## ASU Electronic Theses and Dissertations

This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree information, committee members, an abstract, supporting data or media.

In addition to the electronic theses found in the ASU Digital Repository, ASU Theses and Dissertations can be found in the ASU Library Catalog.

Dissertations and Theses granted by Arizona State University are archived and made available through a joint effort of the ASU Graduate College and the ASU Libraries. For more information or questions about this collection contact or visit the Digital Repository ETD Library Guide or contact the ASU Graduate College at gradformat@asu.edu.

Subject
Date Range
2010 2019

## Recent Submissions

This dissertation will cover two topics. For the first, let $K$ be a number field. A $K$-derived polynomial $f(x) \in K[x]$ is a polynomial that factors into linear factors over $K$, as do all of its derivatives. Such a polynomial is said to be {\it proper} if its roots are distinct. An unresolved question in the literature is whether or not there exists a proper $\Q$-derived polynomial of degree 4. Some examples are known of proper $K$-derived quartics for a quadratic number field $K$, although other than $\Q(\sqrt{3})$, these fields have quite large discriminant. (The second known field is $\Q(\sqrt{3441})$.) …

Contributors
Carrillo, Benjamin, Jones, John, Bremner, Andrew, et al.
Created Date
2019

The close relationship between mathematics and music has been well documented in Western cultures since at least the time of the ancient Greeks. While many connections have been made between math and music over the centuries, it seems that many modern researchers have attempted to create interdisciplinary bridges between these disciplines by using mathematical principles to explain several essential aspects of music: harmony, melody, form, and rhythm. Using these established connections, in addition to several of my own, I have created an undergraduate level survey of Western music course for a population of mathematically inclined students. This approach makes music …

Contributors
Cueva, Darren Luis, Norton, Kay, Wells, Christopher, et al.
Created Date
2019

Extremal graph theory results often provide minimum degree conditions which guarantee a copy of one graph exists within another. A perfect $F$-tiling of a graph $G$ is a collection $\mathcal{F}$ of subgraphs of $G$ such that every element of $\mathcal{F}$ is isomorphic to $F$ and such that every vertex in $G$ is in exactly one element of $\mathcal{F}$. Let $C^{3}_{t}$ denote the loose cycle on $t = 2s$ vertices, the $3$-uniform hypergraph obtained by replacing the edges $e = \{u, v\}$ of a graph cycle $C$ on $s$ vertices with edge triples $\{u, x_e, v\}$, where $x_e$ is uniquely assigned …

Contributors
Oursler, Roy, Czygrinow, Andrzej, Kierstead, Hal A, et al.
Created Date
2019

Diophantine arithmetic is one of the oldest branches of mathematics, the search for integer or rational solutions of algebraic equations. Pythagorean triangles are an early instance. Diophantus of Alexandria wrote the first related treatise in the fourth century; it was an area extensively studied by the great mathematicians of the seventeenth century, including Euler and Fermat. The modern approach is to treat the equations as defining geometric objects, curves, surfaces, etc. The theory of elliptic curves (or curves of genus 1, which are much used in modern cryptography) was developed extensively in the twentieth century, and has had great application …

Contributors
Nguyen, Tho Xuan, Bremner, Andrew, Childress, Nancy, et al.
Created Date
2019

The dynamics of a fluid flow inside 2D square and 3D cubic cavities under various configurations were simulated and analyzed using a spectral code I developed. This code was validated against known studies in the 3D lid-driven cavity. It was then used to explore the various dynamical behaviors close to the onset of instability of the steady-state flow, and explain in the process the mechanism underlying an intermittent bursting previously observed. A fairly complete bifurcation picture emerged, using a combination of computational tools such as selective frequency damping, edge-state tracking and subspace restriction. The code was then used to investigate …

Contributors
Wu, Ke, Lopez, Juan, Welfert, Bruno, et al.
Created Date
2019

In the 1980's, Gromov and Piatetski-Shapiro introduced a technique called "hybridization'' which allowed them to produce non-arithmetic hyperbolic lattices from two non-commensurable arithmetic lattices. It has been asked whether an analogous hybridization technique exists for complex hyperbolic lattices, because certain geometric obstructions make it unclear how to adapt this technique. This thesis explores one possible construction (originally due to Hunt) in depth and uses it to produce arithmetic lattices, non-arithmetic lattices, and thin subgroups in SU(2,1). Dissertation/Thesis

Contributors
Wells, Joseph, Paupert, Julien, Kotschwar, Brett, et al.
Created Date
2019

In this work, I present a Bayesian inference computational framework for the analysis of widefield microscopy data that addresses three challenges: (1) counting and localizing stationary fluorescent molecules; (2) inferring a spatially-dependent effective fluorescence profile that describes the spatially-varying rate at which fluorescent molecules emit subsequently-detected photons (due to different illumination intensities or different local environments); and (3) inferring the camera gain. My general theoretical framework utilizes the Bayesian nonparametric Gaussian and beta-Bernoulli processes with a Markov chain Monte Carlo sampling scheme, which I further specify and implement for Total Internal Reflection Fluorescence (TIRF) microscopy data, benchmarking the method on …

Contributors
Wallgren, Ross Tod, Presse, Steve, Armbruster, Hans, et al.
Created Date
2019

Rabies is an infectious viral disease. It is usually fatal if a victim reaches the rabid stage, which starts after the appearance of disease symptoms. The disease virus attacks the central nervous system, and then it migrates from peripheral nerves to the spinal cord and brain. At the time when the rabies virus reaches the brain, the incubation period is over and the symptoms of clinical disease appear on the victim. From the brain, the virus travels via nerves to the salivary glands and saliva. A mathematical model is developed for the spread of rabies in a spatially distributed fox …

Contributors
Alanazi, Khalaf Matar, Thieme, Horst R., Jackiewicz, Zdzislaw, et al.
Created Date
2018

Earth-system models describe the interacting components of the climate system and technological systems that affect society, such as communication infrastructures. Data assimilation addresses the challenge of state specification by incorporating system observations into the model estimates. In this research, a particular data assimilation technique called the Local Ensemble Transform Kalman Filter (LETKF) is applied to the ionosphere, which is a domain of practical interest due to its effects on infrastructures that depend on satellite communication and remote sensing. This dissertation consists of three main studies that propose strategies to improve space- weather specification during ionospheric extreme events, but are generally …

Contributors
Durazo, Juan Alberto, Kostelich, Eric J., Mahalov, Alex, et al.
Created Date
2018

Since the seminal work of Tur ́an, the forbidden subgraph problem has been among the central questions in extremal graph theory. Let ex(n;F) be the smallest number m such that any graph on n vertices with m edges contains F as a subgraph. Then the forbidden subgraph problem asks to find ex(n; F ) for various graphs F . The question can be further generalized by asking for the extreme values of other graph parameters like minimum degree, maximum degree, or connectivity. We call this type of question a Tura ́n-type problem. In this thesis, we will study Tura ́n-type …

Contributors
Yie, Jangwon, Czygrinow, Andrzej, Kierstead, Henry, et al.
Created Date
2018