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Fall 2013

Keating, John William

This thesis introduces a new temporally second-order accurate direction-splitting scheme for implicitly solving parabolic or elliptic partial differential equations in complex-shaped domains. While some other splitting schemes can be unstable in such domains, numerical evidence suggests that the...

Fall 2016

Fedoruk, John P

In an increasingly data-driven society, there is a growing need to simplify high-dimensional data sets. Over the course of the past three decades, the Johnson and Lindenstrauss (JL) lemma has evolved from a highly abstract mathematical result into a useful tool for dealing with data sets of...

Fall 2012

Kroll, Jeffrey P

This thesis is interested in the topological recursion first introduced in \cite{CEO} and generalized to algebraic curves in \cite{Eynard:2007,Eynard:2008}. A presentation of the Hermitian matrix model is given and includes a derivation of this topological recursion. The second part introduces a...

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 2014

Chi, Michael

Solar updraft towers offers a simple and alternative method of generating electricity. However, it is unclear on how to build a tall, free standing structure that can withstand the unpredictable and destructive force of the wind. A tower consisting of stacked inflatable toroidal elements have...

Fall 2018

Rhodes, Adam R

Metastasis - the spread of cancer from a primary to a distant secondary location - is implicated in over 90% of all cancer related deaths. Despite its importance in patient outcome, a full understanding of the metastatic process remains elusive, largely because of the difficulty in studying the...

Fall 2015

Kang, Jiayin

In this thesis we organize the contents in three parts. The first part is about portfolio rebalancing with changing benchmarks and the second part is about modeling of fractional Brownian motion in financial market while the last part is the conclusion. In the first part, we introduce...

Fall 2020

Davies, Colleen M

Ecological stoichiometry is a framework that allows explicit consideration of nutrient restrictions on growth, and can be used to answer important ecological questions. First, we consider the impact of the turnover rate of producer biomass on ecosystems, since it is usually much faster in aquatic...

Spring 2014

Li, Hao

It is well known that the normal return estimation for financial asset prices is defective. In order to find better models to estimate the prices behavior of financial assets, people need probabilistic distribution that can capture fat-tails, non-constant moments, etc. This thesis find some...

Fall 2013

Zhang, Xuechen

Various analytical methods are available to analyze repeated measures data for both continuous and discrete data. In the case of discrete data, most methods are based on the assumption of asymptotic normality, requiring large samples. Naturally, their small sample performance may not match the...