Physical Sciences and Mathematics Commons^™

Measuring Cosmic Expansion From Early To Late Times Using Quasars, Galaxies, & Local Supernovae, Rajeev Vaisakh

Physics Theses and Dissertations

This dissertation investigates the evolution of cosmic expansion across a wide redshift ($z$) range by combining measurements from quasars \& galaxies in the distant universe $(z > 0.8)$ with those obtained from stripped-core collapse supernovae observations from the nearby universe $(z < 0.1)$. Using the DESI spectroscopic survey, we analyze large-scale clustering from quasars over $0.8 < z < 2.1$ and emission line galaxies over $0.8 < z < 1.6$, contributing to DESI DR2 BAO and full-shape measurements of cosmic expansion and structure growth. Combined with BBN in flat $\Lambda$CDM, DESI DR2 BAO gives $H_0 = 68.51 \pm 0.58$ km s$^{-1}$ Mpc$^{-1}$, while combinations of DESI BAO with CMB and supernova data show a preference for evolving dark energy, with representative constraints such as $w_0 = -0.752 \pm 0.057$ and $w_a = -0.86^{+0.23}_{-0.20}$ for DESI+CMB+DESY5. Using the ROTSE-III Supernova Survey and the expanding photosphere method (EPM), we measure distances to a sample of six supernovae for which the thermal phase can be clearly identified. This analysis focuses on testing whether reliable EPM distances can be obtained for this population. The resulting distances will eventually be compared with independent estimates from the literature. Establishing consistency with these external measurements represents an important step toward applying this methodology to larger samples, with the eventual goal of using ROTSE supernova distances to provide an independent measurement of the local Hubble constant.

Statistical Methodologies For Count Time Series Analysis And Topological Data Analysis Of Medical Images, Yuhyeong Jang

Statistical Science Theses and Dissertations

This dissertation addresses two distinct topics related to count time series analysis and topological medical image analysis, respectively. The first part of the dissertation comprises an application of a count time series model to analysis of US monthly sex trafficking data and development of a new model for multivariate count data that exhibits serial dependence and overdispersion. By imposing a family of multivariate mixed Poisson distributions on the count random vector, the proposed model can accommodate a broad range of overdispersion as well as positive contemporaneous correlations. For maximum likelihood estimation, a computationally feasible EM-type algorithm is derived based on …

Dynamics Of Microscale Droplets In Respiratory Airways, Md Shamser Ali Javed

Mathematics Theses and Dissertations

We investigate trajectories of microscale evaporating droplets in a stagnation point flow near a wall of a respiratory airway. The configuration is motivated by the problem of advection and deposition of microscale droplets of respiratory fluids in human airways during transmission of infectious diseases such as tuberculosis and COVID-19. Laminar boundary layer equations are solved to describe the air flow while the equations of motion of the droplet include contributions from gravity, aerodynamic drag, and Saffman force. Evaporation is accounted for at both the droplet surface and the wall of the respiratory airway and is shown to delay droplet deposition …

Ai And The Music Industry: Its Current Status And A Speculative Projection Of Its Evolutionary Trajectory, Rhett D. Morris, Clayton Rosati, Stefan Fritsch

Honors Projects

Music serves as one of society's biggest cultural outlets, allowing millions to share in what used to be a uniquely human form of expression. The commodification of music has built a huge industry full of companies and platforms that have used technology and property laws to shape music's relationship with the public. This study aims to look into the future to see how AI and its implementation could affect the structure of the music industry. To look into the future, this piece establishes two of the most pressing kinds of AI technology for the music industry and looks to contextualize …

Properties Of Enjoyable Mathematical Contexts From The Student Perspective, Emilie Nadine Hendrickson

Theses and Dissertations

Researchers continue to grapple with how to meaningfully engage students in mathematical content. Many students report disengagement due to perceptions that mathematics is difficult, irrelevant, boring, or anxiety-inducing. This study sought to understand how students interpret and respond to different mathematical problem contexts, with particular attention to the reasons students describe certain problems as enjoyable or unenjoyable. Using semi-structured interviews, this research examined student responses to a variety of mathematical problem types primarily across affective engagement. Students reflected on specific problem contexts and explained which features supported or hindered their enjoyment and engagement. Students described that contexts were enjoyable have …

Sentinel: Evaluating Occlusion-Centered Next-Best-View Selection Using Rgb-Derived Pseudo-Geometry, Paul Nassar

Master's Theses

Three-dimensional cameras provide direct geometric measurements, but their cost, weight, power requirements, and calibration constraints can limit their use in various lightweight or large-scale sensing systems. A potential alternative is to use conventional two-dimensional RGB cameras together with geometric reconstruction models that infer a partial three-dimensional representation from images. This thesis evaluates that possibility for next-best-view (NBV) selection through Sentinel, an occlusion-centered system for static, object-centric scenes with known camera poses and intrinsics. Sentinel converts source RGB observations into pseudo-geometry using monocular depth or point-map predictions, combines those predictions with camera-ray evidence, identifies occluded unknown regions, and selects a candidate …

Predicting Student Belonging In Computing Education: A Multimodal Machine Learning Approach Using Eeg And Survey Data, Hannah Moshtaghi

Master's Theses

Measuring students’ sense of belonging, characterized by feelings of acceptance, inclusion, and encouragement from teachers, remains a significant challenge in computing education. Prior research has associated this multidimensional construct with positive academic outcomes and has identified instructors’ growth- and fixed-mindset messaging as a potential influence. However, belonging is a complex and deeply personal experience that is difficult to capture through direct observation alone. Current measurement methods rely on self-report surveys, which may not capture every aspect of an experience that can also involve emotional and cognitive responses.

This thesis investigates whether combining EEG data recorded during a belonging questionnaire with …

Synthesis And Characterization Of Carbon Quantum Dots And Gold Nanoparticles For Norovirus Biosensing Applications In Water Systems, Breanne Evans

Master's Theses

Rapid, reliable detection of viral pathogens remains a significant challenge across water-treatment and environmental monitoring systems, including drinking-water, wastewater, water reuse, and environmental surveillance applications. Waterborne viral contamination can pose substantial public-health risks, making early detection essential for protecting water quality and responding quickly to treatment failures or contamination events. Direct potable reuse (DPR) is one particularly demanding example because it requires continuous verification of treatment performance and the broader need for rapid virus monitoring extends across many water-treatment and environmental surveillance applications. Norovirus is a priority target because of its widespread occurrence in wastewater, environmental persistence, and exceptionally low …

Criticality In A Heterogeneous Neutron Transport Rod Model, Samuel Kaleb Crowford

All Graduate Reports and Creative Projects, Fall 2023 to Present

This work studies the stochastic behavior of neutron populations in a one-dimensional rod model using Monte Carlo simulation. The first part of this project reproduces the computational results of Dumonteil, Horton, Kyprianou, and Zoia (2025) by independently implementing the Monte Carlo algorithm described in their article, with the asymptotic behavior of the first moment analyzed in relation to the dominant eigenvalue and adjoint eigenfunction of the neutron transport operator. The model is then extended to a heterogeneous setting by introducing a central region where fission is suppressed. A global expectation over initial positions and directions is used to estimate the …

Temperature And Salinity Effects On The Physiology Of Bullfrog Tadpoles (Lithobates Catesbeianus) From A Suburban Temperate Wetland, Angela Brown

Theses, Dissertations and Culminating Projects

One of the most robust amphibians is the American Bullfrog, Lithobates catesbeianus, which is a widespread species that is invasive worldwide, and is broadly tolerant of a range of environmental conditions. Despite this tolerance, survival and performance of adult L. catesbeianus can be negatively affected by increasing temperatures and salinity resulting from anthropogenic impacts, such as climate change and road salts. This study focuses on the effects of acute salinity exposure (mimicking road salt influx into a pond) on L. catesbeianus tadpoles at different larval stages. Increased salinity was predicted to negatively affect two physiological performance measures. Critical maximum temperature …

Magnetic Properties And Ultrafast Spin Dynamics In Quantum Materials, Trung Kien Mac

All Graduate Theses and Dissertations, Fall 2023 to Present

Modern electronics mostly work by moving electric charge, which generates heat and hence wastes energy, especially as devices become smaller and faster. An alternative is to use the spin of electrons (a tiny magnetic property) and related “valley” states in certain atomically thin materials to store and process information more efficiently. This thesis explores how magnetism and spin behavior can be created and measured in a family of ultra-thin materials known as van der Waals quantum materials. Three kinds of materials are studied. First, atomically thin semiconductors are shaped into narrow nanoribbons. Because of their narrow size, their edges can …

A Social-Ecological Systems Approach To Integrating Outdoor Recreation And Black Bear Management: A Michigan Case Study, Megan Dorothy Stone

All Graduate Theses and Dissertations, Fall 2023 to Present

Outdoor recreation sits at the intersection of social and ecological systems, representing one of the primary ways in which humans directly interact with their natural environment. As a result, outdoor recreation management must balance providing high-quality outdoor recreation opportunities while simultaneously protecting natural resources in protected areas. Balancing these concurrent management goals has become more challenging in recent years as participation in outdoor recreation increases. This can lead to numerous negative impacts on the environment, such as wildlife disturbance. In this study, I explore the challenges and opportunities for collaboration between managers of outdoor recreation and black bears in the …

Effects Of Bidisperse Gold Nanoparticles On Near-Infrared Surface-Enhanced Raman Spectroscopy (Sers) In Quick-Freezing-Induced Gold Nanoparticle Aggregates (Qfiaas), Elissa M. Dojka

Forensic Science Master's Projects

Gold nanoparticle (AuNP) aggregates formed via rapid freezing in liquid nitrogen exhibit strong near-infrared (NIR) plasmonic coupling. These quick-freezing-induced AuNP aggregates (QFIAAs) form moderately sized, colloidally stable structures that remain suspended for over three months, supporting a variety of analytical applications. Mechanistically, QFIAA formation arises from the confinement of nanoparticles and ions within advancing ice grain boundaries during freeze-concentration. This mechanical crowding promotes extreme physical proximity while simultaneously elevating local ionic strength, which screens electrostatic barriers to drive the assembly of dense, tightly coupled plasmonic networks.

This study investigates the plasmonic and surface-enhanced Raman scattering (SERS) behavior of bidisperse QFIAA …

A Simulation Assessment Of The 'Law Of One Price', Caleb Wilkins

Computational and Data Sciences (MS) Theses

The ‘law of one price’ is an appealing notion regarding pricing of tradeable commodities that are priced in different currencies. It states that the prices of the same good in different markets should be equal after adjustment for exchange rates and that equality should persist through exchange rate fluctuations.

My research simulates the market conditions that should precipitate the ‘law of one price.’ Data was obtained from the simulated trade between algorithmic artificial intelligence agents that operated under induced boundedly rational market behaviors. Trade took place in two initially separate markets, a high-price market with a higher equilibrium price and …

Viability Assessment Of Bovine Embryos: A Public Dataset And Deep Learning Baselines, Erfan Khayyati

All Graduate Theses and Dissertations, Fall 2023 to Present

Improving the success rates of cattle breeding is essential for sustainable agriculture, global food security, and high-quality livestock production. Currently, determining whether a lab-grown bovine embryo is healthy enough for a successful pregnancy requires highly trained experts to manually evaluate days of continuous time-lapse video footage. This process is not only incredibly time-consuming but also highly subjective; human reviewers often suffer from visual fatigue when tracking subtle, microscopic cellular changes over a seven-day period, leading to significant disagreement among even top experts on an embryo’s true potential. Furthermore, assessing bovine embryos is notoriously difficult due to their dark, lipid-dense cellular …

Integrating Hydrology And Human Water Footprints: A Case Study Of The Great Salt Lake Basin, Rachel Lynne Seeley

All Graduate Theses and Dissertations, Fall 2023 to Present

Global demand for water is outrunning supply, and how we account for water is part of the problem. Many water management frameworks are based solely on how much physical water moves through rivers, aquifers, and other water bodies, missing the water that is embedded in food and other products a region produces and exports. This study developed a new, generalizable water accounting framework that incorporates this “hidden water,” known as virtual water, into water management and applied the framework in the Great Salt Lake Basin.

The Great Salt Lake is shrinking, and an often-overlooked driver of the lake’s decline is …

Mining Time Series Shapelets And Association Rules For Solar Flare Prediction, Drew Watson

All Graduate Theses and Dissertations, Fall 2023 to Present

Solar flares are the largest explosions in the solar system; they are caused by changes in the Sun’s magnetic field. Strong solar flares can disrupt power systems, damage satellites, and interfere with radio communication, so improving flare prediction is important. This thesis develops a way to predict severe solar flares while also helping researchers understand why those predictions are made. The approach looks for short patterns in solar magnetic field data that are linked to future flare activity. It then studies how these patterns appear together and in what order they happen over time. By doing this, the research not …

Spatial Prediction Under Uncertainty: Methodological And Computational Advances In Bayesian Maximum Entropy, Kinspride K. Duah

All Graduate Theses and Dissertations, Fall 2023 to Present

Environmental decisions such as infrastructure design, water management, and snow load estimation depend on spatial data that are often incomplete or uncertain. In many cases, measurements are not exact values but ranges, reflecting limitations in data collection methods. Traditional mapping techniques typically simplify these uncertain measurements, which can lead to less accurate predictions. This dissertation introduces improved statistical tools for making spatial predictions when data are uncertain or partially known. By utilizing a framework called Bayesian Maximum Entropy (BME), this research demonstrates how exact measurements and range-based data can be combined in a mathematically consistent way. The work demonstrates that …

Learning Latent Structure In High-Dimensional Data Via Geometry And Graphs, Haozhe Chen

All Graduate Theses and Dissertations, Fall 2023 to Present

Modern datasets often contain many measured variables for each observation, such as gene-expression levels, brain activity signals, or features in tabular data. These data are also often noisy, meaning that useful patterns are mixed with measurement error or irrelevant variation. Although such datasets can appear complex, they are frequently represented by simpler hidden structures, such as trajectories, clusters, or relationships between observations. This dissertation develops methods for uncovering these hidden structures by learning geometric and graph-based representations directly from data. The first part introduces Functional Information Geometry, which represents local patterns in high-dimensional data using functional features and constructs a …

Unifying And Expanding Global And Local Variable Importance Methods For Explainable Machine Learning, Kelvyn K. Bladen

All Graduate Theses and Dissertations, Fall 2023 to Present

Machine learning methods are powerful analytical tools used across all scientific disciplines and many other fields of investigation for prediction and inference from diverse data sources. Despite their broad applicability, machine learning methods are often highly complex and difficult to interpret. Developing a greater understanding of which variables most influence a response is essential for increasing the interpretability of these models and supporting informed decision-making. This research focuses on improving how we evaluate the importance of these variables.

One common approach is to shuffle the values of a variable and see how much the model accuracy gets worse. Another approach …

Hidden Symmetries And Higher Dimensional Rotating Black Holes, Luis Fernando Temoche Hurtado

All Graduate Theses and Dissertations, Fall 2023 to Present

A standard approach to probing the dynamics of a physical system is to expose it to an external perturbation—such as an incident wave—and analyze its response after the interaction. Mathematically, this procedure is formulated in terms of differential equations governing the evolution of the perturbation.

In the context of black hole physics, an analogous strategy can be employed by studying the response of the event horizon to external perturbations. The differential equations describing these interactions are often invariant under nontrivial transformations, revealing hidden symmetries that help explain distinctive features of higher-dimensional black holes.

By exploiting these hidden symmetries in the …

The Role Of Heterogeneity In Earthquake Rupture Dynamics: Insights From Friction Experiments On A 1-Meter Laboratory Fault, Alejandro Aguilar

All Graduate Theses and Dissertations, Fall 2023 to Present

Tectonic faults are made of many kinds of rocks and minerals, creating natural weak and strong zones along faults where earthquakes occur. These differences can affect how faults move, including whether slip occurs slowly and quietly or suddenly and destructively during an earthquake. However, it is not fully understood how these variations influence when earthquakes start, how fast they spread, and whether they stop or grow into large ruptures. This research studies how different fault materials interact during earthquake slip. Using a large laboratory machine that simulates fault movement under realistic conditions, we recreate earthquake processes and closely measure how …

Counterfactual Explanations For Time Series Classification: From Localized Perturbations To Realistic Generation, Peiyu Li

All Graduate Theses and Dissertations, Fall 2023 to Present

Machine learning models are often used to classify signals collected over time, such as heart rhythms, movement recordings, industrial sensor measurements, and scientific observations. These models can be accurate, but they are often difficult to understand. Users may need to know not only what a model predicted, but also what would have needed to change for the model to reach a different decision.

This dissertation studies counterfactual explanations for time series data. A counterfactual explanation answers a “what-if” question. For example, if a model classifies a signal as one activity instead of another, the explanation shows how the signal would …

Investigation Of Yy Production Methods For Invasive Channel Catfish Ictalurus Punctatus Population Management, Andrew M. Wisniewski

All Graduate Theses and Dissertations, Fall 2023 to Present

Aquatic invasive species are one of the leading causes of native fish declines in the Southwestern United States. Channel Catfish Ictalurus punctatus were introduced into the Colorado River Basin, including the San Juan River, New Mexico, Colorado, and Utah for fishery enhancement during the 20th century. This introduction has contributed to the decline of native species and despite intensive mechanical removal efforts, the Channel Catfish population has persisted in the San Juan River. The Trojan Sex Chromosome approach is a promising eradication strategy that proposes the production and release of Trojan sex chromosome carriers (YY) to skew a targeted population’s …

Mapler: An R Package For Estimating The Impact Of Climate Change On Maple Syrup Production, Matthew T. White

All Graduate Theses and Dissertations, Fall 2023 to Present

Successful maple sap tapping depends on the freeze/thaw cycle (i.e., temperatures fluctuating above/below freezing) during the winter and spring. Climate change threatens to alter the timing and duration of the tapping season. This necessitates research into how maple sap tapping will be impacted by climate change in order to help maple syrup producers prepare for the future. We define a sap day as a day where the freeze/thaw cycle occurred. Using information climate scientists use to predict future temperatures, we calculate how many sap days could occur each year. We develop software to analyze these sap day calculations to determine …

Fostering Safe Space For Children In Online Navigation And Parent-Child Interactions, Rizu Paudel

All Graduate Theses and Dissertations, Fall 2023 to Present

As children and teenagers spend increasingly more time online, digital devices have become a major source of family friction. Disagreements frequently arise over privacy boundaries, and online activities. When these conflicts are unresolved, they often lead to broken trust and secretive behavior, leaving children vulnerable to digital harms like cyberbullying, toxic content, or account hacking. Therefore, it is important to create a safe and open environment for children where in order for them to share their feelings with parents. This dissertation investigates the human and technological dynamics of parent-child interactions, developing new ways to support collaborative conflict resolution and online …

A Data-Driven Nutrient Density Scoring Framework For Beef Using Principal Component Analysis, Teja Vuppala

All Graduate Theses and Dissertations, Fall 2023 to Present

Beef is one of the most nutrient-rich foods in the human diet, providing high-quality protein, iron, omega-3 fatty acids, B vitamins, and a wide range of other compounds important to health. However, current nutrition scoring systems used on food labels were designed to compare different foods to one another — for example, beef versus broccoli — and do not work well for judging the nutritional quality of different beef samples relative to each other. A grass-fed steak and a conventionally-finished steak can carry nearly identical Nutrition Facts panels while differing substantially in their content of omega-3 fatty acids, vitamins, and …

Causal Discovery In Photospheric Magnetic Field Time Series For Interpretable Solar Flare Prediction, Nathan W. Nelson

All Graduate Theses and Dissertations, Fall 2023 to Present

Solar flares are capable of damaging many valuable resources, including satellites, power grids, and even human lives. Being able to predict solar flares can allow for proactive measures to be taken that can prevent that damage. Many new deep learning methods for predicting solar flares have shown promise in this task, but the decisions they make are harder to explain to humans. This makes understanding why these models make mistakes difficult, which in turn makes fixing and maintaining them more challenging. We test a recent deep learning method that helps discover relationships between different measurements of the Sun as they …

Advantages Of Dynamic Representation For Related Rates Problems In Calculus, Eri Osuna

Electronic Theses, Projects, and Dissertations

Related-rates problems are a standard yet persistently difficult topic in first-semester calculus. Research increasingly recommends dynamic visualization tools such as GeoGebra, but direct comparisons of static and dynamic representations in related-rates settings remain scarce. This qualitative study examines how representation type shapes the quality of students' reasoning and their perceived experience during related-rates problem solving. Six mathematics students who had completed Calculus —a group of four undergraduates and a pair of graduate students—completed a static sliding-ladder task and a dynamic airplane-and-camera task supported by an interactive GeoGebra applet, followed by an interview. Findings indicate that the two representations supported reasoning …

Geodesic Completeness And The Hopf-Rinow Theorem, Christopher Farias

Electronic Theses, Projects, and Dissertations

Differential geometry is concerned with the properties of calculus and geometry on curved n-dimensional manifolds. As a result, thinking about such a space often runs counter to the Euclidean geometer's intuition of distances, angles, and transformations. This thesis aims to build up to proving an important result in the study of Riemannian manifolds: the Hopf-Rinow theorem.

In Chapter 2, we begin by defining what a manifold is and showing that the collection of directional derivatives at a point on the manifold spans a tangent vector space. After defining a basis and a metric for this space, in Chapter 3, we …