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Fall 2013

Che, Menglu

It is well known that most information of an image is contained in its edges. Therefore capturing edges in an image is of fundamental importance in image processing. Tensor product real-valued wavelets only capture edges along the horizontal and vertical direc- tions. Hence they are only...

Fall 2010

Ashander, Jaime

Human food production activities can dominate natural systems, altering ecological and evolutionary aspects of the environment. Disease-mediated interactions are of particular concern. For example, parasites may "spill-over'' from farms to wildlife. Parasites isolated on farms can evolve...

Fall 2017

Morrill, Ryan W

In this thesis, we formulate and prove the theorem of quadratic reciprocity for an arbitrary number field. We follow Hecke and base our argument on analytic techniques and especially on an identity of theta functions called theta inversion. From this inversion formula and a limiting argument, we...

Fall 2018

Dong Yang

With the development of modern technology, researchers in various fields are equipped with powerful tools to collect ultrahigh dimensional data, where the number of features p could grow exponentially with the sample size n. It is challenging to extract useful information due to the huge number...

Spring 2019

Taylor, Mitchell A.

Suppose $X$ is a vector lattice and there is a notion of convergence $x{\alpha} \xrightarrow{\sigma} x$ in $X$. Then we can speak of an ``unbounded" version of this convergence by saying that $x{\alpha} \xrightarrow{u\sigma} x$ if $\lvert x\alpha-x\rvert \wedge u\xrightarrow{\sigma} 0$ for every...

Fall 2018

Alsemary, Haya

This thesis investigates the important statistical tool of Esscher transform with its applications in mathematical finance for various environments. This transformation was introduced by F. Esscher and it became very popular afterwards, in both actuarial sciences and finance due to its role in...

Fall 2011

Yaraee, Kate

Functional data analysis (FDA) is a fast-growing area in statistics with the aim of estimating a set of related functions or curves rather than focusing on a single entity, like estimating a point, as in classical statistics. FDA has a wide range of applications in different fields such as...

Spring 2016

Liu, Boxiao

This thesis investigates efficient and robust estimators for binomial regression models. For this purpose, I have made use of two minimum distance estimation methods developed for discrete data, namely Minimum Hellinger Distance Estimation (MHDE) and Symmetric Chi-squared Distance Estimation...

Fall 2015

Gao, Jueyu

Quantile, composite quantile regression with or without regularization have been widely studied and applied in the high-dimensional model estimation and variable selections. Although the theoretical aspect has been well established, the lack of efficient computation methods and publicly available...

Fall 2012

Lin, Xihui

Most recent studies on delay differential equations are mainly focused on local stability analysis, stability switches, and local existence of Hopf bifurcations with only one delay included, while the global existence of Hopf bifurcation and stability analysis with two delays are hardly...