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Fall 2014

Shi, Qian

This thesis develops an efficient quantile-adaptive framework for linear and nonlinear variable screening with high-dimensional heterogeneous data. Inspired by the success of various variable screening methods, especially in the quantile-adaptive framework, we develop a more efficient variable...

Fall 2021

Farkhutdinov, Tagir

In this thesis, I developed the ideas of applying the variational method in geometric mechanics to the porous media described as solid elastic materials with embedded ideal (incompressible) fluid, also known as Eulerian fluid. The work includes four chapters and a conclusion. In the Introduction,...

Fall 2010

Pivovarov, Peter

This thesis is based on three papers on selected topics in Asymptotic Geometric Analysis. The first paper is about the volume of high-dimensional random polytopes; in particular, on polytopes generated by Gaussian random vectors. We consider the question of how many random vertices (or ...

2004

Liu, Songtao

Spring 2016

Wang, Xingpu

In this thesis, we first introduce two basic problems of filter, the nonlinear filtering and model selection problem. We show that both of them can be solved by the unnormalized filter approach. Then several web based particle filter algorithms will be discussed. We extend the resampled and...

Fall 2013

Feng, Han

One of the main aims in this thesis is to establish analogues of the classical Hardy-Littlewood-Sobolev (HLS) inequality for weighted orthogonal polynomial expansions (WOPEs) on the unit sphere, the unit ball and the simplex. An optimal condition for which this inequality holds is obtained....