Applied Mathematics Commons^™

Novel Generative And Language Model Architectures With Applications, Edison Mucllari

Theses and Dissertations--Mathematics

This dissertation investigates novel architectures to address fundamental challenges in machine learning, particularly focusing on transformer models, recurrent neural networks, GAN and continual learning and their applications in natural language processing and computer vision. We propose the Neumann-Cayley Gated Recurrent Unit (NC-GRU), which leverages a Neumann series-based Scaled Cayley transformation to maintain orthogonal weight matrices, effectively mitigating exploding gradients problems while improving long-term memory retention across prediction tasks. We demonstrate the practical applications of NC-GRU by implementing our proposed architecture into an autoencoder to derive neural molecular fingerprints. Building upon these advancements, we turn our attention to the transformer architecture, …

Weathering And Beyond: Leveraging Mathematical Modeling To Simulate Erosion In Digital Media, Fiona Irving-Beck

Scripps Senior Theses

How might we bring an idea to life from both a mathematical and an artistic perspective? Within Weathering, I use imagery of environmental erosion to explore the differences between physical and digital forms of representation. I created a physical painting of an abandoned copper mine, digitized the work, and then used a mathematical model to digitally “erode” it, which I re-translated into paintings. While the explicit texture present in physical work speaks best to my practice/intent, the mathematical framework that is the basis for my digital work affords a powerful mode of temporal flexibility. Used in conjunction, these two …

Bound Preserving Discontinuous Galerkin Methods For Euler Equations And Nonequilibrium Flows, Fangyao Zhu

Dissertations, Master's Theses and Master's Reports

This dissertation is composed of four chapters in which we will closely examine the high order bound preserving discontinuous Galerkin methods for solving partial differential equations, specifically non-equilibrium chemical reacting flows and Euler equations under gravitational fields. A shared requirement between the two is the necessity for positive values of both density and pressure. Due to this physical nature of the two systems, constructing a positivity preserving scheme become very essential in our research.

For non-equilibrium flows where multi-reactions and multi-species are involved, we are also required to keep the bounds of the mass fraction of each species in between …

Theory And Applications Surrounding Markov Chains, Joseph J. Quisito Jr., Gallean Brown, Elijah Yoder

Capstone Showcase

This capstone project explores the Markov Chain – a mathematical model used to describe systems that transition between states based on probabilities. It begins by introducing the fundamental concepts, including transition matrices, state classifications, and stationary distributions. The paper then applies Markov Chain theory to real-world scenarios, such as simulating Snakes and Ladders games, predicting soccer match outcomes for Manchester United, and generating texts from movie lines. Finally, it discusses key findings, challenges, and potential areas for future research in the field.

A Mathematical Modeling Approach To Investigate The Impacts Of Post-Infection Mortality And Partial Immunity On Disease Endemicity, Brendan M. Shrader

Honors Undergraduate Theses

A number of infectious diseases cause post-infection conditions or complications, such as COVID- 19, Q fever, and Polio. These conditions result in recovered individuals having a higher mortality rate than susceptibles, and this can impact disease dynamics. An existing mass-action model in the literature that incorporated post-infection mortality was shown to have limit cycles, or persistent oscillations, in the infected population. To better understand what causes these limit cycles, we develop and analyze a new epidemiological model with standard incidence. We show standard results, including the existence, uniqueness, and stability of the disease-free and endemic equilibria, and we rule out …

Time-Marching Quantum Algorithm For Simulation Of Nonlinear Lorenz Dynamics, Efstratios Koukoutsis, George Vahala, Min Soe, Kyriakos Hizanidis, Linda Vahala, Abhay K. Ram

Electrical & Computer Engineering Faculty Publications

Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by developing an explicit quantum algorithm that implements the time evolution of a second-order time-discretized version of the Lorenz model. The Lorenz model is a celebrated system of nonlinear ordinary differential equations that has been extensively studied in the contexts of climate science, fluid dynamics, and chaos theory. Our algorithm possesses a recursive structure and requires only a linear number of copies of the initial state …

Scalable Parallel-In-Time Integration For Equations Of Motion, Nathan W. Chapman

All Master's Theses

Physical simulations always need to balance accuracy and run-time. This work implements the Parareal Algorithm using graphics processing units across a distributed system to accurately simulate time-dependent physics while attempting to minimize runtime. Data-transfer latency is identified as the primary bottleneck, for which mitigation methods are provided. Benchmarks comparing single-GPU and distributed implementations on a spectrum of coarse and fine discretizations are analyzed.

Harnessing Electroosmotic Hybrid Nanofluid Dynamics In Curved Arteries: Insights Into Biomedical Flow Enhancement, M. A. El Kot, A. M. Alsharif, Y. Abd Elmaboud, Sara Abdelsalam

Basic Science Engineering

No abstract provided.

Match Accuracy Of Burned Teeth: A Pilot Study Of Allied Dental Professionals, Brenda T. Bradshaw, Marsha A. Voelker, Samantha C. Vest, Sinjini Sikdar

Dental Hygiene Faculty Publications

Purpose: The purpose of this pilot study was to assess allied dental professionals' match accuracy of burned teeth; a skill required by disaster victim identification (DVI) team members.

Methods: This cross-sectional study used a convenience sample of registered dental hygienists (RDH) (n=15) and dental assistants (DA) (n=15) to assess their match accuracy of burned teeth with simulated antemortem (AM) and postmortem (PM) images. Fifteen human teeth were heated at 400°C for 15 minutes. Prior to and following heat alteration, each tooth was photographed and radiographed. Images were presented to participants in randomized order, and they were instructed to correctly match …

A New Simulation Framework For Analyzing Neutrosophic Data In Experimental Design, Muhammad Aslam, Nasrullah Khan, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

A recent simulation-based classical analysis has been developed for interval data. However, a review of the literature indicates that these existing simulations have notable limitations and fail to conform to the neutrosophic statistical framework. In this paper, we propose a novel simulation process designed to analyze neutrosophic data within an appropriate and rigorous neutrosophic framework. We demonstrate that the proposed simulation is more comprehensive and aligns closely with the principles of neutrosophic theory. The results will be obtained through simulation and compared with those of existing methods, with the expectation that the proposed approach provides substantial improvements and is better …

Modeling Energetic Electron Precipitation: Radiation Belt Loss, Its Drivers, And Atmospheric Impacts, Zhi Gu Li

Graduate Theses, Dissertations, and Problem Reports (ETD)

Energetic electrons in the terrestrial outer radiation belt present significant hazards to spacecraft systems and human operations in space. The intensity of these electrons can vary rapidly and dramatically during geomagnetic storms, governed by a complex competition between acceleration and loss processes. Among these, precipitation into the atmosphere via resonant wave-particle interaction acts as a key loss mechanism. This dissertation focuses on improving the quantification of energetic electron precipitation using physics-based modeling constrained by low-altitude satellite observations.

We begin by developing and validating the Drift-Diffusion model, which simulates low-altitude electron dynamics while accounting for azimuthal drift, pitch-angle diffusion, and atmospheric …

Weakly Reversible Deficiency Zero Realizations Of Polynomial Dynamical Systems, Neal Ryan Buxton

Graduate Theses, Dissertations, and Problem Reports (ETD)

Weakly reversible, deficiency zero (WR0) systems form a large class of polynomial ODEs modeling chemical reaction networks. Their behavior is exceptionally stable: they have unique positive steady states, which are locally asymptotically stable (they are also conjectured to be globally asymptotically stable). This powerful result (the Deficiency Zero Theorem) applies to a large class of high dimensional, nonlinear polynomial dynamics, and is independent of the choice of parameters in the model. In this dissertation we present two algorithms that expands the scope of the Deficiency Zero Theorem to:

1. Networks with WR0 realizations, i.e. networks that are not necessarily WR0 …

Rapid Inference Of Atmospheric Feature Parameters From Light Curves Using Bayesian Neural Networks, Eugenio A. Diaz

Honors Undergraduate Theses

Mapping atmospheres using rotationally modulated light curves offers insights into cloud structures and dynamics. Current retrieval methods, primarily based on Markov Chain Monte Carlo (MCMC) techniques like Aeolus, can infer atmospheric features but are computationally prohibitive for large datasets. This project proposes a neural network (NN) framework for the rapid, variational inference of atmospheric structure from light curves, particularly those of brown dwarfs. The primary approach focuses on training a Bayesian NN (BNN) to perform regression, predicting the spot parameters that describe the object's surface brightness map. Given the scarcity of suitable observational training data, the BNN is trained on …

0th Order Solutions Of The Wavefunctions For The Quantum Elliptical Box And Microstrip Antenna, Nishtha Tikalal

Honors Undergraduate Theses

For a quantum particle confined to a two-dimensional elliptical box or electromagnetic wave in a microstrip antenna, geometrical and boundary condition interplay result in a spectrum of spatial patterns. Due to the asymmetrical nature of the ellipse, we are faced with continuous symmetry reductions, leaving both degenerate and nondegenerate solutions. Here, we present a complete derivation of an analytical solution and visualizations of the fundamental wavefunctions for both Dirichlet and Neumann boundary conditions respectively corresponding to the quantum elliptical box and the elliptical microstrip antenna.

We demonstrate that the eigenmodes, governed by eccentricity, directly correspond to the modal field distributions …

Mathematical Modeling Of Lead Climbing Falls, Rosemary Christmas Evans

EWU Masters Thesis Collection

This thesis presents a force-based mathematical model for simulating dynamic falls in lead sport climbing, with an emphasis on physical realism and empirical validation. The system is modeled as a mass–spring–damper, incorporating gravity, nonlinear rope stiffness, internal damping, and Capstan-style friction at protection points. The goal is to predict peak forces and rope elongation while capturing the complex dynamics of real climbing ropes. Several novel features are introduced. Activation switches ensure forces only engage when the rope is tensioned, preventing premature response. A velocity-sensitive stiffness transition function allows the rope to stiffen smoothly with increasing fall speed, reflecting rate-dependent rope …

Wildfire Modeling Using Systems Of Odes And Pdes, Michael A. Quindlen

EWU Masters Thesis Collection

No abstract provided.

Ultrasonic Sensor-Based Sound Synthesis Using Raspberry Pi Pico W, Niraj Jaishwal

Williams Honors College, Honors Research Projects

At the intersection of Human Computer Interaction and digital art, this project transforms simple motion into musical expression. It explores an interactive real-time sound synthesis system using ultrasonic sensors to generate continuous audio. The objective is to design a system that maps physical distances into musical parameters such as pitch and amplitude, which will create a responsive audio environment. Two ultrasonic sensors are used in combination with the Raspberry Pi Pico W microcontroller running CircuitPython and Adafruit Audio Hat for real-time sound output. One sensor controls the pitch of the generated tone, while the other controls volume. This enables expressive …

Improving The Accuracy Of Neighborhood Median Pixel Method (Nmpm) In Classifying Landsat-8 Oli Images By Optimizing The Scoring System’S Point Values, Abraham T. Magpantay, Proceso L. Fernandez Jr

Department of Information Systems & Computer Science Faculty Publications

The Neighborhood Median Pixel Method has previously been introduced as an image processing technique in remote sensing, developed to classify Landsat-8 OLI satellite image pixels into categories of vegetation, water, and built-up areas. This method relies on a lookup table based on the median pixel values within a pixel’s neighborhood and a scoring system that assigns point values for classification. While a 9x9 neighborhood size was originally proposed, a succeeding study suggested a 13x13 neighborhood for better classification accuracy. This study focuses on refining the scoring system used in the Neighborhood Median Pixel Method, particularly the original set of arbitrary …

The Inverse Scattering Transform For The Nonlinear Schrödinger Equation, Ivan Casas-Rocha

Honors Undergraduate Theses

The Nonlinear Schrödinger (NLS) Equation, iψ_t + 1/2 ψ_xx ± |ψ|²ψ = 0, is a nonlinear partial differential equation which is used to model several physical phenomena including nonlinear effects inside optical fibers and the formation of rogue waves in shallow water. It is particu- larly difficult to study solutions to this equation due to the nonlinearity, and the nonlinearity leads to incredibly interesting solutions not found in linear PDEs such as solitons. In this thesis, we highlight two methods of obtaining solutions to the (NLS) equation: the Inverse Scattering Transform and the Dressing Method. Furthermore, …

Modified Equations Of Conformal Symplectic Exponential Time Differencing Methods, Taylore M. Keesler

Honors Undergraduate Theses

Planetary orbits, pendulums, and hurricanes are everyday examples of nonlinear systems, often studied using differential equations. However, their exact solutions can not always be computed, and thus, we use numerical methods to approximate their solutions. Certain methods are better suited to preserve special properties of the system like energy and geometry. Through previous numerical simulations, a conformal symplectic method proves more effective in this preservation. To understand why, we find the modified equation of a nonlinear system with damping, which is a differential equation for which the numerical solution is exact. Through backward error analysis, we obtain these modified equations, …

Solvability Of Stochastic Linear-Quadratic Optimal Control Problems Under Partial Stabilizability Conditions, Al-Sadh Rahman Imadh

Honors Undergraduate Theses

Optimal Control Theory, a branch of Control Theory, is applicable in fields such as engineering, operations research, and economics. Stochastic Optimal Control deals with noisy systems and data using Ito’s formulation. Given a noisy system and a cost functional, the goal is to find a control that will minimize the cost. This thesis focuses on linear quadratic stochastic optimal control, and we explore state equations that are not stabilizable. We first address measurability concerns arising from the semigroup property of the state trajectory. The notions of partial stability and partial stabilizability are introduced, and we formulate their corresponding Lyapunov and …

Quantized Average Agreement Algorithms With Error Correction For Digraphs, Shuaib A. Mughal

Honors Undergraduate Theses

Multi-agent systems have become more and more prevalent as technology increasingly gets integrated into our daily lives. Some of these technological systems are large in size; for example, the smart grid where multiple devices are used to monitor and control different aspects of the energy grid. Another example is a team of autonomous systems deployed for a specific task. When these systems are spatially distributed, an important component of distributed algorithms is the ability for the agents to reach consensus on the global state of the system. Reaching agreement enables the spatially distributed agent make decisions or determine the next …

Centralized Deep Reinforcement Learning For Homogeneous Multi-Component Maintenance Optimization, Joseph W. Wittrock

Theses and Dissertations

This thesis explores an application of reinforcement learning (RL) in maintenance optimization. Recent advances in hardware-accelerated computation and deep learning have made RL a powerful tool for solving optimization problems which are too complex for traditional methods. Maintenance optimization involves improving the efficiency and effectiveness of maintenance activities through data-driven approaches, ultimately reducing costs and increasing asset availability. Making informed maintenance decisions is crucial to long-term sustainability.

A desirable maintenance policy maximizes a utility signal while minimizing the cost of maintenance. Techniques in sequential decision making such as dynamic programming (DP) and RL have found success in optimizing these maintenance …

Cfd Analysis Of Hydrodynamic Cavitation Through An Orifice: Influence Of Different Inlet Pressures And Number Of Orifice Holes, Lemthong Chanphavong, Vongsavanh Chanthaboune, Keophousone Phonhalath

ASEAN Journal on Science and Technology for Development

Hydrodynamic cavitation (HC) is considered an energy-efficient process with high potential for utilization in many chemical processes. This study presents a computational fluid dynamics (CFD) analysis of cavitating flow through an orifice with a constant flow area. The Reynolds-Averaged Navier-Stokes (RANS) equations, coupled with turbulence and cavitation models, are employed to capture the complex flow behaviors. The effects of inlet pressures and number of orifice-holes on cavitation behavior are investigated. Result of the numerical simulation is validated with the existing experimental data from the literature. The CFD study revealed that cavitation initiates just behind the inlet edge of the orifice …

Mathematical Contributions To The Study Of Chemotaxis And Cell Signaling, Hajr Zam

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation presents results from two mathematical projects concerned with the biology of cells. Chapter 1 provides biological background and places the two mathematical problems in the context of cell signaling. The larger project, with Prof. H. Hattori on a chemotaxis model is presented in Chapters 3 and 4. Work with Prof. \'{A}. Hal\'{a}sz on a chemical reaction network system with linear multimers and two types of labels is presented in Chapter 2. The chemotaxis system describes the one-dimensional dynamics of a species of cells with two chemical species, a chemo-attractant and chemo-repellent. The goal is to analyze the behavior …

Individual And Collective Properties Of Tunable Photochemical Belousov-Zhabotinsky Micro-Reactors, Kudakwashe Benedict Shumba

Graduate Theses, Dissertations, and Problem Reports (ETD)

Cell-like model chemical systems are powerful tools that can be used to explore the role of intercellular coupling on population level behaviors in communities of biological cells. Firstly, we present a new method for fabricating such micro-reactors using the photosensitive Belousov–Zhabotinsky (BZ) reaction system employed in silica microparticles. These BZ micro-reactors have a tunable response to photochemical coupling, varying from a fully excitatory response to a fully inhibitory response. Their response can be tuned through variations in either the reactive mixture or, on an individual micro-reactor level, by changes in the synthesis temperature used during the fabrication of the silica …

Application Of Semantic Segmentation To An Automatic Target Recognition Problem, Bruce W. Rush Jr.

College of Graduate Studies: Theses & Dissertations

Synthetic Aperture Radar (SAR) is an active remote sensing system commonly used in aerial reconnaissance. SAR penetrates cloud cover and vegetation by recording reflected energy pulses. The resulting information content is difficult to interpret due to vast clutter data and sparse target data. The time-consuming process of analyzing SAR imagery can be greatly reduced by implementing an Automatic Target Recognition (ATR) algorithm. Convolutional Neural Networks (CNN) are capable of extracting identification features from SAR data content. Further research in this field indicates that high performing models are insufficiently robust due to high clutter correlation among classes in the Moving and …

Majority Decision Using Top-Performing Neural Networks Models For Improved Credit Risk Prediction, Vincent Dey

College of Graduate Studies: Theses & Dissertations

Credit risk prediction remains both a challenging and high-interest problem due to the inherently unbalanced nature of financial datasets and the continuous drive for higher pre- dictive precision. In this work, I build upon previous advancements in credit risk modeling and introduce an ensemble-based Artificial Neural Network (ANN) architecture designed to enhance classification performance. By leveraging a selective ensemble of decision net- works, this approach not only improves prediction accuracy but also mitigates the chal- lenges posed by imbalanced data distributions. While the primary focus is on credit risk prediction, my analysis demonstrates that the proposed model can be effectively …

Applying The Lagrangian Variational Method To Atom Interferometry, Jeffrey W. Heward

College of Graduate Studies: Theses & Dissertations

Atom interferometry in Bose-Einstein condensate systems has emerged as a promising technique for precision metrology. The dynamics of these systems are well-described by the Gross-Pitaevskii equation (GPE), but direct numerical solution of this equation is infeasible for realistic systems. We use the Lagrangian Variational Method (LVM) to approximate solutions of the GPE in 1D and 3D, and we compare the LVM results to the exact solutions. We also present 3D LVM results for a case where numerical solution of the GPE is infeasible.

Towards Understanding Thermal Management In Unsteady Boundary Layer Flow With Ac/Dc Electric Fields, Sara Abdelsalam, M. A. Dagher, Y. A. Elmaboud, A. I. Abdellateef

Basic Science Engineering

Unsteady boundary layer flow induced by alternating current (AC) or direct current (DC) electric field through a porous layer is investigated numerically. The finite difference method based on Crank-Nicolson is applied to solve the nonlinear system. The governing equations are built with fractional shear stress and the Cattaneo heat flux model, and time fractional derivatives are computed using the Caputo fractional derivative. The numerical results are presented to demonstrate the effects of varying parameters on momentum and thermal boundary layer. The results reveal that the time delay in the velocity profile occurs for larger values of both the velocity fractional …