Physical Sciences and Mathematics Commons^™

Optimization Strategies For Political Redistricting, Blake Splitter

All Dissertations

Political redistricting has remained a hot-button issue in the United States for several decades. Every ten years, most states need to redraw their districts to account for changing populations. Sometimes, these district plans can be drawn with the malevolent intention of aiding one political party over another. This dissertation summarizes four distinct methods of drawing these districts using computer algorithms while keeping several objectives in mind. We test these approaches on the case study state of South Carolina, since it provides a sufficiently challenging problem for us to test various algorithms. We find that many of these approaches improve upon …

Optimization Strategies To Enhance Performance In Matrix/Tensor Factorization And Multi-Source Data Integration, Mengyuan Zhang

All Dissertations

Optimization in the realm of machine learning constitutes a fundamental process aimed at refining the parameters of models to enhance their performance. It serves as the backbone of various machine learning techniques, encompassing diverse algorithms and methodologies tailored to address specific tasks and objectives.

In machine learning, datasets are commonly structured as matrices or tensors, making techniques like matrix factorization and tensor factorization indispensable for extracting meaningful representations from intricate data. Furthermore, datasets commonly comprise multiple sets of features, which has inspired our exploration of effective strategies for leveraging information from diverse sources during optimization. Additionally, the interconnected nature of …

Some Experiments In Additive Number Theory, Yunan Wang

All Dissertations

This dissertation explores fundamental conjectures in number theory, focusing on the distribution patterns of representation functions in prime pairs. The work concentrates on twin primes, cousin primes, and primes separated by six units, offering a fresh heuristic interpretation of the Hardy-Littlewood correction factor. The analysis progresses to investigate the partition function for prime pairs in the form $(p, p+k)$, specifically for $k = 2, 4, 6$. The study culminates in the derivation of a general formula for prime pairs $(p, p+d)$, where $d$ is an even integer. Drawing on the insights gleaned from examining the correction factor, this dissertation proposes …

We Train Ai, Why Not Humans, Too? An Exploration Of Human-Ai Team Training For Future Workplace Viability, Caitlin M. Lancaster

All Dissertations

The integration of Artificial Intelligence (AI) in the workforce is transforming team dynamics, leading to the emergence of Human-AI Teams (HATs). These teams offer opportunities to capitalize on human strengths with AI's prowess, offering significant opportunities for innovation and efficiency. Effective HAT functioning requires aligning human expectations with AI capabilities and bridging knowledge gaps between teammates. Despite this potential, key integration challenges remain, such as developing shared mental models, addressing skill limitations, and overcoming negative AI perceptions. Existing training efforts often apply human-human teaming principles directly to HATs, overlooking AI's role as a teammate and limiting the development of HAT-specific …

Relating Elasticity And Other Multiplicative Properties Among Orders In Number Fields And Related Rings, Grant Moles

All Dissertations

This dissertation will explore factorization within orders in a number ring. By far the most well-understood of these orders are rings of algebraic integers. We will begin by examining how certain types of subrings may relate to the larger rings in which they are contained. We will then apply this knowledge, along with additional techniques, to determine how the elasticity in an order relates to the elasticity of the full ring of algebraic integers. Using many of the same strategies, we will develop a corresponding result in the rings of formal power series. Finally, we will explore a number of …

Efficient First-Order Methods For Some Smooth Nonlinear Optimization Problems, Yunheng Jiang

All Dissertations

none

Physics-Informed Machine Learning Methods For Inverse Design Of Multi-Phase Materials With Targeted Mechanical Properties, Yunpeng Wu

All Dissertations

Advances in machine learning algorithms and applications have significantly enhanced engineering inverse design capabilities. This work focuses on the machine learning-based inverse design of material microstructures with targeted linear and nonlinear mechanical properties. It involves developing and applying predictive and generative physics-informed neural networks for both 2D and 3D multiphase materials.

The first investigation aims to develop a machine learning method for the inverse design of 2D multiphase materials, particularly porous materials. We first develop machine learning methods to understand the implicit relationship between a material's microstructure and its mechanical behavior. Specifically, we use ResNet-based models to predict the elastic …

Probabilistic Frames And Concepts From Optimal Transport, Dongwei Chen

All Dissertations

As the generalization of frames in the Euclidean space $\mathbb{R}^n$, a probabilistic frame is a probability measure on $\mathbb{R}^n$ that has a finite second moment and whose support spans $\mathbb{R}^n$. The p-Wasserstein distance with $p \geq 1$ from optimal transport is often used to compare probabilistic frames. It is particularly useful to compare frames of various cardinalities in the context of probabilistic frames. We show that the 2-Wasserstein distance appears naturally in the fundamental objects of frame theory and draws consequences leading to a geometric viewpoint of probabilistic frames.

We convert the classic lower bound estimates of 2-Wasserstein distance \cite{Gelbrich90, …

On Weak Solutions And The Navier-Stokes Equations, Aryan Prabhudesai

Mathematical Sciences Undergraduate Honors Theses

In this paper, I will discuss a partial differential equation that has solutions that are discontinuous. This example motivates the need for distribution theory, which will provide an interpretation of what it means for a discontinuous function to be a “solution” to a PDE. Then I will give a detailed foundation of distributions, including the definition of the derivative of a distribution. Then I will introduce and give background on the Navier-Stokes equations. Following that, I will explain the Millennium Problem concerning global regularity for the Navier-Stokes equations and share mathematical results regarding weak solutions. Finally, I will go over …

Assessing The Reactivity Of Amino Acids To Chlorination Using Capillary Electrophoresis, Pedro De Allende

Electronic Theses, Projects, and Dissertations

Amino acids (AA) are ubiquitous in wastewater systems. One of the most popular wastewater treatments is chlorination which is effective at eradicating bacteria and overall treating the wastewater, but it can also produce disinfection by-products (DBPs). Certain DBPs have been classified as Class B Carcinogens to humans and are therefore highly regulated and monitored. Past studies have shown that natural organic matter (NOM), specifically amino acids, can be precursors to DBPs if chlorinated to the correct dose. This thesis project explored AA chlorination's mechanism(s) to understand further which products arise. In particular, the investigation detailed which steps of the mechanism …

Enhancing Cybersecurity For Unmanned Systems: A Comprehensive Literature Review, Jonathan Gabriel Mardoyan

Electronic Theses, Projects, and Dissertations

This culminating experience project addresses the pressing cybersecurity challenges encountered by unmanned autonomous vehicles. The research provides a comprehensive literature review on how hybrid encryption techniques can improve the security of its communication systems. The chosen research questions guiding this study are: (Q1) How can we enhance cybersecurity measures to safeguard the communication and transmission of sensitive data from unmanned systems, thereby preventing unauthorized access by malicious actors? (Q2) How can we ensure the confidentiality and integrity of messages exchanged with unmanned systems to a command-and-control center operating on the tactical edge? (Q3) How can hybrid encryption tackle the consumption …

Methods For Improving Low Frequency Selection And Electrode Firing Order In Cochlear Implants, James H. Keen Jr.

University of New Orleans Theses and Dissertations

The Advanced Bionics cochlear implant devices allocate static frequency bins to electrode channels based on the natural tonotopic organization of the cochlea. These frequency bins are wide and limited, especially in the lower range. Considering that the fundamental tones of the human voice and the primary melodic tones in music are in this lower range, it is important to have accurate representation of this frequency content. Here, adjustments to the frequency bin allocation algorithm used in the crowdsourced CI Hackathon code are made to allow a more accurate representation of the original signal. First, the frequency bins allocated to each …

Rock Wall Fracturing As A Potential Control On River Valley Width In The Buffalo National River, Arkansas, Kindle Hon

Graduate Theses and Dissertations

Quantifying bedrock properties that control the persistence of fallen rock material (talus) along bedrock walls bounding river valleys may be a key factor in understanding what controls the rate at which these river valleys widen. My work is a component of a collaborative research project focused on the overarching hypothesis that the persistence vs. erodibility of talus that buffers river valley walls can be a first-order control on valley widening rates. I hypothesize that the primary control for creating erodible or persistent talus is the fracture spacing of bedrock valley walls as it sets the maximum block size of collapsed …

Struvite Effects On Greenhouse Gas Emissions From Flood- And Furrow-Irrigated Rice In The Greenhouse, Chandler Arel

Graduate Theses and Dissertations

Over time, as the influences of climate-change and declining, mineable, global phosphorus (P) reserves begin to impact agricultural production systems, alternative fertilizer sources and management practices, such as struvite (MgNH4PO4 · 6H2O) and furrow-irrigation, will be necessary to accommodate nutrient and water demands. The precipitation and use of struvite as a fertilizer-P source could reduce environmental damages caused by nutrient-rich wastewater streams, supplement domestic P supply, and improve the sustainability of flood-, and furrow-irrigated rice production by reducing greenhouse gas emissions. The study of struvite from both chemical and electrochemical precipitation processes is well documented, but currently there is a …

Quantum Modeling & Experimental Studies Of Radical Chemistry, Justin Michael Barrett

Graduate Theses and Dissertations

This work describes two projects centered around radical chemical mechanisms. The first investigation generalized the utility of a C-N bond homolysis followed by a [1,3] – rearrangement synthetic strategy found possible in N-alkylated thiazole & benzothiazole species onto analogous systems. Computational investigation guided the inquiry on structurally analogous systems that would favor a radical, [1,3] – rearrangement. Herein, we describe the implementation of that mechanism to transform Breslow Intermediate-like substrates into tertiary alcohol and amide products under facile conditions. We confer on the proficiency of this strategy with 2-pyridinemethanol and the problematic implementation with 2-(aminomethyl)pyridine. The second investigation solved a …

Controls On The Development Of Hummocky Topography On Debris-Covered Glaciers, Ryan M. Strickland

Graduate Theses and Dissertations

Rock debris covers many glaciers in Earth’s highest mountains and the debris impacts glacier response to changes in climate. Interactions between debris, drainage, glacier dynamics, and climate produce contrasts in melt rates that cause debris-covered glaciers to develop complex, hummocky topography. Contrasts in melt rate produce thousands of hills–hummocks–and depressions. Ponds and ice cliffs often form in the depressions. Although ponds and ice cliffs occupy only a small fraction of the surface, they account for nearly half of glacier melt. Understanding the processes that control the development of hummocky topography is key to predicting the evolution of debris-covered glaciers. In …

Investigation Of Optically Pumped Gesn Quantum Well Lasers, Grey Steven Abernathy

Graduate Theses and Dissertations

Silicon photonic integrated circuits enable the capability of producing on-chip processing of photonic signals, including both emission and detection. Emission materials, however, have been limited for monolithic integration due to high processing temperatures, indirect bandgap materials, and material integration complications. The (Si)GeSn material system has recently attracted attention due to the bandgap transition from the Si and Ge, naturally indirect bandgap, to direct bandgap with sufficient Sn incorporation. Additionally, the low growth temperature (CMOS compatible; <400 >°C) of (Si)GeSn materials can enable the monolithic integration of the highly desired mid-infrared light emission on the Si Photonic platform. This dissertation first discusses …

Investigating The Applications Of Peps To The Measurement Of The Stabilities Of Staphylococcal Nuclease (Stw) And Human Acidic Fibroblast Growth Factor (Hfgf1), Motolani Omolade Matthew

Graduate Theses and Dissertations

This dissertation presents a detailed investigation into the applications of Protein Equilibrium Population Snapshot H/D Exchange Electrospray Ionization Mass Spectrometry (PEPS-H/D exchange or PEPS) method. This method is based on protein equilibrium unfolding, and its fundamental capability is to capture a "snapshot" of the protein's state, allowing us to monitor the ratio of the unfolded to folded populations at different chemical denaturant concentrations. First, to increase the accuracy of PEPS data analysis for assessing protein stability, the traditional linear extrapolation method (LEM) was replaced. Instead of using LEM, which calculates free energy change based on the peak ratio of unfolded …

Understanding And Control Of Frustration And Topological Defects In Ferroic Matter, Suyash Rijal

Graduate Theses and Dissertations

Ferroic matter are of great importance as they provide a platform to extend the understanding of many-body physics and also for their amazing functional properties relevant for technological advancements. The work in this dissertation is dedicated to two of such ferroic materials. First is CrGeTe3 (CGT), a two dimensional (2D) magnet discovered in 2017. The discovery of two-dimensional magnetism has invigorated the research community as their low dimensionality offers a unique avenue to understand and investigate the origin of magnetism in these atomically thin systems and harvest diverse application such as information processing, storage and transfer using their magnetic spins. …

Cover-Crop Effects On Near-Surface Soil Properties Over Time In The Lower Mississippi River Valley, Cooper Fanning

Graduate Theses and Dissertations

Human population growth and climate change are present stressors that continue to put pressure on current agricultural production systems, where typical row-crop agricultural practices can negatively impact soil health. Extensive use of cover crops (CC) to increase soil health remains widely unrealized. Soil health in Arkansas is a major concern for sustaining agricultural output, therefore research into CC implementation across Arkansas to maintain or improve soil health is needed. The objective of this study was to evaluate the effects of CC (i.e., with and without CC) across various physical, hydraulic, biological, and chemical soil indicators in the Lower Mississippi River …

The Gavel And The Camera: Environmental Law And Photojournalism's Relationship To Appalachian Identity, Emily S. Patton

Honors Theses

Both the federal government and photojournalism have played a substantial role in the “othering” of Appalachia while simultaneously attempting to save it. Examining both institutions demonstrates the exploitative processes that alter the perception of rural communities and their surrounding environment. Stacey Kranitz’s archival exhibit, As It Was Give(n) To Me, internalizes this precarious role of the camera in a region heavily journalized. By inhabiting the area for years, establishing close relationships, and researching the documented history of Appalachia, Kranitz’s work becomes her livelihood in the dissolution of profession vs. personal. She is critical of past projects whose objective portrayal of …

Metal Assisted O2-Dependent Carbon-Carbon Bond Cleavage Of Β-Diketones And Flavonols, Stephen N. Anderson

All Graduate Theses and Dissertations, Fall 2023 to Present

Almost everything we interact with on a daily basis has been synthesized by chemists ranging from plastics, food preservatives, and medications. The diversity of synthetic molecules are achieved by the formation of new bonds between existing molecules and/or through the cleaving of bonds found in a molecule. There are uncountable amount of conditions reported to facilitate chemical reactions which all depend on the nature of molecules being used and the environment it is used in.

In recent years, more attention has been paid to identify chemical reactions that can use more environmentally favorable conditions and reduce the use of limited …

Hydrogen Stable Isotope Constraints On Hydration Of Colorado Plateau Lower Crust From Oligocene-Miocene Navajo Volcanic Field Xenoliths, Shelby Dianne Litton

All Graduate Theses and Dissertations, Fall 2023 to Present

Understanding flat-slab subduction is crucial as it involves the horizontal movement of an oceanic plate beneath a continental margin over a long distance. This tectonic process is widespread yet not fully understood, particularly regarding how it influences the chemical makeup of the continental plate and recycling in the hydrosphere. By analyzing isotopes, which are variations of certain elements found in minerals and water, we can gain insights into the sources of chemicals and geological processes at play. Our study area included six locations within the Navajo volcanic field (NVF), a region in the Colorado Plateau. We analyzed 23 lower crustal …

Functional Electrolytes Designing And Studying For Lithium Metal And Non-Aqueous Zinc Metal Batteries, Liping Zhang

All Graduate Theses and Dissertations, Fall 2023 to Present

Our current energy policy relies heavily on burning fossil fuels, raising serious concerns due to CO₂-related global warming. Consequently, significant progress is being made in pursuing renewable and green energy sources, such as solar, wind, and geothermal energy. These renewable energies require rechargeable batteries as energy storage systems to compensate for their intermittent nature.

Over the decades, lithium-ion batteries (LIBs) have become the dominant power sources for portable electronic devices. Current LIBs rely on graphite anodes with a limited theoretical capacity (372 mAh g^-1), which restricts their advanced applications. Li metal (Li⁰) anodes, with …

Enabling Iov Communication Through Secure Decentralized Clustering Using Federated Deep Reinforcement Learning, Chandler Scott

Electronic Theses and Dissertations

The Internet of Vehicles (IoV) holds immense potential for revolutionizing transporta- tion systems by facilitating seamless vehicle-to-vehicle and vehicle-to-infrastructure communication. However, challenges such as congestion, pollution, and security per- sist, particularly in rural areas with limited infrastructure. Existing centralized solu- tions are impractical in such environments due to latency and privacy concerns. To address these challenges, we propose a decentralized clustering algorithm enhanced with Federated Deep Reinforcement Learning (FDRL). Our approach enables low- latency communication, competitive packet delivery ratios, and cluster stability while preserving data privacy. Additionally, we introduce a trust-based security framework for IoV environments, integrating a central authority …

Convex Ancient Solutions To Anisotropic Curve Shortening Flow, Benjamin Richards

Doctoral Dissertations

We construct ancient solutions to Anisotropic Curve Shortening Flow, including a
noncompact translator and compact solution that lives in a slab. We then show that
these are the unique ancient solutions that exist in a slab of a given width.

Probabilistic And Data-Driven Methods For Numerical Pdes, Johannes Krotz

Doctoral Dissertations

This dissertation consists of three integral self-contained parts. The first part develops a novel Monte Carlo algorithm, called the near-Maximal Algorithm for Poisson-disk Sampling (nMAPS), to efficiently generate the nodes of a high-quality mesh for the calculation of flow and the associated transport of chemical species in low-permeability fractured rock, such as shale and granite. A good mesh balances accuracy requirements with a reasonable computational cost, i.e., it is generated efficiently, dense where necessary for accuracy, and contains no cells that cause instabilities or blown-up errors. Quality bounds for meshes generated through nMAPS are proven, and its efficiency is demonstrated …

Tales In The Teeth: Using Isotopic Analysis To Understand The Paleoecology And Social Behavior Of Brontotheres Of The Intermountain Basins During The Middle Eocene, John Michael Michalski

All Graduate Reports and Creative Projects, Fall 2023 to Present

Isotopic analysis has been a common practice used in paleontology to study ancient ecosystems, and the lives of animals therein. Oxygen isotopic analysis is of particular importance not only because of its use in studying paleoecology, diet, and migration, but also its use in studying mountain elevation, and its impact on ancient ecosystems. I use stable oxygen isotopic analysis to study the habits and ecology of brontotheres from intermountain basins surrounding the Uinta Mountains of Utah and Wyoming, USA. I studied the oxygen isotopes from 16 fossil specimens of teeth, most of which belonged to brontotheres, including the genera Palaeosyops …

Simulation Study On Confidence Interval Estimation For Standard Deviation With Non-Normal Distributions, Theophilus Oppong Kyeremeh

Electronic Theses and Dissertations

This study explores innovative approaches to constructing confidence intervals for the population standard deviation, σ, in non-normal data scenarios. While the sample standard deviation, s, is widely used, its reliability is compromised when dealing with skewed or heavy-tailed distributions and exhibits sensitivity to outliers. Our research addresses these limitations by investigating alternative estimation methods that offer greater robustness and accuracy.

Shaking Off The Rust: Unraveling The Depositional And Diagenetic History Of Enigmatic Ferroan Dolostones In The Cambrian Bright Angel Formation, Tonto Group, Grand Canyon, Joseph J. Clevenger

All Graduate Theses and Dissertations, Fall 2023 to Present

Within the siliciclastic-sediment-dominated Bright Angel Formation (BAF) of the iconic Cambrian sedimentary strata (Tonto Group) in Grand Canyon National Park, Arizona, workers have identified and named prominent reddish-brown cliffs breaking up the generally slope-forming unit near, but separated from, its upper contact with the limestone-dominated Muav Formation, the "Rusty Brown Dolostones" (RBDs). Previous hypotheses suggest that the RBDs are chemically and physically altered tongues of the Muav Formation intercalated with the BAF at increasingly higher stratigraphic positions from west to east within the Canyon. A genetic association between the Muav Formation and the RBDs, as well as between the RBDs …