Digital Commons Network^™

Classical And Quantum Computational Methods For Predicting Fluid Transport In Fracture Networks, John Kath

CGU Theses & Dissertations

This dissertation addresses the challenge of modeling complex geophysical systems by developing efficient surrogate models and scalable quantum algorithms. Our approaches provide uncertainty quantification, assessing confidence in estimates while accounting for subsurface heterogeneity. These innovations are designed to replace costly solvers with parsimonious emulators. In combination with multi-fidelity and quantum techniques, they make physics-informed modeling computationally feasible. One of our studies involves the use of Gaussian process regression to generate Bayesian predictions for gas transport in 3D discrete fracture networks. This provides accurate estimates while offering substantial savings over computationally intensive high-fidelity simulations. Additionally, we study multi-fidelity modeling through the …

Optimization Of Free-Time Controlled Constrained Sweeping Processes And Applications, Thi Dai Trang Nguyen

Wayne State University Dissertations

Optimization and optimal control have a wide range of applications across fields like engineering, biology, data science, and economics. This dissertation is devoted to advanced optimal control problems discontinuous constrained differential inclusions of the sweeping type involving the duration of the dynamic process into optimization, which are truly challenging and underinvestigated in control theory while being highly important for various applications. To attack such problems, we use the method of discrete approximation while establishing its well-posedness and strong convergence to optimal solutions of the controlled sweeping process. This approach, married to advanced tools of variational analysis, enables this research to …

Examining Student Understanding Of Series Convergence Using Script Writing, Eduardo Torres Manzanarez

Mathematics Dissertations - Archive

This exploratory study investigates second-semester calculus students’ understanding of series convergence using both nonscripting and scripting-based tasks. Researchers recognize that students encounter difficulties with learning series, including series convergence, and that there is a need for more meaningful tasks that aid students’ learning of series. Script writing, used mainly with prospective mathematics teachers, can be used to explore mathematical understandings. Thus, this study examines how script writing, in the form of a scripting task, elicits students’ understanding of series convergence in contrast to nonscripting-based tasks to determine the potential of script writing in assessing this student understanding. We examine students’ …

Enhancing The Accuracy Of Image Classification For Degenerative Brain Diseases With Cnn Ensemble Models Using Mel-Spectrograms, Sang-Ha Sung, Michael Pokojovy, Do-Young Kang, Woo-Yong Bae, Yeon-Jae Hong, Sangjin Kim

Mathematics & Statistics Faculty Publications

Alzheimer’s disease (AD) and Parkinson’s disease (PD) are prevalent neurodegenerative disorders among the elderly, leading to cognitive decline and motor impairments. As the population ages, the prevalence of these neurodegenerative disorders is increasing, providing motivation for active research in this area. However, most studies are conducted using brain imaging, with relatively few studies utilizing voice data. Using voice data offers advantages in accessibility compared to brain imaging analysis. This study introduces a novel ensemble-based classification model that utilizes Mel spectrograms and Convolutional Neural Networks (CNNs) to distinguish between healthy individuals (NM), AD, and PD patients. A total of 700 voice …

Construction Techniques For Linear Realizations Of Multisets With Small Support, M. A. Ollis

Emerson Authors, Researchers, & Creators

The Buratti-Horak Rosa Conjecture is a problem in graph theory asking when we can find a Hamiltonian path in the complete graph that has various properties to do with edge lengths. In this paper, we use constructive methods to show that the conjecture is true for various parameter sets where it was previously unknown.

Random Graph Models For Dual Graphs, Anne Friedman

Scripps Senior Theses

This paper aims to better characterize dual graphs derived from state districting maps by developing random graph models that replicate their structural properties. Dual graphs provide a simplified way to represent districting maps, making it computationally feasible to analyze their structure. These representations enable researchers, legislators, and courts to assess district compactness, detect signs of gerrymandering, and generate alternative districting plans. A deeper understanding of the structural patterns of these dual graphs can help researchers choose or design more effective algorithms for redistricting analysis. The random graph models developed in this study serve as testbeds for evaluating algorithmic approaches to …

Analyzing Patterns In Chicago Motor Vehicle Crashes Using Time-Series Techniques, Christina Trotta

Senior Honors Theses and Projects

This project explores time series forecasting of daily traffic crash rates in Chicago from 2018 to 2024, with a focus on understanding how past crash patterns and external conditions influence future risk. The primary research question asks: To what extent does yesterday’s crash rate help predict today’s? Using a combination of Holt-Winters exponential smoothing, Prophet forecasting, and SARIMAX models, we assess the role of autoregression, seasonality, and exogenous variables such as weather and roadway conditions. Daily crash data was cleaned, aggregated, and enriched with engineered features including holiday indicators, weather metrics from O’Hare and Midway airports, and binary flags for …

A New Formulation Of Hardy-Type Dynamic Inequalities On Time Scales, Martin Bohner, Irena Jadlovská, Ahmed I. Saied

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we introduce a novel formulation of dynamic Hardy-type inequalities on a time scale, motivated by a recently established convexity approach in the Haar measure. The classical Hardy inequality is refined so that the classical Lebesgue-measure constant is replaced by the sharp constant 1. We obtain time-scale analogues on finite intervals with best constants, and, for nonincreasing and nondecreasing functions, reversed inequalities with explicit weights described by incomplete β-functions. To establish our results, we employ two distinct time scales and apply the chain rule, together with the substitution rule, the derivative of inverse functions, and Fubini's theorem for …

Self-Tor Persistence Of Modules Over Determinantal Rings, Tatheer F. Ajani

Mathematics Dissertations - Archive

Tor-persistence is the claim that Tor of a module with itself is only zero if the module has finite projective dimension. Work done by Avramov, Iyengar, Nasseh, Sather-Wagstaff, and various other authors have proved Tor-persistence of modules over certain rings. In this work, we will prove Tor-persistence for certain modules over determinantal rings, specifically for the hypersurface defined by the determinant of a generic matrix. We will then give an explicit proof that Tor^R_2(M,M) is never zero, that Tor^R_1(M,M)=0, and due to the periodicity of the given free resolution, our result can be extended to the entire complex, showing that …

Adding Libraries To The Equation: Mathematical Sciences’ Underutilization Of Academic Librarians, Jennifer Lc Burke, Elizabeth C. Novosel, Daniel G. Kipnis, Rasitha Jayesekere

Scholarship and Professional Work

Academic librarians do not engage with all disciplinary departments equally. Despite equal or even greater efforts, some departments are less responsive to librarian outreach. One such department is mathematics. To understand mathematics departments’ relationships with their academic librarians, three mathematics librarians created a 20-question survey that was disseminated to mathematics faculty, instructors, and instructional staff in the United States and Canada. Of the 188 survey participants, more than a third reported that they never engage with their librarians, approximately half only do so occasionally, and a mere eight percent of participants collaborated with librarians to provide information literacy instruction (IL) …

Modeling Deductive Inference: A Historico-Philosophical Introduction To First-Order Logic, David J. Buller

Faculty Books & Book Chapters

This book is a companion text for lectures on first-order logic and its elementary metatheory (used in Intermediate Logic at Northern Illinois University). It covers the basic concepts of set theory necessary for a mathematical development of first-order logic; develops a formal language of first-order logic; presents a classical Tarskian semantics for the language and the “semantic” conception of logical consequence; presents a Gentzenian proof system and the “syntactic” conception of logical consequence; develops a partial decision procedure for logical consequence in the language; demonstrates applications of the formal system to modeling deductive inference expressed in natural language; and extends …

Designing An Affordable Motion Capture System For Multi-Robot Research And Education, Hojune Kim , '25

Senior Theses, Projects, and Awards

In this work, we propose a low-cost motion capture system for real-time tracking of multiple robots’ positions and orientations in indoor environments, specifically tailored for research and educational applications. Precise localization is essential for evaluating robotics algorithms such as decentralized multi-agent control, cooperative path planning, and collision avoidance. [1-3] However, commercial motion capture systems like Vicon and OptiTrack cost between $50,000 and $150,000, making them inaccessible for many smaller institutions, student clubs, and low-resource labs. To address this challenge, we developed an affordable alternative based on three ceiling-mounted 1080p USB cameras and AprilTags. Our system operates at 30 Hz and …

Runner Locating With Multiple Probes, Kola Akinrele, Axel Brandt, Elizabeth Breen, Catherine Erbes, Matthew Lee, Patrick O’Doherty, Weston Rainer

2025 Faculty Bibliography

In the runner locating variation of cops and robbers on a graph, a chaser attempts to locate an invisible runner by probing a single vertex v each turn, from which the chaser learns the runner’s distance. The runner is then permitted to stay at his current vertex or move to an adjacent vertex other than v. A graph is locatable if the chaser is able to locate the runner in a finite number of turns, and the location number of a graph is the minimum number of turns necessary to determine the runner’s location regardless of the runner’s evasion strategy. …

Rings With Q-Torsionfree Canonical Modules, Naoki William Endo, Laura P. Ghezzi, Shiro S. Goto, Jooyoun Hong Phd, Shin-Ichiro Iai, Toshinori Kobayashi, Naoyuki Matsuoka, Ryo Takahashi

Publications and Research

Let A be a Noetherian local ring with canonical module K A . We characterize A when K A is a torsionless, reflexive, or q-torsionfree module for an integer q ≥ 3 . If A is a Cohen–Macaulay ring, H.-B. Foxby proved in 1974 that the A-module K A is q-torsionfree if and only if the ring A is q-Gorenstein. With mild assumptions, we provide a generalization of Foxby’s result to arbitrary Noetherian local rings admitting the canonical module. In particular, since the reflexivity of the canonical module is closely related to the ring being Gorenstein …

Vanishing Of Local Cohomology With Applications To Hodge Theory, Scott Hiatt

Mathematics Faculty Publications

Let H = ((H, F •), L) be a polarized variation of Hodge structure on a smooth quasi-projective variety U . By M. Saito’s theory of mixed Hodge modules, the variation of Hodge structure H can be viewed as a polarized Hodge module M ∈ HM (U ). Let X be a compactification of U , and j : U ↪→ X is the natural map. In this paper, we use local cohomology with mixed Hodge module theory to study j+M ∈ DbM HM (X). In particular, we study the graded pieces of the de Rham complex GrF p DR(j+M) …

Ms-Yolo: Infrared Object Detection For Edge Deployment Via Mobilenetv4 And Slideloss, Jiali Zhang, Thomas S. White, Haoliang Zhang, Wenqing Hu, Donald C. Wunsch, Jian Liu

Mathematics and Statistics Faculty Research & Creative Works

Infrared imaging has emerged as a robust solution for urban object detection under low-light and adverse weather conditions, offering significant advantages over traditional visible-light cameras. However, challenges such as class imbalance, thermal noise, and computational constraints can significantly hinder model performance in practical settings. To address these issues, we evaluate multiple YOLO variants on the FLIR ADAS V2 dataset, ultimately selecting YOLOv8 as our baseline due to its balanced accuracy and efficiency. Building on this foundation, we present MS-YOLO (MobileNetv4 and SlideLoss based on YOLO), which replaces YOLOv8's CSPDarknet backbone with the more efficient MobileNetV4, reducing computational overhead by 1.5% …

Optimizing Decision-Making In A Cerebral Palsy Model Using Reinforcement Learning, Richard Ampah

Pitzer Senior Theses

This study presents an original interdisciplinary investigation into how reinforcement learning (RL) can model motor and cognitive defects and potentially improve motor and cognitive functions in individuals with cerebral palsy (CP), a non-progressive neurological disorder that impairs movement and adaptability. Integrating computational neuroscience and machine learning, the research applies policy gradient methods and Markov Decision Processes (MDPs) to simulate adaptive learning in agents with and without CP-related constraints.

The central aim is to compare the cumulative rewards of optimal policies, derived from value iteration, and human-like learning policies using the REINFORCE algorithm, both with and without the Bellman baseline. The …

The Anatomy Of A Reconstruction: From Fourier Space To Image Recovery In Computed Tomography, Charlotte P. Maurer

Honors Theses

This thesis develops the mathematical foundations of computed tomography (CT) reconstruction through the lens of harmonic analysis. Beginning with the Schwartz class, we introduce the Fourier transform and its role in expressing the Radon transform and its inversion via a fractional Laplacian. After constructing the Radon transform in general dimension R^d, we specialize to the cases d = 2 and d = 3, demonstrating explicit inversion formulas and the associated instability in lower dimensions. For its computational advantages, we study filtered back-projection using classical low-pass filters (Ram-Lak, Shepp–Logan, Cosine, Gaussian) and formulate a discrete reconstruction algorithm grounded in …

Local Limit Theorems On Finitely Generated Abelian Groups, Yutong Yan

Honors Theses

In this thesis, we classify the pointwise behavior of finite-range random walks on finitely generated abelian groups in terms of local limit theorems. Random walks are central objects of research in probability theory, and the theory has found applications in statistics, physics, and even card shuffling. One significant topic in this line of study is random walks on finitely generated groups. Starting from the pioneering work of G. Pólya and H. Kesten, random walks on finitely generated groups have been studied extensively. However, many notable results on the subject (local limit theorems, for example) make assumptions about periodicity and irreducibility …

Affine Groups: A Functorial Perspective, Vladimir Khabaev

Honors Theses

A familiar construction associated to any commutative ringRwith1is its group of units, traditionally denoted by R^x= {u in R | uv = 1 for some v in R}. This is but one out of many ways to get a group from a ring. To see at least one other way, we need a mild change in perspective: units may instead be characterized as elements for which the linear transformation f(r) = u ⋅ r is an isomorphism of R as a module over itself. That is to say, R^x = GL(1, R …

A Comparative Analysis Of Data-Driven And Model-Based Neutrosophication Methods: Advancing True Neutrosophic Logic In Medical Data Transformation, Maikel Yelandi Leyva Vázquez, Lorenzo Cevallos-Torres, Omar Mar Cornelio, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic logic extends fuzzy logic by explicitly modeling indeterminacy (I), offering a robust framework for uncertainty representation. The transformation of crisp data into neutrosophic triplets {T, I, F}—known as neutrosophication—is crucial for applying neutrosophic models in real-world analysis. However, comparative evaluations of existing neutrosophication methods remain limited. This study presents a systematic comparison of five approaches: three model-based methods (Parabolic, Threshold Distance, Fuzzy Membership), one density-based method (Kernel Density Estimation), and a proposed data-driven K-Means clustering method integrating sigmoid membership functions. Using a medical dataset of 299 patients and six continuous clinical variables, we assessed statistical behavior, consistency, and alignment …

Knörr Lattices For Elementary Abelian Groups Over Unramified Extensions Of Z_P, Marie Swartz

Graduate Research Theses & Dissertations

In this dissertation, we examine the existence of positive height Knörr RD-lattices for D an elementary abelian p-group and R an unramified extension of the p-adics Zp. Knörr lattices form an important subclass of the absolutely indecomposable lattices and have close connections to modular representation theory’s “local to global” behavior. We generalize many prior results, shown only when p = 2, to odd p when |D| = p3. Further, when p = 3, we show that a positive height Knörr RD lattice must have a projective summand when restricted to any maximal subgroup of D. The proof of this requires …

Geometric Function Theory On Uniformly Quasiconformally Homogeneous Domains, Allyson Mackenzie Hahn

Graduate Research Theses & Dissertations

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Uniformly quasiconformally homogeneous domains in $\mathbb{R}^n$ carry a transitive collection of $K$-quasiconformal maps for a fixed $K\geq 1.$ In this dissertation we investigate three questions in this setting. The first is to show that quasiconformality and quasisymmetry with respect to the quasihyperbolic metric are equivalent. The second is to study normal quasiregular maps from such a domain into $S^n$ or $\mathbb{R}^n$ and determine they hold geometric properties such as a uniform Hölder condition. The third is to study preimages of a power-type mapping and show they are well-distributed in a precise sense.

Efficient Algorithms For Nearest Correlation Matrix Computation With Missing Data, Ibrahim Eniola Oyeyinka

Graduate Research Theses & Dissertations

This thesis investigates efficient algorithms for computing the Nearest Correlation Matrix (NCM) under incomplete financial data. Correlation matrices are vital in portfolio optimization and risk management, yet empirical estimates often violate symmetry, positive semidefiniteness, and unit diagonal conditions due to missing observations. Two projection-based methods are analyzed: the Modified Alternating Projections (MAP) and Anderson Acceleration (AA). Theoretical analysis using convex optimization and normal cone characterization supports numerical evaluation on synthetic and real-world stock-return matrices (550×550, 2020–2025). Missing data are modeled through Missing Completely at Random (MCAR) and Not Missing at Random (NMAR) mechanisms. The results show that AA converges faster …

Bytes, Banter, And The Bible: An Interdisciplinary Account Of Objective Meaning, Cameron Bonin

Senior Honors Theses

The claim that the Bible has objective meaning is contested in a postmodern world. This claim can be more persuasively defended when it is addressed by insights from multiple disciplines. In particular, the field of computer science is apt to illuminate the concept of meaning through its reflection on the nature of languages and its concern with the accurate transmission of information. By synthesizing insights from the field of computer science, such as that of Claude Shannon, with Nicholas Wolterstorff’s use of speech-act theory, the concept of meaning can be understood more clearly. Consequently, this synthesis assists in answering questions …

Estimating The Gender Wage Gap: A Comparative Analysis Of Different Estimators, Xinran Zhang

Mathematics, Statistics, and Computer Science Honors Projects

The gender wage gap between males and females has been well studied by labor economists. We take a multi-prong approach to evaluate three estimators —a regression-imputation estimator, a weighting estimator, and a doubly robust estimator—in estimating the gender wage gap. Using the Panel Study of Income Dynamics, we conduct an empirical study of the estimators’ performances. In a simulation study, we evaluate the properties of estimators and study whether bootstrapping is an appropriate measure of the uncertainty of each estimator. The findings show that while the estimators provide different results, the doubly robust estimator provides reliable and consistent results under …

Action This Day: The Mathematics And Machinations That Bested The German Enigma, Jonah Weinbaum

Dartmouth College Master’s Theses

This thesis presents a comprehensive and chronological overview of cryptographic techniques designed to break Enigma, beginning in 1932 and culminating in the creation of the Turing-Welchman Bombe. We discuss the mathematical theory and electromechanical implements used to decode one of history's greatest ciphers.

Reexamining the Bombe through the lens of modern group theory, we critique Alan Turing's estimation of the number of "stops" that the Bombe produces for various plaintext-ciphertext pairing structures. To address its limitations, we introduce a new framework for estimating the number of stops by extending John Dixon's theorem concerning the probability that uniformly distributed elements of …

The Local Deep Galerkin Method Applied To The (2+1)-D Cahn-Hilliard Equation, Caden Fischer

Schultz-Werth Award Papers

Physics-informed Neural Networks (PINNs) are an alternative approach to solving Partial Differential Equations. This study examines the Local Deep Galerkin Method (LDGM), and its application to the (2+1)-Dimensional Cahn-Hilliard Equation (2D-CH). The 2D-CH models phase separation. One application of this is to modeling biofilm. The LDGM is trained on a loss function that minimizes the sum of the squares of the residuals of the system of equations. The LDGM is compared to a numerical simulation based on the Finite Element Method. The results of this study show that LDGM does not produce accurate results for the 2D-CH equation for large …

Empirical Analysis Of Political Districting Splitability Via Uniform Spanning Trees In Polynomial Time, Brooke C. Feinberg

Scripps Senior Theses

This work expands a recently proven conjecture that a polynomial fraction of all uniform spanning trees (USTs) are splittable into k balanced partitions on grid graphs to real-world political districting plans. We investigate whether similar structural properties hold for the planar dual graphs of U.S. counties (cnty) and tracts (t), using Wilson’s algorithm to generate uniform random spanning trees and Breadth- First Search (BFS) to check for splitability into balanced partitions. Our empirical findings suggest that real-world districting plans can be split into 2-balanced, connected partitions in a fraction of polynomial time. This result highlights the potential for scalable redistricting …

Reasoning Through Change: Exploring Covariational Thinking In Student Exponential Graph Interpretation, Samantha Lynn Pearson

Honors Theses and Capstones

This study explores how life science students reason about exponential functions in the context of an introductory physics course. While exponential functions are essential in both physics and biology—appearing in scenarios like population growth and temperature cooling—students often encounter challenges in interpreting them. Using a resources framework, we examined the cognitive resources these students bring to exponential reasoning, focusing on what ideas and strategies they already possess. Our methodology involved conducting think-aloud interviews with nine students from PHYS 402. Interviews were coded using a framework informed by prior research on covariational reasoning and exponential understanding. Results show that students generally …