successfully to problems with constant boundaries. The method is `geometrically flexible' and `strictly stable'. In this work, these properties are used to solve problems in evolving bounded domains, whose boundary curve/surface is given by a known smooth time dependent function with a uniformly bounded normal derivative.
An analysis of the diffusion equation is carried, in a semi-discrete setting, that allows the use of a Cartesian grid on smoothly evolving complex geometries, yet maintains the order of accuracy with an `almost strict stability'.
Numerical examples, for the diffusion equation in 1-D and 2-D are presented, and demonstrate the efficiency of the method for a 2nd and 4th order accurate schemes.
PDE Seminar
Department of Mathematics Colloquium
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