Physical Sciences and Mathematics Commons^™

Analyzing Sleep Architecture And Brain State Transitions Via Hidden Markov Models On Fmri Data, Brileigh Jay Cates

Masters Theses

Sleep is associated with systematic changes in brain activity and functional connectivity observable in functional magnetic resonance imagining (fMRI) signals. Because subjects often fall asleep during resting-state experiments, the absence of vigilance monitoring can confound the interpretation of resting-state dynamics. Although electroencephalography (EEG) is the gold standard for sleep staging, simultaneous EEG-fMRI acquisition is not always feasible.

This study investigates whether sleep stages can be inferred directly from fMRI using a probabilistic latent-state framework. Hidden Markov Models (HMMs) are applied to blood-oxygen-level-dependent (BOLD) time series to identify latent brain states and their temporal transitions. Inferred states are aligned with EEG-derived …

A Geospatial Assessment Of Groundwater Salinization In A Multi-Aquifer System: Durango, Mexico, Juan Lopez-Sierra

Graduate Theses/Dissertations

Groundwater salinization poses a critical environmental concern for water resource sustainability in arid and semi-arid regions. This study evaluates spatial and temporal patterns of groundwater salinity across the state of Durango, Mexico, using total dissolved solids (TDS), sodium adsorption ratio (SAR), as salinity indicators and nitrate-nitrogen (NO₃–N) as an anthropogenic indicator. Groundwater quality data were obtained from (CONAGUA), a Mexican water agency. To assess salinity variations with respect to time, while minimizing interannual sampling bias, two multi-year sampling periods were selected: 2012-2013, and 2020-2021. Final datasets consisted of 122 wells for 2012–2013 and 131 wells for 2020–2021. The wells were …

Essays On Accelerated Failure Time Models For Recurrent Event Data, Emmanuel Masavo Djegou

Doctoral Dissertations

Recurrent event data arise in many fields such as medicine, reliability, insurance, and economics, where the same event may occur repeatedly for a subject. Accelerated Failure Time (AFT) models provide an intuitive framework for relating covariates to event times and offer a useful alternative to proportional hazards models, allowing direct prediction of event timing under right censoring. However, existing AFT extensions for recurrent events, such as accelerated gap time (AGT) models, often fail to account for interventions between events and may not capture complex temporal patterns.

In this work, we first propose a class of semiparametric AGT models incorporating an …

Enhancing Team Science By Training Collaborative Biostatisticians To Have A Strong Statistical Voice, Gina-Maria Pomann, Steven C. Grambow, Marissa C. Ashner, Bibhas Chakraborty, Nan Liu, Megan L. Neely, Sarah Peskoe, Lacey Rende, Emily Slade, Tracy Truong, Lexie Zidanyue Yang, Greg P. Samsa, Jesse D. Troy

Biostatistics Faculty Publications

Strong statistical voice is defined as the ability to advocate and negotiate for good and ethical statistical practices, including integrating and resolving differing scientific approaches. This skill is crucial for biostatisticians who work on biomedical research teams, as it ensures the integrity and accuracy of statistical analyses and fosters productive collaborations with non-statisticians. Despite its importance, new graduates often lack targeted training opportunities. This manuscript presents a scalable training approach through the development of online videos. Preliminary didactic materials focused on two key applications: providing written comments on manuscripts and engaging in study design discussions. To evaluate this training approach, …

An Ensemble Classifier For Ordinal Outcomes In High-Dimensional Genomics Data, Heranga K. Rathnasekara, Sinjini Sikdar

Mathematics & Statistics Faculty Publications

Analysis of genomics data for predicting disease outcomes is a fast-growing field in medical research. There often exist categorical, specifically, ordinal outcomes that need to be predicted based on genomic profiles. This has led to recent development of some high-dimensional ordinal classification methods that can address the large dimensionality of the genomic covariate set. These high-dimensional ordinal models tend to vary widely in their performance depending on the data they are applied to and the evaluation criteria used. In this article, we outline an ensemble ordinal classifier that integrates different ordinal modeling approaches through bootstrap-based model evaluation, multi-metric performance assessment, …

Investigating The Connection Between Als Through The Mutation R522s In The Rna Binding Protein, Dennia Estrella-Vargas, Lydia Uptain

Mathematics

Amyotrophic lateral sclerosis (ALS) is a fatal disease that causes the deterioration of motor neurons , death is usually due to respiratory paralysis. The variant R522S was chosen because it is near a hot spot of pathogenic variants. It is an arginine-to-serine swap, this swap is present in pathogenic variants near the 522 position, such as R514S, R521S, R524S. Recent evidence suggests that arginine-deficiency can influence disease progression.

Using Camera-Based Unmarked Spatial Capture-Recapture Modeling To Estimate Reintroduced Elk (Cervus Canadensis) Population Parameters And Distribution In Southeastern Kentucky, Claire Marie Muia

Theses and Dissertations--Forestry and Natural Resources

Estimation of population parameters is important for wildlife management decisions. Elk reintroduced to southeastern Kentucky experienced early irruptive population growth and are currently monitored using a statewide harvest-based statistical population reconstruction model (SPR) across the Kentucky Elk Restoration Zone (KERZ). Because the SPR model is spatially coarse and difficult to scale to the smaller management units comprising the KERZ, we conducted a spatially explicit capture-recapture study using a clustered camera-trapping array deployed for 10 weeks from June–August 2024 to estimate elk population parameters within Management Unit 4. Due to a lack of resights of GPS-marked elk, population parameters were estimated …

Volatility Modeling With An Application To Risk Parity Portfolios, Kenneth Hou

CMC Senior Theses

This thesis studies volatility modeling in the context of risk parity portfolio construction. I compare three risk parity portfolios that differ only in their underlying volatility model: a historical covariance baseline, a Bayesian stochastic volatility model, and a GRU–GARCH hybrid neural network. Using daily returns on Kenneth French’s five industry portfolios from January 2016 through December 2025, I construct monthly rebalanced portfolios under each model, with the SV and GRU forecasts embedded in hybrid covariance matrices that combine forecasted volatilities with rolling historical correlations. The results document a divergence between forecast accuracy and portfolio performance: the SV model is the …

Rank Rebalancing In Commodity And Foreign Exchange Markets, Prateek D. Vyas

CMC Senior Theses

This thesis empirically tests the rank-rebalancing mechanism of Stochastic Portfolio Theory (SPT) across commodity futures, foreign exchange futures, and equity ETFs. The Reverse Price-Weighted strategy (RPW) assigns, to each asset, the market weight of the asset at the opposite price rank, and generates an annualized excess return of 2.90% over the price-weighted (MKT) commodity benchmark, during the period of November 1977 to October 2025 (HAC t = 2.058, p = 0.040). The differential Sharpe ratio (dSharpe) of 0.245 is confirmed by a stationary block bootstrap, with a 𝑝-value of 0.015, and factor regressions controlling for carry, momentum, and value yield …

All Games Have Equilibria, M. Ali Khan, Arthur Paul Pedersen, Maxwell B. Stinchcombe

Publications and Research

Research on Nash equilibrium existence for infinite games has grown into a patchwork of technical preconditions and counterexamples. This paper presents a unified program in equilibrium theory by revising the predominant model of mixed strategies based on countable additivity. A game is specified by a nonempty set of players and, for each player, a nonempty action set and a bounded von Neumann-Morgenstern utility function. Every such game is shown to admit a Nash equilibrium in finitely additive mixed strategies. In addition, the equilibrium correspondence for any such game is shown to be nonempty, compact-valued, and upper hemicontinuous, and the same …

Body Mass Index Has No Impact On Complications And Mortality For Patients With Stage Iv Pancreatic Ductal Adenocarcinoma, Ren Bryant, Hannah Darnell, Megan Hall, Kelsey N. Karnik, Kristen J. Mcquerry, Ruben R. Plentz

Biostatistics Faculty Publications

Background: Pancreatic ductal adenocarcinoma (PDAC) is one of the leading causes of United States (USA) cancer death. Overweight and obesity developing into a growing global medical and socio-economic problem, affecting approximately 42% of adults in the USA population. The aim of our analysis was to evaluate the influence of overweight and obesity on complications and clinical outcome in patients with stage IV PDAC.

Methods: We retrospectively reviewed electronic health records of patients diagnosed with stage IV PDAC (n=162) who followed with the University of Kentucky from January 2017–October 2024. Comparisons were based on the body mass index (BMI): low BMI …

Bayesian Analysis Of Nominal Outcomes With Missing Values Using Multinomial And Multivariate Multinomial Probit Models, Suwash Silwal

Dissertations, Master's Theses and Master's Reports

Nominal outcomes frequently arise in health sciences, transportation, economics, market research, and related fields. These data often contain missing values, while longitudinal and panel studies generate multiple correlated nominal responses. Bayesian estimation of multinomial probit (MNP) and multivariate multinomial probit (MMNP) models provides a flexible framework for analyzing such data but remains computationally challenging due to high-dimensional likelihood integration, restrictive covariance identification constraints, and poor mixing of Markov chain Monte Carlo (MCMC) algorithms, particularly in the presence of missing data. This dissertation develops parameter-expanded data augmentation (PX-DA) methods for MNP and MMNP models with missing nominal outcomes by incorporating parameter …

Beyond The Lace Index: Benchmarking Machine Learning Architectures And Explaining 30-Day Hospital Readmission Risk With Shap Analysis, Carl E. Hughes Iii

Williams Honors College, Honors Research Projects

Unplanned 30-day hospital readmission remains a fundamental challenge in US healthcare, associated with increased risk to patient recovery and representing an estimated $52.4 billion in annual expenses (Beauvais et al., 2022). While the rigorously validated LACE index serves as the clinical standard for readmission modeling, its linear structure and four explanatory variables lack the complexity to capture the high-dimensional and interactive nature of patient risk. This study utilizes an admission granularity level cohort of the MIMIC-IV database to develop and compare machine learning architectures against the baseline LACE index. Due to the imbalanced prevalence of readmission, the penalized logistic regression, …

Modeling Housing Prices: Which Features Matter Most?, Alex Ruvolo

Williams Honors College, Honors Research Projects

This paper attempts to find the biggest factors and traits that influence the cost of housing. This will include the lot size, type of street, utilities, neighborhood, year built, heating, electrical, yard size, number of different rooms, age, condition, and others. I will attempt to answer the question of whether the prices of houses have changed within the last 5 to 10 years, and obviously this is an easy question to answer. However, the bigger question beyond this is are the main factors affecting housing prices all important in explaining this relationship? Is one factor more important than the rest …

Equilibrium Stability Under Nuclear Confrontation, Martin Bohner, A. A. Martynyuk

Mathematics and Statistics Faculty Research & Creative Works

This article proposes and analyzes mathematical models of confrontation between two and n countries, including countries with nuclear weapons. The proposed models are based on a generalization of Richardson's well-known mathematical model of the arms race. Namely, the factor of hostility is filled with expanded content, including public opinion and the armed forces of the opposing countries. Qualitative analysis of confrontation models is carried out by the method of Lyapunov functions and by applying nonlinear integral inequalities. As a result of the analysis, the conditions for the stability of the equilibrium state of the opposing countries are established, and the …

Threshold Asymmetric Conditional Autoregressive Range (Tacarr) Model, Isuru Ratnayake, V. A. Samaranayake

Mathematics and Statistics Faculty Research & Creative Works

This paper introduces a Threshold Asymmetric Conditional Autoregressive Range (TACARR) model for analyzing the daily price ranges of financial assets. The proposed formulation assumes that the conditional expected range switches between two regimes, representing upward and downward market states, with the disturbance distribution also allowed to vary across regimes. A self-adjusting threshold component, determined by past values of the series, is used to identify the prevailing market regime. In this way, the model is able to capture asymmetric and heteroscedastic volatility behavior in financial markets. The TACARR model is designed to address several limitations of existing price range models, including …

A Variance Decomposition Approach To Inconclusives In Forensic Black Box Studies, Amanda Luby, Joseph B. Kadane

Mathematics and Statistics Faculty Work

In the USA, ‘black box’ studies are increasingly being used to estimate the error rate of forensic disciplines. A sample of forensic examiner participants is asked to evaluate a set of items whose source is known to the researchers but not to the participants. Participants are asked to make a source determination (typically an identification, exclusion, or some kind of inconclusive). We study inconclusives in two black box studies, one on fingerprints and one on bullets. Rather than treating all inconclusive responses as functionally correct (as is the practice in reported error rates in the two studies we address), irrelevant …

Barriers To Immunity: Understanding Covid-19 Vaccine Uptake In Africa, Emilia Blechschmidt

Honors Theses

This thesis examines the factors influencing COVID-19 vaccine uptake across African countries, with a focus on structural, informational, and behavioral barriers to immunization. Drawing on cross-country data, the study analyzes how access to transportation, reliable information, and healthcare resources shape vaccination rates, alongside the effect of demographics and institutional factors in shaping individual perceptions of risk and vaccine safety.

The findings emphasize that the broader strength and preparedness of national health systems strongly influence vaccine uptake. Countries that demonstrated higher coverage of routine childhood immunizations, such as polio and hepatitis B, also tended to perform better in COVID-19 uptake efficiency …

Feasibility, Acceptability, And Preliminary Efficacy Of A Pilot Study To Integrate Buprenorphine Into A Harm-Reduction Drop-In-Center In Kampala, Uganda, Julia Dickson-Gomez, Sergey Tarima, Wamala Twaibu, Dan Katende, Latifah Kyeswa, Laura Glasman, Arthur Kiconco, Sarah Krechel, Bryan Johnston, Moses Ogwal, Brian Byamah Mutamba, Peter Mudiope, Stella Alamo, Rhoda Wanyenze, Geofrey Musinguzi

Biostatistics Faculty Publications

Illicit drug use has been increasing rapidly in Sub-Saharan Africa in the past decade. However, until recently HIV prevention has largely ignored people who inject drugs and medications to treat opioid use disorder (MOUD) were largely absent. This paper reports results of a pilot intervention that integrated buprenorphine into a harm-reduction drop-in-center for people with opioid use disorder (OUD) in Kampala, Uganda. We collected implementation outcomes and changes in self-reported drug use after buprenorphine initiation. We conducted qualitative interviews with a subset of 14 participants who had initiated buprenorphine. Sixty-two participants were screened for OUD, of whom 57 were eligible …

Artificial Intelligence In Biomedical Team Science: Perceptions, Practices, And Training Needs, Emily Slade, Kelsey N. Karnik, Caitline Phan, Megan E. Hall, Yana Feygin, Kristen J. Mcquerry

Biostatistics Faculty Publications

Introduction: Artificial intelligence (AI) is increasingly used in biomedical research, yet limited empirical work has described how researchers use AI tools on collaborative research teams and how they view their role within team-based research. This study examines researchers’ experience with and attitudes toward AI use in collaborative research environments.

Methods: A cross-sectional survey was administered to 178 investigators engaged in collaborative research at the University of Kentucky. Questions assessed AI use across research and communication tasks, team-related decision-making practices, perceived benefits and concerns, and preferences for training and frameworks.

Results: Thirty-nine participants responded (22%). AI use was heterogeneous: 26% had …

Understanding Motivations And Health Outcomes Of College-Aged Triathletes During Covid-19: A Mixed-Methods Study, Patrick Wilson, Eddie Hill, Justin Haegele, Xihe Zhu

Human Movement Studies & Special Education Faculty Publications

A triathlon is a multi-sport event that consists of three simultaneous events: swimming, biking, and running. This sport has experienced significant growth in the past few decades, with colleges and universities now participating. This exploratory mixed-methods study examined the motivations and perceived health benefits of college triathletes during the COVID-19 pandemic, using the Means-Ends of Recreation Scale and the Perceived Health Outcomes of Recreation Scale (N = 29), as well as semi-structured interviews (N = 4). Results indicate no difference in motives or health outcomes between male and female survey respondents. The thematic analysis of open-ended interview questions highlighted lived …

Inferential Statistics For Industrial Organizational Psychologists: A Practical Guide For Testing Hypotheses Using R, Caitlin Lapine

Open Touro Created

2026

This text aims to provide a practical guide for students in industrial organizational psychology or related fields to complete inferential statistics using R open-source programming language. It provides information about when to use particular statistical analyses and how to perform those with statistical software.

Designing A Research Study: Controlling For A Variable And Using Chatgpt, Fritz Umbach

Open Educational Resources

This assignment uses a hypothetical society to help students understand the idea of “controlling for a variable” and practice applying it to a real-world research question. Students design a research approach to examine whether income differences are better explained by family background or by systemic prejudice, working within clear data limits. ChatGPT is used as a research guide to help students brainstorm, test, and revise their methods, while encouraging them to critically evaluate the usefulness and limits of AI-generated suggestions. The assignment emphasizes careful reasoning, clear research design, and thoughtful use of AI as a support for learning rather than …

I Think, Therefore I Can: Self-Efficacy, Self-Regulation, And Sense Of Belonging In Introductory Physics, Danielle Christine Maldonado

Graduate Theses, Dissertations, and Problem Reports (ETD)

Cognitive and affective beliefs in physics classrooms are important indicators of student success beyond traditional measurements of academic performance. This body of work explores major beliefs and processes, including self-efficacy, self-regulation, and sense of belonging, as they relate to academic achievement among introductory undergraduate physics students. First, this dissertation explores the development of physics self-efficacy and physics sense of belonging, two highly correlated variables. This work identifies unique sources of physics self-efficacy and sense of belonging development from current and prior academic experiences, personality factors, and demographic variables. Then, relationships between early- semester self-efficacy and sense of belonging, mid-semester …

Likelihood-Based Inference For Random Networks With Changepoints, Daniel Cirkovic, Tiandong Wang, Xianyang Zhang

Mathematical and Statistical Science Faculty Research and Publications

Generative, temporal network models play an important role in analyzing the dependence structure and evolution patterns of complex networks. Due to the complicated nature of real network data, it is often naive to assume that the underlying data-generative mechanism itself is invariant with time. Such observation leads to the study of changepoints or sudden shifts in the distributional structure of the evolving network. In this paper, we propose a likelihood-based methodology to detect changepoints in undirected, affine preferential attachment networks where, upon introduction, a new node selects one old to attach to with probability proportional to its degree. In particular, …

Infimum Dimension Nash Embeddings For 2d Projective Shape Analysis, Robert L. Paige, Vic Patrangenaru

Mathematics and Statistics Faculty Research & Creative Works

Vector embeddings make complicated data extracted from networks, words and images, more amendable to data science applications. At the present time, the Veronese-Whitney (VW) matrix embedding of the real projective space is the state of the art for making inference about digital images from an uncalibrated camera, such as a cell phone or security camera. In this work we consider vector embeddings for the projective shape data and in particular determine the minimum dimension isometric (distance-preserving or Nash) vector embedding for a projective space. We determine such an embedding for the projective plane in closed-form. From this embedding we determine …

Gender Differences In The Association Between Adverse Childhood Experiences And Drug Use: Findings From A Community-Based Survey In China, Hongyun Fu, Elizabeth Monk-Turner, Xiushi Yang

Department of Pediatrics Faculty Publications

Background

While adverse childhood experiences (ACEs) are widely recognized risk factors for behavioral health problems, including drug use, prior research has largely been conducted in Western countries, focused primarily on males, and relied on convenience samples without comparison groups of nonusers. Limited work has examined the impact of ACEs on drug use in non-Western contexts. This study examines gender differences in the relationship between ACEs and drug use in China, using data from a population-based probability sample survey.

Methods:

Cross-sectional data were collected in 2019 from one city in Yunnan Province in Southwest China and one city in Guangdong Province …

Integer-Valued Time Series Model Via Copula-Based Bivariate Skellam Distribution, Mohammed Alqawba, Norou Diawara, Mame Mor Sene

Mathematics & Statistics Faculty Publications

Time series analysis is crucial for modeling and forecasting diverse real-world phenomena. Traditional models typically assume continuous-valued data; however, many applications involve integer-valued series, often including negative integers. This paper introduces an approach that combines copula theory with the bivariate Skellam distribution to handle such integer-valued data effectively. Copulas are widely recognized for capturing complex dependencies among variables. By integrating copulas, our proposed method respects integer constraints while modeling positive, negative, and temporal dependencies accurately. Through simulation and an empirical study on a real-life example, we demonstrate that our class of models performs well. This approach has broad applicability in …

Propensity Score Matching Accounting For Longitudinal Trends Before Baseline With Group-Based Trajectory Modeling, Dustin R. Bastaich

Theses and Dissertations

Propensity score matching is used in observational studies to balance baseline attributes between a treatment of interest and a control group. Propensity score matching typically relies on baseline variables, but longitudinal trends in patient characteristics can also influence treatment decisions and subsequent health outcomes. This dissertation extends standard approaches by explicitly incorporating longitudinal trajectories of key variables into the propensity score estimation process.

Trends in a longitudinal variable prior to baseline were characterized using group-based trajectory modeling. A two-step modeling approach was implemented where trajectory groups of a key variable were first estimated and then included as covariates in the …

Identifying Mobility Hub Suitability In The Mid-Sized United States Urban Area Using Weighted Overlay And Percentile Based Local Peak Analysis, Eric Asplund

Theses and Dissertations

IDENTIFYING MOBILITY HUB SUITABILITY IN THE MID-SIZED UNITED STATES URBAN AREA USING WEIGHTED OVERLAY AND PERCENTILE‑BASED LOCAL PEAK ANALYSIS

By Eric Asplund

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Urban and Regional Planning at Virginia Commonwealth University.

Virginia Commonwealth University, 2026.

Major Director: Dr. Ivan Suen, Ph. D., Associate Professor, Faculty of Urban and Regional Studies and Planning

Shared mobility hubs are increasingly posited in transportation planning as interventions supporting multimodality, sustainability, and equitable access, but guidance on evaluation of potential hub locations remains uneven, particularly in mid-sized United States cities where …