Physical Sciences and Mathematics Commons^™

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 …

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 …

From Lap To Map: How Musical Scale, Place, And Play Drive The Interconnected Mario Kart World, Cameron Cummins

Honors Undergraduate Theses

With their deserts, castles, and ghost houses, the environments of Super Mario games are colorful, whimsical, and charming, but why are they so compelling, and what happens when our analysis of these environments extends beyond individual levels to expansive game worlds? Drawing on Cresswell’s theory of place (2014) and recent work on musical place-building in Mario Kart 8 (Heazlewood-Dale, 2024), I propose a spectrum between localized and globalized scale in games. As game environments become increasingly globalized, the music may be similarly altered to account for this shift in scale. Consequently, players may then encounter a broader, less musically congruent …

Hybrid Patchtst And Physics-Based Framework For Predicting Lithium-Ion Battery State Of Health, Pavan Ravuri

Honors Undergraduate Theses

Accurately forecasting the state of health of lithium-ion batteries is critical for improving performance, reliability and lifetime in energy storage applications. Battery capacity degrades into a nonlinear pattern over cycling due to electrochemical processes where neither purely data driven nor physics-based models can capture alone. This study looks at a hybrid framework combining that PatchTST patch-based transformer architecture with physics-based features derived from the solid electrolyte interphase and pseudo two-dimensional models. Physics inspired proxy features were computed from cycling data and concatenated with electrochemical measurements as added input channels before patch segmentation. There are five model configurations that were evaluated …

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 …

Machine Learning-Based Spatio-Temporal Modeling Of Climate Dynamics And Desertification In The Sahara–Sahel Region, Stephen M. Tivenan

Theses and Dissertations

Arid climate classifications are threshold-dependent and easily interpretable mappings that are widely used in ecological, agricultural, and climate-related studies. These classifications inform scientific understanding, support policy and land management decisions, and provide an intuitive summary of environmental conditions. Despite their usefulness, traditional arid climate classifications often fail to quantify uncertainty, incorporate spatial context, or account for complex relationships among relevant environmental variables. Existing approaches to uncertainty assessment have largely relied on comparing classifications across multiple datasets or alternative formulas, but these methods generally overlook important spatial dependence and latent structure in the data.

This dissertation develops three machine learning-based statistical …

Challenges And Applications Of Fine-Grained Temporal Action Understanding: Modeling Temporal Granularity And Data Efficiency, Halil I. Helvaci

Theses and Dissertations--Electrical and Computer Engineering

Fine-grained Temporal Action Segmentation (TAS) has become a cornerstone of video understanding, offering dense frame-level predictions essential for clinical assessment, surgical skill evaluation, and human-computer interaction. While TAS methods have delivered strong results on coarse-grained benchmarks, two fundamental challenges persist: (1) global attention mechanisms dilute boundary information critical for subsecond precision, a phenomenon we term the temporal granularity bottleneck, and (2) dense frame-level annotation remains prohibitively expensive, with most datasets requiring exhaustive labeling of lengthy untrimmed videos. These challenges are particularly pronounced in medical domains, where sub-second primitives define clinical outcomes while expert annotation remains scarce. In this dissertation, we …

Advancing Periodic Time Series Analysis: Application, Bias Assessment, And Optimal Window Selection In The Variable Bandpass Periodic Block Bootstrap Method, Yanan Sun

Electronic Theses & Dissertations (2024 - present)

Time series analysis is essential for understanding long-term patterns, periodic behavior, and underlying correlations in complex datasets. The periodically correlated (PC) time series is a type of time series where the correlation structure repeats over fixed intervals. The Variable Bandpass Periodic Block Bootstrap (VBPBB) has recently been proposed as a resampling method that preserves PC structures through the use of periodogram, bandpass filters, and block bootstrap resampling. Although promising, VBPBB remains underutilized, and its limitations have not been fully examined. This dissertation advances both the application and methodological development of the VBPBB.

The first project applies the VBPBB to a …

Entropic Foundation Of Finance And Physics: Securities Price Dynamics And Quantum Theory, Mohammad Abedi

Electronic Theses & Dissertations (2024 - present)

In many scientific and financial contexts, we must reason and make predictions under conditions of incomplete information. This dissertation develops Entropic Dynamics (ED) as a unified framework for deriving dynamical laws directly from principles of inference. Within this approach, probability distributions represent states of knowledge, and their evolution is determined through entropy maximization subject to relevant constraints. This leads to a novel concept of entropic time and a formulation of dynamics as an inferential process. In this talk, I will present how ED provides a common foundation across multiple domains. In physics, quantum dynamics for particles and scalar fields in …

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 …

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 …

Changepoint Analyses Confirms Global Tropical Cyclone Frequency Decline, Michael Wehner, Thomas Fisher, Norou Diawara, Robert Lund

Mathematics & Statistics Faculty Publications

Changes in tropical cyclone frequencies as the climate warms is a topic of significant current debate [1, 2]. There is no accepted theory of how tropical cyclogenesis might respond to a warmer ocean-atmosphere system as multiple controlling factors exist [3–7]. Anthropogenic warming of surface ocean temperatures due to increased greenhouse gas concentrations [8] increases the potential for tropical cyclogenesis [9–11]; however, realized cyclogenesis also requires an initial local disturbance [12–16] to develop. Most multi-decadal tropical cyclone permitting climate models (i.e. resolutions of 15-50km) exhibit frequency decreases in warmer climates, despite the increase in tropical cyclogenesis potential [17–25]. In this paper, …

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 …

Machine Learning Prediction Of Federal Appellate Court Outcomes: A Multi-Circuit Analysis With Administrative Law Implications, Nicky Nuertey Apenahier

Dissertations and Theses

Federal appellate courts are the final arbiters in many cases, yet systematic machine learning analysis across all twelve circuits remains largely absent from the computational law literature. With courts of appeals deciding tens of thousands of cases annually and the Supreme Court reviewing only a fraction, understanding what predicts reversal outcomes has both theoretical importance and practical consequences for litigants, attorneys, and judicial administrators. This study addresses that gap using eleven years of federal appellate decisions from the Federal Judicial Center’s Integrated Database. A systematic comparison of twenty-five machine learning models, spanning five algorithms and five class-imbalance correction strategies, identifies …

All Games Have Equilibria, Arthur Paul Pedersen, M. Ali Khan, 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 …

The Maxima Method For Identification Of Principal Periodic Components In Time Series Analysis, Megan Di Maio

Electronic Theses & Dissertations (2024 - present)

This dissertation investigates methods for mean estimation in periodically correlated time series, focusing on the Variable Bandpass Periodic Block Bootstrap (VBPBB) and a novel data-driven maxima method. Time series require specific methods because of the temporal correlation in the data. Traditional methods like the General Seasonal Block Bootstrap (GSBB) account for this correlation but often produce wide confidence intervals because they cannot isolate multiple periodicities, allowing noise and other frequencies to interfere with analysis. The VBPBB method addresses this by applying a Kolmogorov-Zurbenko Fourier Transform (KZFT) filter to the data before bootstrapping, which suppresses interfering frequencies and results in narrower, …

Bayesian Modelling On Periodically And Multiple Periodically Correlated Time Series Data, Jie Yao

Electronic Theses & Dissertations (2024 - present)

Time series with multiple periodically correlated (MPC) components present a complex challenge, with relatively limited prior research. Most existing models are designed for simpler periodically correlated (PC) components and often struggle with over-parameterization, optimization issues, and capturing complex PC patterns within a time series. Frequency separation techniques can help preserve the correlation structure of individual PC components, while Bayesian methods can integrate new and prior information to refine beliefs about these components. This study proposes a two-stage approach that combines frequency separation and Bayesian techniques to forecast PC and MPC time series data. This method aims to demonstrate improved effectiveness …

Applications Of Machine Learning For Evaluating Downward-Coupled Stratosphere-Troposphere Interactions And Subseasonal Forecasts Of Opportunity, Elena M. Fernandez

Electronic Theses & Dissertations (2024 - present)

Wintertime stratospheric dynamics provide key information for understanding atmospheric teleconnections and improving subseasonal-to-seasonal (S2S) predictions on timescales of two weeks to two months. Periods of enhanced predictability, often referred to as forecasts of opportunity, arise from large-scale teleconnected variability, within which the stratosphere serves as an important precursor for tropospheric states, such as near-surface temperatures. While traditional diagnostics of downward coupled stratosphere-troposphere interactions typically rely on zonal-mean representations of wind and geopotential height, this dissertation presents an alternative vortex-centric framework through metrics that capture the daily geometric and dynamical evolution of the stratospheric polar vortex. The proposed stratospheric …

Hidden Markov Models For Stock Market Regime Prediction, Meghan Blanch

Electronic Theses & Dissertations (2024 - present)

Hidden Markov Models (HMMs) are a powerful mathematical system used for analyzing time sequences in which the underlying states are unable to be directly observed. This project strives to develop the theory and computation of such models, including deriving the forward and backward variables, the Baum-Welch algorithm, and the Viterbi algorithm. Each of these HMM components are derived and explained to demonstrate the probabilistic principles that allow HMMs to be effective for modeling sequential data.

To demonstrate its practical relevance, the HMM is applied to financial time series. The observable stock market returns tend to be influenced by market regimes …

Symbolic Logistic Regression For Interval-Valued Predictors: A Simulation Study And Application To Health Data, Soad Abdullah

Graduate Research Theses & Dissertations

This thesis investigates symbolic logistic regression for interval-valued predictors through simulation studies and a real health data application. Classical logistic regression assumes exact predictor values, whereas in many practical settings variables are available only in interval form due to coarsening or reporting uncertainty. Two simulation studies examine the impact of interval uncertainty under asymmetric intervals and measurement error. Symbolic models based on midpoint and midpoint-plus-width representations are compared with the classical approach. Results show that midpoint modeling captures the general relationship but introduces bias under asymmetry, while incorporating width reduces this distortion. Under measurement error, classical logistic regression exhibits attenuation …

Bayesian Inference For A 12-Level Galton Board Using Terminal Bin Counts, Ace Frieders

Graduate Research Theses & Dissertations

A Galton board is a physical device in which a ball passes through a triangular array of pegs and is deflected left or right before landing in one of several bins. Under an idealized model, deflections are independent with probability 0.5 of moving right, implying a binomial distribution for the terminal bin location. Physical boards may deviate from this ideal due to asymmetries and other sources of bias. This thesis develops a Bayesian model for a 12-level Galton board in which each peg has its own right-move probability. Independent Beta priors are assigned to peg probabilities, and terminal bin counts …

Time Series Decomposition And Forecasting Of Alzheimer’S Disease Mortality Using A Kolmogorov-Zurbenko Filter, Jack D. Farrell

Electronic Theses & Dissertations (2024 - present)

Alzheimer’s disease mortality has substantially risen in recent history, placing a significant burden on public health infrastructure and highlighting the need for improved analytical methods to better understand mortality data patterns and offer reliable predictions. Time series methods often struggle to balance both accuracy and interpretability, which hinders the ability to gather meaningful insights from time series data. To address these limitations, this study applies the Kolmogorov-Zurbenko (KZ) filter to monthly U.S. Alzheimer’s mortality data spanning from 1999 to 2023 and decomposes the series into long-term trend, seasonal, and noise components on a logarithmic scale. Long-term trend accounts for 86.49% …

Spectral Analysis Of Traffic Accidents In New York's Capital Region, Michael Barr

Electronic Theses & Dissertations (2024 - present)

In this paper we estimate the spectral density of traffic accident events in the Capital Distict, NY area using a band-pass filter known as the Kolmogorov-Zurbenko Fourier Transform (KZFT). The source data is provided by Moosavi, et al. (2019) and originally captured from various public entities and sensors in the road network. Spectral density estimation with KZFT suppresses noise to reveal the constituent frequencies embedded in the noisy signal. Signal reconstruction based on KZFT produces an approximate weekly accident arrivals for this noisy signal, or in other words a pattern which is proportionate to the event expectation viewed over a …

Entropic Dynamics Approach To The Classical Limit Of Quantum Mechanics: Decoupling Of The Center Of Mass Motion For A Mesoscopic Particle, Fatimah Judayba

Electronic Theses & Dissertations (2024 - present)

In the Entropic Dynamics (ED) approach, quantum mechanics is derived from the principles of entropic inference and information geometry. The ED approach differs from other interpretations by making a clear commitment to distinguishing which variables are ontic (real) and which are epistemic. The classical limit for the center of mass (CM) coordinate is achieved for a large number of particles, M →∞, while Planck’s constant ℏ remains finite. Typically, the emergence of the classical limit requires decoherence through interactions with the external environment. In this work, we investigate whether the classical behavior of the CM coordinate in a mesoscopic system …

Variance Shrinkage In Dunnett-Type Multiple Comparisons With Missing Data, Md Habibullah

UNF Graduate Theses and Dissertations

Dunnett’s procedure is widely used for comparing multiple treatments with a control, but its application becomes challenging in the presence of missing data and multiple com- parisons. An improved Dunnett-type procedure addresses this by using multiple imputation under Rubin’s framework and constructing unified confidence intervals based on a multi- variate t distribution, allowing valid simultaneous inference while controlling the family-wise error rate (FWER). This work further extends the method by incorporating shrinkage-based variance estimation. Specifically, individual group variances are shrunk toward a common value to improve stability. This approach is particularly effective when group variances are similar or moderately different, …

Ridit-Based Adaptive Allocation In Two-Stage Clinical Trials With Binary Outcomes, Dewan Fahim

UNF Graduate Theses and Dissertations

This study explores better ways to assign patients to treatments in clinical trials with binary outcomes, such as success or failure. Adaptive methods are used to learn from early results and adjust treatment assignments during the trial, helping more patients receive better performing treatments while maintaining reliable conclusions. We focus on trials comparing multiple treatments using a two-stage design. In the first stage, several treatments are tested to identify the most promising one; in the second stage, that treatment is compared with a control. Unlike traditional equal assignment, we use adaptive allocation in the second stage to make better use …

Two-Stage Response-Adaptive Randomization Designs For Multi-Arm Trials With Normal Outcome, Tanjin Tamanna Happy

UNF Graduate Theses and Dissertations

This study focuses on improving how clinical trials compare new treatments with a standard treatment, when the response is quantitative (normally distributed). In a common two-stage design, several new treatments are first evaluated, and the best-performing one is selected if it appears better than the standard. In the second stage, this selected treatment is compared again with the standard using additional data to confirm its effectiveness. This approach is known to be efficient in terms of accuracy and sample size savings. We extend this design by introducing an adaptive method for assigning patients to treatments in the second stage. Instead …

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 …