Applied Mathematics Commons^™

A Modeling Scenario For Cooling A Hot Vehicle In Florida, Jared Bunn, Bernadette Mullins, Elizabeth Hale, Jaeyoun Oh

CODEE Journal

This paper presents a group project assigned in a Calculus 2 course that has students work to develop, analyze, and draw conclusions about a modeling scenario for cooling a hot car. Using a modeling-first approach, instructors supported the students in class throughout the beginning of the project, enabling the groups to complete the remainder of the project on their own. Students used parameter estimation to tune their models to provided data: one for windows being up, and one for windows being down. This project provides an example of how modeling can be introduced early in a calculus course, rather than …

Dynamics Of Microscale Droplets In Respiratory Airways, Md Shamser Ali Javed

Mathematics Theses and Dissertations

We investigate trajectories of microscale evaporating droplets in a stagnation point flow near a wall of a respiratory airway. The configuration is motivated by the problem of advection and deposition of microscale droplets of respiratory fluids in human airways during transmission of infectious diseases such as tuberculosis and COVID-19. Laminar boundary layer equations are solved to describe the air flow while the equations of motion of the droplet include contributions from gravity, aerodynamic drag, and Saffman force. Evaporation is accounted for at both the droplet surface and the wall of the respiratory airway and is shown to delay droplet deposition …

On A Classification Of Goy/Sabra-Type Shell Models Of Turbulence, Austin Ho

Theses and Dissertations

Since their inception in the 1970s, shell models have proved to be a fruitful testbed for studying theories of turbulence. This thesis considers variations of two classical shell models: the Gledzer–Ohkitani–Yamada (GOY) model and the Sabra model. Up to conjugacy classes, we classify all possible GOY-type and Sabra-type models. We numerically approximate the scaling exponents for the newly identified models and develop their mathematical well-posedness.

From Homogeneous To Heterogeneous Adaptive Bounded-Confidence Opinion Dynamics On Networks, Sally Hafez, Fatma R. Farag, Amira S. N. Tawadros

Northeast Journal of Complex Systems (NEJCS)

Adaptive bounded-confidence models (ABCMs) elucidate the coevolution of agent states and network structure via local interactions and rewiring mechanisms. Traditional formulations assume uniform interaction parameters, leading to distinct regime shifts encompassing fragmentation, polarization, and consensus. A symmetric heterogeneous extension of the adaptive bounded-confidence model is introduced, in which interaction parameters vary according to whether agents belong to the same or different groups. The model retains the original update and rewiring protocols but integrates within-group and between-group confidence bounds alongside tolerance thresholds. Initially, the classic homogeneous model is replicated to establish a reference point. Subsequently, the heterogeneous extension is assessed under …

Improving Tensorsketch Using Complex Random Variables, Amit Sharma, Mohammad Azhar Khan, Rameshwar Pratap, Keegan Kang

Faculty Conference Papers and Presentations

TensorSketch by Pham and Pagh [2013], Kar and Karnick [2012] provides efficient sketching algorithms for highdimensional polynomial kernels $\vec{x}^{\otimes p} \in \R^{d^p}$. Kar and Karnick [2012] uses dense Johnson-Lindenstrauss (JL)-type projections with computational cost $O(pDd)$, whereas Pham and Pagh [2013] extends the sparse CountSketch [Charikar et al., 2024] algorithm, yielding a faster algorithm for high-dimensional sparse inputs with running time $O\left(p(\nnz{\vec{x}} + D \log D)\right)$. However, the variance of both estimators grows exponentially with the polynomial degree $p$, scaling as $3^{p}/D$, where $D$ denotes the sketch dimension. Recent work by Wacker et al. [2023] showed that using complex-valued distribution reduces …

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 …

Parameter Dependent Chen-Fliess Series And Their Nonrecursive Interconnections, Natalie T. Pham

Electrical & Computer Engineering Theses & Dissertations

In control theory, a Chen-Fliess functional series is a weighted sum of iterated integrals constructed from a given set of input functions. Such series can be used to represent nonlinear input-output systems. In applications, they have been employed to characterize interconnected nonlinear systems, to solve system inversion and tracking problems, and to design predictive and adaptive controllers.

Distributed parameter systems exhibit spatial dependence along with temporal dependence. Such systems are typically represented in terms of partial differential equations. In control theory, there appears to be no existing method for representing the input-output map of a distributed system via a Chen-Fliess …

Criticality In A Heterogeneous Neutron Transport Rod Model, Samuel Kaleb Crowford

All Graduate Reports and Creative Projects, Fall 2023 to Present

This work studies the stochastic behavior of neutron populations in a one-dimensional rod model using Monte Carlo simulation. The first part of this project reproduces the computational results of Dumonteil, Horton, Kyprianou, and Zoia (2025) by independently implementing the Monte Carlo algorithm described in their article, with the asymptotic behavior of the first moment analyzed in relation to the dominant eigenvalue and adjoint eigenfunction of the neutron transport operator. The model is then extended to a heterogeneous setting by introducing a central region where fission is suppressed. A global expectation over initial positions and directions is used to estimate the …

Convergence Theory For Deep And Multi-Grade Neural Architectures, Lei Huang

Mathematics & Statistics Theses & Dissertations

This dissertation studies two complementary notions of convergence arising in modern neural network models: the convergence of recursively constructed neural network architectures and the convergence of optimization algorithms used for training neural-network-based image restoration models. The first part develops a convergence theory for deep neural networks (DNNs) viewed as recursively generated sequences of functions. Within an Lp framework motivated by statistical learning, sufficient conditions are established under which increasing-depth neural network sequences converge to well-defined limiting functions. The analysis covers both bounded-width and unbounded-width architectures, establishes explicit convergence rates, and motivates a network initialization strategy derived from the convergence conditions. …

The Role Of Non-Symmetric Weights In Hermite–Hadamard Inequalities For Coordinated Ga-Convex And Ga-Quasi-Convex Functions, Muhammad Amer Latif, Ayesha Shabbir

Publications and Research

This paper establishes new Fejér and Hermite–Hadamard-type inequalities for functions of two variables whose mixed second-order partial derivatives satisfy coordinated GA-convexity or coordinated GA-quasi-convexity on a rectangle in the positive quadrant. Our main results are formulated for non-negative continuous weight functions that are not necessarily symmetric with respect to the geometric means of the interval endpoints, thereby extending the classical framework to genuinely asymmetric weights. However, to obtain explicit and sharp integral bounds in certain cases, we also employ a technical lemma that assumes a special symmetric setting where the weight function is symmetric on each coordinate with respect to …

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 …

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 …

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 …

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 …

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 …

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.

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 …

Open Neighbourhood Edge Degree And Metric Descriptors Qspr And Multi Criteria Analysis Of Chemicals And Antiviral Drugs, Gayathri A Ms

Theses and Dissertations

Chemical Graph theory offers powerful computational methods for evaluating chemical structures, significantly impacting cheminformatics and drug analysis. It provides a robust mathematical framework to represent, model, and analyse molecular systems through topological indices and graph invariants. These indices serve as effective numerical descriptors, encapsulating significant structural information that enhances the prediction of physicochemical and biological properties. This thesis utilizes mathematical modeling, algorithmic computation, and decision making process to derive extensive insights to drug discovery and molecular analysis.

The thesis introduces a new class of topological indices ONE1, ONE2, ONE3, ONE4, ONE5,ONE6 and ONE7 based on open-neighbourhood-edge-degree and it evaluates the …