Applied Mathematics Commons^™

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 …

Decomposition And Coordination For Multiobjective Optimization: A Framework And Methodology, Philip J. De Castro

All Dissertations

In this work, we consider finding Pareto efficient solutions for complex multiobjective optimization problems (MOPs). Complex MOPs are unique in the literature because they have many more objective functions than is typically considered. In fact, such complex MOPs will have 30+ objective functions. This large problem size presents computational and coginitive difficulties. Computationally, standard techniques for solving MOPs are often ineffective and cognitively it is difficult for a decision maker (DM) to handle all of the information provided in such a large problem. To address these challenges, we develop a decomposition and coordination framework. This framework will allow us to …

The Little Diagram That Could: Geometric Properties And Statistical Applications Of Persistence Diagrams In Topological Data Analysis, Eugene Kler

McKelvey School of Engineering Graduate Student Theses & Dissertations

Topological Data Analysis (TDA) is a collection of techniques for data analysis that leverages topological invariants of spaces formed from data points. These methods excel at extracting useful information from noisy or sparse data, making them attractive to many mathematicians, statisticians, and scientists. In this thesis, we explore TDA on three fronts: algebraic foundations, statistical applications, and metric properties. Throughout, the central object of study is the Persistence Diagram (PD), a summary of the changes in homology that occur as one builds simplicial complexes from the data by increasing a parameter.

Mathematics-Ai Based Phylogenetic Analysis Of Influenza Virus Mutation Data, Emilee Walden

Mathematical Sciences Undergraduate Honors Theses

The influenza virus is one of the most common viral infections each year and can mutate rapidly. Viral mutations pose significant threats to public health by increasing infectivity and strengthening vaccine resistance. To track these evolving patterns, agencies like the CDC annually evaluate thousands of virus strains to understand viral mutagenesis and evolution in depth. Therefore, a computational method for analyzing high-dimensional, noisy virus data could aid in the rapid identification of antigens essential for an effective influenza vaccine for the upcoming season. Through the integration of genomic analysis, clustering, and dimensionality reduction methods, this study specifically aims to develop …

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.

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 …

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 …

Conformable Regulator Problems With Fixed Delay, Seth Baur, Joseph E. Smith, Nick Wintz

2025 Student Academic Showcase

In this project, we consider processes guided by a conformable derivative first introduced by Khalil et al in 2014. This time-weighted derivative has many of the same properties as the classical derivative but lacks the semigroup property for the exponential. Here, we study a conformable linear system where the state and control are subject to the same fixed delay. Our process is also subject to wear and tear, represented by a cost functional. Our goal is to find an optimal control that minimizes this cost. This control is propagated by a quasi-Ricatti equation, which itself includes a time delay. Finally, …

Applications For The Conformable Information Filter, Sophia Hungerford, Joseph E. Smith, Nick Wintz

2025 Student Academic Showcase

In this project, we offer application to our previously constructed information filter. The information filter is an algorithm used to estimate the information of a process corrupted in some way. The information filter is mathematically similar to the Kalman filter, widely used in navigation. Unlike the Kalman filter, the information filter propagates backwards in time and is more effective in smoothing. Here, our corrupted system is in terms of conformable derivative introduced by Khalil et al. in 2014. This time-weighted derivative shares many of the same properties as the classical derivative but lacks the usual semigroup property associated with the …

Developing An Unfolding-Incorporated Coarse-Grained Polymer Model For Fibrinogen To Study The Mechanical Behaviour, Vivek Sharma, Poulomi Sadhukhan

Northeast Journal of Complex Systems (NEJCS)

Fibrinogen is a protein found in blood that forms Fibrin polymer network to build a clot during wound healing process when there is a cut in the blood vessel. The fibrin fiber is highly stretchable and shows a complex mechanical properties. The fibrin monomer, Fibrinogen, has a very complex structure which is responsible for its unusual elastic behaviour. In this work, we focus on mechanism of unfolding of D-domain of Fibrinogen, and study its effect in the mechanical behaviour. We develop a coarse-grained (CG) bead-spring model for Fibrinogen which captures the unfolding of folded D-domains along with other necessary structural …

Automating Course Scheduling With Linear Programming And The Python Pulp Framework: First Steps, George K. Thiruvathukal

Computer Science: Faculty Publications and Other Works

This article presents a pragmatic approach to automating course scheduling in an academic setting using linear programming.

We explore how linear optimization via current open-source tools can efficiently handle scheduling constraints such as instructor preferences, teaching loads, course section requirements, and specific time slots. Using Python’s PuLP library and matplotlib for visualization, we built a flexible and accessible scheduling system.

Our research prototype balances course assignments while addressing department-specific needs, demonstrating how linear programming can simplify academic scheduling and improve efficiency.

Although this is a research prototype, our results already demonstrate the ability to generate a correct course schedule that …

Meta-Clustering For Specialized Language Models: Enhancing Contextual Adaptation And Mitigating Hallucinations In Diverse Healthcare Environments, Joshit Mohanty, Vaishali Vaishali, Sandeep Kumar Nayak, Sumit Lahiri

Graduate Student Government Association Research Conference

Large Language Models (LLMs) have significantly advanced conversational AI by enabling dialogic information-seeking and task execution across diverse domains. However, their extensive parameters and broad domain scope lead to “data hallucinations.” These shortcomings are particularly evident in dynamic and diverse environments like India’s healthcare sector, where myriad languages, regional practices, and cultural nuances demand specialized, localized expertise rather than one-size-fits-all generalist models. This paper introduces a meta-clustering framework that integrates Distilled Language Models (DLMs) and Small/Specialized Language Models (SLMs) with meta-learning principles to address these limitations. By drawing on evidence from works such as MedHalu and Med-HALT, the framework seeks …

Existence And Nonexistence Of Positive Solutions For Fractional Boundary Value Problems With Lidstone-Inspired Fractional Conditions, Jeffrey Lyons, Jeffrey T. Neugebauer, Aaron G. Wingo

EKU Faculty and Staff Scholarship

This paper investigates the existence and nonexistence of positive solutions for a class of nonlinear Riemann–Liouville fractional boundary value problems of order 𝛼 +2⁢𝑛, where 𝛼 ∈(𝑚 −1,𝑚] with 𝑚 ≥3 and 𝑚,𝑛 ∈ℕ. The conjugate fractional boundary conditions are inspired by Lidstone conditions. The nonlinearity depends on a positive parameter on which we identify constraints that determine the existence or nonexistence of positive solutions. Our method involves constructing Green’s function by convolving the Green functions of a lower-order fractional boundary value problem and a conjugate boundary value problem and using properties of this Green function to apply the Guo–Krasnosel’skii …

Using Mathematical Modeling To Study The Dynamics Of Legionnaires’ Disease And Consider Management Options, Mark Z. Wang, Christina J. Edholm, Lihong Zhao

Faculty Articles

Legionnaires' disease (LD) is a largely understudied and underreported pneumonic environmentally transmitted disease caused by the bacteria \textit{Legionella}. It primarily occurs in places with poorly maintained artificial sources of water. There is currently a lack of mathematical models on the dynamics of LD. In this paper, we formulate a novel ordinary differential equation-based susceptible-exposed-infected-recovered (SEIR) model for LD. One issue with LD is the difficulty in its detection, as the majority of countries around the world lack the proper surveillance and diagnosis methods. Thus, there is not much publicly available data or literature on LD. We use parameter estimation for …

Numerical Analysis Of The Seir Model, Abigail R. Beckelhimer

Departmental Honors & Graduate Capstone Projects

Epidemiological models delineate the spread of diseases within a population. In this research project, the Susceptible-Exposed-Infected-Recovered (SEIR) Model was examined numerically for comparison between several methods. Approximations were obtained through Euler’s Method, Taylor’s Method, Runge-Kutta Methods, and Multi-step Methods. Hypothetical situations with parameter alterations were considered in order to better understand the effects the parameters have on the model. The goal of this project was to portray the usefulness of numerical approximations for predicting the behavior of the SEIR model and thus the course of a pandemic.

Learning With Errors Parameter Analysis, Archana Parameswaran

Cybersecurity Undergraduate Research Showcase

We implement a systematic approach for generating, evaluating, and benchmarking Learning with Errors implementations in Sage Math by varying lattice dimensions, moduli, error standard deviations, and multiple error distributions to observe concrete security-efficiency tradeoffs. The security estimator maps parameter sets to concrete security levels and bits, while performance metrics measured computational efficiency and memory requirements. Results indicate that various distribution types do not significantly impact security, though binomial distributions require more computational overhead than discrete gaussian or uniform. Memory requirements increased when modulus q increased from 12289 to 65537. Larger dimensions have an exponentially growing requirement for memory, but this …