Applied Mathematics Commons^™

(R2135) System Dynamical Analysis For Ann-Based Numerical Solutions Of A Compartmental Model: A Bio-Mathematical Model Of Drug Diffusion Through The Compartments Of Blood And Tissue, Rakesh Kumar, Sudarshan Dhua

Applications and Applied Mathematics: An International Journal (AAM)

This paper provides a considerably efficient numerical approach to acquire the solutions of a biomathematical model administrating oral and intravenous distribution of pharmaceuticals in the human body. The proposed numerical approach based on an artificial neural network is employed to extract numerical solutions for a detailed set of ordinary differential equations and analyze the change in concentration of drug diffusion via the compartments of blood and tissue medium. We primarily focus on analyzing three different models established on the diffusion process, exercising laws of mass action and Fick’s principle. In this work, the existing model is reformulated as an optimization …

(R2107) Analysis Of A Bivalent Vaccine Model With Peer Influence Effect On Testing, Manoj Kumar Singh, Anjali .

Applications and Applied Mathematics: An International Journal (AAM)

The coronavirus caused havoc around the world. There was a terrible situation in villages and cities, and no one knew how to deal with it. Although the governments of each country tried their best to save the common people, vaccination programs and testing centers were built everywhere. However, people were not utilizing it due to fear. Because of this, the infection spread rapidly. The qualitative study of the mathematical model here is in context with the situation when bivalent vaccination and testing are available for an epidemic. The mathematical model combines the exposed period and influenza model with vaccination included …

(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.

Deep Reinforcement Learning For Adaptive Mesh Refinement: A Training Parameter Study, Antone Chacartegui

Boise State University Theses and Dissertations

Adaptive mesh refinement (AMR) enables efficient solution of partial differential equations by dynamically allocating computational resources to regions requiring higher resolution. It has been demonstrated that deep reinforcement learning agents could learn effective mesh adaptation policies. However, practical deployment requires a systematic understanding of how training parameters affect performance across diverse computational scenarios.

This thesis presents a parameter optimization study analyzing the relationship between deep reinforcement learning for adaptive mesh refinement (DRL-AMR) training parameters and model performance. We implement an independent DRL-AMR system with a discontinuous Galerkin solver and actor-critic (A2C) algorithm for one-dimensional linear advection. The study explores four …

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.

Clustering 24-Hour Ambulatory Blood Pressure Time Series With Dynamic Time Warping And Time Warp Edit Distance, John Knight

Theses and Dissertations

Ambulatory blood pressure monitoring (ABPM) captures dynamic circadian changes in blood pressure (BP) that are not reflected in static clinic readings. This study applied time-series clustering with two elastic distance measures—Dynamic Time Warping (DTW) and Time Warp Edit Distance (TWED)—to identify distinct phenotypes in 2,155 24-hour ABPM time series from participants in the Maracaibo Aging Study. DTW and TWED both yielded three clusters corresponding to non-dipping, moderate-dipping, and strong-dipping patterns. The non-dipping group showed elevated nighttime BP, associated with greater cardiovascular and cognitive risk, while the strong-dipping group was associated with higher education and younger age in baseline clinic measurements. …

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 …

On Sobolev Spaces And The Existence Of Weak Solutions To Boundary Value Problems, Skye X. Paul

Master's Theses

Many boundary value problems that arise in mathematical models have close connections to second order elliptic partial differential equations. This thesis introduces the idea of weak derivatives and Sobolev Spaces to generalize possible solutions. Using functional analysis centered around the Lax-Milgram theorem, we show the existence of these generalized solutions to boundary value problems including Laplace's Equation, 2nd order linear ODEs, and ultimately a general second order elliptic PDE. The work cumulates with recovering a number of central theorems of functional analysis in the context of Sobolev Spaces, creating a new perspective on the solvability of these boundary value problems.

Grokking Applied To Chaotic Iterates Of The Logistic Map, Felix Donkoh

Electronic Theses and Dissertations

This thesis investigates grokking, the delayed transition from memorization to generalization in neural networks trained on deterministic chaotic data. Using an integer–arithmetic discretization of the logistic map, yn+1 =( a yn(p − yn))/ p 2 , bounded aperiodic sequences were generated across control parameters α ranging from 3.0 to 4.0. Transformer-based models displayed characteristic grokking curves. In periodic and chaotic regimes, validation accuracy rose suddenly after long plateaus, while at the Feigenbaum boundary (α ≈ 3.57) generalization failed completely. Increasing data diversity restored learning in chaotic domains, and explicit α–conditioning enabled a single network to generalize across all regimes. A …

An Income Subsystem As A Discrete Stochastic Leslie System: A Simulation-Based Approach, Fahd Nii Okantah Cobblah

Electronic Theses and Dissertations

This thesis formulates the household-income engine of an integrated population sim- ulator as a Discrete Stochastic Leslie System (DSLS). The nonnegative state vector nt ∈ Rk + aggregates income, savings, debt, employment, and transfers. (Here, the subscript + denotes the positive cone, i.e., vectors with nonnegative components). Annual evolution is linear in state, stochastic in coefficients: nt+1 = Ttnt + εt, with Tt : Rk + → Rk + cone-preserving. Exogenous macro drivers (inflation, employment, tax, salary inflation, mortgage) are forecast via ARIMA; forecasts multiply entries of Tt, preserving linearity in expectation while introducing realistic temporal correlation. The discrete-event implemented …

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 …

Modeling And Analysis Of Electric Signal In Neurons, Kevin J. Roberts

All Graduate Reports and Creative Projects, Fall 2023 to Present

Neurons in humans and other species transmit information by sending electric signals via axons. This process relies on the generation and propagation of action potentials—rapid changes in the membrane potential of the axon. Understanding the mechanisms of action potentials, including how they are generated and influenced by the axon geometry and material parameters, is crucial for gaining insight into neurological diseases such as Alzheimer’s and Multiple Sclerosis (diseases highly correlated to demyelination). In this work, we review and summarize mathematical models for signal transmission–including the classical Hodgkin-Huxley model, the Single Cable (SC) model, and the Double Cable (DC) model. We …

Role Of Competition In Avoiding Social Collapse, Gabriel M. Tonks

All Graduate Reports and Creative Projects, Fall 2023 to Present

Historical examples suggest that isolated, resource-scarce societies are prone to increased hostility and social disasters. The research in this report explores the role of intrasocietal competition in avoiding resource collapse. Two resource-consumer models are proposed with competition which depends on the level of available resources. One of these models is selected for in-depth analysis, and the region in the parameter space where saddle-node bifurcations emerge is computed numerically. The effects of environmental noise on resource growth are simulated, showing that the increased noise usually has negative long-term effects which might be mitigated via increased consumer competition.

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 …

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 …

Estimation Of 3d Facial Dynamics With Nonlinear Filters For Position Tracking, Thoa Thieu, Roderick Melnik

School of Mathematical & Statistical Sciences Faculty Publications

This study presents a comparative evaluation of three nonlinear state estimation filters, the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Particle Filter (PF), for the task of 3D facial landmark tracking. Using a publicly available dataset, we assess each filter's performance under both deterministic (noise-free) and stochastic (noisy) conditions. Metrics such as mean squared error (MSE), convergence rates of state and covariance estimates, and consistency over time are used to quantify tracking performance. Results show that the EKF consistently outperforms the UKF and PF, achieving faster convergence and lower estimation error, particularly in scenarios characterized by mild nonlinearity. …

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 …

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 …