Applied Mathematics Commons^™

Evaluating Risk And Return Of Corn And Soybean Marketing Strategies Using Monte Carlo Simulation Methods, Johanna Ilves

Department of Agricultural Economics: Dissertations, Theses, and Student Research

This study evaluates the performance of pre-harvest marketing strategies for corn and soybeans, using Monte Carlo simulation techniques. Given the increasing volatility in commodity prices and the evolving landscape of agricultural markets, producers face growing challenges in developing effective marketing plans that manage risk and enhance profitability. This thesis examines thirteen marketing strategies from 2008 to 2024, including benchmark harvest-only sales and various pre-harvest futures contract approaches. Historical futures price data for December corn and November soybean contracts were used to simulate 1,000 marketing outcomes per strategy per year, capturing a broad range of market conditions. Key performance indicators such …

Physics Embedded Neural Network: A Novel Data-Free Numerical Method For Solving Computational Physics Problems, Pawan Gaire

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

A novel approach for solving partial differential equations (PDEs) using neural networks for scientific computing is introduced. The proposed approach, referred to as physics-embedded neural network (PENN), features a unique architecture that incorporates the PDE and boundary conditions information directly within the final fully-connected layer of the feed-forward neural network (NN). The key aspect of PENN is the parallel numerical embedding of a differential equation associated with physical problems within the activation function of the network’s final layer. This integration leads to a new class of computational solvers competitive with classical methods like the Finite Element Method (FEM) and capable …

Using Permutation Groups To Identify Families Of Capacity Achieving Codes, Daniel Welchons

Department of Mathematics: Dissertations, Theses, and Student Research

When communicating over a noisy channel, the probability of message interference sets a maximum possible transmission rate known as the channel capacity. Any family of codes which have rates converging to the channel capacity and arbitrarily low probability of decoding failure is called capacity achieving. Such codes have been known to exist since the birth of information theory, but are difficult to find explicitly. It has recently been shown that the permutation groups of a family of codes can be used to show that the family is capacity achieving on the q-ary erasure channel.

This thesis seeks to apply the …

Car Price Prediction Using Machine Learning: Analyzing The Dvm-Car Dataset, Yaman Abu Ghareebaih

Electronic Theses and Dissertations

The objective of this study is to predict car prices using machine learning models and the DVM-CAR dataset, which includes over 1.4 million images and car specifi- cations from 899 car models. Key factors such as mileage, engine power, and year of registration were analyzed for their correlation with car prices. Extensive data cleaning was performed, including filling missing values, identifying outliers, and normalizing numerical variables. Discrete variables like car make and body type were encoded using one-hot encoding. Linear relationships were analyzed with Multiple Logistic Regression, and Random Forest models were used for nonlinear patterns. Model performance was evaluated …

Random Processes With High Variance Produce Scale Free Networks, Josh Johnston

Boise State University Theses and Dissertations

The degree distribution of a real world network --- the number of links per node --- often follows a power law, so some hubs have many more links than traditional graph generation methods predict. For years, preferential attachment and growth have been the proposed mechanisms leading to these scale free networks, exemplified by the Barabási–Albert model. This dissertation provides an alternative model using a randomly stopped linking process, showing that mixtures of geometric distributions can lead to power laws, an intuition suggested by the Central Limit Theorem for distributions with infinite variance. Having a collection of Bernoulli trials with high …

The Herzog-Takayama Resolution Over A Skew Polynomial Ring, Linoy Utkina

Theses and Dissertations

Let k be a field, and let I be a monomial ideal in the polynomial ring R = k[x1,..., xn]. In her thesis, Taylor introduced a complex that yields a finite free resolution of R/I as an R-module. Building on Taylor’s work, Ferraro, Martin, and Moore extended this construction to monomial ideals in skew polynomial rings. Because the Taylor resolution is typically not minimal, subsequent research efforts went into identifying specific classes of ideals whose minimal free resolutions can be constructed more simply. In 1990, Eliahou and Kervaire devised an approach for handling minimal resolutions of …

Congruences In Arithmetic Progression For Coefficients Of Gaussian Polynomials And Crank Statistics, Joselyne Aniceto

Theses and Dissertations

The study of partition congruences, inspired by Ramanujan’s discoveries for ��(��) over a century ago, remains a central topic in this field. This dissertation examines congruence properties in two restricted partition functions: ��(��,��), which counts partitions of �� into at most �� parts, and ��(��,��,��), which further limits the size of the largest part to be at most ��. Building on Kronholm’s 2007 result, now known as the Interval Theorem, and a recent result by Eichhorn, Engle, and Kronholm, we establish new infinite families of congruences for ��(��,��,��). This dissertation extends not only the recent results of Eichhorn, Engle, …

Implementing And Evaluating An Ai-Powered Visual Decision Support System To Improve Antibiotic Usage Among Physicians With A Built-In Early Warning System, Akua Sekyiwaa Osei-Nkwantabisa

Theses and Dissertations

The widespread misuse and excessive prescription of antibiotics have played a pivotal role in the emergence and proliferation of antibiotic-resistant bacteria, posing a critical global public health crisis. Addressing this challenge necessitates innovative solutions that enhance antimicrobial stewardship. This study presents the development and implementation of a visual decision support system designed to monitor and optimize antibiotic usage among healthcare providers. The proposed system integrates advanced machine learning algorithms with real-time data analytics to provide a dynamic, evidence-based decision support tool. Specifically, a neural network model was developed after evaluating multiple machine learning approaches, including Random Forest, Logistic Regression and …

Investigating The Privacy-Utility Trade-O↵ In Synthetic Data Generation Using Correlated Attribute Mode, Kofi Sarfo

Electronic Theses and Dissertations

This thesis explores the privacy-utility trade-off in synthetic data generation using the Correlated Attribute Mode of DataSynthesizer, which employs Bayesian networks to model attribute dependencies. It focuses on integrating differential privacy mechanisms, particularly the Laplace mechanism, to inject controlled noise into synthetic data and enhance privacy protection. As organizations face challenges balancing data-driven decision-making with privacy regulations such as the General Data Protection Regulation and the California Consumer Privacy Act, synthetic data offers a solution by creating artificial datasets that preserve statistical properties while balancing data privacy and utility. This research investigates how different differential privacy parameters epsilon affect data …

Divergence-Free Smoothed Particle Hydrodynamics In A Stream Digital Twin, Austin Hartley

All Theses

Digital Twins (DT) are being explored by the South Carolina (SC) water community to simulate how SC streams will flow at various water levels. Currently, a DT called Gilligan simulates these streams utilizing weakly-incompressible Smoothed Particle Hydrodynamics (SPH). This method does not strictly enforce incompressibility, which leads to unrealistic water flows and unwanted visual artifacts that require post-processing effects to hide. To address these problems and simulate more realistic water flows, the Gilligan stream logic is updated and a state-of-the-art SPH method that enforces incompressibility—Divergence-Free SPH (DFSPH)—is implemented within the Gilligan framework. DFSPH is able to make use of two …

Quantitative Runtime Monitoring Of Ethereum Transaction Attacks, Xinyao Xu, Ziyu Mao, Jianzhong Su, Xingwei Lin, David Basin, Jun Sun, Jingyi Wang

Research Collection School Of Computing and Information Systems

The rapid growth of decentralized applications, while revolutionizing financial transactions, has created an attractive target for malicious attacks. Existing approaches to detecting attacks often rely on predefined rules or simplistic and overly-specialized models, which lack the flexibility to handle the wide spectrum of diverse and dynamically changing attack types. To address this challenge, we present a general and extensible framework, MoE (Monitoring Ethereum), that leverages runtime verification to detect a wide range of attacks on Ethereum. MoE features an expressive attack modeling language, based on Metric First-order Temporal Logic (MFOTL), that can formalize a wide range of attacks. We integrate …

Identifying And Characterizing Transition Cells In Developmental Processes From Scrna-Seq Data, Yuanxin Wang

Dissertations and Theses (Open Access)

During the development of multicellular organisms, individual cells make distinct decisions about their cell types and states. Understanding the molecular mechanisms underlying cellular state transitions at different developmental stages provides deep insights into physiology, morphology and the etiology of diseases. Single-cell RNA-sequencing (scRNA-seq), which is widely used to study complex cell states and dynamic gene expression patterns, enables us to investigate molecular mechanisms of cellular state transitions. Currently, however, computational tools available for identifying cellular states and state transitions remain limited.

Although trajectory-based methods such as Monocle and Slingshot assume that state transitions generate continuous expression profiles, they cannot distinguish …

Using Gaussian Process Regression To Learn Thermodynamic Equations Of State With Uncertainty Quantification, Austen T. Lee

Chemical Engineering Undergraduate Honors Theses

This study investigates the use of derivative-informed Gaussian Process (GP) models to estimate thermodynamic behavior across temperature and density by building a Helmholtz-based equation of state. Argon, a stable monatomic gas, was chosen as a case study within the vapor region. The GP model was trained using values of experimentally measurable properties found by taking first and second derivatives of the original potential function. Results show that while the GP model offered uncertainty quantification and informed thermodynamic behavior, it predicted values that deviated from the ground truth depending on the property. The model exhibited high confidence in regions with substantial …

Numalyze: Numerical Analysis Web Application, Dev Kapupara

Electronic Theses, Projects, and Dissertations

Numalyze is an online platform that allows users to run and apply different numerical methods in real time. The application is built using Python and the Flask web framework. It provides an interface where users input mathematical functions and parameters to see the results for root-finding and integration methods, and to also perform reductions on matrices. By using a light-weight web framework and self-coded algorithms which removes dependency on massive external libraries—this application connects theoretical concepts to their practical implementation. It enables students and researchers to visualize the series of steps that each algorithm takes to compute results. Moreover, the …

Robust And Efficient Solvers For Physics-Based Pde’S, Elizabeth Hawkins

All Dissertations

This work was partially supported by the U.S. Department of Energy under award DE- SC0025292, by NSF grant DMS 2152623, and by NSF grant DMS 2011490.

This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Mathematical Multifaceted Integrated Capability Centers (MMICCs) program, under Field Work Proposal 22-025291 (Multifaceted Math- ematics for Predictive Digital Twins (M2dt)), Field Work Proposal 23-020467, and Computing and Information Sciences (CIS) investment area in the Laboratory Directed Research and Development program at Sandia National Laboratories. This written work is authored by an employee …

Domain Decomposition For Coupled Systems Of Fluid-Structure Interaction And Numerical Modeling For Thin Film Polymers, Amy De Castro

All Dissertations

We consider two primary areas of physical application in this work: fluid interaction systems with either linear elastic structures or with poroelastic structures, and thin film polymers, where the majority of the work focuses on the fluid-structure interaction systems.

In the first chapter, we present a strongly coupled partitioned method for fluid structure interaction (FSI) problems based on a monolithic formulation of the system which employs a Lagrange multiplier (LM). We prove that both the semi-discrete and fully discrete formulations are well-posed. To derive the partitioned scheme, a Schur complement equation, which implicitly expresses the Lagrange multiplier and the fluid …

Sliding Window Method For Simulating Action Potentials In Axons, Hayden Reed

Honors Theses

ABSTRACT Hodgkin and Huxley’s nonlinear partial differential equations model the excitation and propagation of action potentials in neurons, and there have been numerous attempts at finding the best numerical solution method. This thesis proposes a novel approach to solving these equations: the Sliding Window method, in which a fixed sub-interval is found through capturing the signal’s head and tail. The system is then solved on the sub-interval instead of the entire interval. Using the Sliding Window technique also involves implementing the backward and forward Euler methods and the finite difference method. It will be demonstrated that, in utilizing the Sliding …

A Profile Wald Test In M-Estimation, Reagan Kesseku

Open Access Theses & Dissertations

Despite the growing popularity of machine learning-based inference, classical statistical inference remains highly relevant in modern data science due to its interpretability and theoretical rigor. Among its core tools, the likelihood ratio test, Wald test, and score test are foundational methods for hypothesis testing within the maximum likelihood framework. Although these tests are asymptotically equivalent under regularity conditions, each offers distinct advantages depending on the context, computational demands, and the availability of parameter estimates. In this dissertation, we introduce a fourth method, the Profile Wald Test (PWT), within the broader M-estimation framework. The PWT is based on profile estimators of …

Simulations Of Richtmyer-Meshkov Instability Using High Order Weno Methods, Ryan Holley

Graduate Theses and Dissertations

Turbulent mixing due to hydrodynamic instabilities occurs in a broad spectrum of engineering, astrophysical and geophysical applications. Theory, experiment, and numerical simulation help us to understand the dynamics of interface instabilities between two fluids. This thesis presents an increasingly accurate and robust front tracking method for the numerical simulations of shock-induced turbulent mixing known as Richtmyer-Meshkov Instability (RMI). Front tracking is an adaptive computational method, where the interface instability is explicitly represented as lower dimensional manifolds moving through a rectangular grid. All the cell-center states (density, velocity and pressure) are updated using higher order weighted essentially non-oscillatory (WENO) scheme. Performance …

A Dg-Algebra Structure With Divided Powers On The Generalized Taylor Resolution, Raul F, Alvarez

Theses and Dissertations

This thesis investigates the construction of a DG Γ-algebra structure on the Generalized Taylor Resolution (GTR) associated with monomial ideals. The classical Taylor resolution is known for providing a free but generally non-minimal resolution, leading to computational challenges and inefficiencies in algebraic analysis. In contrast, the GTR preserves essential algebraic structures while optimizing the resolution process, offering a more efficient and comprehensive framework for studying monomial ideals.

We introduce a novel DG Γ-structure that incorporates divided powers into the GTR, enhancing its multiplicative and homological properties. This structure preserves strict graded commutativity and is fully compatible with the differential graded …