Applied Mathematics Commons^™

Taut And Dupin Submanifolds (Updated Version), Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

This is an updated version of the paper [29] by the author which originally appeared in 1997. The original paper was a survey of the closely related fields of taut and Dupin submanifolds of Euclidean space, and this updated version includes many results in the field that have appeared since the publication of the original version. The emphasis is on stating results in their proper context and noting areas for future research, and relatively few proofs are given. The important class of isoparametric hypersurfaces is surveyed in detail, as is the relationship between the two concepts of taut and Dupin. …

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

Computational and Data Sciences (MS) Theses

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

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

A Mathematical Decision-Making Framework For Athlete Development In A Collegiate Taekwondo Community: Prioritizing Coaching Interventions Using Statistical Analysis And The Analytic Hierarchy Process, King Harold A. Recto, Hazel Jade L. Antonio, Jhyrald Anthony P. Dalida

Electronics, Computer, and Communications Engineering Faculty Publications

Athlete development within collegiate sports communities requires informed decisions regarding the prioritization of coaching interventions and allocation of developmental resources. However, such decisions are frequently guided by experience and intuition, limiting opportunities for systematic and evidence-based decision-making. This study develops a mathematical decision-making framework for athlete development by integrating statistical analysis and the Analytic Hierarchy Process (AHP) within a collegiate taekwondo community. Data were collected from 25 collegiate taekwondo athletes who satisfied established eligibility criteria, including participation in University Athletic Association of the Philippines (UAAP) competitions during the previous three seasons. Athletes evaluated coaching practices across five dimensions: Training and …

Information Theory Analysis Of Water Vapor Stable Isotopes From The Sail Campaign, Matthew John Rybecky

Earth and Planetary Sciences ETDs

Understanding the processes that control water vapor isotopic composition in mountain environ- ments is essential for interpreting isotope records and predicting water resource responses to cli- mate change. This thesis applies information theory to continuous, high-resolution water vapor stable isotope measurements from the Surface Atmosphere Integrated Field Laboratory (SAIL) campaign in the East River watershed of Colorado’s Upper Gunnison Basin, spanning the winter- to-spring transition of 2022–2023. The analysis employs Shannon entropy, mutual information, transfer entropy, and joint transfer en- tropy (JTE) to quantify how environmental variables, including surface meteorology, radiation, tur- bulent fluxes, and ERA5 reanalysis products, transfer information …

Stylometric And Formal Patterns In The Scholarly Impact Of Scientific Literature, Joshua Ange, Eric Godat, Rajani Sudan

SMU Journal of Undergraduate Research

Scientific communication is typically tied to promoting public engagement and interest in science, increasing scientific literacy, and playing an essential role in policymaking. The success of public communication of scientific findings is largely associated with secondary characteristics of research (e.g. the style of writing and presentation), rather than the primary content or research quality. But it is unclear to what extent the success of scientific literature intended for working scientists is influenced by those same secondary characteristics. Does the writing style of scientific articles impact their success in academic spheres? In this study, we explore the stylometric and formal characteristics …

Cdt-1d Cnn Integration With Simpson-Sobolev Regularization For High-Frequency Options Trading: With Fem-Based Heston Option Pricing, Daniel M. Margolis, Johannes Tausch, Arthur K. Selender

Mathematics Theses and Dissertations

This dissertation presents a computational framework for high-frequency options trading that combines Cross-Data-Type 1-D Convolutional Neural Networks (CDT-1D CNN) with Simpson-Sobolev regularization for directional prediction, and finite element methods (FEM) for realistic option pricing during backtesting. The core innovation lies in developing a mathematically rigorous regularization approach that maintains the adaptability of modern deep learning while enabling accurate evaluation through stochastic volatility models. The primary contribution is the Simpson-Sobolev regularization scheme, which extends traditional Sobolev regularization by incorporating Simpson’s rule for numerical integration. This approach achieves higher-order accuracy in approximating the Sobolev norms that control function smoothness. Simpson’s rule attains …

Enhancing Community Engagement Through ‘Nitunze Kilombero’ Mobile App: Case Of Climate Land Use And Cover Management For Kilombero Basin, Ghanima Chanzi, Subira Munishi

Tanzania Journal of Engineering and Technology (TJET)

The Kilombero Basin in southeastern Tanzania faces significant challenges due to rapid land use and land cover (LULC) changes driven by climate change, population growth, and unsustainable farming practices. This study assessed the role of community engagement and digital reporting through the 'NITUNZE KILOMBERO', mobile application in supporting water resources management in the basin. The App facilitates real-time reporting of environmental issues, provides educational resources, and enables collaboration between local communities and authorities. A mixed-methods approach, including household surveys and key informant interviews, was employed to assess the app's effectiveness. Results indicate high community awareness of LULC impacts, with 85% …

(R2077) Enhancing Queue Management: Dynamic Server Allocation And Optional Services In Stochastic Modeling, G. Ayyappan, S. Sankeetha

Applications and Applied Mathematics: An International Journal (AAM)

Consider a queueing system with a single server, where customer arrivals follow a Markovian arrival process and service times follow a phase-type distribution. The main server has the capability to recruit an additional server when the number of customers in the system exceeds a certain threshold, denoted as L. Both servers provide normal service to customers, and optional service is provided upon request. The main server takes multiple vacations, with the durations following an exponential distribution with rate parameter η, until there is at least one customer in the system. This system can be represented as a Markov chain process, …

Analysis And Machine Learning Adaptation Of A Cognitive Model For Human Memory, Trevor Cross, Aihua W. Wood

Faculty Publications

In this paper, we use the Duolingo SLAM dataset to analyze several cognitive models of second language acquisition and develop new approaches for enhanced performance. In particular, we consider the Predictive Performance Equation and some of its underlying power laws. Leveraging insights from machine learning, we develop simple one-feature models as building blocks for combined models that match or in certain cases outperform the existing models at much reduced computational cost. In addition, a neural network with one fully connected hidden layer is constructed that outperforms all other models on sufficiently large datasets.

A System For The Prediction Of Election Results Using Vader And Hybridized Machine Learning Model, Abraham E. Evwiekpaefe, Khadijah Kabir, Georgina N. Obunadike

Tanzania Journal of Science

Integrating different classifiers along with sentiment lexicons like Vader, can enhance the performance of sentiment analysis systems. However, such a hybrid model remains underexplored, particularly in the context of regional elections in developing countries like Nigeria. The aim of this research is to develop a hybrid model that combines three machine learning classifiers and Vader lexicon to possibly achieve a higher accuracy. A case study of the 2023 governorship election in Kogi, Bayelsa and Imo State, Nigeria was examined. Twitter API library was utilized to extracted public and personal tweets using hashtags and keywords related to the target data from …

Conditional Product Sampling For Gaussian Process Implicit Surfaces, Song Shi

Dartmouth College Master’s Theses

Gaussian Process Implicit Surfaces (GPISes) provide a powerful and unified stochastic geometry representation for rendering surfaces, volumes, and the rich continuum between them. Recent work has shown that GPISes can model a broad space of visual appearances under a unified light transport framework. However, practical rendering with GPISes remains challenging: existing estimators can become inefficient for particular correlation structures, and highly anisotropic or heightfield-like GPISes require specialized treatment to obtain robust variance reduction.

This thesis extends recent work on GPIS rendering by introducing a new next-event estimation (NEE) technique for anisotropic GPISes.We show that standard NEE provides diminishing benefits as …

An Analytical Framework For Quantifying Urban And Community Resilience To Natural Hazards From Cell-Phone Gps-Location And Traffic-Flow Data, Georgios Chatzikyriakidis

Civil and Environmental Engineering Theses and Dissertations

Urban areas are increasingly exposed to natural hazards while accommodating a growing share of the global population, yet a consistent science-based framework for quantifying urban and community resilience remains lacking. This dissertation develops a physics-based analytical framework grounded in statistical mechanics and the quantitative theory of Brownian motion. A city is conceptualized as a complex medium in which citizens move analogously to Brownian particles within a viscoelastic environment, influenced by socioeconomic interactions and infrastructure functionality.

A central premise is that urban resilience, interpreted as engineering resilience (an outcome), can be quantified through a single metric: the mean-square displacement MSD=⟨r²(t)⟩, of …

Largest 2-Regular Subgraphs In Complete S-Partite Graphs, Yiyang Jiang

McKelvey School of Engineering Graduate Student Theses & Dissertations

In this thesis, we focus on the class of complete $S$-partite graphs, for $S$ an undirected graph possibly with self-loops, and address the problem of finding largest $2$-regular subgraphs of these graphs, which can be formulated as an integer linear program. Roughly speaking, a complete $S$-partite graph is obtained by replacing every single node of $S$ with a number of nodes, preserving the edge/non-edge relations of $S$. Our motivation in studying largest $2$-regular subgraphs is rooted in the structural systems theory, particularly in the problem of finding largest subnetworks that can sustain controllability or asymptotic stability of the corresponding subsystems. …

Machine Learning For Handwritten Character Recognition, Hannah Freitag

Honors Capstones

Handwritten character recognition remains a challenging problem in machine learning due to the high variability of handwriting across individuals and the visual similarity between certain character classes. This project explores whether Singular Value Decomposition (SVD)-based dimensionality reduction can serve as an effective preprocessing step for a fully connected neural network trained on the EMNIST Balanced dataset, a 47-class benchmark of handwritten digits and letters. By projecting 784- dimensional pixel inputs onto the top 70 principal components, approximately 90% of the total variance is preserved while reducing input dimensionality by 91%. The resulting SVD-based model achieves approximately 94% test accuracy, outperforming …

Adaptive Artificial Potential Field Guidance And Control For Autonomous Docking With Uncooperative And Unknown Spacecraft, Steven Holmberg

Theses and Dissertations

The increasing demand for on-orbit servicing (OOS), active debris removal (ADR), and space domain awareness (SDA) missions has increased the need for autonomous spacecraft rendezvous and proximity operations (RPO) with uncooperative and unknown targets. Traditional guidance and control methods are typically designed for cooperative systems with known geometry and state information. This work builds on previous research to develop and evaluate an artificial potential field (APF)-based control framework capable of autonomous operation with minimal prior target knowledge and applicability to both relatively static and tumbling spacecraft.

The proposed APF formulation incorporates established safety constructs from cooperative docking systems, including an …

The Digital Neuron: Neural Cellular Automata For Neural–Symbolic Translation, Nicole Assenza

SMU Data Science Review

A neural cellular automata (NCA) architecture, referred to as Pluto’s NCA, was developed to characterize bilateral communication and semantic reciprocity between symbolic representations and a spatially distributed update field. The architecture employs an encoder–automata–decoder pipeline that maps symbolic inputs into a multichannel state field and reconstructs them through agreement-driven attractor convergence within a stable semantic attractor landscape. System behavior was evaluated under controlled perturbations, including rhythmic desynchronization, graded ablations, correlated and independent noise, and percolation-based structural degradation. Quantities such as Agreement(t), internal coherence Aᵢ(t), the recovery time constant τ, and the critical percolation threshold pc were measured to assess stability, …

Low-Complexity Structured Neural Networks And Their Usage In Image And Signal Processing, Adam Kuzmicki

Doctoral Dissertations and Master's Theses

Conventional neural networks face significant challenges due to high computational costs, large parameter counts, and reliance on backpropagation, which restricts their application in resource-constrained and real-time settings. To address these challenges, this thesis proposes three structured neural network (NN) architectures grounded in the theories of sparse and self-contained factorizations of transforms, with applications to image compression, reconstruction, classification, encryption, and also adaptive wideband multi-beam beamforming. The first neural network architecture, named DCTrix-Net, replaces conventional spatial con- volution with highly sparse factorization of the discrete Cosine transform (DCT) complemented by Toeplitz-structured weight initialization, achieving at least 97% FLOP reduction over CNNs, …

An Odd Protocol For An Agent-Based Model Of Hepatitis C Virus Transmission In A Homogeneous Syringe-Sharing Network, Seun Ale, Que Thi Nguyet Nguyen Dr., John D. Kelleher Prof., Elizabeth Hunter Dr.

Reports

The model described in this ODD is an agent-based model of hepatitis C virus (HCV) transmission among people who inject drugs (PWID). The model assumes homogeneous mixing among syringe-sharing agents, without any form of heterogeneity in the agents interactions or syringe-sharing attitude. All syringe-sharing PWID are treated as identical in terms of their interaction frequency and syringe-sharing probability. Interactions are generated dynamically using proximity-based sampling at each timestep (one day), allowing agents to form syringe-sharing interactions based on spatial closeness. The number of daily interaction events is fixed at the population level, and each syringe-sharing agent has the same probability …

An Odd Protocol For An Agent-Based Model Of Hepatitis C Virus Transmission With Inter- And Intra-Group Structural And Behavioural Heterogeneous Syringe-Sharing Networks (5), Seun Ale, Que Nguyen Dr., John D. Kelleher Prof., Elizabeth Hunter Dr.

Reports

The model described in this ODD is an agent-based model of hepatitis C virus (HCV) transmission among people who inject drugs (PWID). The model incorporates structural heterogeneity through a three-group interaction framework and behavioural heterogeneity through group-specific syringe-sharing rates with additional intra-group variability. The syringe-sharing population in the model is divided into core, inner, and outer circle groups representing individuals with high, moderate, and low levels of syringe-sharing interaction intensity, respectively. In addition to differences in the number of daily interaction opportunities across groups, agents in each group are assigned syringe-sharing probabilities that vary at the individual level around their …

An Odd Protocol For An Agent-Based Model Of Hepatitis C Virus Transmission In A Two-Group Structural Heterogeneous Syringe-Sharing Network (M2), Seun Ale, Que Nguyen Dr., John D. Kelleher Prof., Elizabeth Hunter Dr.

Reports

The model described in this ODD is an agent-based model of hepatitis C virus (HCV) transmission among people who inject drugs (PWID). The model extended a baseline homogeneous model by incorporating structural heterogeneity via a two-group interaction framework. The syringe-sharing population in the model is divided into inner and outer circle groups representing individuals with differing levels of syringe-sharing interaction intensity. While all agents share the same syringe-sharing probability and epidemiological processes remain identical across agents, the number of daily interaction opportunities differs between the two groups. Interactions in the model are generated dynamically using proximity-based sampling at each timestep …

An Odd Protocol For An Agent-Based Model Of Hepatitis C Virus Transmission In A Three-Group Structural Heterogeneous Syringe-Sharing Network (M3), Seun Ale, Que Nguyen Dr., John D. Kelleher Prof., Elizabeth Hunter Dr.

Reports

The model described in this ODD is an agent-based model of hepatitis C virus (HCV) transmission among people who inject drugs (PWID). The model incorporates structural heterogeneity through a three-group interaction framework. The syringe-sharing population in the model is divided into core, inner, and outer circle groups representing individuals with high, moderate, and low levels of syringe-sharing interaction intensity, respectively. While the syringe-sharing rate and all epidemiological processes remain identical across agents, the number of daily interaction opportunities differs by agent grouping, capturing variation in structural position within the syringe-sharing network. Interactions are generated dynamically using proximity-based sampling at each …

An Odd Protocol For An Agent-Based Model Of Hepatitis C Virus Transmission With Inter-Group Structural And Behavioural Heterogeneous Syringe-Sharing Networks (M4), Seun Ale, Que Nguyen Dr., John D. Kelleher Prof., Elizabeth Hunter Dr.

Reports

The model described in this ODD is an agent-based model of hepatitis C virus (HCV) transmission among people who inject drugs (PWID). The model incorporates structural heterogeneity through a three-group interaction framework and behavioural heterogeneity through group-specific syringe-sharing rates. The syringe-sharing population in the model is divided into core, inner, and outer circle groups representing individuals with high, moderate, and low levels of syringe-sharing interaction intensity, respectively. In addition to differences in the number of daily interaction opportunities across groups, agents in each group are assigned distinct syringe-sharing probabilities, reflecting variation in risk-taking behaviour across structural groups within the syringe-sharing …

On Cartan’S Examples Of Isoparametric Hypersurfaces And Their Focal Submanifolds, Thomas E. Cecil, Patrick J. Ryan

Mathematics and Computer Science Department Faculty Scholarship

This paper is a survey of Cartan’s examples of isoparametric hypersurfaces in spheres and their focal submanifolds that were described in his fundamental work on the subject, which appeared in four papers [2]–[5] published during the period 1938–1940.

Detecting And Repairing Conflicting Constraints In Co-Trained Physics-Informed Neural Networks For Composite Curing Processes, Cooper J. Evans

Dissertations, Master's Theses and Master's Reports

Composite materials have become a critical component of modern manufacturing, especially in the automotive and aerospace industries. The curing process for these composites has been modeled using a variety of partial differential equations representing the heat transfer and composite curing kinetics. Optimizing the applied temperature profile is critical for maximizing the efficiency and capacity of composite part manufacturers. Constraints must be placed on the inputs and outputs of the model, including but not limited to, the applied temperature profile, part temperature, and final degree of cure. Conflicting sets of constraints are easy to unknowingly impose due to the highly coupled …

Design And Analysis Of Modern Quantum Neural Network Architectures For Intelligent Systems, Lakshmi Chandrakanth Kasireddy, Prabhakara Rao Kapula, Dineshkumar Rajendran, Neha Bharani, Srikanth Pulipeti, Islombek Khushvaktov

Computer Science Faculty Publications

Quantum neural networks (QNNs) offer a principled pathway for integrating quantum computation with machine learning through superposition- and entanglement-based representations. This chapter proposes an architecture-aware design and evaluation framework for modern QNNs, emphasizing robustness and system feasibility alongside predictive performance. Multiple architectures variational QNNs, quantum convolutional neural networks, tensor-network hybrids, and fully quantum models—are assessed under a unified protocol. Experimental analysis shows that the proposed architecture-search–guided QNN achieves 91.8% classification accuracy and an F1-score of 0.914, outperforming fixed-template variational QNNs by approximately 5.6 percentage points. Under depolarizing noise with probability p = 0.10, the proposed model retains 85.3% accuracy, whereas …

Stochastic Fractional-Order Memristive Fuzzy Bam Neural Networks With Time Delays And Leakage Term For Finite-Time Stability Analysis, J. Kumar, M. Syed Ali, Sumaya Sanober, Mohammad Yarish, Abeer M. Alotaibi, Tarek F. Ibrahim

Computer Science Faculty Publications

In this study, a finite-time stability analysis with time delays and a leakage term is conducted on stochastic fractional-order memristive fuzzy BAM neural networks. FOMFBAMNNs are developed using set-valued map theories as well as differential inclusion. We obtained several significant adequate criteria of uniform stability in the mean square of such networks by using analytical methods and inequality approaches, such as Cauchy–Schwarz inequality and Burkholder–Davis–Gundy inequality. In addition to examining two different fractional-order derivatives between the U-layer and V-layer synchronously with fractional order, the existence, uniqueness, and stability of its equilibrium point are also shown ½ ≤ α ≤ 1. …

Robust Deep Learning One-Class Classification, Shahd Alnofaie

Graduate Studies Theses and Dissertations 2026

One-Class Classification (OCC) focuses on learning the characteristics of normal data and identifying observations that deviate from this learned pattern as anomalies. It is commonly used in applications such as medical diagnosis, cybersecurity, industrial monitoring, and fraud detection, where abnormal examples are often rare or unavailable during training. Classical approaches such as SVDD and LS-SVDD describe normal data using a hypersphere. While effective in some settings, these methods rely on shallow representations and can be sensitive to noise and contaminated observations. To address these limitations, this dissertation introduces a Deep LS-SVDD framework that combines hypersphere-based data description with deep neural …

Beyond Full Fine-Tuning: The New Playbook For Adapting Deep Neural Networks, Cristian S. Mcgee

Honors Undergraduate Theses

Fine-tuning is the process of teaching and specializing a pre-trained neural network on a downstream task. Fine-tuning is a rapidly growing topic in artificial intelligence domains; however, many fine-tuning endeavors are highly specialized without a coherent framework connecting them. This work presents a unified perspective on fine-tuning methods and performance metrics. Our perspective organizes the methods in terms of how they are applied to fine-tuning. This framework showcases methods that (i) update effective subspaces of the pre-trained model, (ii) change the adaptation optimization procedure, and (iii) alter the representations of the embedded input. Additionally, we present unconventional metrics such as …

A 1d Symmetric Interior Penalty Discontinuous Galerkin Solver In Rust, William Aey

Williams Honors College, Honors Research Projects

This honors project will build a 1D Symmetric Interior Discontinuous Galerkin (SIPDG) solver in Rust for Stum-Liouville type problems such as the Poisson equation, with Robin, Dirichlet, and Neumann boundary conditions. The work will cover the full pipeline: starting from the strong form of the PDE, deriving the DG weak form, implementing element and interface operators, and assembling or apply the discrete operator. Rust's safety and concurrency (e.g, via Rayon) will be used to explore serial and parallel performance. A test-driven development approach will be used to maintain a strong suite of tests. The project will result in a documented …

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 …