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Differences In Sideerophore Production During The Growth Of Phytoplankton In Southern Ocean Incubation Experiments Under High- And Low-Iron Conditions, Randelle M. Bundy, Kristen N. Buck, Bethany D. Jenkins, P. Dreux Chappell, Daniel J. Repeta, Alexa Sterling, Shannon M. Yang, Laura Holland, Léo Mahieu, Laura E. Moore Jan 2026

Differences In Sideerophore Production During The Growth Of Phytoplankton In Southern Ocean Incubation Experiments Under High- And Low-Iron Conditions, Randelle M. Bundy, Kristen N. Buck, Bethany D. Jenkins, P. Dreux Chappell, Daniel J. Repeta, Alexa Sterling, Shannon M. Yang, Laura Holland, Léo Mahieu, Laura E. Moore

OES Faculty Publications

Iron is an important micronutrient required by marine microorganisms. The Southern Ocean is an ecosystem where primary production is limited by the availability of iron, but how microorganisms in this region adapt to low-iron conditions or respond to episodic iron inputs is understudied. We tested how external iron additions would impact bacterial production of siderophores during phytoplankton growth using shipboard incubation experiments under a range of iron conditions. Similar heterotrophic bacteria communities and phytoplankton biomass were observed whether iron was added from the continental margin or as inorganic iron. Under both high- and low-iron conditions, the heterotrophic bacteria community remained …


The Distribution Of A-Numbers Of Hyperelliptic Curves In Characteristic Three, Derek Garton, Jeffrey Lin Thunder, Colin Weir Jan 2026

The Distribution Of A-Numbers Of Hyperelliptic Curves In Characteristic Three, Derek Garton, Jeffrey Lin Thunder, Colin Weir

Mathematics and Statistics Faculty Publications and Presentations

In this paper we present a new approach to counting the proportion of hyperelliptic curves of genus g defined over a finite field Fq with a given a-number. In characteristic three this method gives exact probabilities for curves of the form Y 2 = f(X) with f(X) ∈ Fq[X] monic and cubefree, probabilities that match the data presented by Cais et al. in previous work. These results are sufficient to derive precise estimates (in terms of q) for these probabilities when restricting to squarefree f. As a consequence, for positive integers a and g we show that the nonempty strata …


Numerics: A .Net Library For Numerical Computing, Statistical Analysis, And Risk Assessment, C. Haden Smith, Woodrow L. Fields, Julian Gonzalez, Sadie Niblett, Brennan Beam, Brian Skahill Jan 2026

Numerics: A .Net Library For Numerical Computing, Statistical Analysis, And Risk Assessment, C. Haden Smith, Woodrow L. Fields, Julian Gonzalez, Sadie Niblett, Brennan Beam, Brian Skahill

Mathematics and Statistics Faculty Publications and Presentations

Numerics is a free and open-source numerical computing library for .NET, developed by the U.S. Army Corps of Engineers Risk Management Center (USACE-RMC). The library provides 43 univariate probability distributions with L-moment and maximum likelihood parameter estimation, eight Markov Chain Monte Carlo (MCMC) samplers for Bayesian inference, bootstrap uncertainty quantification, bivariate copulas, optimization algorithms, and numerical methods for integration, differentiation, root finding, and linear algebra. Numerics targets engineers, scientists, and analysts working in infrastructure risk assessment, flood frequency analysis, and Monte Carlo simulation within .NET-based enterprise systems. The library supports .NET 8.0 through 10.0 and .NET Framework 4.8.1 and is …


Legal Ethics Of Ai Snake Oil: Navigating The Hype, Harm, And Hope Of Legal Ai, Drew Simshaw Jan 2026

Legal Ethics Of Ai Snake Oil: Navigating The Hype, Harm, And Hope Of Legal Ai, Drew Simshaw

Scholarly Works

This paper argues that the legal ethics of AI extend far beyond competence and hallucinations. It shows how AI often functions as a mirror, exposing deeper ethical questions about institutional incentives, lawyer wellbeing, access to justice, and AI's broader social and environmental impacts.


An Empirical Framework For Evaluating Semantic Preservation Using Hugging Face, Nan Jia, Anita Raja, Raffi Khatchadourian Jan 2026

An Empirical Framework For Evaluating Semantic Preservation Using Hugging Face, Nan Jia, Anita Raja, Raffi Khatchadourian

Publications and Research

As machine learning (ML) becomes an integral part of high-autonomy systems, it is critical to ensure the trustworthiness of learning-enabled software systems (LESS). Yet, the nondeterministic and run-time-defined semantics of ML complicate traditional software refactoring. We define semantic preservation in LESS as the property that optimizations of intelligent components do not alter the system's overall functional behavior. This paper introduces an empirical framework to evaluate semantic preservation in LESS by mining model evolution data from HuggingFace. We extract commit histories, $\textit{Model Cards}$, and performance metrics from a large number of models. To establish baselines, we conducted case studies in three …


All Games Have Equilibria, M. Ali Khan, Arthur Paul Pedersen, Maxwell B. Stinchcombe Jan 2026

All Games Have Equilibria, M. Ali Khan, Arthur Paul Pedersen, Maxwell B. Stinchcombe

Publications and Research

Research on Nash equilibrium existence for infinite games has grown into a patchwork of technical preconditions and counterexamples. This paper presents a unified program in equilibrium theory by revising the predominant model of mixed strategies based on countable additivity. A game is specified by a nonempty set of players and, for each player, a nonempty action set and a bounded von Neumann-Morgenstern utility function. Every such game is shown to admit a Nash equilibrium in finitely additive mixed strategies. In addition, the equilibrium correspondence for any such game is shown to be nonempty, compact-valued, and upper hemicontinuous, and the same …


Resilience For Whom? A Study In Pathways And Production Of Unequal Risk In The Rockaways, Aaryan M. Nair Jan 2026

Resilience For Whom? A Study In Pathways And Production Of Unequal Risk In The Rockaways, Aaryan M. Nair

Publications and Research

This paper investigates how climate adaptation policies in the Rockaway Peninsula of New York City produce unequal outcomes despite their ostensibly neutral design, framing resilience as an environmental and climate justice problem. Situated within a landscape marked by stark socioeconomic disparities, aging housing stock, and high exposure to coastal flooding, the study demonstrates that existing adaptation strategies—centered on uniform technical standards, insurance frameworks, and large-scale coastal infrastructure—systematically advantage actors with greater financial and institutional capacity while leaving low-income residents, particularly renters, disproportionately vulnerable.

The analysis identifies three core dynamics underlying this “unequal-by-design” resilience regime: (1) the stratified feasibility of compliance …


Quantifying Uncertainty In Landscape Evolution And Provenance Analysis: Insights From Statistical And Numerical Modelling, Vivian Carmello Grom Jan 2026

Quantifying Uncertainty In Landscape Evolution And Provenance Analysis: Insights From Statistical And Numerical Modelling, Vivian Carmello Grom

LSU Doctoral Dissertations

Landscape evolution models (LEMs) and detrital zircon provenance are widely used to investigate Earth surface processes, yet both face challenges related to quantifying model behavior and interpreting sedimentary signals under realistic, heterogeneous conditions. This thesis addresses these challenges through analysis and case studies that develop and apply new approaches for analyzing landscape dynamics and assessing uncertainties in sediment provenance.

Chapter 1 introduces a quantitative framework for evaluating LEM outputs using Shannon Entropy, Moran’s I, and Geary’s C. Applied to simulations with steady uplift, periodic uplift, spatially variable uplift, and a timeseries of DEMs, these metrics capture spatial organization and information …


Key To Spartina Of The West Coast Based On Vegetative Characteristics, Mary Pfauth, Mark D. Sytsma, Mitchell Kloer, Jennifer Riddle, Jacob Rose, Gabriel E. Campbell Jan 2026

Key To Spartina Of The West Coast Based On Vegetative Characteristics, Mary Pfauth, Mark D. Sytsma, Mitchell Kloer, Jennifer Riddle, Jacob Rose, Gabriel E. Campbell

Center for Lakes and Reservoirs Publications and Presentations

In their natural condition, Pacific Coast estuaries have extensive open mudflats in the intertidal area that are important shorebird feeding habitat and are used for oystering and recreational fishing. Several non-native cordgrass species are invading Pacific estuaries and damaging these functions and uses. Early detection is critical to effective management of cordgrass infestation. This key is intended to provide an easy-to-use reference for quick identification of Spartina (synonym: Sporobolus) species on the Pacific coast. We choose to focus on vegetative characteristics here, since flowers are not always visible when it can be advantageous to survey.

This publication is intended to …


Inferential Statistics For Industrial Organizational Psychologists: A Practical Guide For Testing Hypotheses Using R, Caitlin Lapine Jan 2026

Inferential Statistics For Industrial Organizational Psychologists: A Practical Guide For Testing Hypotheses Using R, Caitlin Lapine

Open Touro Created

2026

This text aims to provide a practical guide for students in industrial organizational psychology or related fields to complete inferential statistics using R open-source programming language. It provides information about when to use particular statistical analyses and how to perform those with statistical software.


Investigating Effects Of The Macroalga Caulerpa Prolifera On Restoration Of The Seagrass Halodule Wrightii In The Indian River Lagoon, Florida, Luciana M. Banquero Jan 2026

Investigating Effects Of The Macroalga Caulerpa Prolifera On Restoration Of The Seagrass Halodule Wrightii In The Indian River Lagoon, Florida, Luciana M. Banquero

Graduate Studies Theses and Dissertations 2026

Seagrass restoration efforts have been motivated by global decreases in coverage associated with anthropogenic influences on the environment. In the Indian River Lagoon (IRL), FL, seagrass declined by 75% between 2011 and 2021. During this time, abundance of the macroalga Caulerpa prolifera increased substantially in the IRL. The macroalga is native to this estuary, however C. prolifera abundance has fluctuated widely in the past few decades. Being highly opportunistic, C. prolifera took advantage of areas formerly inhabited by seagrass. It is not known how dense, continuous beds of C. prolifera impact seagrass restoration projects or natural recovery of seagrass. Previous …


Using Inferences From Natural Language Narratives To Improve Video Question Answering, Hoang Bao Truong Jan 2026

Using Inferences From Natural Language Narratives To Improve Video Question Answering, Hoang Bao Truong

Graduate Studies Theses and Dissertations 2026

The purpose of this thesis is to examine how structured narrative representation and reasoning strategies jointly affect the performance of Video Question Answering (VideoQA). Although recent advances in large multimodal and language models have improved video description and retrieval, causal and counterfactual reasoning remain challenging. This thesis studies an inference-only pipeline in which videos are converted into natural-language narratives, and those narratives may optionally be transformed into a structured NarrativeML format before multiple-choice questions are answered without task-specific fine-tuning. NarrativeML is a machine-readable narrative representation that explicitly encodes entities, events, and their causal and temporal relations. Three representational contexts are …


Holographic Sensors For The Detection Of Volatile Organic Compounds, Graceson Antony Jan 2026

Holographic Sensors For The Detection Of Volatile Organic Compounds, Graceson Antony

Doctoral

Volatile organic compound (VOC) monitoring at parts-per-million (ppm) concentration levels is essential for occupational safety, indoor air quality, and regulatory compliance. Although holographic gas sensors have been widely investigated, most operate in reflection mode as qualitative visual indicators, with limited quantitative evaluation of sensing mechanisms and scarce systematic demonstrations of repeatable multi-cycle validation for VOCs at ppm concentrations. A physics-based optimisation framework for transmission-mode holographic gas sensors which can bridge this gap has remained largely undeveloped.

This thesis presents the development and optimisation of real-time transmission-mode volume phase transmission holographic grating (VPTHG) sensors for ppm-level VOC detection. A comprehensive theoretical …


The Colorado River: Searching For Solutions In The Face Of Uncertainty: Conference Summary, Emilia Endara, Douglas Kenney Jan 2026

The Colorado River: Searching For Solutions In The Face Of Uncertainty: Conference Summary, Emilia Endara, Douglas Kenney

Books, Reports, and Studies

The Colorado River is facing unprecedented change and uncertainty. Average annual flows continue to decline, and negotiations to craft post-2026 guidelines to manage the river have repeatedly bogged down in disagreements about delivery obligations, sharing shortages, and mandatory conservation. While some clarity may emerge in the coming months, the ability to sustain many existing municipal and agricultural water users is already being compromised. Meanwhile, there is growing recognition that a durable resolution must also address the water rights of sovereign Tribal Nations and better integrate environmental values into river management. All sovereigns, stakeholders, and sectors must work together now more …


Thirst For Data: State Responses To Data Center Water Use, Daniel Anderson, Sydney Stellato Jan 2026

Thirst For Data: State Responses To Data Center Water Use, Daniel Anderson, Sydney Stellato

Books, Reports, and Studies

No abstract provided.


Predicting Oil Contamination In Water Using Machine Learning On Microbial Compositions, Tong Gao, Isaac Bigcraft, Stephen Techtmann, Issei Nakamura Jan 2026

Predicting Oil Contamination In Water Using Machine Learning On Microbial Compositions, Tong Gao, Isaac Bigcraft, Stephen Techtmann, Issei Nakamura

Michigan Tech Publications

We present a compact and generative machine-learning framework that predicts oil contamination based on microbial community compositions from experimental samples. Our method combines dimensionality reduction with data augmentation and generative modeling to address high-dimensional, non-linear, and sparse microbial data. To reduce the 503-dimensional bacterial composition dataset, we compared three dimensionality reduction techniques: feature importance from random forest, principal component analysis (PCA), and t-distributed stochastic neighbor embedding (t-SNE). Feature importance outperformed PCA and t-SNE, improving predictive performance and identifying microbial species most strongly correlated with oil contamination. To mitigate data scarcity, we augmented the training data using an augmented data neural …


Evaluating Llms For Cpe Identification In Iot Reconnaissance, Christopher Davisson Jan 2026

Evaluating Llms For Cpe Identification In Iot Reconnaissance, Christopher Davisson

EWU Masters Thesis Collection

Vulnerability identification during penetration testing relies on rigid string-matching to map network scan data to Common Platform Enumeration (CPE) identifiers and downstream Common Vulnerabilities and Exposures (CVEs). The approach frequently fails on physical Internet of Things (IoT) devices, which produce non-standard, irregular service banners that resist deterministic parsing. Large Language Models can reason through these fuzzy associations, but cloud-hosted models introduce cost, latency, and operational security concerns when processing reconnaissance data from live networks. This thesis asks whether locally-hosted open-weight Large Language Models (LLMs) can perform this task well enough to be useful, and how performance varies with model scale, …


Tree-Based Graph Neura Networks For Natural Language Inference: From Structure-Only To Hybrid Architectures, Jason P. Lunder Jan 2026

Tree-Based Graph Neura Networks For Natural Language Inference: From Structure-Only To Hybrid Architectures, Jason P. Lunder

EWU Masters Thesis Collection

Large transformer models achieve strong performance on natural language understanding tasks but require hundreds of millions of parameters and extensive pretraining. This thesis investigates whether graph neural networks operating on dependency parse trees can provide more parameter-efficient sentence representations for natural language inference, evaluated on two NLI tasks: entailment classification and semantic textual similarity.

Tree Matching Networks (TMN) adapt Graph Matching Networks to linguistic dependency trees with rich node and edge features, evaluated against a BERT baseline at matched parameter counts on identical training data. Tree Transformer Networks (TTN) extend TMN with transformer-based aggregation and tree-aware positional encodings, with component …


Macroinvertebrate Taxonomic And Functional Diversity In The Spokane River Watershed, Kaitlin L. Abell Jan 2026

Macroinvertebrate Taxonomic And Functional Diversity In The Spokane River Watershed, Kaitlin L. Abell

EWU Masters Thesis Collection

Changes in land use, such as agricultural expansion, have impacted stream systems by modifying discharge, substrate diversity, channel morphology, and nutrient inputs. The Spokane River Watershed is heavily impacted by human activity, including urban and agricultural development. Rehabilitation efforts are being organized to reintroduce Salmonidae species in the Spokane River Watershed. The first step of this reintroduction is to perform habitat studies to inform allocation of restoration efforts. As part of this effort, I performed benthic macroinvertebrate surveys throughout the watershed.

The objective of my research was to use the macroinvertebrate community as a biological indicator to determine which habitat …


Relationships Between Benthic Macroinvertebrate Communities And Environmental Conditions In Headwater Tributaries Of The Pend Oreille Lake Watershed, Idaho, Devlin Mee Jan 2026

Relationships Between Benthic Macroinvertebrate Communities And Environmental Conditions In Headwater Tributaries Of The Pend Oreille Lake Watershed, Idaho, Devlin Mee

EWU Masters Thesis Collection

Benthic macroinvertebrates are widely used indicators of stream condition, and their communities respond to thermal and land-use conditions in headwater streams. This study characterized macroinvertebrate biomass, community composition, and diversity across forested headwater tributaries of the Pend Oreille lake watershed in northern Idaho, and examined their relationships with summer temperature, land development, and road proximity. Samples from thirteen streams collected in 2024 were identified to genus, measured, and converted to estimated biomass using published length–mass regressions; ten streams had recovered temperature loggers. Because environmental variables were characterized once per stream, all analyses were conducted at the stream level.

Estimated total …


Microgravity-Induced Alterations In Left Atrial Hemodynamics And Thrombogenic Risk: Insights From Healthy And Atrial Fibrillation Models, Grace M. Hoeppner Jan 2026

Microgravity-Induced Alterations In Left Atrial Hemodynamics And Thrombogenic Risk: Insights From Healthy And Atrial Fibrillation Models, Grace M. Hoeppner

Dissertations, Master's Theses and Master's Reports

Background: Microgravity exposure alters cardiovascular loading, yet its impact on left atrial flow dynamics and thrombotic risk remains poorly understood. This study investigates how spaceflight-relevant microgravity-induced changes in cardiac outflow affect left atrial hemodynamics in healthy individuals and patients with atrial fibrillation.

Methods: Patient-specific left atrial models were generated for three healthy individuals and three AF patients. Computational fluid dynamics (CFD) simulations were performed using each patient’s baseline mitral outflow waveform and two modified waveforms representing short- and long-duration post-flight cardiac loading changes derived from echocardiographic observations. Hemodynamic metrics included left atrial velocity, time averaged wall shear stress, oscillatory shear …


Geospatial Analysis Of Sinkhole Density And Characteristics In West Virginia, Marissa Shannon Loftus Jan 2026

Geospatial Analysis Of Sinkhole Density And Characteristics In West Virginia, Marissa Shannon Loftus

Graduate Theses, Dissertations, and Problem Reports (ETD)

Creation of a sinkhole map of West Virginia provides useful data to help identify areas susceptible to sinkhole related hazards, as well as allowing for detailed analysis of factors controlling karst development. Newly available, statewide LiDAR-derived digital elevation data have made mapping sinkholes over larger spatial extents feasible. For this study, sinkholes were mapped for all areas of West Virginia that are underlain by carbonate rocks; then the distribution and characteristics were evaluated overall and in four focus areas (Berkeley and Jefferson counties, Pendleton County, Greenbrier County, and Monroe County). These areas correspond to broader physiographic regions, with Berkeley, Jefferson, …


Comparison Of Push-Pull Air Curtain To Overhead Downdraft Systems On Aerosol Containment And Distribution In Controlled Environments, Manal Mutairi Jan 2026

Comparison Of Push-Pull Air Curtain To Overhead Downdraft Systems On Aerosol Containment And Distribution In Controlled Environments, Manal Mutairi

Graduate Theses, Dissertations, and Problem Reports (ETD)

Abstract

Comparison of Push-Pull Air Curtain to Overhead Downdraft Systems on Aerosol Containment and Distribution in Controlled Environments.

This dissertation looks at the ongoing issue of tiny airborne particles created during medical and dental procedures and evaluates ways to reduce the risk of exposure for healthcare workers and patients to these particles. The first study focuses on the size, how long particles stay in the air, and how far they travel from common medical procedures that create aerosols, showing that tiny particles (less than 5 µm) can stay in the air long enough to escape basic droplet controls. As a …


Timing, Spectral, And Single-Pulse Properties Of Radio Pulsars, Evan Francis Lewis Jan 2026

Timing, Spectral, And Single-Pulse Properties Of Radio Pulsars, Evan Francis Lewis

Graduate Theses, Dissertations, and Problem Reports (ETD)

Radio pulsars are highly magnetized, rapidly rotating neutron stars which emit beams of radio waves from their magnetic poles. Their incredible rotational stability allows for their use in a variety of high-energy astrophysical studies, though the details of their internal structure and emission mechanisms are still unknown. We use observations of a cross-section of the pulsar population in order to investigate the nature of their evolution, their emission properties, and their environments.

First we derive timing solutions for three pulsars discovered through their sporadic single pulses. It was possible to obtain timing solutions through a set of single-pulse times of …


Preliminary Analysis Of Soil Volatile Organic Compounds As Soil Health Indicators, Thorne Taul Jan 2026

Preliminary Analysis Of Soil Volatile Organic Compounds As Soil Health Indicators, Thorne Taul

Graduate Theses, Dissertations, and Problem Reports (ETD)

Over the past decade, soil health (SH) has gained popularity due to the novelty of sustainable soil use related to human wellbeing. Soil health describes the overall quality of soil and its capacity to function over time. As interest in SH grows, researchers continue to explore new soil health indicators that can improve knowledge on how soil health is assessed and managed. Some indicators directly reflect soil health status, and some indirectly relate to processes and functions occurring within the soil. Volatile organic compounds (VOCs) are naturally occurring compounds that play a role in multiple soil processes. They are associated …


The Deposition, Prevalence, And Persistence Of Gunshot Residue In Standard And Less Lethal Ammunition, Liliana Claire Barbosa Jan 2026

The Deposition, Prevalence, And Persistence Of Gunshot Residue In Standard And Less Lethal Ammunition, Liliana Claire Barbosa

Graduate Theses, Dissertations, and Problem Reports (ETD)

During the discharge of a firearm, gunshot residue (GSR) is released and settles into nearby surfaces, leaving traces that can provide valuable information for forensic investigations. This study aims to improve understanding of the deposition, prevalence, and persistence of standard and less-lethal ammunition through an analytical framework that examines collection and analysis protocols, revealing connections among multiple traces for effective use in investigations and courtroom proceedings.

Research into the chemical residues of less lethal ammunition (LLA) is a critical frontier in shooting investigations. While standard leaded ammunition has over a century of established literature, the chemical fingerprints of LLA residues …


Sedimentological And Geochemical Investigation Of The Origin Of Upper Pennsylvanian Black Shales, East-Central Appalachian Basin, Tyler Hickey Jan 2026

Sedimentological And Geochemical Investigation Of The Origin Of Upper Pennsylvanian Black Shales, East-Central Appalachian Basin, Tyler Hickey

Graduate Theses, Dissertations, and Problem Reports (ETD)

In the east-central Allegheny foreland basin, laminated black shales overlying Upper Pennsylvanian Glenshaw Fm. coal seams record paleoenvironmental conditions associated with the termination of peat swamp deposition before, during, and after the Carboniferous Coal Forest Collapse (CCFC), a major paleobotanical evolutionary event during the Late Paleozoic Ice Age (LPIA) that contributed to extinction of lepidodendrons near the Desmoinesian-Missourian boundary (~306 Ma). Previous investigations of the CCFC commonly implicate an episode of aridification during intensification of LPIA glaciation that stressed the lepidodendrons beyond their ecological tipping point; however, the cause of this aridification is unclear. An investigation of Glenshaw Fm. black …


Deposition And Diagenesis Of Permo-Triassic Gypsum From Wyoming And Texas: Saline Lake And Groundwater Systems Of Equatorial Pangea, Maya Yamei Bradford Jan 2026

Deposition And Diagenesis Of Permo-Triassic Gypsum From Wyoming And Texas: Saline Lake And Groundwater Systems Of Equatorial Pangea, Maya Yamei Bradford

Graduate Theses, Dissertations, and Problem Reports (ETD)

Knowledge of gypsum textures and the processes that yield them is important for interpreting the history of environments, climates, and life on Earth. This is because gypsum textures are products of specific environmental, microbiological, and diagenetic processes, and because gypsum is relatively common in the Earth’s sedimentary record. Despite this significance, gypsum is relatively understudied. The fundamental goal of this dissertation is to advance our understanding of gypsum textures by presenting detailed, petrography-based investigations of Permo-Triassic gypsum from the continental interior of Pangea.

Gypsum is typical in the Permo-Triassic sedimentary record of tropical Pangea, where it is associated with red …


High-Resolution Laser Diagnostics For Ion Measurements In Magnetized Plasmas, Katey Stevenson Jan 2026

High-Resolution Laser Diagnostics For Ion Measurements In Magnetized Plasmas, Katey Stevenson

Graduate Theses, Dissertations, and Problem Reports (ETD)

In this work, we investigate ion heating in two plasma systems (helicon plasmas and flux rope plasmas) using the PHAse Space MApping (PHASMA) experiment. Our studies rely on high-resolution laser diagnostics, specifically laser-induced fluorescence (LIF), to measure ion velocity distribution functions (IVDFs). The temperature and bulk flow of each species are inferred from their respective VDFs. This dissertation is organized into three main parts: the study of ion heating in helicon plasmas, pulsed LIF modeling and diagnostic development, and the study of ion heating in flux rope plasmas. Helicon plasma sources efficiently generate high-density plasmas and are widely used to …


Studies On The Depth Formula And On Reducing Dimensions, Brian Mccourt Laverty Jan 2026

Studies On The Depth Formula And On Reducing Dimensions, Brian Mccourt Laverty

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation presents the author’s recent research, conducted under the supervision of Professor Olgur Celikbas, and based on two articles—one published and one in progress. These works develop two closely related research directions in commutative algebra. Together, they contribute to the subject by addressing aspects of existing conjectures, establishing new results, and introducing methods for studying homological invariants.

The first research direction concerns the depth formula, namely the equality \[ \depth_R(M)+\depth_R(N)=\depth(R)+\depth_R(M\otimes_RN) \] where $M$ and $N$ are finitely generated $R$-modules. A classical result of Auslander \cite{Aus} shows that the depth formula holds provided that either $M$ or $N$ has finite …