Applied Mathematics Commons^™

Inhomogeneous Branching Random Walks: Incorporating Genealogy And Density Effects, Lauren Ajax, Beatrice Durham, Pratima Hebbar, Cade Johnston, Jiayi Zhang

Spora: A Journal of Biomathematics

We introduce a novel framework using inhomogeneous branching random walks (BRWs) to model biological processes, specifically by introducing genealogy-dependence in branching rates and displacement distributions to model bacterial colony growth. Current stochastic models often either assume independent and identical behavior of individual agents or incorporate only spatiotemporal inhomogeneity, ignoring the effect of genealogy-based inhomogeneity on the long-time behavior of these processes. Such asymptotics are of independent mathematical interest and are crucial in understanding the emergence of patterns. We propose several inhomogeneous BRW models in 2D space where displacement distributions and branching rates vary with time, space, and genealogy. A combined …

Comparative Machine Learning Models For Disease Risk Prediction, Mercy Mawusi Agbley

Theses, Dissertations and Capstones

Accurate prediction of disease outcomes is crucial for improving clinical decision-making and enabling early intervention. This study compares the performance of various statistical and machine learning models for clinical risk prediction using two healthcare datasets: diabetic retinopathy and heart disease. The models assessed include Logistic Regression, LASSO, k-Nearest Neighbors (KNN), Support Vector Machines (SVM), Neural Networks, Random Forests, Gradient Boosting Machines (GBM), and a stacked ensemble model. Prior to modeling, datasets were split into train and test sets. Standardization was applied to numeric features whilst categorical features were one-hot encoded. These transformations were later applied to the test set. Principal …

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 …

Uncertainty Quantification, Propagation & Conjunction Assessment In Orbital Mechanics Using Generalized Polynomial Chaos Expansion & 2-Dimensional Conjunction Plane Analysis Techniques, Monalisa Karim

Mechanical and Aerospace Engineering Theses

Uncertainties, that are inherent to dynamic models, can be associated with state initial conditions, force modelling errors, navigation and actuation errors. In system modelling stochastic differential equations are used to represent dynamic phenomena with uncertainties, for which the solutions are probability density functions of quantities of interest characterizing the realization of the stochastic processes. In Polynomial Chaos Expansion (PCE) propagation, these solutions are represented as weighted sums of multivariate spectral polynomials that are functions of the input random variables. Generalized polynomial chaos expansion (gPC) is an extension to the original homogenous PCE which projects the random solution onto a basis …

Investigating The Connection Between Als Through The Mutation R522s In The Rna Binding Protein, Dennia Estrella-Vargas, Lydia Uptain

Mathematics

Amyotrophic lateral sclerosis (ALS) is a fatal disease that causes the deterioration of motor neurons , death is usually due to respiratory paralysis. The variant R522S was chosen because it is near a hot spot of pathogenic variants. It is an arginine-to-serine swap, this swap is present in pathogenic variants near the 522 position, such as R514S, R521S, R524S. Recent evidence suggests that arginine-deficiency can influence disease progression.

Type Ii Diabetes Treatment Comparison Via Compartment Modeling, Abigail M. Collins

Theses and Dissertations

Type II diabetes mellitus affects one in ten adults worldwide, yet the effects of treatment type and adherence level on developing complications and quality of life have not been well characterized at the population level, and mathematical modeling offers a structured way to examine these dynamics. This thesis adapts the Boutayeb et al. (2004) model to incorporate dynamic treatment types and levels of adherence, producing nine scenarios in which complication development rate and complication recovery rate differed, to compare peak complications and quality of life across treatment and adherence conditions. Using a system of ordinary differential equations and compartment modeling, …

Applications Of Machine Learning For Evaluating Downward-Coupled Stratosphere-Troposphere Interactions And Subseasonal Forecasts Of Opportunity, Elena M. Fernandez

Electronic Theses & Dissertations (2024 - present)

Wintertime stratospheric dynamics provide key information for understanding atmospheric teleconnections and improving subseasonal-to-seasonal (S2S) predictions on timescales of two weeks to two months. Periods of enhanced predictability, often referred to as forecasts of opportunity, arise from large-scale teleconnected variability, within which the stratosphere serves as an important precursor for tropospheric states, such as near-surface temperatures. While traditional diagnostics of downward coupled stratosphere-troposphere interactions typically rely on zonal-mean representations of wind and geopotential height, this dissertation presents an alternative vortex-centric framework through metrics that capture the daily geometric and dynamical evolution of the stratospheric polar vortex. The proposed stratospheric …

Machine Learning-Based Intrusion Detection System For Iot Networks Using The Rt-Iot 2022 Dataset, Bukunmi Ebenezer Afolabi

Theses, Dissertations and Capstones

The rapid expansion of the Internet of Things (IoT) has transformed modern computing by enabling seamless connectivity among heterogeneous devices across diverse application domains. However, this increased interconnectivity has significantly enlarged the attack surface of IoT networks, exposing them to a wide range of sophisticated cyber threats. Conventional security mechanisms often lack the capability to detect emerging attacks in real time, thereby necessitating the development of intelligent Intrusion Detection Systems (IDS) capable of accurately identifying malicious network activities. This study developed and evaluated a machine learning-based intrusion detection framework for multiclass IoT attack detection using the RT-IoT2022 dataset. The dataset …

Entropic Foundation Of Finance And Physics: Securities Price Dynamics And Quantum Theory, Mohammad Abedi

Electronic Theses & Dissertations (2024 - present)

In many scientific and financial contexts, we must reason and make predictions under conditions of incomplete information. This dissertation develops Entropic Dynamics (ED) as a unified framework for deriving dynamical laws directly from principles of inference. Within this approach, probability distributions represent states of knowledge, and their evolution is determined through entropy maximization subject to relevant constraints. This leads to a novel concept of entropic time and a formulation of dynamics as an inferential process. In this talk, I will present how ED provides a common foundation across multiple domains. In physics, quantum dynamics for particles and scalar fields in …

Data-Driven Partitioning In Distributed Optimization For Networked Systems, Prosper Azameti

Theses and Dissertations

The convergence behavior of distributed optimal power flow (OPF) depends strongly on how the power network is partitioned into regions. Classical graph-based methods such as METIS are widely used, but they rely mainly on static topological criteria and do not explicitly incorporate operating-point-dependent information that may affect distributed optimization performance. This thesis develops a data-driven partitioning framework for distributed OPF using graph neural networks (GNNs). Each OPF scenario is represented as a graph in which buses are nodes and transmission lines are edges. Node and edge features capture both structural and operational characteristics of the network. Partition prediction is formulated …

Theoretical Analysis Of Filtering And Smoothing Techniques In Stochastic Time Series, Kaosarat Bola Azeez

Theses and Dissertations

Polynomial-preserving linear filters are fundamental tools for smoothing and trend extraction in noisy time series, particularly when the objective is to reduce short-run variation without distorting underlying low-degree structure. This thesis develops a general framework for such filters based on local polynomial approximation and least-squares estimation. In particular, we establish that the resulting estimators can be represented as symmetric linear filters whose weights satisfy moment conditions that ensure exact polynomial reproduction up to a specified degree. Building on this framework, we derive explicit coefficient vectors for several classical smoothing filters, including the Savitzky-Golay filters SG(5,2) and SG(7,3), as well as …

Performance Of Numerical Methods Applied To The Black–Scholes Model, Scott Cameron Williams

UNF Graduate Theses and Dissertations

We compare five numerical approaches for approximating solutions to the Black–Scholes partial differential equation for pricing European call options: FTCS, BTCS, Crank– Nicolson, Monte Carlo simulation, and a physics–informed neural network (PINN). These methods span finite difference techniques, probabilistic simulation, and machine learning. Performance is evaluated based on computational efficiency and accuracy relative to the analytical Black–Scholes solution.

Among the methods, Crank–Nicolson and the PINN demonstrated the strongest overall performance. Crank–Nicolson achieved the highest accuracy but exhibited increased runtime as the number of underlying stock price grid points grew. In contrast, the PINN produced slightly less accurate results but with …

All Games Have Equilibria, M. Ali Khan, Arthur Paul Pedersen, 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 …

On Sharpest Tail Bounds For Functions Of Tail Bounded Random Variables, Stephen Harrison

Mathematics & Statistics ETDs

Consider n real/complex, independent/dependent random variables with respective tail bounds and g a measurable function of the r.v.’s. Consider f the “sharpest” tail bound of g (sharpest in the sense, if f were any less, then for some X1, ..., Xn satisfying the conditions, g(X1, ..., Xn) would not satisfy the tail f). Significant research has been done to approximate f often with high accuracy. These results are often of the form, for g in this family, and tail bounds of Xk in this family, f is bounded by some f′ with high accuracy. However, the question “what would it …

Modeling Private Debt Using U.S. Consumer Expenditure Data, Stsiapan Dziamentsyeu

Honors Capstones

This project models private household debt among U.S. consumers using data from the Consumer Expenditure Survey (CES) between 2013 and 2023. The analysis focuses on identifying how demographic and economic characteristics, such as income, housing expenditures, education, and occupation, relate to non-mortgage “other” loan balances. After initial model development produced poor residual behavior due to zero-inflation from imputed debt values, the analysis was refined to include only households reporting verifiable debt. Multiple modeling techniques, including AIC-based variable selection and Lasso regularization, were compared under a five-fold cross-validation framework. The Lasso model achieved superior predictive accuracy (RMSE = 1.55, MAE = …

The Food Truck: A Multi-Product Newsvendor With Expectile Risk, Sekyiwaah Nuamah

Electronic Theses and Dissertations

The Newsvendor Problem is a fundamental model in Operation Research and Supply Chain Management used to determine the optimal order quantity under uncertain demand to minimize expected costs.
This research extends the classical Newsvendor problem to a multi--product setting, addressing the risk of asymmetric cost structures faced by a food truck. This thesis introduces expectile risk measures to quantify and manage uncertainty in demand, moving beyond traditional risk metrics. To evaluate the impact of expectile-based decision-making, we analyze three types of demand distributions--simple, symmetric, and skewed. For skewed distributions, we apply linear spline inverse interpolation to derive expectile values from …

(R2130) Cusum-Test For Unconditional Variance Change Detection In Bilinear Garch Models, Edoh Katchekpele, Abdou Kâ Diongue, Ben Célestin Kouassi

Applications and Applied Mathematics: An International Journal (AAM)

We examine CUSUM-type test for detecting changes in unconditional variance within Bilinear GARCH models. We derive the asymptotic distribution of the test statistic under both null and alternative hypotheses and assess test effectiveness in identifying single structural breaks. Simulation studies support our theoretical results and demonstrate the practical utility of the test.

Coupled Machine Learning Models: Combining Observations And Numerical Analysis In A Physics-Regularized Approach, Austin B. Schmidt

LSU New Orleans Theses and Dissertations

This dissertation investigates surrogate modeling for fixed-location environmental forecasting using novel data-combination techniques. The work surveys the landscape of observational measurements and numerically generated data, identifying similar research and gaps in current methodologies. The ratio-coupled training framework is introduced to combine two data sources per predicted feature through a tunable parameter that weights training signal strength. An optimization scheme is developed to simultaneously tune surrogate weights and the coupled signal ratio, allowing relative influence between signals to act as an explicit regularizer. Three case studies demonstrate the methodology and approach in a variety of contexts. The first study is based …

Stochastic Functional Data-Driven Models For Real-Time Battery Health Forecasting Under Dynamic Operating Conditions, Joshua Owusu

Electronic Theses and Dissertations

This thesis provides an effective statistical model to predict the real-time state of lithium-ion batteries for reliable Battery Management Systems (BMS). It highlights battery data (voltage, current, temperature) as smooth functional curves. The principal method demonstrates diminishing trends to health outcomes like State of Health (SoH) and Remaining Useful Life (RUL) by employing Functional Principal Component Analysis (FPCA) and Bayesian Functional Linear Models (FLMs). The primary objective is to figure out how uncertain forecasts are. Simulations demonstrate that the highest accuracy (lowest MSE) is achieved through low noise levels along with large sample sizes. The final system provides a highly …

Deep Learning With Kalman Filter, Rexford Julius Quaye

Electronic Theses and Dissertations

This thesis presents an extension of the Kalman filter to handle nonlinear and non-Gaussian systems. The standard Kalman filter is optimal under Gaussian assumptions but struggles with more complex noise models. This work introduces a novel loss function based on the Mahalanobis distance, which incorporates the covariance structure of measurement errors, enabling the filter to adapt to non-Gaussian scenarios. The neural network framework is applied to predict the system’s process model, while retaining the classical Kalman measurement update. The proposed methodology is demonstrated through examples of car position and rocket altitude tracking. The results show that the new approach performs …

A Leslie System For A Demographic Simulation: From An Actuarial Point Of View, David Kings

Electronic Theses and Dissertations

This thesis develops a discrete stochastic linear systems interpretation of age–stage demographic evolution grounded in Leslie operators and realized in a discrete-event simulation implemented with salabim. The central claim is that one annual cycle of the simulation constitutes a cone-preserving, stochastic affine transformation on a high- dimensional population state vector indexed by age, sex, marital status, household type, employment, and education, and that the composition of yearly operators yields a random matrix product whose top Lyapunov exponent is the stochastic counterpart of the Perron–Frobenius growth rate (Caswell, 2001; Tuljapurkar, 1997)[1, 2]. The actuarial bridge is constructed by mapping simulated survival …

Instance-Adaptive Gated Fusion Of Multi-Transform Image Representations, Prince Appiah

Open Access Theses & Dissertations

This dissertation proposes the Instance-Adaptive Gated Fusion (IAGF) framework, a novel deep learning architecture for adaptive and interpretable fusion of multiple time–series image transformations. While existing methods rely on static concatenation or dataset-level optimization, IAGF introduces a learnable gating mechanism that dynamically assigns per-instance weights to Recurrence Plots (RP), Gramian Angular Summation Fields (GASF), and Gramian Angular Difference Fields (GADF). The gating layer performs a convex fusion of transformation-specific embeddings under a softmax constraint, ensuring mathematical stability and interpretability. An entropy-regularized objective prevents dominance collapse and promotes balanced exploration of transformations during training. Comprehensive experiments across eighteen benchmark datasets, spanning …

The Odds Don’T Lie: Mathematical Reasoning And Societal Ignorance In Don’T Look Up, Nysa Vedwan, Shane Carey

LASER Journal

In Adam McKay’s 2021 satirical sci-fi movie Don’t Look Up, two astronomers discover a comet heading directly toward Earth. Despite overwhelming evidence and near-certainty of global extinction, their warnings are ignored and ridiculed. This paper discusses the mathematical and scientific foundations of the movie’s social and political reception, and specifically focuses on orbital prediction and probabilistic modeling as they relate to public understanding of risk. This paper shows how data is often undermined by political and social dynamics, by connecting the fictional events of the movie with real-world crises like the COVID-19 pandemic and the climate emergency. In Don’t Look …

Explainable Post-Operative Patients Recovery Prediction Following Elective Brain Tumor Resection: A Precision Medicine Approach, Eleanor Belkin

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

[Kyda] Biologically Grounded Surrogate-Driven Parameter Inference For Sparsely Observed Dynamical Systems, Joshua C. Macdonald

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mentoring First-Year Stem Students Through Collaborative Research In The Haynes Scholars Program, Alex Capaldi, Laura Tipton

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

[Lele] Incorporating Physiological Constraints In Estimates Of Post-Prandial Insulin Secretion Rate, Justin K. Garrish, Christine L. Chan, Douglas Nychka, Cecilia Diniz Behn

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Teaching Statistical Literacy Through An Excel Class Project, Patricia Berchiolli, Omar Babun Codorniu

Faculty and Staff Publications & Presentations

Lynn University’s core curriculum, The Dialogues, enables students to develop critical thinking, communication, and innovation skills. As part of this curriculum, Introductory Statistics introduces students to key statistical concepts while showing how they can be applied in real-world situations using Excel. The highlight of the course is the Statistics Excel Project, where students create their own dataset with a mix of quantitative and qualitative variables. To keep the focus on learning statistical techniques rather than data collection, students use Excel’s random number generator for quantitative data, which also avoids the need for IRB approval. From there, they calculate statistical measures, …

Simultaneous Application Of Multiple Process Control Rules, Tran B. Ngo

Electronic Theses and Dissertations

Statistical Process Control (SPC) charts are tools used in quality control to monitor and analyze the stability of a process over time. This study evaluates the effectiveness of eight individual Western Electric rules, also known as WECO rules, and the various combinations of these rules with Shewhart rule (or WECO rule 1) to SPC charts. As more rules are added to a process control scheme with Rule 1, there is a trade-off: a higher false out-of-control signal rate but an increase in sensitivity, that is the ability of a specified process control scheme to capture a true out-of-control signal. This …

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 …