Other Applied Mathematics Commons^™

Using Feynman's Technique To Evaluate Non-Elementary Integrals Used In Physics, Dominick Dingus, Christopher Wengert, Madouna Barsoum

Student Scholar Symposium

In numerous physical applications, such as those in the fields of optics and thermodynamics, the quantitative description of various phenomena requires evaluating certain definite integrals whose antiderivatives cannot be expressed using elementary functions. As a result, these integrals are typically evaluated numerically using a suitable program. However, it is possible to evaluate some of these types of integrals using a strategy known as Feynman’s Technique, an approach named after Richard Feynman, the American physicist who popularized the method during the mid-20th century. This project aims to highlight the usage of Feynman’s Technique for evaluating some of these integrals while applying …

Math Meets Climate: The Energy Balance Model, Maria I. Sanchez Muniz

Open Educational Resources

This assignment introduces students to the mathematics of Earth’s climate through the classical energy balance model. Students analyze how incoming solar radiation, outgoing thermal radiation, and temperature-dependent albedo interact to determine Earth’s equilibrium temperature. Using analytical calculations and computational tools, students identify equilibrium states, assess their stability, and interpret the results through the lens of dynamical systems and bifurcation theory. The activity builds conceptual understanding of climate feedbacks, greenhouse effects, and tipping behavior using a transparent, one-variable model. Designed for applied mathematics and interdisciplinary STEM courses, this assignment emphasizes computation, physical interpretation, and real-world relevance. It is released as a …

Understanding Enso Through Mathematical Models, Maria I. Sanchez Muniz

Open Educational Resources

This assignment introduces students to conceptual models of the El Niño–Southern Oscillation (ENSO) and guides them through a structured investigation of their physical and mathematical foundations. Students analyze the recharge–oscillator and delayed–oscillator frameworks, explore how differential equations capture ocean–atmosphere interactions, and evaluate parameter-driven changes in oscillatory behavior. A key component of the work is the guided use of generative AI as a research tool: students employ AI models to locate peer-reviewed literature, interrogate model extensions, and refine their understanding of complex mechanisms, while synthesizing all final explanations in their own words. By blending classical climate modeling with modern AI-supported inquiry, …

Generalizing Threshold-Based Multiparty Computation To Ramp Schemes, Christian Tucker

All Theses

Secure multiparty computation (MPC) enables multiple participants to jointly compute functions over their private inputs without revealing them. Classical threshold based protocols, such as the BGW protocol, perform computations on scalar values using (k,n)-threshold secret sharing. While these protocols provide strong security guarantees, they become computationally expensive when applied to large matrices or multiple secret values. In this work, we investigate the use of ramp schemes, secret sharing schemes that encode sets of secrets with a trade-off between privacy and efficiency, to generalize BGW computations. We show that the linear operations performed on shares (k,n)-threshold schemes in BGW can be …

Reverse (Bio)Engineering: A Machine Learning Approach To Optimize Baseball Pitcher Health And Performance, Robert C. Moore

All Dissertations

Ball tracking systems are becoming ubiquitous in sport, creating an unprecedented opportunity for big data applications to optimize human health and performance. These applications are especially common in baseball, a sport known for analyzing ball flight data to quantify performance. Analysts routinely use ball flight data to identify the attributes of top performing pitchers, finding that the best pitchers throw with optimal combinations of release speed and spin to precise locations. However, for certain pitchers, the throwing motion required to produce optimal ball flight places exceedingly high biomechanical load on the elbow, and consequently injury rates continue to rise. This …

Feedback Strategies In The Market With Uncertainties, Mustapha Nyenye Issah

Graduate Theses and Dissertations (2019 - present)

This paper explores how established firms use strategic advertising to deter new competitors in uncertain markets. Specifically, it models a situation where market demand evolves unpredictably - captured by the CKLS stochastic process, and the incumbent firm may be either strong or weak, a fact hidden from potential entrants. For a company already in the market, advertising is not just about driving immediate sales, it is a strategic tool to project an image of strength and deter potential new competitors. On the other side, a business thinking about entering that market faces a high-stakes, irreversible decision. It will typically hold …

Quantum Entanglement As A Resource For Coordinating Navigation, Aamir Ahmad

Theses and Dissertations

John Clauser, Michael Horne, Abner Shimony, and Richard Holt (CHSH) originally formulated the CHSH game as an experiment to establish entanglement as a quantum mechanical phenomenon that could not be predicted by classical theories. I will apply the quantum strategy used in the CHSH game to demonstrate that it also establishes a structure that employs entanglement as a resource to enable coordination without communication in the context of navigation.

Investigating The Basic Reproduction Number For An Avian Influenza Model, Omar Saucedo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Probabilistic Modeling Of Antibody Kinetics Post Infection And Vaccination, Rayanne Luke, Prajakta Bedekar, Anthony J. Kearsley

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

[Project Insight] [Foag] Data-Driven Machine Learning Approaches To Modeling Pertussis Vaccine Scare Behavior, Gleb Gribovskii

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Histamine And Serotonin Impact Anopheles Stephensi Population Dynamics And Malaria Transmission: Perspectives From Mathematical Modeling, Michael Robert

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Evolution Of Cooperation In A Mobile Population On Random Networks: Network Topology Matters Only For Low-Degree Networks, Igor V. Erovenko

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Sustainable Insecticide Spraying Strategy For Long-Term Chagas Disease Vector Control, Bismark Oduro

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Understanding The Spread Of Black Sigatoka Disease: A Deterministic And Stochastic Modeling Approach, Bernard Asamoah Afful, Luis F. Gordillo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Investigating The Market Dynamics Of Aeroponically Cultivated Products With Delay, Pulak Kundu, Uzzwal Kumar Mallick

Mathematical Modelling and Numerical Simulation with Applications

Aeroponically grown potatoes offer higher yields and year-round production but often face delayed market entry due to high setup costs, technical barriers, and logistical challenges. A delay-based mathematical model has been newly proposed in this study to analyze the dynamics of demand, supply, and pricing for aeroponically grown products. The model’s existence, stability, and sensitivity have been investigated analytically, and numerical simulations have been carried out using the Runge-Kutta 4th order method with the dde23 solver. Findings reveal that market stability is maintained when delays are below seven years, but delays beyond this threshold lead to persistent fluctuations in price, …

Investigating Potential Alzheimer's Disease Therapies Through An Agent-Based Model Of Impaired Microglia Metabolismmodeling Impaired Microglia Metabolism, Cheyenne Ty, Abigail Penland, John Gerving, Martin Mendoza-Ceja, Megan Pratt, Kamila Larripa

Spora: A Journal of Biomathematics

Alzheimer’s disease is the leading cause of dementia globally and is marked by amyloid-β plaque accumulation, decreased brain pH, disrupted metabolism, and increased permeability of the blood-brain barrier. Microglia, the resident immune cells of the central nervous system, are essential for maintaining brain homeostasis and are critically involved in the progression of AD. While microglia can initiate protective immune responses to injury and disease, dysregulated microglial metabolism may contribute to the exacerbation of Alzheimer's pathology. To investigate potential therapeutic strategies, we developed an agent-based model simulating the effects of exercise and metabolic enhancement on dysfunctional microglia. Our findings suggest that …

Building Countably Many Disjoint Stat Sets In Ω1, Jordan Mills

Summer Undergraduate Research Program (SURP) Symposium

The first uncountable ordinal is ω₁. Here, we will describe the process for partitioning ω1 into countably many disjoint stationary (stat) sets. We first partition ω₁ into 2 disjoint stat sets, and then describe the process for continuing to partition ω₁ into infinitely many disjoint stat sets.

Duality Of Quadrilaterals Via Quaternions, Parker Sjomeling

Summer Undergraduate Research Program (SURP) Symposium

A quaternion is number which is hyper-complex, it has the form,

Where a₁, a₂, a₃, and a₄ are real “scalars”. Then i, j, and k are imaginary numbers which have the following properties:

q = a₁ +a₂i + a₃j + a₃k

Relevant operations on these quaternions include taking the conjugate and the norm (or commonly described as the distance).

The norm of q is equal to:

(a₁)² + (a₂)² + (a₃)² + (a₄)²

The conjugate of q is:

¯q = a …

Advancing Real-World Implementation Of The Well Optimized Linear Finder (Wolf) High-Speed Atmospheric Turbulence Compensation Method, Timothy Evan Coon

Theses and Dissertations

This dissertation advances the real-world implementation of the Well Optimized Linear Finder (WOLF) method for high-speed Atmospheric Turbulence Compensation (ATC). Atmospheric turbulence introduces phase aberrations into optical wavefronts and degrades image quality in terrestrial imaging systems. Traditional phase diversity methods are computationally intensive and poorly suited to real-time operation. The WOLF method addresses these limitations through a novel, point-wise formulation of the optical transfer function (OTF) as a structured autocorrelation of the generalized pupil function (GPF). This formulation enables the estimation of phase aberrations at individual spatial coordinates with distributed computational complexity.

The research begins by developing a MATLAB-based simulation …

Quasistatic Peridynamics, Existence Of Unique Solution In The Presence Of Damage, Nuwanthi N. Samarawickrama

LSU Doctoral Dissertations

A mathematical model for damage propagation based on nonlocal potentials is developed within the framework of peridynamics. This model is applied to simulate damage evolution in cyclically loaded structures. By neglecting inertial effects, a well-posed quasistatic formulation for cyclic loading is obtained.\\ The resulting equation is expressed as a nonlocal and nonlinear integral operator that couples damage evolution to the deformation field.\\ This coupling occurs through the product of a damage factor and the derivative of a force potential. The damage factor ranges between zero and one, where one represents undamaged material and zero indicates complete damage.\\ It serves to …

Modifications To The Spiral Array: A Computational Approach To Music Analysis, Rose Bittle

DePaul Discoveries

The Spiral Array is a geometric model of musical tonality and exists as a tool in computer-aided music analysis. The model was first published in 2000 by Elaine Chew, PhD, in her thesis, Towards a Mathematical Model of Tonality. This project aimed to restructure the Spiral Array, limiting user ambiguity and optimizing the application of musical key finding. The existing model defines pitch, chord, and key location to form a series of spirals dependent on a set of flexible weights. In our research we were able to identify potential issues with the pitch definitions themselves and experiment with methods …

Evolutionary Dynamics Of Artificial Agents: Exploration And Learning In Games, Brian Mintz

Dartmouth College Ph.D Dissertations

The natural world abounds with examples of complex behavior in humans and many other species. Evolutionary game theory is a powerful mathematical framework to understand the origins of many such behaviors like cooperation. Since these behaviors are often selected against initially, understanding why they are so widespread has been a longstanding question. Rather than assuming agents' rationality, like in traditional game theory, this approach studies the mutation and selection of strategies themselves. However most behavior is neither perfectly rational nor entirely determined by genetics. This dissertation works to bridge the gap between these two perspectives by analyzing models where individuals …

Filling Gaps In Scientific Data Sets Using Physics Informed Neural Networks: A Case Study In Velocity Fields, Ellen Saunders

Master's Theses

Gaps in scientific data sets are a persistent issue for researchers in a variety of fields, and while nothing makes up for missing out on real data, well-simulated synthetic data can be a useful tool. In the world of image processing, machine learning techniques have become quite sophisticated at taking an image with a missing component and filling in that space with something believable. The aim of this thesis is to take machine learning techniques similar to what gets used in image processing and repurpose them to infill gaps in scientific data sets in a realistic manner. This thesis compares …

Adaptive Volatility Forecasting Models, Jeffrey K. Tan

Master's Theses

In finance, risk is often quantified by volatility, and computing accurate volatility forecasts — while vital to financial decision making — remains one of the most challenging tasks in financial modeling. This thesis, motivated in part by the Black-Scholes-Merton Model and its limitations, adopts a statistical approach to volatility forecasting. The two main models of interest are the Exponential Weighted Moving Average (EWMA) model and the GARCH(1,1) model. Specifically, this work expands upon a potential adaptive lambda algorithm for EWMA models first proposed by Bernard Bollen (2014), and this work also utilizes the Momentum of Predictability (MoP) to generate adaptive …

Applications Of The Mathieu Groups And Information Theory In Dna Encoding Functions, Juan C. Nava Jr

Theses and Dissertations

A foundational idea in mathematics lies in breaking down existing components into their bare fundamentals. As evidenced by prime numbers and composites, we learn this idea at an early age. Categorizing these broken-down components into their simplest form allows mathematicians to construct proofs from emergent patterns. John Conway’s Atlas of Finite Groups in the 1990s was particularly concerned with the categorization of structures known as groups. There are certain axioms a group must adhere to, which amount to the retention of symmetry; ultimately a group helps us to better understand symmetric actions performed on a set with a binary operation. …

Using A Pharmacokinetic Model To Design And Evaluate An Early Ctdna Biomarker For Response To Targeted Therapy, Aaron Li

Spora: A Journal of Biomathematics

Early prediction of response to therapy or lack thereof can help physicians plan treatment more efficiently. Biomarkers based on circulating tumor DNA (ctDNA) are promising. However, biomarkers beyond direct comparison to baseline have not been thoroughly explored. We develop a model for ctDNA shedding under targeted therapy that incorporates pharmacokinetics. Using a simulated cohort of virtual patients with varied parameters, we define and analyze a biomarker based on ctDNA samples at baseline, 12 hours, and 24 hours after initiation of treatment. The biomarker identified patients who would achieve partial or complete response with high sensitivity and specificity and was able …

Mathematics-Ai Based Phylogenetic Analysis Of Influenza Virus Mutation Data, Emilee Walden

Mathematical Sciences Undergraduate Honors Theses

The influenza virus is one of the most common viral infections each year and can mutate rapidly. Viral mutations pose significant threats to public health by increasing infectivity and strengthening vaccine resistance. To track these evolving patterns, agencies like the CDC annually evaluate thousands of virus strains to understand viral mutagenesis and evolution in depth. Therefore, a computational method for analyzing high-dimensional, noisy virus data could aid in the rapid identification of antigens essential for an effective influenza vaccine for the upcoming season. Through the integration of genomic analysis, clustering, and dimensionality reduction methods, this study specifically aims to develop …

Modeling Dna Repair In Escherichia Coli Using A Boolean And Stochastic Framework, Gabrianne Ivey

All Theses

DNA can be damaged through both internal and external sources. Therefore, cells have created methods to repair DNA damage. In Escherichia coli, the system responsible for DNA repair is termed the SOS response. This system consists of more than 50 genes and contains three main repair pathways: nucleotide excision repair, translesion synthesis, and homologous recombination. The response is initiated when DNA lesions result in the accumulation of single-stranded DNA (ssDNA). The protein RecA is activated by binding to ssDNA and is then denoted RecA*. RecA* assists in the auto-cleavage of LexA which is the primary repressor protein involved in …

Decomposition And Coordination For Multiobjective Optimization: A Framework And Methodology, Philip J. De Castro

All Dissertations

In this work, we consider finding Pareto efficient solutions for complex multiobjective optimization problems (MOPs). Complex MOPs are unique in the literature because they have many more objective functions than is typically considered. In fact, such complex MOPs will have 30+ objective functions. This large problem size presents computational and coginitive difficulties. Computationally, standard techniques for solving MOPs are often ineffective and cognitively it is difficult for a decision maker (DM) to handle all of the information provided in such a large problem. To address these challenges, we develop a decomposition and coordination framework. This framework will allow us to …

Decoding The Algorithm: The Mathematics Behind Tiktok’S Short-Form Content Success, Ashley N. Lynch

Honors Scholar Theses

Within the realm of social networks, TikTok has become the central hub for short-form video content. The network’s unique ability to capture individual preferences using predictive analytics has greatly contributed to its massive success, allowing the company to optimize its performance and content personalization. In an age where digital media have such a significant influence on society, it is essential that users develop an understanding of how social network algorithms function to make more informed online decisions. Although TikTok’s technological system is primarily undisclosed, the platform certifiably leverages several key mathematical principles within its algorithm to achieve its core goals …