Physical Sciences and Mathematics Commons^™

The Direct And Inverse Scattering Problems For The Third-Order Operator, Ivan Toledo

Mathematics Dissertations - Archive

We consider the full-line direct and inverse scattering problems for the third-order ordinary differential equation containing two potentials decaying sufficiently fast at infinity. The direct scattering problem consists of the determination of the scattering data set when the two potentials are known. The scattering data set is made up of the corresponding scattering coefficients and the bound-state information. On the other hand, the inverse scattering problem involves the recovery of the two potentials when the scattering data set is available. We formulate the inverse scattering problem via a related Riemann--Hilbert problem on the complex plane. We describe the recovery of …

A Novel K-Nearest Neighbors Method Based On Generalized Feature Optimization For Precipitation Forecasting, Sean Guidry Stanteen

Mathematics Dissertations - Archive

This study introduces a novel k-nearest neighbors (kNN) method of forecasting precipitation at weather-observing stations. The method identifies numerous monthly temporal patterns to produce precipitation forecasts for a specific month. Compared to climatological forecasts, which average the observed precipitation over the prior thirty years, and other existing contemporary iterations of kNN, the proposed novel kNN method produces more accurate forecasts on a consistent basis. Specifically, the novel kNN method produces improved root mean square errors (RMSE), mean relative errors, and Nash-Sutcliffe coefficients when compared to climatological and other kNN forecasts at five weather …

A New Mechanistic Model Of Brain Metabolism With Optimal Parametrization, Alice Lubbe

Mathematics Dissertations - Archive

Models of glucose metabolism in the brain often focus on chemical exchanges and reactions that occur as part of the tricarboxylic acid cycle (TCA cycle). Experiments involving nuclear magnetic resonance (NMR) spectroscopy to detect and measure carbon-labeled isotopomers of metabolites such as glutamate in vivo inform kinetic, mechanistic models used to study metabolic pathways. In the present work, a new model with two compartments, astrocytic and neuronal, is developed using known biochemical processes and fit to experimental data coming from fully labeled glucose infusions. A gradient descent method is introduced and employed to obtain optimal flux parameter values involved in …

Integrating Machine Learning With Cure Models And Associated Inference, Wisdom Aselisewine

Mathematics Dissertations - Archive

Recent advancements in medical treatments have significantly enhanced the rates of recovery for numerous chronic illnesses. This progress has sparked growing interest in developing suitable statistical models capable of handling survival data that includes substantial cure fractions. The mixture cure model finds extensive application in analyzing survival data when there exists a cured subgroup. Standard logistic regression-based approaches for modeling the incidence part of the mixture cure model may suffer from poor predictive accuracy, especially in the presence of high dimensional covariates and/or non-linear covariate effects. To overcome this limitation, we propose the integration of distinct machine learning algorithms with …

Soil Biogeochemistry In Riparian And Restored Tidal Wetlands: Monitoring And Method Evaluation, Joseph Anthony Loffredo

Open Access Master's Theses

Although soils are essential for sustaining ecosystems, they are often overlooked in routine monitoring efforts during restoration projects. This thesis tries to address the interest in and challenges of measuring and monitoring soil biogeochemical properties and processes to evaluate restoration trajectories. In the first part of this thesis (Chapter 1), I monitored tidal marsh vegetation and soil biogeochemical responses to restoration by thin-layer placement (TLP) of dredged sediments in a greenhouse mesocosm study and a parallel field study at an active restoration site in southern RI. In the greenhouse, aboveground plant biomass in mesocosms treated with +5 cm and +10 …

Language Models For Rare Disease Information Extraction: Empirical Insights And Model Comparisons, Shashank Gupta

Theses and Dissertations--Computer Science

End-to-end relation extraction (E2ERE) is a crucial task in natural language processing (NLP) that involves identifying and classifying semantic relationships between entities in text. This thesis compares three paradigms for end-to-end relation extraction (E2ERE) in biomedicine, focusing on rare diseases with discontinuous and nested entities. We evaluate Named Entity Recognition (NER) to Relation Extraction (RE) pipelines, sequence-to-sequence models, and generative pre-trained transformer (GPT) models using the RareDis information extraction dataset. Our findings indicate that pipeline models are the most effective, followed closely by sequence-to-sequence models. GPT models, despite having eight times as many parameters, perform worse than sequence-to-sequence models and …

Recent Paleolimnological History Of Jackson Lake, Grand Teton National Park, Wyoming (Usa), Hillary Johnson

Theses and Dissertations--Earth and Environmental Sciences

This study utilizes a recently acquired, high-resolution CHIRP seismic reflection dataset and a deepwater sediment core to analyze the recent stratigraphy of Jackson Lake (Wyoming, USA). The western shoreline of Jackson Lake is situated adjacent to the Teton fault, a down-to-the-east normal fault that produces the spectacular high topography of Grand Teton National Park. The sediments of Jackson Lake are underexplored and consequently, their value as indicators of hydroclimatic and tectonic changes is unknown. Here, the sedimentary fill of Jackson Lake is explored as a natural archive of environmental change, specifically in reference to the influence of human outlet engineering …

Microstructural, Mineralogical, And Chemical Characterization Of The Handys Bend And Flax Creek Meteorites, Kentucky: Relevance For The Iron Meteorite Record, Ethan S.L. Davis

Theses and Dissertations--Earth and Environmental Sciences

Iron meteorites remain the only material view into planetary cores. Despite their scientific relevance, iron meteorites are relatively rare. In June 2021 and March 2022, the Kentucky Geological Survey received requests to identify two metallic specimens discovered in central Kentucky. The specimens were given the provisional names Handys Bend (3175.2 g) and Flax Creek (286.2 g). The goal of this project is to confirm meteoritic origin, characterize their structures and chemistry, assign genetic classifications, and examine potential relations to previous discoveries. Petrography was conducted using scanning electron microscopy. Mineral phases were examined using X-Ray diffraction crystallography. Chemical compositions were determined …

Thermal Alteration Of The Mineralogy Of Calcium Sulfoaluminate Cements: Implications For The Performance Of Rapid Repair Materials, Jillian Cavellier

Theses and Dissertations--Earth and Environmental Sciences

Calcium sulfoaluminate (CSA) was developed in part to lessen the environmental impact of cementitious materials compared to traditional Portland cements. CSA was first put into production in the 1970s and has been undergoing various performance testing to investigate its durability. Yet to be evaluated is CSA’s response to a rapid, high temperature event. In this study, X-ray diffraction, thermogravimetric analysis, Fourier transform infrared spectrometry and scanning electron microscope imaging were used to analyze alterations in the mineralogy due to such an event. As found in previous studies, after ~125°C, ettringite has been completely dehydrated. Ettringite decomposes into bassanite and calcium …

Assessing Microplastic Contamination Within Karst Groundwater Basins In Kentucky, Maaz Fareedi

Theses and Dissertations--Earth and Environmental Sciences

The input and abrasion of plastic waste in the environment has long been known to form microplastics (MPs). These ubiquitous contaminants are easily mobilized into hydrologic systems. MPs are now being found in karst aquifers around the world, including several across Kentucky, USA. Due to their size (< 5 mm in diameter), chemical properties, abundance, and wide distribution, MPs pose numerous ecological hazards, including uptake by organisms and as substrates for contaminant sorption. Karst groundwater is especially vulnerable to surface contaminants; however, knowledge of the extent of karst MP contamination is limited, with most studies focused on individual sites or small areas. In this study, we created a MP contamination dataset for 30 karst springs and 10 locations where cave sediments were characterized across Kentucky. MP concentrations in groundwater samples ranged from 0 to 41.1 items/L and yielded an average of 4.9 ± 8.7 items/L. Sediment MP concentrations ranged from 0 to 306 items/kg. We performed statistical analyses and linear regressions to examine whether groundwater MP concentrations could be explained by factors including land use, population density, basin area, numbers of sinkholes, and sinking streams. Our models revealed that population density, agrarian land use, sinking stream density, and basin area were related to MP concentrations. All factors except basin area trended positively with MP concentration, while basin area trended negatively. These relations are generally corroborated by existing literature, however they indicate that further studies with considerably larger sample sizes are needed to determine mechanistic relationships.

Visualizing And Automating Past, Real-Time, And Forecast Dynamic Hazard Maps For Shallow Colluvial Landslides In Eastern Kentucky, Nathaniel O'Leary

Theses and Dissertations--Earth and Environmental Sciences

Landslide hazards are a persistent threat to communities and infrastructure in Eastern Kentucky, where steep slopes, shallow colluvial soils, and variable hydrological conditions make slope failures frequent. This thesis presents an integrated approach to landslide hazard mapping (LHM) through the development of dynamic, spatiotemporal LHMs for shallow colluvial landslides. Two studies within this work investigate and refine the use of the Lu and Godt (2008) factor of safety (FS) equation to improve landslide predictions. The first study establishes a novel LHM workflow using Hydrus-1D to simulate soil moisture infiltration and fluctuations from precipitation and evapotranspiration (ET) data. This study also …

Sh-Wave Seismic-Reflection Efficiency Technique For Investigating The Wolf Island Fault, New Madrid Seismic Zone, Usa, Stephanie Vicroy

Theses and Dissertations--Earth and Environmental Sciences

The Reelfoot Fault within the New Madrid seismic zone has displacement at seismogenic depth to which the surface expression has unequal displacement. Previous work identified northeast-oriented transpressional fault strands northeast of a bend in the scarp as evidence for a through-going shear-zone, acting as potential accommodation for the observed strain imbalance. This investigation projected the trend of these faults to their intersection with an industry seismic survey at Wolf Island, Missouri, which exhibits a similarly structured faulted zone. We suggest this structure is the continuation of the through-going shear zone representing a previously unknown 22-km-long Quaternary-active fault that can affect …

Alteration Of Ultramafic Lamprophyres And Its Effect On Rare Earth Element Distribution In The Illinois-Ketucky Fluorspar District, Zachary O. Walton

Theses and Dissertations--Earth and Environmental Sciences

The ultramafic lamprophyres of the Illinois-Kentucky Fluorspar District (IKFD) have been identified as a potential domestic source of rare earth elements (REEs). The present distribution of the REEs and the role of the carbonate alteration in the distribution of the REEs is poorly understood. Petrographic and geochemical analyses were employed to determine the nature of the mantle source region and timing of the carbonate mineralization. Ratios of ¹⁴³Nd/¹⁴⁴Nd vs. ⁸⁷Sr/⁸⁶Sr demonstrate that in addition to the intrusion of primitive magma into the crust, a melt was generated from a mantle source region metasomatized by …

Re-Examination Of A Middle Mississippian Carbonate Mud-Mound Complex From The Fort Payne Formation In South-Central, Kentucky, Maxwell Mickelson

Theses and Dissertations--Earth and Environmental Sciences

This study examines the origin of a 213-m (700-ft) long, Middle Mississippian, carbonate “mud-mound complex” in the Fort Payne Formation of south-central Kentucky. The complex’s well-exposed, easily accessible, and well-preserved nature provides an opportunity to understand how mounds like this developed during a time of sediment starvation, basinward of the largely abandoned Borden-Grainger Delta complex.

The mound complex is formed of small, accretionary mounds that accreted onto the flanks of an eroded structural high and onto the backs of each other, apparently for protection from storms. Each sub-mound is composed of micrite-rich wackestone, comprising one of two biofacies: 1) alternating …

High Resolution Sedimentary Investigations Of Extant Lakes In North America, John Dilworth

Theses and Dissertations--Earth and Environmental Sciences

Investigation of past lake environments forms the discipline of paleolimnology. Paleolimnological studies seek to evaluate geophysical, geochemical, and ecological proxies and indicators contained within lake sediment archives. Using these potential stores of high-resolution environmental information, questions regarding climate, biological, and geochemical changes experienced by a lake and its watershed can be investigated. This dissertation research utilized lake sediment records from two lakes within North America to study different aspects of environmental change. This dissertation consists of three separate studies presented in three chapters.

Chapter Two presents a retrospective environmental assessment of Jackson Lake, Wyoming to investigate the impacts of dam …

Bicategorical Character Theory, Travis Wheeler

Theses and Dissertations--Mathematics

In 2007, Nora Ganter and Mikhail Kapranov defined the categorical trace, which they used to define the categorical character of a 2-representation. In 2008, Kate Ponto defined a shadow functor for bicategories. With the shadow functor, Dr. Ponto defined the bicategorical trace, which is a generalization of the symmetric monoidal trace for bicategories. How are these two notions of trace related to one another? We’ve used bicategorical traces to define a character theory for 2-representations, and the categorical character is an example.

Properties Of Skew-Polynomial Rings And Skew-Cyclic Codes, Kathryn Hechtel

Theses and Dissertations--Mathematics

A skew-polynomial ring is a polynomial ring over a field, with one indeterminate x, where one must apply an automorphism to commute coefficients with x. It was first introduced by Ore in 1933 and since the 1980s has been used to study skew-cyclic codes. In this thesis, we present some properties of skew-polynomial rings and some new constructions of skew-cyclic codes. The dimension of a skew-cyclic code depends on the degree of its generating skew polynomial. However, due to the skew-multiplication rule, the degree of a skew polynomial can be smaller than its number of roots and hence tricky to …

Adams Operations On The Burnside Ring From Power Operations, Lewis Dominguez

Theses and Dissertations--Mathematics

Topology furnishes us with many commutative rings associated to finite groups. These include the complex representation ring, the Burnside ring, and the G-equivariant K-theory of a space. Often, these admit additional structure in the form of natural operations on the ring, such as power operations, symmetric powers, and Adams operations. We will discuss two ways of constructing Adams operations. The goal of this work is to understand these in the case of the Burnside ring.

Pairs Of Quadratic Forms Over P-Adic Fields, John Hall

Theses and Dissertations--Mathematics

Given two quadratic forms $Q_1, Q_2$ over a $p$-adic field $K$ in $n$ variables, we consider the pencil $\mathcal{P}_K(Q_1, Q_2)$, which contains all nontrivial $K$-linear combinations of $Q_1$ and $Q_2$. We define $D$ to be the maximal dimension of a subspace in $K^n$ on which $Q_1$ and $Q_2$ both vanish. We define $H$ to be the maximal number of hyperbolic planes that a form in $\mathcal{P}_K(Q_1, Q_2)$ splits off over $K$. We will determine which values for $(D, H)$ are possible for a nonsingular pair of quadratic forms over a $p$-adic field $K$.

Dirichlet Problems In Perforated Domains, Robert Righi

Theses and Dissertations--Mathematics

We establish W^1,p estimates for solutions u_ε to the Laplace equation with Dirichlet boundary conditions in a bounded C¹ domain Ω_{ε, η} perforated by small holes in ℝ^d. The bounding constants will depend explicitly on epsilon and eta, where epsilon is the order of the minimal distance between holes, and eta denotes the ratio between the size of the holes and epsilon. The proof relies on a large-scale L^p estimate for ∇u_ε, whose proof is divided into two main parts. First, we show that solutions of an intermediate problem for a …

Uniform Regularity Estimates For The Stokes System In Perforated Domains, Jamison R. Wallace

Theses and Dissertations--Mathematics

We consider the Stokes equations in an unbounded domain $\omega_{\epsilon,\eta}$ perforated by small obstacles, where $\epsilon$ represents the minimal distance between obstacles and $\eta$ is the ratio between the obstacle size and $\epsilon$. We are able to obtain uniform $W^{1,q}$ estimates for solutions to the Stokes equations in such domains with bounding constants depending explicitly on $\epsilon$ and $\eta$.

Slₖ-Tilings And Paths In ℤᵏ, Zachery T. Peterson

Theses and Dissertations--Mathematics

An SLₖ-frieze is a bi-infinite array of integers where adjacent entries satisfy a certain diamond rule. SL₂-friezes were introduced and studied by Conway and Coxeter. Later, these were generalized to infinite matrix-like structures called tilings as well as higher values of k. A recent paper by Short showed a bijection between bi-infinite paths of reduced rationals in the Farey graph and SL₂-tilings. We extend this result to higher k by constructing a bijection between SLₖ-tilings and certain pairs of bi-infinite strips of vectors in ℤᵏ called paths. The key ingredient in the proof is the relation to Plucker friezes and …

A Multiple-Case Study On The Impact Of An Introductory Real Analysis Course On Undergraduate Students' Understanding Of Function Continuity, Ryan Joseph Rogers

Theses and Dissertations--Mathematics

Undergraduate students' understanding of function continuity has not been explored broadly in previous research. The relevant findings in the literature are predominantly concerned with calculus students' understanding and misconceptions of continuity. Many of these misunderstandings are tied to the relationships which continuity has with limits and differentiability. This multiple-case study explores how, if at all, an introductory real analysis course impacts undergraduate students' understanding of function continuity and its connections to the notions of limits and differentiability. We embed our findings within the theoretical framework of Tall's three worlds of mathematics, namely, the embodied, symbolic, and formal worlds.

The cases …

Advanced Mathematical Graph-Based Machine Learning And Deep Learning Models For Drug Design, Farjana Tasnim Mukta

Theses and Dissertations--Mathematics

Drug discovery is a highly complicated and time-consuming process. One of the main challenges in drug development is predicting whether a drug-like molecule will interact with a specific target protein. This prediction accelerates target validation and drug development. Recent research in biomolecular sciences has shown significant interest in algebraic graph-based models for representing molecular complexes and predicting drug-target binding affinity. In this thesis, we present algebraic graph-based molecular representations to create data-driven scoring functions (SF) using extended atom types to capture wide-range interactions between targets and drug candidates. Our model employs multiscale weighted colored subgraphs for the protein-ligand complex, colored …

Advancements In Elliptic Mesh Redistribution And Automated Overset Grid Generation For Computational Fluid Dynamics, Chase Ashby

Theses and Dissertations--Mathematics

Automated and robust structured curvilinear overset grid generation remains a significant challenge for the application of computational fluid dynamics. This thesis intro- duces a specialized anisotropic Mach cone aligned adaptation algorithm for low-boom simulations and an automated procedure for generating structured curvilinear overset grids for immersed boundary simulations. Results demonstrate that anisotropic mesh adaptation can reduce computational resource usage by over 50% while maintaining sonic boom prediction accuracy across the entire sonic boom domain compared to user-constructed Mach cone aligned grids. The proposed immersed overset grid gen- eration procedure eliminates the need for complex surface generation algorithms, producing grids suitable …

The Performance Of Marginal Modeling Methods For Rare Events With Application To Opioid Overdose Mortality And Morbidity, Shawn Nigam

Theses and Dissertations--Epidemiology and Biostatistics

Opioid misuse is a nationwide epidemic, with Kentucky having one of the highest opioid overdose-related fatality rates across all US states. These rates have increased significantly over the past decade, with particularly large increases during the COVID-19 pandemic. This dissertation aims to study the behavior of these increases and the methods for the marginal modeling of count outcomes related to opioid overdose.

Opioid overdose-related fatality rates in Kentucky increased significantly during the COVID-19 pandemic. In this chapter, we characterize the changes in opioid overdose fatality rates in Kentucky and identify associations between potential factors and fatality rates. County-level opioid overdose …

A Praxis Towards Social Change Based On Foucault's Conceptualization Of Experience As Relational, Lila Maureen Wakeman

Theses and Dissertations--Philosophy

This project develops a praxis towards social change based on the works of Michel Foucault. It first establishes Foucault’s philosophical assumptions, methods, and political goal of countering “objectivizing” modern Western social forces. It then draws on sources from the three major phases of Foucault’s career to trace his development of a general conceptualization of experience as relational, or as non-exhaustively co-constituted by and through three indispensable kinds of social forces: knowledge, power, and ethics. It then evaluates implications of Foucauldian experience for efforts towards social change to conceptualize a general Foucauldian praxis towards social change. The praxis aims to affect …

Variable Selection For High-Dimensional Data With Interaction Effects: Methods, Applications, And Inferences, Leiyue Li

Theses and Dissertations--Statistics

For high-dimensional data where the number of variables greatly exceeds the number of observations, selecting important variables while maintaining the required heredity conditions can be challenging. This dissertation is structured into three interconnected parts. In the first part, we propose a variable selection method by implementing a well-known optimization technique, the Genetic Algorithm. An R package was developed to simplify the implementation and usage of the proposed method. We then propose another variable selection method by extending the study from the Genetic Algorithm to a different but related optimization technique, Simulated Annealing. We consider three different hierarchical structures in both …

High-Dimensional Tests And Projection Methods: Subvector Analysis And Matrix Variate Data, Shouryya Mitra

Theses and Dissertations--Statistics

In this dissertation, we study projection-based methods to testing problems for high-dimensional data. We also investigate inferential methods for matrix variate data with block compound symmetry (BCS) covariance structure. The research reported in dissertation consists of three projects.

The first project addresses power loss and ill-conditioned error covariance estimates commonly faced by multivariate tests in high-dimensional settings. To overcome these challenges, previous approaches avoided correlations in constructing test statistics, but this required strong assumptions about covariance matrices and dependence structures. More recently, some methods have incorporated correlations by employing random projection into a lower-dimensional space. We develop a unified framework …

Estimation And Testing Of Nonparametric Effects Of Incomplete Multivariate And Repeated Measures Data, Swetalina Maity

Theses and Dissertations--Statistics

In this dissertation, we investigate three distinct but interrelated problems in analyzing repeated measure data with missing values.

The first project is on semiparametric methods for analyzing repeated measures designs with missing values. A closed-form estimator for the parameters and their asymptotic covariance are derived using block partitioning based on the missing data pattern. We also derive the asymptotic distribution of the estimators and construct test statistics to test hypothesis formulated as linear contrasts of the mean vector.

In the second project, we focus on purely nonparametric methods. In this setup, nonparametric treatment effects are defined as functionals of the …