Applied Mathematics Commons^™

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 …

The Pi-Royal Tire, Erik Talvila

Journal of Humanistic Mathematics

In this humorous story, the half-wit proprietor of a tire manufacturing company thinks knowing pi to more digits will allow the production of rounder tires. An applied mathematician is recruited to fulfill a ridiculous industrial research agenda.

Waiting For The Magic: A Historical And Mathematical Study Of Queues In Disney Theme Parks, Nina E. Becket

Journal of Humanistic Mathematics

This paper, written as part of an honors research project in high school, provides an introduction to the line and queuing systems at Disney theme parks. We begin with a brief history of Disney World and its creators. We then introduce the basics of queuing theory and queuing notation. Finally, we examine modern line systems at Disney (as of 2023) and the future of its different queue systems.

Piracy, Terrorism, And The Law: Differential Equations In Hostage Situations, Gabriel Hallevy

Journal of Humanistic Mathematics

Pirates have taken the crew of an American ship hostage. They promise to release the hostages only if another pirate who is held in an American prison for commission of piracy crimes against American citizens, is released. Should the U.S. government enter into negotiations with them? Should they send armed forces and risk the hostages? Should they release the prisoner immediately and unconditionally? The article models and analyzes possible policies regarding sensitive situations involving hostages and other related risks using differential equations. The solutions are surprisingly simple, but not necessarily intuitive. Our analysis aims to demonstrate how powerful mathematics is …

A Method For Folding Origami Rectilinear Polygon Extrusions, Everett L. Jin

Journal of Humanistic Mathematics

We present a method for generating crease patterns for folding any rectilinear polygon extrusion with a specified uniform minimum edge-to-edge distance, using a rectangular sheet of paper. We demonstrate that the resulting models are efficient and watertight. In addition, they achieve optimal efficiency, meaning they attain the smallest possible scale factor from the original sheet of paper to the folded rectilinear polygon extrusion. Finally, we provide a code implementation of the method. Our study not only facilitates crease pattern design for origami artists but also offers an innovative, art-driven pedagogical tool for inspiring interest in mathematics.

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 …

The Uncertainty Principles, Lee Michael Felicetti

Mathematics & Statistics ETDs

The Heisenberg uncertainty principle is a central aspect of quantum mechanics, but also illustrates an essential quality of the Fourier transform. After Heisenberg, a variety of uncertainty inequalities emerged in the fields of physics and mathematics. In this thesis we will analyze the Heisenberg uncertainty principle in both the setting of quantum mechanics and Fourier analysis. We will then look at how the work of Heisenberg has been expanded upon in both physics and mathematics. Particularity, we will see how uncertainty principles can be applied to signal recovery and explore current research in this field.

Boundary Integral Method For A Modified Mullins–Sekerka System, Ly Le

Mathematics & Statistics ETDs

This thesis develops a boundary integral method for a modified Mullins–Sekerka system arising as the sharp-interface limit of a nonreciprocal Cahn–Hilliard model. Nonreciprocal coupling changes the classical Cahn–Hilliard structure by introducing an additional conserved field, leading to coupled elliptic and parabolic dynamics at the interface. Using matched asymptotic expansions, we formally derive the modified Mullins–Sekerka model and then apply the boundary integral method to rewrite it on the moving interface. The elliptic component is represented using the periodic Green’s function for the Laplace equation, while the parabolic component is represented using the periodic heat kernel. This method reduces the bulk …

Nerve Constructions And Mapper, Alexander Bram Fritschi

Mathematics & Statistics ETDs

Mapper is a data visualization tool commonly used in topological data analysis to study large, often high-dimensional datasets. Mapper operates through the selection of a lens function, a clustering algorithm, and a cover. The Mapper graph is constructed using the nerve of the cover after the clustering algorithm is performed; it is therefore useful to study nerves to better understand Mapper. In this thesis, we will utilize the properties of nerves to find the minimal point set that produces a given graph. We will then extend this to Mapper to determine what Mapper graphs may be constructed over a given …

Timelines Over Tokens: Summarization, Prompting, And Explainable Fine-Tuning For User-Level Suicide Risk Detection, Aditya Tekale

Master's Theses

This research presents a two-stage pipeline for user-level suicide risk detection from Reddit: first, inference-only prompting with summarization; second, fine-tuned encoder classification with explainability and expert validation. The data are user-level: each of the 500 C-SSRS Reddit items is one user’s chronologically concatenated posts and comments (a user timeline), annotated by psychiatrists. Stage one: six prompting strategies zero-shot, few-shot, chain-of-thought, tree-of-thought, least-to-most, and self-consistency are evaluated across six LLMs on multi-class and binary formulations; simple zero-shot achieves the highest balanced accuracy (0.53 multi-class). Error analysis shows longer inputs associate with misclassification (p = 0.002); domain-specific summarization (timelines >2,000 tokens) reduces …

Interpretable Case-Control Inference Through Log-Linear General Location Models, Zacharia Stuart

Mathematics & Statistics ETDs

This dissertation analyzes one of the few publicly available NFL injury datasets to study field type and non-contact lower-limb injuries. Field type is studied jointly with other risk factors to understand how these factors interact to affect injury risk. The data were gathered through a case-control sampling scheme, which limits direct inference on absolute injury probabilities. While not the most common approach for case-control data, this dissertation models the retrospective distribution directly through Log-Linear General Location Models (Log-Linear GLOMs). Through a log-linear structure placed on a log-odds-ratio reparameterization, the model provides directly interpretable marginal and interaction contributions to injury log-odds …

Sustainable Consumer Behavior Modeling: A Complex-Systems Approach To Neuromarketing, Preethi Nanjundan, Nupoor Sanjay Bhute, Ragini Topre, Lijo Thomas

Northeast Journal of Complex Systems (NEJCS)

This study examines the application of complex-systems modeling to neuromarketing data for gaining deeper insights into the mechanisms underlying sustainable consumer behavior. It investigates how neural and biometric responses, interpreted through a systems-based perspective, can uncover dynamic interactions, feedback mechanisms, and emergent behavioral patterns influencing sustainable purchase decisions. The research explores the impact of sustainability-oriented marketing stimuli on long-term behavioral intentions by emphasizing the interconnected roles of cognitive processing, emotional engagement, implicit associations, and collective consumer dynamics. Through simulation-based modeling and structural analysis, the study demonstrates how subconscious neural responses and affective mechanisms mediate the relationship between marketing interventions, consumer …

Fundamental Solutions To The Fractional Heat Operator, Jacob Flores

Math Theses

In this thesis, we are interested in showing the existence of a fundamental solution to the fractional heat operator. The fractional heat operator is a nonlocal linear operator used to model the time evolution of anomalous diffusion processes whose applicability arises in a wide variety of fields in the physical sciences, engineering, economics, and finance. Fundamental solutions to a partial differential operator are a class of generalized solutions formulated with rich mathematical analysis grounded in classes of well-behaved smooth functions referred to as test functions and their continuous linear functionals referred to as distributions. A primary tool that we use …

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 …

Cultural Traits May Replace Human Mobility Data In Forecasting Covid-19 Mortality: A Deep Learning Approach, Saif Abbas, Tamer Oraby, Michael G. Tyshenko, Samit Bhattacharyya

School of Mathematical & Statistical Sciences Faculty Publications

The COVID-19 pandemic highlighted the need for accurate epidemic forecasting to support public health decision-making. Most existing approaches depend heavily on human mobility data, while largely neglecting population behavior shaped by socio-cultural norms. In this study, we analyze daily COVID-19 mortality and Google mobility data from 72 countries during the first 130 d of the pandemic, a period characterized by high uncertainty and behavioral heterogeneity. In particular, we examine whether Hofstede’s country-level cultural dimensions can serve as latent behavioral forecasters of mortality in lieu of dynamic mobility indicators. Using 100 d for training and 30 d for forecasting, we employ …

A Bayesian-Optimized Ensemble Deep Learning Framework For Automated Detection And Classification Of Retinal Diseases In Ghana Using Oct Images, Gifty Duah, Eric Nyarko, Gideon Nana Amo, Theophilus Dwamena Frimpong, Anani Lotsi

School of Mathematical & Statistical Sciences Faculty Publications

Retinal diseases pose a significant global health challenge due to their potential to cause severe visual impairment and blindness. This study aimed to develop a robust deep learning ensemble framework for the automated detection and classification of retinal diseases from optical coherence tomography (OCT) images. This study used OCT images from WATBORG Eye Services in Ghana, including glaucoma, macular edema, posterior vitreous detachment (PVD), and healthy eyes. The data preprocessing steps included augmentation, resizing, and one-hot encoding. The dataset was divided into training (56%), validation (14%), and testing (30%) sets using stratified sampling. Six convolutional neural network (CNN) architectures, Visual …

Provocable Forgiveness In Noisy Brand--Consumer Systems:An Agent-Based Study Of Repeated Interaction, Tahere Ahmadiyan, Hamidreza Navidi, Behbod Keshavarzi

Northeast Journal of Complex Systems (NEJCS)

Repeated brand--consumer exchange is often treated as a managerial problem of loyalty, recovery, and trust. It can also be read as a small complex system: many local decisions about cooperation, retaliation, and forgiveness accumulate into market-level selection. This study uses that perspective to examine which relational rules survive when communication is imperfect. Eight canonical Iterated Prisoner's Dilemma strategies are translated into marketing archetypes and evaluated through round-robin tournaments, a six-level noise sweep, proportional-fitness ecological dynamics, and finite-population Moran invasion tests. The tournament leaderboard is calculated without same-strategy self-play, so that reported payoffs reflect inter-archetype competition rather than homogeneous self-coordination. At …

Comparative Analysis Of Traditional And Deep Learning Time Series Architectures For Influenza A Infectious Disease Forecasting, Edmund Fosu Agyemang, Hansapani Rodrigo, Vincent Agbenyeavu

School of Mathematical & Statistical Sciences Faculty Publications

Influenza A remains a major cause of respiratory mortality worldwide, motivating accurate forecasting to support timely preparedness and resource allocation. This study presents a comparative evaluation of two traditional seasonal time series baselines, ARIMA and Holt–Winters exponential smoothing (ETS), and six deep learning (DL) architectures (Simple RNN, LSTM, GRU, BiLSTM, BiGRU, and a Transformer) for forecasting monthly Influenza A case counts in the United States. Data from January 2009 to December 2023 were analyzed, using January 2009 to December 2022 for training and January 2023 to December 2023 for out-of-sample testing. Models were tuned using a validation split and assessed …

Pseudodifferential Absorbing Boundary Conditions For Waves, Lauren Taylor

Mechanical Engineering Theses

Absorbing boundary conditions (ABCs) are required to truncate the computational domain when performing Finite Element Analyses of exterior acoustic problems where physical domain is unbounded. ABC is applied on a fictitious boundary containing the scatterer and ideally allows outgoing waves to leave without non-physical reflections. Preventing artificial reflections is essential to benefit from the accuracy of the numerical method used. Otherwise, ABC acts as a reflective surface, and artificial reflections distort the solution in the entire domain which is not recoverable by any type of refinement. Pseudodifferential ABCs were used to describe the Dirichlet-to-Neumann map which maps known boundary values …