Mathematics Commons^™

A Data-Driven Approach To Time Series Forecasting And Clustering Of U.S. Regional Drug Overdose Mortality, Koshali Hamy Muthunama Gonnage

Mathematics & Statistics ETDs

The increasing rate of drug overdose deaths in the United States poses a critical public health challenge, particularly due to the surge in synthetic opioids and other high-risk substances. This study presents a data-driven framework that integrates time series forecasting and clustering techniques. Monthly mortality data for five key drug types: cocaine, fentanyl, heroin, methamphetamine, and oxycodone were analyzed using four time series forecasting models: ARIMA, ETS, TBATS, and NNAR. These models were evaluated using standard accuracy metrics RMSE, MAPE, and MAE to assess predictive performance. Signal decomposition approach based on Singular Value Decomposition and subspace modeling was employed to …

Minimal Error Functions On Irregular Subsets Of The Real Line, Robert Michael Dukes

Mathematics & Statistics ETDs

Chebyshev Polynomials, those that minimize the maximal error on a compact set, are one of the most practical tools for approximating smooth functions. The classical results are on the set [-1, 1]; in this paper, we extend to more complicated subsets of the real line. We demonstrate some classical results and then take the result from [2] on regular Parreau-Widom Sets and extend it to semi-regular sets, defined as sets whose regular part is closed. We introduce the Regularity Coefficient as a series formed by evaluating the Green’s Function at irregular points. This new machinery is applied to the lower …

Exact Sampling Of The Six-Vertex Model Using Coupling From The Past, Malaeka Amir

DePaul Discoveries

This paper aims to explore the six-vertex model through simulations designed to investigate the behavior of configurations under specific domain wall boundary conditions. To generate random configurations, we employ the Markov Chain Monte Carlo method while addressing the challenge of mixing times by utilizing the Coupling from the Past (CFTP) algorithm. Implemented in Python, our approach leverages CFTP to ensure exact sampling, avoiding the uncertainty of convergence in traditional Monte Carlo methods. We explore the monotonicity property within this framework and prove that it is only maintained by the steps of this algorithm for very particular values of the parameters.

Dice Math And Probability, Warren Campbell

SEAS Faculty Publications

The manufacture of dice for tabletop games is a billion-dollar industry. In gaming circles and online forums, the concept of “cursed dice” is a popular topic. Dice are inherently unfair due to the difficulty of manufacturing them with perfect geometric tolerances and uniform material densities. A common method for testing dice fairness is the chi-square statistic, which is typically assumed to follow the chi-square distribution. However, this assumption is only asymptotically valid.

Exact distributions of the statistic can be computed for dice with few sides and a limited number of rolls—such as 2-sided (D2) and 4-sided (D4) dice—but the computational …

Torus Probabilistic Principal Component Analysis, Anahita Nodehi, Mousa Golalizadeh, Mehdi Maadooliat, Claudio Agostinelli

Mathematical and Statistical Science Faculty Research and Publications

Analyzing data in non-Euclidean spaces, such as bioinformatics, biology, and geology, where variables represent directions or angles, poses unique challenges. This type of data is known as circular data in univariate cases and can be termed spherical or toroidal in multivariate contexts. In this paper, we introduce a novel extension of probabilistic principal component analysis (PPCA) designed for toroidal (or torus) data, termed torus probabilistic PCA (TPPCA). We provide detailed algorithms for implementing TPPCA and demonstrate its applicability to torus data. To assess the efficacy of TPPCA, we perform comparative analyses using a simulation study and three real datasets. Our …

Graph Convolutional Networks Enable Fast Hemorrhagic Stroke Monitoring With Electrical Impedance Tomography, J. Toivanen, V. Kolehmainen, A. Paldanius, A. Hänninen, A. Hauptmann, Sarah J. Hamilton

Mathematical and Statistical Science Faculty Research and Publications

Objective: To develop a fast image reconstruction method for stroke monitoring with electrical impedance tomography with image quality comparable to computationally expensive nonlinear model-based methods. Methods: A post-processing approach with graph convolutional networks is employed. Utilizing the flexibility of the graph setting, a graph U-net is trained on linear difference reconstructions from 2D simulated stroke data and applied to fully 3D images from realistic simulated and experimental data. An additional network, trained on 3D vs. 2D images, is also considered for comparison. Results: Post-processing the linear difference reconstructions through the graph U-net significantly improved the image quality, resulting in images …

A Study On Fuzzy Time-Series And Its Applications To Stock Price Forecasting, Takeshi Stormer

University Honors Theses

Fuzzy mathematics looks to incorporate the vagueness that exists within the real world, specifically regarding imprecise classes, or non-numerical information expressed as "linguistic" variables. Since most traditional mathematical theories do not have the ability to be applied with the exactness that is otherwise seen in mathematics. As such, there had been many applications of fuzzy mathematics throughout many different fields of mathematics, including that of forecasting. By exploring the fundamentals of fuzzy mathematics, including fuzzy sets, operations of fuzzy sets, the surface level introduction to fuzzy logic, fuzzy relations, operations of fuzzy relations, and fuzzy time-series, this work looks to …

Some Results In Thermodynamic Formalism, C. Evans Hedges

Electronic Theses and Dissertations

This dissertation investigates several key questions at the intersection of dynamical systems, computability theory, and thermodynamic formalism. In the symbolic setting, we establish novel results regarding the statistical properties of equilibrium states, deriving bounds on probabilities of configurations and relating these bounds to the Gibbs property through the homoclinic relation. Additionally, we examine the computability of thermodynamic quantities such as pressure, ground state energy, and residual entropy. We show that topological pressure is computable from above for general subshifts and computable for strongly irreducible shifts, with similar results extending to ground state energy and residual entropy.

Extending beyond subshifts, we …

Forecasting Influenza Rates Using Machine Learning: A Study Of Chatgpt's Predictive Accuracy, Sara Saleh

University Honors Theses

This study evaluates ChatGPT's ability to forecast influenza rates, such as the number of flu cases, hospitalizations, and death during peak season periods using CDC data, and comparing forecasts against actual results to calculate statistical accuracy and consistency. Influenza forecasting is essential for public health planning, but traditional methods may not always provide timely or accurate predictions. In this research study, ChatGPT was utilized to predict the influenza rates for the following week based on the previous week's data obtained from the FluView surveillance system. The predicted rates were compared to the actual influenza rates to assess the model's overall …

Ceno: Non-Uniform, Segment And Parallel Zero-Knowledge Virtual Machine, Tianyi Liu, Zhenfei Zhang, Yuncong Zhang, Wenqing Hu, Ye Zhang

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we explore a novel Zero-knowledge Virtual Machine (zkVM) framework leveraging succinct, non-interactive zero-knowledge proofs for verifiable computation over any code. Our approach divides the proof of program execution into two stages. In the first stage, the process breaks down program execution into segments, identifying and grouping identical sections. These segments are then proved through data-parallel circuits that allow for varying amounts of duplication. In the subsequent stage, the verifier examines these segment proofs, reconstructing the program's control and data flow based on the segments' duplication number and the original program. The second stage can be further attested …

A Bayesian Approach To Grappa Parallel Fmri Image Reconstruction Increases Snr And Power Of Task Detection, Chase J. Sakitis, Daniel B. Rowe

Mathematical and Statistical Science Faculty Research and Publications

In fMRI, capturing brain activation during a task is dependent on how quickly k-space arrays are obtained. Acquiring full k-space arrays, which are reconstructed into images using the inverse Fourier transform (IFT), that make up volume images can take a considerable amount of scan time. Undersampling k-space reduces the acquisition time but results in aliased, or “folded,” images. GeneRalized Autocalibrating Partial Parallel Acquisition (GRAPPA) is a parallel imaging technique that yields full images from subsampled arrays of k-space. GRAPPA uses localized interpolation weights, which are estimated prescan and fixed over time, to fill in the missing …

Radiation-Induced Cardiotoxicity In Hypertensive Salt-Sensitive Rats: A Feasibility Study, Dayeong An, Alison Kriegel, Suresh N. Kumar, Heather A. Himburg, Brian Fish, S. Klawikowski, Daniel B. Rowe, Marek Lenarczyk, John Baker, El Sayed H. Ibrahim

Mathematical and Statistical Science Faculty Research and Publications

Radiation therapy (RT) plays a vital role in managing thoracic cancers, though it can lead to adverse effects, including significant cardiotoxicity. Understanding the risk factors like hypertension in RT is important for patient prognosis and management. A Dahl salt-sensitive (SS) female rat model was used to study hypertension effect on RT-induced cardiotoxicity. Rats were fed a high-salt diet to induce hypertension and then divided into RT and sham groups. The RT group received 24 Gy of whole-heart irradiation. Cardiac function was evaluated using MRI and blood pressure measurements at baseline, 8 weeks and 12 weeks post-RT. Histological examination was performed …

Property Testing Ai: An Efficient Frontier, Paul Sopher Lintilhac

Dartmouth College Ph.D Dissertations

In this dissertation, we take a step towards addressing the major problem of a lack of standardized and rigorous approaches to testing and evaluation of AI systems. Taking inspiration from both the fields of Property Testing and Property Based Testing (for programs), we develop a novel taxonomy of partially overlapping classes of properties of AI systems, including simple properties, compound properties, higher order properties, data relation properties, and architecture-utility properties. We argue that this taxonomy categorizes a diverse set of AI traits -- including accuracy, fairness, robustness, monotonicity, point-wise and global privacy properties, sensitivity, and more -- according to the …

Statistics - What Does My Data Say About Me?, Taylor Gadsden-Deterville

Student Scholar Symposium Abstracts and Posters

For my Introduction to Statistics Class, I have been tasked with collecting unique, personal data to give insight into my daily routine. I decided to record nine different outcomes (two qualitative and seven quantitative). On February 6, 2025, I began with a blank Excel sheet, and so far, I have 57 full days of data collected. I will continue monitoring my findings for the remainder of the Spring 2025 Semester. Per my project instructions, I must include tables and graphs for my qualitative and quantitative outcomes. So far, I have collected daily quantitative data on my screen time (Instagram and …

Modeling Literary Connections: Exploring Transregional Resistance In Dalit Poetry, Antara Bhattacharyay

Mathematics, Statistics, and Computer Science Honors Projects

Structuring socio-political identities, the caste system (a graded form of hierarchy) remains entrenched in contemporary Indian society. Dalits, marginalized by the caste system, have expressed their resistance through literature, envisioning substantive equality and social change. In this thesis, I draw on digital humanities methods to examine regional variation in translated Dalit poetry from Bengali, Hindi/Urdu, Marathi, and Tamil languages. I utilize topic modeling—a machine learning algorithm that detects latent semantic structures in a text—as a point of departure for poetry analysis. I observe how topic modeling enables newer readings of the poems, revealing regionally resonant and broader Dalit themes.

Development Of Saddlepoint Methodologies For Sparse Sample Multiple Parameter Generalized Linear Models And Correlated Data Scenarios, Christopher Johnson

All Graduate Theses and Dissertations, Fall 2023 to Present

Parameter estimation using maximum likelihood techniques may be biased when sample sizes are small, event rates are low, or otherwise sparse counts exist in a parametric model. This in turn may lead researchers to draw invalid statistical conclusions when conventional methods are utilized. The saddlepoint approximation has potential to lessen the degree of bias in sparse data conditions through its use of moments beyond the mean and variance, which allows for more accurate approximations using a smaller number of observations. We propose two novel saddlepoint methods for use in practical analysis scenarios, as an alternative to maximum likelihood estimation. First, …

Computer Vision In Soccer: Yolov11 Analytics Engine For Quantifying Game Strategy, Connor S. Maurer

Data Science Undergraduate Honors Theses

Single-shot object detection capabilities significantly reduce computational overhead for real-time computer vision in sports analytics at 60 FPS. YOLO11’s lightweight CNN gives promising accuracy while meeting the low-latency demand of dynamic soccer matches. As data-driven approaches take over the sport of soccer, efficient player tracking systems become critical for informing coach’s strategies. I prototype the ETL (Extract, Transform, Load) process of data collected from a single- shot detection program and evaluate its viability for estimating player fatigue. YOLO11 detects players, the ball, and other characteristics, with the output transformed by homography to estimate the positions in the real world. These …

Maximal Independent Set Algorithms Within Procedural Planar Maps: A Large-Scale Evaluation, Chaucer Ihrig

Honors College Theses

Analysis of a childhood game has led us to the problem of maximum independent sets in planar graphs. We wrote a graph creation utility using R to generate a random planar map and its dual graph. This utility then finds a graph’s maximal independent set using a variety of six algorithms. We investigate statistical connections between graph structure, colorability, and the maximal independent sets found using these algorithms over an incredibly large and procedurally generated dataset. We find one can always win the coloring game if the resultant graph is two-colorable. The algorithms perform statistically and practically significantly better on …

Efficient Fully Bayesian Approach To Brain Activity Mapping With Complex-Valued Fmri Data, Zhengxin Wang, Daniel B. Rowe, Xinyi Li, D. Andrew Brown

Mathematical and Statistical Science Faculty Research and Publications

Functional magnetic resonance imaging (fMRI) enables indirect detection of brain activity changes via the blood-oxygen-level-dependent (BOLD) signal. Conventional analysis methods mainly rely on the real-valued magnitude of these signals. In contrast, research suggests that analyzing both real and imaginary components of the complex-valued fMRI (cv-fMRI) signal provides a more holistic approach that can increase power to detect neuronal activation. We propose a fully Bayesian model for brain activity mapping with cv-fMRI data. Our model accommodates temporal and spatial dynamics. Additionally, we propose a computationally efficient sampling algorithm, which enhances processing speed through image partitioning. Our approach is shown to be …

Car Price Prediction Using Machine Learning: Analyzing The Dvm-Car Dataset, Yaman Abu Ghareebaih

Electronic Theses and Dissertations

The objective of this study is to predict car prices using machine learning models and the DVM-CAR dataset, which includes over 1.4 million images and car specifi- cations from 899 car models. Key factors such as mileage, engine power, and year of registration were analyzed for their correlation with car prices. Extensive data cleaning was performed, including filling missing values, identifying outliers, and normalizing numerical variables. Discrete variables like car make and body type were encoded using one-hot encoding. Linear relationships were analyzed with Multiple Logistic Regression, and Random Forest models were used for nonlinear patterns. Model performance was evaluated …

Yield Prediction Of Pv Solar Energy Systems And Its Application In The Energy Grid For Operational Efficiency, Pablo Bustamante

Open Access Theses & Dissertations

The generation of power from photovoltaic (PV) solar panels is influenced by a multitude of factors. These include the tilt and orientation of the solar panels, the latitude of their location, and the prevailing climate and weather conditions. Additionally, shading at specific locations, particularly if the panels are not part of a solar facility, can significantly impact their efficiency. The quality and efficiency of the panels themselves, along with the preventive maintenance of both the solar panels and associated components such as inverters and trackers, are also critical. Finally, the overall system design and installation play a vital role in …

Analyzing The Sentiment Of Feminist And Non-Feminist Works, Jasmine Borie, Megan G. Falschlehner

Mathematics, Computer Science & Statistics Presentations

This presentation focuses on a group of texts that advocate for a change in the current belief system. These texts are the Feminist Manifesto, Sojourner Truth: Ain’t I a Woman?, and Civilization and Its Discontents. These first two texts advocate for women’s rights, while Freud’s book is focused on civilization’s decline and how our understanding of community can affect this. Through our presentation, we want to examine the differences in sentiment and language between the feminist texts and Freud’s texts to pinpoint whether or not sentiment changes when advocating for different beliefs.

A Text Mining And Sentiment Analysis Of Valuable Cie Texts Using R, Eric Sugarman, Ethan Turber-Ortiz, Hannah Quinn

Mathematics, Computer Science & Statistics Presentations

The purpose of this project was to perform a sentiment analysis of three texts used in Ursinus College's Common Intellectual Experience (CIE) course: Between the World and Me by Ta-Nehisi Coates, The New Jim Crow by Michelle Alexander and Discourse on Method by Rene Descartes. Word count and word cloud analysis were also performed on the texts as well as term frequency and bigram analysis.

Evaluating The Performance Of Bayesian Removal Models For Estimating Population Density And Detecting Trends With Variable Detection Probability, David R. Stewart

Mathematics & Statistics ETDs

Removal models have long been used to estimate population abundance by progressively capturing and removing individuals from a closed population. These models provide a valuable tool for ecological monitoring, but their accuracy depends heavily on assumptions about detection probability, which may decline over successive sampling passes. Traditional removal models assume constant detection probabilities, an assumption that is often violated in real-world applications. This thesis aims to advance hierarchical Bayesian models by accounting for variable detection probabilities, improving the reliability of abundance estimates and trend detection. By integrating simulation-based analyses with empirical data from Lahontan Cutthroat Trout (Oncorhynchus clarkia henshawi …

Robust Multifidelity Operator Learning For Partial Differential Equations, Jacob Hauck, Yanzhi Zhang

Miners Solving for Tomorrow Research Conference

No abstract provided.

Unraveling The Impact Of Curricular Complexity On Graduation Time: A Causal Analysis In Higher Education, Ameer Slim

Mathematics & Statistics ETDs

This study examines the causal relationship between program complexity and graduation time at UNM. While program complexity is recognized as a factor influencing student outcomes, its precise impact on graduation timelines remains underexplored. Using comprehensive cohort data, this study employs causal inference methods, including generalized propensity scores, to estimate the effect of complexity on time-to-degree. Findings reveal that higher program complexity extends graduation timelines, even after controlling for demographics and academic preparedness. Socioeconomic factors also play a role. Specifically, programs with more Pell Grant recipients and lower median high school GPAs tend to have lower complexity levels. These results provide …

Quarterback Statistics Vs. Season Success, Brendan Woods

Mathematics Senior Capstone Papers

The purpose of this research is to determine which quarterback statistic most significantly impacts team success in the National Football League. By analyzing data from quarterbacks with at least 100 pass attempts per season from 2006 to 2023, we examine the relationship between quarterback rating, passer rating, completion percentage, and TD-INT ratio with end-of-season power rankings. We ran the data through multiple linear regression models to identify which statistic has the strongest correlation with team performance. Our model considers variations across different seasons and accounts for statistical trends over time. With over 17 seasons of data analyzed, further exploration could …

The Effect Of Internal Consistency On Ncaa Women’S Gymnastics Scores, Jordan Williams

Mathematics Senior Capstone Papers

The aim of my research is to examine internal consistency in relation to the validity of scores in NCAA Women’s Gymnastics. This study focuses on scores from the now infamous 2024 Tennessee Collegiate Classic. Patterns from several different deviations and correlation coefficients are analyzed, and a “gold standard” score to test against is created. This allows me to identify several patterns in results that could signify invalid scores.

Faculty Diversity And Minority Enrollment In Advanced Stem Courses: A Case Study At Neville High School, Anaya Cormier

Mathematics Senior Capstone Papers

This study investigates the correlation between the diversity of STEM faculty and the enrollment rates of minority students in honors, Advanced Placement (AP), and dual enrollment STEM courses at Neville High School. Recognizing the long-standing underrepresented minority students in advanced STEM education, this research explores whether a more diverse faculty positively influences student participation in these courses. Using a quantitative correlational design, data on faculty demographics and student enrollment patterns were analyzed through descriptive statistics and chi-square tests of independence. The results are expected to provide information on the role of faculty diversity in fostering equitable academic opportunities. The findings …

An Analysis Of The Alaskan Salmon Harvest, Carson Allen

Mathematics Senior Capstone Papers

The objective of this paper is to analyze the annual Alaskan salmon harvest and the variables that effect the harvest differently each year. Every year, thousands of workers’ livelihoods depend on the annual salmon harvest to provide for themselves and their families. This paper takes this reality and aims to use data gathered from previous fishing seasons to understand what variables affect the salmon population. To analyze the salmon harvest, multiple linear regression will be used over a 41 year period with variables including water temperature, air temperature, yearly harvest, and species of salmon. By modeling these and other variables, …