Physical Sciences and Mathematics Commons^™

Pt-Symmetry And Eigenmodes, Tamara Gratcheva

University Honors Theses

Spectra of systems with balanced gain and loss, described by Hamiltonians with parity and time-reversal (PT) symmetry is a rich area of research. This work studies by means of numerical techniques, how eigenvalues and eigenfunctions of a Schrodinger operator change as a gain-loss parameter changes. Two cases on a disk with zero boundary conditions are considered. In the first case, within the enclosing disk, we place a parity (P) symmetric configuration of three smaller disks containing gain and loss media, which does not have PT-symmetry. In the second case, we study a PT-symmetric configuration …

Einstein Field Equations And The Solutions For Uncharged Black Holes, Yogesh Mahat

Masters Theses

The General Theory of Relativity, formulated by the brilliant mind of Albert Einstein, stands as one of the most fundamental and revolutionary pillars of modern physics. This elegant theory of gravity not only offers a comprehensive explanation of the workings of the universe on a large scale, but it has also paved the way for groundbreaking advancements in the field of mathematics. This thesis begins by providing a concise overview of the key mathematical principles that are crucial to understanding Einstein’s theory. These principles form the basis for deriving the field equations that Einstein introduced. From there, these equations are …

Recursive Marix Game Analysis: Optimal, Simplified, And Human Strategies In Brave Rats, William A. Medwid

Master's Theses

Brave Rats is a short game with simple rules, yet establishing a comprehensive strategy is very challenging without extensive computation. After explaining the rules, this paper begins by calculating the optimal strategy by recursively solving each turn’s Minimax strategy. It then provides summary statistics about the complex, branching Minimax solution. Next, we examine six other strategy models and evaluate their performance against each other. These models’ flaws highlight the key elements that contribute to the effectiveness of the Minimax strategy and offer insight into simpler strategies that human players could mimic. Finally, we analyze 123 games of human data collected …

Predicting Rheology Of Uv-Curable Nanoparticle Ink Components And Compositions For Inkjet Additive Manufacturing, Cameron D. Lutz

Master's Theses

Inkjet additive manufacturing is the next step toward ubiquitous manufacturing by enabling multi-material printing that can exhibit various mechanical, electronic, and thermal properties. These characteristics are realized in the careful formulation of the inks and their functional materials, but there are many constraints that need to be satisfied to allow optimal jetting performance and build quality when used in an inkjet 3-D printer. Previous research has addressed the desirable rheology characteristics to enable stable drop formation and how the metallic nanoparticles affect the viscosity of inks. The contending goals of increasing nanoparticle-loading to improve material deposition rates while trying to …

Semantic Structuring Of Digital Documents: Knowledge Graph Generation And Evaluation, Erik E. Luu

Master's Theses

In the era of total digitization of documents, navigating vast and heterogeneous data landscapes presents significant challenges for effective information retrieval, both for humans and digital agents. Traditional methods of knowledge organization often struggle to keep pace with evolving user demands, resulting in suboptimal outcomes such as information overload and disorganized data. This thesis presents a case study on a pipeline that leverages principles from cognitive science, graph theory, and semantic computing to generate semantically organized knowledge graphs. By evaluating a combination of different models, methodologies, and algorithms, the pipeline aims to enhance the organization and retrieval of digital documents. …

Accessible Real-Time Eye-Gaze Tracking For Neurocognitive Health Assessments, A Multimodal Web-Based Approach, Daniel C. Tisdale

Master's Theses

We introduce a novel integration of real-time, predictive eye-gaze tracking models into a multimodal dialogue system tailored for remote health assessments. This system is designed to be highly accessible requiring only a conventional webcam for video input along with minimal cursor interaction and utilizes engaging gaze-based tasks that can be performed directly in a web browser. We have crafted dynamic subsystems that capture high-quality data efficiently and maintain quality through instances of user attrition and incomplete calls. Additionally, these subsystems are designed with the foresight to allow for future re-analysis using improved predictive models, as well as enable the creation …

Dehn's Problems And Geometric Group Theory, Noelle Labrie

Master's Theses

In 1911, mathematician Max Dehn posed three decision problems for finitely

presented groups that have remained central to the study of combinatorial

group theory. His work provided the foundation for geometric group theory,

which aims to analyze groups using the topological and geometric properties

of the spaces they act on. In this thesis, we study group actions on Cayley

graphs and the Farey tree. We prove that a group has a solvable word problem

if and only if its associated Cayley graph is constructible. Moreover, we prove

that a group is finitely generated if and only if it acts geometrically …

Qwixx Strategies Using Simulation And Mcmc Methods, Joshua W. Blank

Master's Theses

This study explores optimal strategies for maximizing scores and winning in the popular dice game Qwixx, analyzing both single and multiplayer gameplay scenarios. Through extensive simulations, various strategies were tested and compared, including a scorebased approach that uses a formula tuned by MCMC random walks, and race-to-lock approaches which use absorbing Markov chain qualities of individual score sheet rows to find ways to lock rows as quickly as possible. Results indicate that employing a scorebased strategy, considering gap, count, position, skip, and likelihood scores, significantly improves performance in single player games, while move restrictions based on specific dice roll sums …

Pain Points: Cluster Analysis In Chronic Pain Networks, Iris W. Ho

Master's Theses

Chronic pain is a pervasive health issue, affecting a significant portion of the population and posing complex challenges due to its diverse etiology and individualized impact. To address this complexity, there is a growing interest in grouping chronic pain patients based on their unique treatment needs. While various methodologies for patient grouping have emerged, leveraging graph-based approaches to produce and evaluate such groupings remains largely unexplored. Recent studies have shown promise in integrating knowledge graphs into exploring patient similarity across different biological domains, indicating potential avenues for research. Additionally, there is a growing interest in investigating patient similarity networks, highlighting …

Unraveling The History Of Deforestation In The Amazon Rainforest With Statistical Modeling, Ryan Destefano

Master's Theses

The Amazon rainforest, a vital ecosystem of immense biodiversity and global climate significance, faces the ongoing threat of deforestation driven by agricultural expansion. This thesis employs remote sensing techniques, focusing on the Enhanced Vegetation Index (EVI) derived from Landsat satellite imagery, to track land cover dynamics within the Amazon. The study examines historical land cover changes in current plantations in Peru and Brazil, regions where the exact timing of deforestation is uncertain. By analyzing EVI measurements dating back to 1984, inflection points indicative of deforestation events preceding plantation establishment are identified. Statistical modeling techniques, including spline fitting to analyze time …

Matrix Approximation And Image Compression, Isabella R. Padavana

Master's Theses

This thesis concerns the mathematics and application of various methods for approximating matrices, with a particular eye towards the role that such methods play in image compression. An image is stored as a matrix of values with each entry containing a value recording the intensity of a corresponding pixel, so image compression is essentially equivalent to matrix approximation. First, we look at the singular value decomposition, one of the central tools for analyzing a matrix. We show that, in a sense, the singular value decomposition is the best low-rank approximation of any matrix. However, the singular value decomposition has some …

Assessing The Efficacy Of Hydraulic Pumping As A Remediation Method Of A Subsurface Light Non-Aqueous Phase Liquid Spill In Arroyo Grande, California, James M. Raney

Master of Science in Environmental Sciences and Management Projects

The efficacy of hydraulic pumping as a remediation method of a petroleum, or Light Non-Aqueous Phase Liquid (LNAPL) spill in Arroyo Grande, California will be assessed by determining aquifer properties, assessing the chemical properties of the contaminant, recovering the contaminant from the subsurface, and proposing alternative remediation techniques. Soil, groundwater and contaminant characteristics, cumulative volume of LNAPL skimming test data, pumping rates, and LNAPL thicknesses in wells installed within the contaminant plume were collected. Sediments around the LNAPL source are contaminated with hydrocarbons in the gas and diesel range. Pumping efficacy is expected to continue to decrease at the site, …

Santa Maria Climate Action Plan Recommendations: Building Energy And Transportation, Thomas Zimmerman, Elena Blewett

City and Regional Planning

The Santa Maria Climate Action Plan Recommendations addresses GHG emissions reduction for the largest sectors in the City of Santa Maria- Building Energy and Transportation. The project includes GHG forecasts and reduction targets from the City’s Draft 2020 Community-Wide Greenhouse Gas Inventory Report. The reduction targets are met through a series of actionable measures to help the City meet aggressive reduction targets by 2030 and 2045.

On Near-Linear Cellular Automata Over Near Spaces, Abdul-Rahman M. Nasser

Dissertations

Cellular Automata can be considered as examples of massively parallel machines. They are computational mathematical objects consisting of a grid of cells, each of which can exist in a finite number of states. These cells evolve over discrete time steps according to a set of predefined rules based on the states of neighboring cells. The notion of cellular automata was first introduced by Ulam and von Neumann and then popularized by John H. Conway in the 1970s with one of the most famous examples being The Game of Life.

This research builds on and generalizes the work of Tullio Ceccherini-Silberstein …

Alternative Adjacency Matrices And Spatial Analysis, Jaeseong Hwang

Dissertations

Spatial analysis is essential for comprehending the spatial distribution of diseases and various phenomena across geographic regions. This study investigates the utilization of alternative adjacency matrices in spatial analysis, with a specific focus on implementing Poisson regression models. This study intricately explores the methodology behind constructing alternative weight matrices, specifying weight matrices, and comparing the performance of Poisson models using five different weight matrices.

The popular Poisson model model is described, and five different definitions of weight matrices are defined, which are the following: binary weight matrix, inverse distance weight matrix using Euclidean distance, Graph distance matrix, Path matrix, and …

Quasi-Monte Carlo Estimation For Functional Generalized Linear Mixed Models., Ruvini Kumari Jayamaha Hitihamilage

Dissertations

Functional Data Analysis (FDA) is a topic of growing interest in the statistics community and is applied in a wide range of fields such as Anthropology, Epidemiology, Meteorology, Neurology and Engineering. The data in FDA are smooth curves or surfaces in time or space which can be conceptualized as functions. Because of the smooth nature of the data and the measurements are highly correlated, making the classical methods such as univariate or multivariate analysis are infeasible for such data. Functional data Analysis (FDA) deals with these kinds of more detailed, complex, and structured data.

In this dissertation, we propose a …

A Microgenetic Learning Analysis Of Contextuality In Reasoning About Exponential Modeling, Elahe Allahyari

Dissertations

This work explores the complex cognitive processes students engage in when addressing contextual tasks requiring linear and exponential models. Grounded within Piagetian constructivism and the Knowledge in Pieces (KiP) epistemological perspective (diSessa, 1993, 2018), this empirical study in a clinical setting develops a Microgenetic Learning Analysis (MLA) of the reasoning of 14 students from an Algebra II course. It reveals the critical role of cognitive disequilibrium as an essential cognitive state for conceptual development and the process of reorganizing knowledge systems. The study uncovers the fluctuations in students’ reasoning patterns and the significant impact on students’ reasoning patterns of task-specific …

An Experimental Study Of Supervised Machine Learning Techniques For Minor Class Prediction Utilizing Kernel Density Estimation: Factors Impacting Model Performance, Abdullah Mana Alfarwan

Dissertations

This dissertation examined classification outcome differences among four popular individual supervised machine learning (ISML) models (logistic regression, decision tree, support vector machine, and multilayer perceptron) when predicting minor class membership within imbalanced datasets. The study context and the theoretical population sampled focus on one aspect of the larger problem of student retention and dropout prediction in higher education (HE): identification.

This study differs from current literature by implementing an experimental design approach with simulated student data that closely mirrors HE situational and student data. Specifically, this study tested the predictive ability of the four ISML classification models (CLS) under experimentally …

Remediating History: A Review Of Restoration For Creeks Polluted From Historical Mining Sites, With The Red Boy Mine As A Primary Case Study, Kara Atiyeh

University Honors Theses

I conducted a literature review to examine the key aspects of restoring watersheds affected by pollution from historical mining. This review is then applied to a case study discussion of the Red Boy Mine and Clear Creek remediation project in Granite, Oregon. The goal of this discussion is to explore how an analysis of site conditions along with current literature on management practices can help guide these projects. Thousands of abandoned hard rock mines remain throughout the country, and many pose serious environmental health effects. Heavy metals like cadmium, nickel, and copper are brought to the surface from mining activity, …

The Cascading Effects Of Database Design, Liam Mccracken

University Honors Theses

This paper details how a relational database influenced the design of the rest of a software project. The software project in question is WonderTix, an open-source ticketing and donation platform for the use of Portland Playhouse under continuous development by teams of Portland State students as their computer science capstone project. The paper, a capstone review thesis, examines WonderTix as an instantiation of the Model-View-Controller design pattern, noting how the model, a relational database based on the SQL standard, influenced the design of the view and controller components. This influence is explored from three angles. First, when the implementation of …

Comparison Between Galfit And Lenstronomy To Analyze The Host Galaxies Of Reverberation Mapped Active Galactic Nuclei, Samantha Kay Allen

Physics

Active Galactic Nuclei (AGN) are some of the brightest objects within our Universe. Most galaxies contain a supermassive black hole (SMBH) at their center, but not all are powered by active accretion which can form an AGN. Due to the conservation of angular momentum, dust and gas rotate around the SMBH to form a disk. The large gravitational potential energy from the SMBH is converted into heat through friction, which produces a hot and luminous source of light. As a result, the SMBH is unresolved. Through a technique known as reverberation mapping (RM), the mass of the SMBH has been …

Investigating The Relationship Between Single And Multiple Sersic Models Of Active Galaxies Using Galfit, Ellie H. Johnson

Physics

Supermassive Black Holes (SMBHs) can be found in the center of almost every galaxy, and in some cases, can form Active Galactic Nuclei (AGNs). AGNs are some of the brightest objects in our observable Universe and are distinguished from quiescent galaxies by accretion onto the central SMBH, which forms a disk where the luminosity is produced. Reverberation mapping (RM) of broad-line AGNs determines the mass of the SMBH by resolving the gravitational sphere of influence of the BH ``in time". In this study, GALFIT is used to fit 2D analytic functions to existing Hubble Space Telescope (HST) images for 23 …

Identifying Ion-Scale Waves In Parker Solar Probe Sub-Alfvénic Intervals, Nicholas Henry Androski, Kristoff Paulson

Physics

Identification of coherent quasi-parallel ion-scale (1-32 Hz) wave activity in sub-Alfvénic regions of the solar wind observed by NASA's Parker Solar Probe during perihelion encounters 8 to 16. Wave activity is filtered computationally by coherency, circular polarization and propagation angle with respect to the mean magnetic field. Initial statistical results are presented with suggestions for future improvements and studies. A general overview of the heliosphere and the context of ion-cyclotron waves (an ion-scale wave) in the coronal heating problem. Along the way to identify ion-scale wave activity, tables of sub-Alfvénic intervals and current sheet crossings for encounters 8 to 16 …

Parabolic And Non-Parabolic Surfaces With Small Or Large End Spaces Via Fenchel-Nielsen Parameters, Michael Antony Pandazis

Dissertations, Theses, and Capstone Projects

We consider conditions on the Fenchel-Nielsen parameters of a Riemann surface X that determine whether or not a surface X is parabolic. Fix a geodesic pants decomposition of a surface and call the boundary geodesics in the decomposition cuffs. For a zero or half-twist flute surface, we prove that parabolicity is equivalent to the surface having a covering group of the first kind. Using that result, we give necessary and sufficient conditions on the Fenchel-Nielsen parameters of a half-twist flute surface X with increasing cuff lengths such that X is parabolic. As an application, we determine whether or not each …

Environmental Fate And Transport Of Pfas In Wastewater Treatment Plant Effluent Discharged To Rapid Infiltration Basins, Kai M. Trobisch

Masters Theses

Fate and transport of per- and polyfluoroalkyl substances (PFAS) in wastewater treatment plant (WWTP) effluent discharged to rapid infiltration basins (RIBs) is investigated using data from 26 WWTPs in Michigan and numerical modeling to assess the role of air-water interface (AWI) sorption in modulating mass fluxes to the saturated zone. Analysis of RIB physical properties yields a median separation distance of 6.5 meters between land surface and the water table, and a continuum of area-normalized effluent fluxes ranging from 0.01 to 0.62 meters per day. A subset of WWTPs with RIBs indicate higher PFAS concentrations in groundwater than effluent with …

Moral Responsibility And Other Visceral Attitudes Of Western Michigan University Students Toward Food Waste, Quinn Heiser

Masters Theses

Despite the large number of people that go hungry on a regular basis in America, food waste remains a looming issue, globally and nationally. Both American college students and the universities themselves contribute a large portion to the national food waste totals. A dichotomy that is especially curious is the difference between students who live on-campus and whose main source of meals is the dining centers, versus students who live off campus and rely mainly on groceries to make meals independently. However, food waste has seldom been studied in the context of the fact that college is a major transition …

Causal Inference Using Bayesian Network For Search And Rescue, Amanda Belden

Master's Theses

People who are considered missing have much higher probabilities of being found dead compared to those who are not considered missing in terms of Search and Rescue (SAR) missions. Dementia patients are incredibly likely to be declared missing, and in fact after removing those with dementia the probability of the mission being regarded as missing person case is only about 10%. Additionally, those who go missing are much more likely to be on private land than on protected areas such as forests and parks. These and similar associations can be represented and investigated using a Bayesian network that has been …

Auditory Ace Mobile Application Capstone Review, Layla Smith

University Honors Theses

This paper describes the development process and outcomes of my 2023-2024 Capstone Project, Auditory Ace, a self-directed auditory training mobile application for individuals with cochlear implants. Recognizing the limitations of current market offerings, Dr. Timothy Anderson created a Capstone project proposal to develop an accessible auditory training mobile application. The Capstone team that took on this proposal consisted of Darya Haines, Dustin Huynh, Jordan Nguyen, Nihar Koppolu, Scott Thorkelson, Sienna Day, and myself, Layla Smith. This paper is structured to follow the Agile software development methodology, which we used to develop Auditory Ace, reviewing in detail every major choice we …

Development Of A Two-Photon Imaging System, Jesseca Hollenbaugh

University Honors Theses

The objective of this project was to convert a Sarastro 2000 confocal laser scanning microscope (CLSM) into a system capable of far-field two-photon excitation (TPE) imaging for the use of the PSU Biology department. TPE microscopy operates on the ability of fluorophores to accept two photons each with half the energy of a desired transition in a single quantum event via a virtual energy state and then emit a higher energy photon upon relaxation. This is preferable to single-photon excitation (SPE) imaging due to lower photon imaging, causing less damage to delicate biological samples, as well as the inherent localization …

Virtual Field Environments Capstone Software Review, Ashton Sawyer

University Honors Theses

This is a review of the Virtual Field Environments computer science capstone project, sponsored by geology professor Rick Hugo. The tool aims to create and render VFEs, interactable 360° environments hosted on the web that are used as virtual field trips for K-12 students. This essay discusses the development process, including understanding requirements, tool and technology selection, problem-solving, and decision-making strategies. It also highlights the differences between the capstone and the other core computer science courses, and how those differences help to prepare students for the workforce. The project was completed over the course of twenty weeks by a team …