Applied Mathematics Commons^™

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 …

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 …

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 …

Studies Of Pathways To T2d And Interventions Through A Dynamical System Model., Rafiqul Islam

Electronic Theses and Dissertations

Existing mathematical models investigating the progression of type 2 diabetes (T2D) over time primarily focus on glucose, insulin, β-cell mass, and other related factors, while often omitting fatty acids (FA) as an explicit variable—despite FA being a major energy source for the body. There exists a complex network of dynamical interactions among glucose, insulin, FA, and β-cell mass. To gain deeper insights into the metabolic dynamics and pathophysiology of T2D, it is essential to incorporate FA into such models. In this study, we extend the classic Topp’s GIβ model by explicitly incorporating FA and exploring its interactions with glucose, insulin, …

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 …

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 …

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 …

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 …

Towards Advancing Streamflow And Peak Flow Prediction With Machine Learning: Identifying Infrastructure At Risk, Sudan Pokharel

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

Due to climate change and its impact, the need for adaptive strategies for natural disaster mitigation and resource management has never been more urgent. Central to this is water resource management, which is essential for sustainable human activities, ecological balance, and the mitigation of natural hazards like floods. Streamflow is a crucial element of water resource management and plays a vital role in planning and building water infrastructure, implementing emergency response plans, supporting flood mitigation initiatives, and regulating agricultural and industrial use. However, accurate prediction of streamflow still remains a challenge due to the complex non-linear and non-stationary interaction between …

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 …

Properties Of Eigenvalues Of The Fractal Laplacian, Eric Stachura, Andrew Chincea

Symposium of Student Scholars

We investigate the properties of the eigenvalues of the fractal Laplacian. We begin by defining the fractal Laplacian operator in one dimension and formulate the corresponding Dirichlet eigenvalue problem. Analytical solutions are obtained for specific fractal parameters, and computational results illustrate the structure of eigenvalues and their associated eigenfunctions. We extend our analysis to two dimensions using separation of variables. Our findings contribute to a deeper understanding of how fractal geometry affects the spectral characteristics of differential operators.

Improving Image Quality In Electrical Capacitance Tomography Using Otsu Thresholding, Josiah Nombo

Tanzania Journal of Engineering and Technology (TJET)

Electrical Capacitance Tomography (ECT) is an imaging technique used in industrial process monitoring, particularly for monitoring and measuring the composition of multiphase flows. Despite its widespread application, the commonly used Linear Back Projection (LBP) algorithm often produces low-quality images due to its limited ability to handle high permittivity contrasts and nonlinearities. This study investigates the use of Otsu thresholding as a post-processing technique to enhance ECT image quality. By maximizing inter-class variance in the image histogram, Otsu thresholding improves contrast, clarity, and structural definition, enabling more effective segmentation of oil and gas components in multiphase flows. The proposed Otsu-based reconstruction …

Development Of A Microcontroller-Based Intelligent Traffic Light Control System For Vehicular Movement In T-Junctions, Frederick O. Ehiagwina

Tanzania Journal of Engineering and Technology (TJET)

This research is devoted to the issue of regulating traffic congestion in major cities using light-dependent resistors coupled with the PIC16F877A microcontroller. This study proposes an intelligent traffic control system for T-Junctions, utilizing sensing and control to optimize traffic flow through dynamic phase adjustments and congestion reduction, enabled by a microcontroller-based decision-making system. The proposed system reduces traffic congestion, automates control, and enhances safety, minimizing accidents and lowering infrastructure costs. Under simulated environment, it demonstrates an average response time of 50 ms and achieves 99% accuracy in displaying the correct countdown. Finally, the number of state transitions handled per minute …

Stability Of Space-Time Finite Element Discretizations Of Subdiffusive Time-Fractional Differential Equations, Gabriel Kenneth Staton

Theses and Dissertations

The study of anamolous diffusion, and in particular of subdiffusive time-fractional differential equations, is of great interest for its ability to describe transport of particles through porous media. The time-fractional derivatives in these problems are nonlocal, which notably hinders performance of classical time-stepping methods. As a result, there is significant interest in using simultaneous space-time discretizations for these subdiffusive problems, which have the additional benefit of significantly relaxing the regularity requirements for candidate solutions. These types of Petrov-Galerkin schemes require a careful choice of discretized trial and test spaces in order to guarantee stability; in particular, the usual Galerkin choice …

Developing Predictive Mathematical Model For Optimizing Coating Weight Variation In Galvalume Production: A Case Study Of A Metal Industry, Victoria Mahabi

Tanzania Journal of Engineering and Technology (TJET)

Variations in coating weight for galvanized steel sheets can result in notable differences between batches. Such variations may cause various issues, such as diminished corrosion resistance, lower mechanical strength, and visual defects, which can ultimately drive-up costs, lead to customer dissatisfaction, and pose safety risks. Even with attempts to manage elements like air knife pressure and line speed, coating weight inconsistencies remain challenging. The research focuses on developing a predictive mathematical model designed to optimize variations in coating weight during Galvalume production. The critical parameters influencing coating weight variation were identified and analysed using a systematic literature review, primary data …

Design And Performance Analysis Of Fiber Bragg Grating Temperature Sensor For Industrial Processes Sensing Applications, Paul Stone Stone Brown Macheso S.B.

Tanzania Journal of Engineering and Technology (TJET)

The Fiber Bragg Grating (FBG) sensor has become a widespread sensing device because of its small size, passive design, immunity to electromagnetic interference, and direct ability to measure physical properties like temperature and strain. Recently, femtosecond infrared laser processing and regeneration techniques have resulted in the development of stable high-temperature gratings, which are a powerful tool in smart factories, an aspect of the fourth Industrial Revolution (4IR), and show promise for application in harsh environments like high pressure, high temperature, or ionizing radiation. The development of stable high-temperature gratings that can withstand harsh environmental factors like high temperatures, pressures, and …

A Fuzzy Based Framework For Sustainable Technology Selection In Small-Scale Gold Mining Operations, John M. Kafuku

Tanzania Journal of Engineering and Technology (TJET)

Small-scale gold mining (SSGM) operations in Tanzania has been operating inefficiently due to inadequate mining processing technologies, poor working tools, lack of enough capital, and insufficient electricity. Despite the efforts made by different stakeholders in boosting the sustainability of SSGM yet the sector has not reached the expected goal. This paper proposes a framework for appropriate technology selection to help small scale gold miners in evaluating various gold mineral processing technologies. The framework utilizes the fuzzy logic set theory for technology evaluation and selection. The developed framework for technology selection upon validation provided results that technology adequacy of more than …