Physical Sciences and Mathematics Commons^™

Computing The Canonical Ring Of Certain Stacks, Jesse Franklin

Graduate College Dissertations and Theses

We compute the canonical ring of some stacks. We first give a detailed account of what this problem means including several proofs of a famous historical example. The main body of work of this thesis expands on our article \cite{Franklin-geometry-Drinfeld-modular-forms} in describing the geometry of Drinfeld modular forms as sections of a specified line bundle on a certain stacky modular curve. As a consequence of that geometry, we provide a program: one can compute the (log) canonical ring of a stacky curve to determine generators and relations for an algebra of Drinfeld modular forms, answering a problem posed by Gekeler …

Unraveling Public Evacuation Likelihood: Structural Equation Models And The Extended Parallel Process Model In Focus, Molly Margaret Myers

Graduate College Dissertations and Theses

This study explores the intricate relationships between risk perception, efficacy appraisal, and evacuation likelihood in the context of flooding among the United States public. The Extended Parallel Process Model (EPPM) developed by Witte (1992) serves as the theoretical framework for this study, emphasizing the two-pronged appraisal process of threat and efficacy, influencing individual responses to risk messaging. Analysis of the data delves into the relationships between risk perception and evacuation likelihood, offering insights into the public's understanding of flood risk and readiness for impending flood events. This study used Structural Equation Modeling (SEM) to discern the impact of threat and …

Investigating The Effect Of Relative Humidity On Organic New Particle Formation From The Dark Ozonolysis Of Biogenic Volatile Organic Compounds, Austin Callum Flueckiger

Graduate College Dissertations and Theses

Solid or liquid particulate matter suspended in the air, also known as atmospheric aerosols, are a ubiquitous component of Earth’s atmosphere. It is important to understand the chemical and physical processes that lead to the formation of these aerosols as they have an impact on climate health and human health. An important subset of atmospheric aerosols are secondary organic aerosols (SOA) that form from the gas-phase oxidation of volatile organic compounds (VOCs). VOCs can be emitted via biogenic and anthropogenic pathways, however, global estimates place biogenic sources as the major contributor. Although widely studied, some of the fundamental mechanisms that …

Ring Learning With Errors, Sarah Days-Merrill

Graduate College Dissertations and Theses

Over the last twenty years, lattice-based cryptosystems have gained interest due to their levelof security against attacks from quantum computers. The main cryptosystems are based on the hardness of Ring Learning with Errors (RLWE). The Learning with Errors (LWE) problems were first introduced in 2005 by Regev [Reg09] and in 2010, [LPR10] developed the Ring Learning with Errors (RLWE) problems as candidates for safe encryption against quantum computers. Let K be a number field with ring of integers OK. For a prime q, the RLWE problems rely on samples of the form (a, b) ∈ OK/qOK × OK/qOK where a …

Effective Drag Coefficient Prediction On Single-View 2d Images Of Snowflakes, Cameron Hudson

Graduate College Dissertations and Theses

The drag coefficient of snowflakes is an crucial particle descriptor that can quantify the relationships with the mass, shape, size, and fall speed of snowflake particles. Previous studies has relied on estimating and improving empirical correlations for the drag coefficient of particles, utilizing 3D images from the Multi-Angled Snowflake Camera Database (MASCDB) to estimate snowflake properties such as mass, geometry, shape classification, and rimming degree. However, predictions of the drag coefficient with single-view 2D images of snowflakes has proven to be a challenging problem, primarily due to the lack of data and time-consuming, expensive methods used to estimate snowflake shape …

Robust Interventions In Network Epidemiology, Erik Weis

Graduate College Dissertations and Theses

Which individual should we vaccinate to minimize the spread of a disease? Designing optimal interventions of this kind can be formalized as an optimization problem on networks, in which we have to select a budgeted number of dynamically important nodes to receive treatment that optimizes a dynamical outcome. Describing this optimization problem requires specifying the network, a model of the dynamics, and an objective for the outcome of the dynamics. In real-world contexts, these inputs are vulnerable to misspecification---the network and dynamics must be inferred from data, and the decision-maker must operationalize some (potentially abstract) goal into a mathematical objective …

Organic Fouling Mitigation In Forward Osmosis Technology Through The Use Of Oscilatting Alternating Current Electric Fields, Logan Werner

Graduate College Dissertations and Theses

Forward osmosis (FO) is the term given to osmosis in water filtration applications. FO has many advantages to conventional membrane filtration processes. The lack of external pressure needed to force solvent through the membrane is dramatically decreased in FO, resulting in a lower cost of operation compared to reverse osmosis. Lower external pressures also result in decreased fouling on the membrane surface and improved permeate flux. Fouling is one of the foremost challenges within the membrane filtration industry and is one of the biggest contributors to operating costs. While FO results in less fouling than RO, fouling remains a major …

Role Of Relative Humidity In New Particle Formation From Ozonlysis Of Atmospheric Volatile Organic Compounds, Christopher Snyder

Graduate College Dissertations and Theses

The impact of relative humidity (RH) on organic new particle formation (NPF) from ozonolysis of biogenic volatile organic compounds (BVOCs) remains an area of active debate. Previous reports provide contradictory results indicating both depression and enhancement of NPF under conditions of moderate RH, while others ignore the potential impact. Only several reports have suggested that the effect may depend on absolute mixing ratio of the precursor volatile organic compound (VOC, ppbv). However, before any experiments could be completed, development of new methods was necessary to overcome the limitation of sampling ultrafine nanoparticles (<50 nm aerodynamic diameter) with aerosol mass spectrometry. This dissertation includes a report on a new Particle Growth Apparatus (PaGA) that artificially grows particles from as small as 17 nm to over 110nm. Considerable effort was made to identify the most suitable growth matrix (squalane) and optimize particle growth for reproducibility and sensitivity.

The PaGA was then utilized in the …

Employing Genetic Algorithms For Energy-Efficient Data Routing In Internet Of Things Networks, Farzana Akhter

Graduate College Dissertations and Theses

The Internet of Things (IoT) connects a vast number of smart objects for various applications,such as home automation, industrial control, and healthcare. The rapid advancement in wireless technologies and miniature embedded devices has enabled IoT systems to be deployed in various environments. However, the performance of IoT devices is limited because of the imbalance of data traffic on different router nodes. Nodes that experience high data volume will have a higher energy depletion rate and, as a result, will reach the end of their life quicker than other routers that have less data traffic. Genetic Algorithms are a well-known technique …

A Computational Journey Through Conspiracy Theories: A Genealogical Approach, Mohsen Ghasemizade

Graduate College Dissertations and Theses

In an era where misinformation and conspiracy theories (CTs) proliferate, this study presents an approach to understanding and categorizing CTs through the development of a detailed `family tree'. By adopting different definitions, we explore CTs as efforts to explain events through the lens of hidden, malevolent forces, distinguishing between actual conspiracies and theoretical beliefs without empirical proof. Leveraging an analysis of 1769 articles from fact-checking websites and employing Keyphrase Extraction, we compiled a dataset that led to the identification of 769 unique conspiracies. A RoBERTa-based binary classifier was developed, achieving an F1 score of 87\%, to distinguish CTs from non-CT …

Community Science And Coyote Stories: Capturing And Communicating Nature's Non-Material Values For Use In Decision-Making, Joshua Wright Morse

Graduate College Dissertations and Theses

The reasons and ways that nature matters underlie every part of environmental decision-making. Yet, there are disparities in how different kinds of benefits from and values about nature are represented in policy and practice. This dissertation explores how decision-makers and community members value nature broadly and also in the context of a specific human-wildlife interaction in Vermont, United States.

In my first chapter, I conduct semi-structured interviews with environmental sector practitioners in Vermont to learn about their awareness of non-material values from nature. I find that practitioners talk readily about both material and non-material ecosystem services as well as multiple …

Edge Colored And Edge Ordered Graphs, Per Gustin Wagenius

Graduate College Dissertations and Theses

In this work, the current state of the field of edge-colored graphs is surveyed. Anew concept of unshrinkable edge colorings is introduced which is useful for rainbow subgraph problems and interesting in its own right. This concept is analyzed in some depth. Building upon the linear edge ordering described in a recent work from Gerbner, Methuku, Nagy, Pálvölgyi, Tardos, and Vizer, edge-ordering graphs with the cyclic group is introduced and some results are given on this and a related counting problem.

Developing Muscle Synergy Functions For Remote Gait Analysis, Nicole Marie Donahue

Graduate College Dissertations and Theses

Digital medicine promises to improve healthcare and enable its delivery to rural and underserved communities. A key component of digital medicine is accurate and robust remote patient monitoring. For example, remote monitoring of biomechanical measures of limb impairment during daily life could allow near real-time tracking of rehabilitation progress and personalization of rehabilitation paradigms in those recovering from orthopedic surgery. Wearable sensors have long been suggested as a means for quantifying muscle and joint loading, which can provide a direct measure of limb impairment. However, current approaches either do not provide these measures or require unwieldy wearable sensor arrays and/or …

Data-Driven Reachability Of Non-Linear Systems Via Optimization Of Chen-Fliess Series, Ivan Perez Avellaneda

Graduate College Dissertations and Theses

A reachable set is the set of all possible states produced by applying a set of inputs, initial states, and parameters. The fundamental problem of reachability is checking if a set of states is reached provided a set of inputs, initial states, and parameters, typically, in a finite time. In the engineering field, reachability analysis is used to test the guarantees of the operation’s safety of a system. In the present work, the reachability analysis of nonlinear control affine systems is studied by means of the Chen-Fliess series. Different perspectives for addressing the reachability problem, such as interval arithmetic, mixed-monotonicity, …

Assessing The Drivers Of Legacy Phosphorus Loading And Distribution In Shallow Eutrophic Lake Sediments And The Impacts Of Intervention, Ashton P. Kirol

Graduate College Dissertations and Theses

The eutrophication of freshwater lakes from excessive nutrient runoff leads to decreased water quality and worsening cyanobacteria blooms. Water quality improvements in shallow eutrophic lakes can be delayed by decades due to the seasonal recycling of legacy phosphorus (P) enriched lake sediments, even when external nutrient loads are addressed. It is critical to understand the drivers of internal P loading to suppress this source of P through intervention to meet water quality goals. This study contrasts two shallow eutrophic systems, Lake Carmi and Missisquoi Bay in Lake Champlain, impacted by legacy P loading driven by the occurrence of low dissolved …

Riparian Buffer Establishment Using Different Management Techniques, Stever H. Bartlett

Graduate College Dissertations and Theses

ABSTRACT

In riparian areas of the northeastern United States, well-established reed canary grass (Phalaris arundinacea) stands are common and have proven to be a challenge for the success of tree plantings during riparian forest restoration projects. The impacts of reed canary grass (RCG) on the habitats it invades are numerous. Reed canary grass reduces biological diversity by homogenizing habitat structure, richness, and environmental variability. Its rapid growth rate and invasive nature limits tree regeneration in riparian forests by shading and crowding out seedlings. Riparian forests improve water quality, wildlife habitat, flood control, and provide a variety of other ecosystem services. …

Socio-Ecological Economic Impact Analysis Of Food Systems Initiatives Using Mixed Methods And Community-Based Research Approaches, Josiah J. Taylor

Graduate College Dissertations and Theses

Many NGO and government community development programs seek to alleviate complex problems related to food systems and agriculture. Yet, without integrated social, ecological, and economic impact analysis we cannot understand or communicate the value of such interventions. For this research, we partnered with food and agriculture organizations using participatory action research approaches to co-develop and test tools for holistic program analysis. We then used these tools to conduct and co-produce a holistic analysis and evaluation of program impacts. The first chapter provides background and context for the body of the dissertation. Chapter two details work with Hunger Free Vermont to …

Forest Management Tradeoffs: Examining Relationships Between Timber Harvest, Carbon Sequestration And Storage, Bioenergy, And Wildlife, Michelle L. Brown

Graduate College Dissertations and Theses

Timber harvesting is the leading cause of adult tree mortality in forests of the northeastern United States. While current rates of harvest are generally sustainable, there is considerable pressure to increase harvest to meet timber production, climate, and energy goals. Maximizing one of these values may compromise other forest resources, including a wide range of ecosystem services and the conservation of native species. This dissertation investigates the effects of timber harvest on carbon sequestration and storage, bioenergy, and wildlife. First, I estimated current harvest regimes for different forest types and regions across the U.S. states of New York, Vermont, New …

An Analysis Of A Linear Algebra Based Group Key Exchange Protocol, Annie Zhang

Graduate College Dissertations and Theses

Group key exchange protocols are used to establish session keys, which can then be used as encryption keys to set up secure channels of communication, between more than two parties simultaneously. Many different group key exchange protocols exist and require security proofs in order to determine the strength of the protocol and answer the following questions: does the protocol provide authentication, and if so, to what degree? Does the protocol provide key secrecy? In this thesis we examine a particular group key exchange protocol that we call the \textit{vector space projection protocol} as first described in “A Group Key Establishment …

Analyzing The Impact Of Cultural Factors On Happiness Levels In Arabic Language Tweets, Parisa Suchdev

Graduate College Dissertations and Theses

Culture is a fundamental force shaping our view of the world. Filtered through the stories we share on social media, our collective behavior both reflects and amplifies cultural impacts. The present study seeks to describe the effect of cultural factors, such as religion, on happiness scores in Arabic language tweets from January 2010 to June 2023. Our methodology involves using present tools called Hedonometer (https://hedonometer.org/) to study happy and sad events and StoryWrangler (https://storywrangling.org/) to study the usage of keywords related to those events. Our findings reveal a notable pattern of Twitter happiness declining following the start of the Arab …

Bayesian Experimental Design For Control And Surveillance In Epidemiology, Bren Case

Graduate College Dissertations and Theses

Effective public health interventions must balance an array of interconnected challenges, and decisions must be made based on scientific evidence from existing information. Building evidence requires extrapolating from limited data using models. But when data are insufficient, it is important to recognize the limitations of model predictions and diagnose how they can be improved. This dissertation shows how principles from Bayesian experimental design can be applied to surveillance and control efforts to allow researchers to get more out of their data and direct limited resources to best effect. We argue a Bayesian perspective on data gathering, where design decisions are …

Estimation In Generalized Estimating Equation Measurement Error Models Using Instrumental Variables/ Estimating The Cardinality Of Latent Defective Edges In Hypergraphs, Damin Zhu

Graduate College Dissertations and Theses

This dissertation consists of two studies. The first develops theory for a new method for estimating regression parameters using generalized estimating equations (GEE) with panel data prone to covariate measurement error. The focus is on logistic regression, though the method is applicable to other models. The method requires availability ofinstrumental variables (IV) to identify model parameters. Simulations are performed to assess the performance of the proposed estimator. The method, abbreviated GEEIV, is able to accurately estimate logistic regression parameters masked by measurement error in a variety of population configurations.

In the second study, an algorithm is proposed to estimate the …

Anaerobic Soil Disinfestation And Vermicompost To Manage Rhizoctonia Solani In Organic Lettuce, Anna Rissland Brown

Graduate College Dissertations and Theses

Rhizoctonia solani Kühn is an aggressive saprophytic soilborne fungal plant pathogen that is distributed globally and infects many crops including Solanaceae, Fabaceae, and Asteraceae. The lack of effective organic methods to control R. solani and the resulting yield losses contribute to the economic insecurity of farms and farmers. The overall aim of this study was to compare two organic certifiable approaches to manage bottom rot caused by R. solani (subspecies AG1-IB) in field-grown organic lettuce: anaerobic soil infestation (ASD) and thermophilic compost cured by vermicompost (vermicompost). A commercially available biocontrol product and an untreated control were used as references.

Two …

Drivers Of Soil Organic Carbon In Rich Northern Hardwood Forests, Sophia Rebecca Marinace

Graduate College Dissertations and Theses

Forests are increasingly being managed for their carbon sequestration potential. As such, an understanding of the factors controlling carbon dynamics across and within sites is becoming increasingly important for guiding carbon management strategies. Given that much of a forest’s carbon is stored in soils, identifying the factors that control how much carbon is stored in soils is critical. This study used detailed vegetation and soil measurements across a rich northern hardwood forest in Corinth, Vermont to identify factors that drive soil carbon storage in a northern hardwood forest, a common type in New England, and investigated how multiple non-native species …

Data Science And Mathematical Modeling For Humanitarian Response, Ollin Demian Langle Chimal

Graduate College Dissertations and Theses

This dissertation focuses on the exploration of societal responses to crises, with a par-ticular interest in existing socio-economic disparities, using tools of data science and mathematical modeling. The scope of the research is comprised predominantly around the COVID-19 pandemic, incorporating an in-depth analysis across six middle-income countries; Brazil, Colombia, Indonesia, Mexico, Philippines, and South Africa. With GPS data of approximately three million users, we found significant differences in the adherence to stay-at-home guidelines, revealing a great contrast between individuals in high-wealth and low-wealth areas, showing the disparities of who were more able to stay at home without risking their livelihood. …

In-Situ Weathering Of Calcium Bearing Minerals In Forested Ecosystems, Victoria Treto

Graduate College Dissertations and Theses

Timber harvests in the northeastern United States are integral to its economy but shifts in land management, biotic stresses, and nutrient limitations are diminishing forest productivity levels. The effects of harvesting severity and repeated harvests result in net losses of base cation nutrients which decreases woody biomass, potentially as much as 20%. Calcium (Ca) serves to regulate critical processes linked to tree growth and ecosystem health, but it is the quickest depleting base cation from northeastern forest soils. As a result, the quantification of nutrient-bearing minerals in forest soils is fundamental in predicting long-term sustainability of wood production. Further, the …

Investigations Of Low-Frequency Vibrations In Crystalline Organic Semiconductors And Their Impact On Material Properties, Peter Alexander Banks

Graduate College Dissertations and Theses

An increasing amount of attention has been dedicated to small-molecule based crystalline organic semiconducting materials, with regular reports of newly-designed molecules that are specifically engineered to produce high-performance organic devices. Commonly, these molecules contain distinct chemical characteristics that are specifically incorporated to inhibit the large-amplitude, low-frequency vibrational motions that occur about intermolecular van der Waals contacts. These molecular motions have been historically considered a primary factor that uniquely limits the semiconducting performance of these materials, as the large displacements induced by these vibrations strongly diminish the electronic coupling between molecules in the lattice. This phenomenon is denoted as electron-phonon coupling, …

On The Construction Of More Lifelike Devices, Shawn Lawrence Beaulieu

Graduate College Dissertations and Theses

Devices which blur the distinction between the living and the inanimate are being reported with heightened frequency. But what forms of organization, and what modes of internal change and worldly interaction, are required for truly lifelike devices, rather than ones which abstractly mimic life in simulation? This thesis presents results from two publications which attempt to mitigate a problem known to limit the performance of artificial neural networks, called ``catastrophic forgetting"; and a third paper which tries to articulate a vision for the construction of more lifelike devices—whose form, function, and putative environment are not conclusively specified prior to their …

Estimating Particle Velocity From Dual-Camera Mixed Reality Video Images Using 3d Particle Tracking Velocimetry, Thomas Chivers

Graduate College Dissertations and Theses

Mixed reality (MR) systems integrate diverse sensors, allowing users to better visualize and quantify surrounding environmental processes. Some existing mixed reality headsets include synchronized front-facing cameras that, among other things, can be used to track naturally occurring tracer particles (such as dust or snowflakes) to estimate particle velocity field in real time. The current work presents a 3D particle tracking velocimetry (PTV) method for use with MR systems, which combines various monocular cues to match particles between corresponding stereo images. Binocular disparity is used to estimate particle distance from an observer. Individual particles are tracked through time and used to …

How To Analyze Parental Conversation Online: A Computational Stack For Studying Vaccine Hesitancy., Carter Willets Ward

Graduate College Dissertations and Theses

Despite national and international organizations such as the CDC and WHO recognizing the value of vaccines and their importance in addressing public health concerns, there has been a decline in coverage for even the most established vaccines over the past three years. The global COVID-19 pandemic has contributed to this decline via decreases in medical resource accessibility and an increase in vaccine hesitancy. Even before the COVID-19 pandemic, WHO had recognized vaccine hesitancy as one of the top ten threats to public health. In the present work, we introduce a background account of (1) vaccine hesitancy and (2) anti-vax activism, …