Applied Mathematics Commons^™

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.

Multi-Grade Deep Learning, Yuesheng Xu

Mathematics & Statistics Faculty Publications

Deep learning requires solving a nonconvex optimization problem of a large size to learn a deep neural network (DNN). The current deep learning model is of a single-grade, that is, it trains a DNN end-to-end, by solving a single nonconvex optimization problem. When the layer number of the neural network is large, it is computationally challenging to carry out such a task efficiently. The complexity of the task comes from learning all weight matrices and bias vectors from one single nonconvex optimization problem of a large size. Inspired by the human education process which arranges learning in grades, we …

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 …

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 …

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 …

Dataless Neural Networks For Boolean Satisfiability And Network Optimization, Andrew Evan Gautier

Graduate Theses, Dissertations, and Problem Reports (ETD)

Combinatorial optimization problems (COPs) require searching over a finite solution space subject to constraints, with the goal of satisfying an objective function. They arise in operations research, scheduling, resource allocation, circuit design, and many other fields. Many problems in combinatorial optimization (including satisfiability and network design) are NP-hard. Traditionally, researchers have built approximate solvers that return near- optimal solutions efficiently by developing increasingly sophisticated heuristics and meta- heuristics. Deep learning has provided new opportunities for improving combinatorial solvers by leveraging neural guidance to prune the search space. Traditional neural networks have distinct drawbacks in this context: separate training and …

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 …

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. …

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 …

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 …

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 …

An Empirical Comparison Of K-Nearest-Neighbors And Logistic Regression Classification Models, Jackson Cushing

Graduate Studies Theses and Dissertations 2026

This thesis presents an empirical comparison of two classification methods: Logistic Regression and K Nearest Neighbors (KNN). The primary objective of this research is to evaluate the strengths and limitations of each method when applied to real-world datasets. Several publicly available datasets on diabetes, breast cancer, heart attack risk, and cardiovascular disease, were analyzed. For each dataset, K Nearest Neighbors models were implemented in the same way logistic regression had already been applied. The results demonstrate that while logistic regression offers interpretable parameter estimates and performs well when the underlying predictor and outcome relationship is approximately linear, however KNN can …

Stability Analysis Of Thermohaline Convection With A Time-Varying Shear Flow Using The Lyapunov Method, Kalin Kochnev

Honors Scholar Theses

This work applies the Lyapunov method to identify instabilities and compute the growth rate of a linear time-varying system. The linear system studied describes cold fresh water on top of hot salty water with a periodically time-varying background shear flow. A time-dependent weighting matrix is employed to construct a Lyapunov function candidate. The resulting linear matrix inequalities are discretized in time using the forward Euler method. As the number of temporal discretization points increases, the growth rate predicted by the Lyapunov method or Floquet theory, used for comparison, will converge to the same value obtained from numerical simulations. Furthermore, the …

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 …

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 …

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 …

Universal Systems Simulation Via Constraint Hypergraphs With Applications To Digital Twins, John Morris

All Dissertations

The characterization of systems encompasses a variety of modeling frameworks designed to capture specific behaviors and components of various system domains. Whatever the framework, the core elements of a system representation are the information of the system and a description of how that information is related. The relations in deterministic systems are functions, which, when composed to form executable processes, can be used to simulate system data. A declarative modeling framework is one that encodes mechanisms for preparing these simulations within the model structure, allowing an external agent to form the execution processes required for a given context. To date, …

On The Scalability Of Anisotropic Mesh Adaptation On Distributed And Shared Memory Architectures For Numerical Approximations, Kevin Mark Garner Jr.

Computer Science Theses & Dissertations

Mesh generation is a critical component in numerical approximations of Partial Differential Equations (PDEs). One such example includes Computational Fluid Dynamics (CFD), as CFD simulations in turn are crucial for applications in many industries, such as personalized healthcare and the design of aerospace vehicles. Generating high quality meshes for large-scale CFD problems presents a significant bottleneck in the CFD workflow. This dissertation proposes “fast,” parallel 3D mesh generation methodologies that are designed to leverage the concurrency offered by emerging High-Performance Computing (HPC) architectures. First, a distributed memory method is presented that integrates a sequential state-of-the-art isotropic, advancing front local reconnection-based …

Ai-Driven Optimization Of Wind Energy Distribution In Texas Using Multi-Agent Reinforcement Learning, Waleed Amer, Owolabi Oluwadamilola, Bassey Ogbonnaya

SMU Data Science Review

Abstract. The integration of large-scale wind power into modern electrical grids presents persistent challenges due to variability, curtailment, and compliance with operational constraints. This study proposes a multi-agent reinforcement learning (MARL) framework for optimizing wind energy distribution within the Texas power grid. The system employs three specialized agents—managing wind curtailment, storage utilization, and load adjustments—to collaboratively balance supply and demand under dynamic grid conditions. Using historical operational data from the Electric Reliability Council of Texas (ERCOT), the framework was trained and evaluated on a range of scenarios encompassing both typical and extreme operating conditions. Results demonstrate substantial performance improvements compared …

Towards Robust Autonomous Systems: Handling Multi-Modal Uncertainties In Gps-Denied Environments, Vivya Kalidindi

Doctoral Dissertations

This dissertation focuses on designing a robust and uncertainty-aware framework for autonomous systems operating in GPS-denied environments, such as indoor infrastructures, underground tunnels, and lunar surfaces. The proposed framework addresses the challenges posed by multi-modal uncertainties, including sensor noise, distributional shifts under adverse conditions, and conflicting decision-making preferences. These challenges compromise the reliability and adaptability of autonomous platforms. To overcome these challenges, the proposed framework adopts a layered architecture that integrates advanced methodologies across the sensing, perception, and decision-making layers. At the sensing layer, an Edge-Kalman Filter combined with a density ratio-based update mechanism is employed to reduce aleatoric uncertainty …

Multi-Resolution Graph Neural Networks For Spread Prediction, Petr Kisselev

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling Synaptic Dysfunction As Neural Contagion: A Graph-Based Sedr Framework For Simulating Signal Spread, Michelle Marfo, Dr. Padmanabhan Seshaiyer, Alonso Ogueda-Oliva

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling The Cancer Cell Growth Predictions Based On Classical Mathematical Models With Physics-Informed Neural Network, Widodo Samyono

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Quantification Of Parameters To Predict The Rupture Of Intracranial Saccular Aneurysms Using Physics Informed Neural Networks, Alonso Gabriel Ogueda, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Problem Of Identification Of Linear Stationary Objects With Distributed Parameters By Their Experimental Transient Characteristics, Miraziz Vorisovich Sagatov

Chemical Technology, Control and Management

A wide class of control system elements can be described with reasonable accuracy by the concept of a linear stationary dynamic object. Several mathematical descriptions of such an object are known. The traditional mathematical model is a high-order ordinary linear differential equation. In the Laplace image space, this corresponds to a fractional-rational transfer function. The latter can be decomposed into elementary fractions. Then, using the convolution theorem and tables of elementary Laplace transform functions, one can access the originals. It is crucial to ensure precise alignment of the parameters of the mathematical model of the object used in the corrector …

Tight Spherical Embeddings (Updated Version), Thomas E. Cecil, Patrick J. Ryan

Mathematics and Computer Science Department Faculty Scholarship

This is an updated version of the paper [14] which appeared in the proceedings of the 1979 Berlin Colloquium on Global Differential Geometry. This paper contains the original exposition together with some notes by the authors made in 2025 (as indicated in the text) that give references to descriptions of progress made in the field since the time of the original version of the paper. The main result of this paper is that every compact isoparametric hypersurface Mⁿ ⊂ Sⁿ⁺¹ ⊂ Rⁿ⁺² is tight, i.e., every non-degenerate linear height function ℓ_p, p ∈ …

Cnn-Based Hybrid Model For Detecting Blight Diseases In Potato Crops With Advanced Image Processing Techniques, Farian S. Ishengoma

Tanzania Journal of Engineering and Technology (TJET)

Potato production plays a vital role in global agriculture as a major food source for large populations. However, potato crops are highly susceptible to diseases, particularly Early Blight and Late Blight, which result in substantial yield losses. Timely detection and effective control of these diseases are essential for maintaining stable crop output. This study explores the integration of Convolutional Neural Networks (CNNs) and advanced image processing techniques to differentiate between diseased and healthy potato plants accurately. Two datasets comprising original and enhanced images were used to train four CNN models: InceptionV3, Xception, Densenet201, and Resnet152V2. The original images underwent background …