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Full-Text Articles in Physical Sciences and Mathematics

Numerical Simulations Of An Inductively Coupled Plasma Torch, Samuel Whitmore Jan 2020

Numerical Simulations Of An Inductively Coupled Plasma Torch, Samuel Whitmore

Graduate College Dissertations and Theses

During entry into a planetary atmosphere, a blunt body (e.g. a spacecraft) traveling at hypersonic velocity creates a bow shock in front of it. In the highly energetic post shock environment, the body experiences heat transfer due to convective, chemical, and radiative processes. To protect the payload against this heating, a thermal protection system (TPS) is employed. Because a given propulsion system has a set amount of mass that it can launch to orbit, reducing the amount of mass used for TPS is desirable as this mass is freed up for mission-oriented payload. At the present, uncertainties in the flow …


Energy Justice, Just Transitions, And Renewable Energy Policies: Examining Energy Transitions In The State Of Vermont, Walter Keady Jan 2020

Energy Justice, Just Transitions, And Renewable Energy Policies: Examining Energy Transitions In The State Of Vermont, Walter Keady

Graduate College Dissertations and Theses

In the United States, sub-national state policies play outsized roles in renewable energy policy. Vermont is considered a leader in renewable energy transitions, exemplified by its goal of a 90% reduction in greenhouse gas emissions by 2050. While scholars have praised Vermont’s transition policies, few studies analyze it using energy justice or just transition principles. This is a crucial omission, as justice in energy transition has both moral and instrumental importance – unjust transitions may thwart themselves by failing to achieve widespread societal support. I make initial contributions to this study using original research conducted as a member of an …


Complex Systems Analysis In Selected Domains: Animal Biosecurity & Genetic Expression, Luke Trinity Jan 2020

Complex Systems Analysis In Selected Domains: Animal Biosecurity & Genetic Expression, Luke Trinity

Graduate College Dissertations and Theses

I first broadly define the study of complex systems, identifying language to describe and characterize mechanisms of such systems which is applicable across disciplines. An overview of methods is provided, including the description of a software development methodology which defines how a combination of computer science, statistics, and mathematics are applied to specified domains. This work describes strategies to facilitate timely completion of robust and adaptable projects which vary in complexity and scope. A biosecurity informatics pipeline is outlined, which is an abstraction useful in organizing the analysis of biological data from cells. This is followed by specific applications of …


The Energetic Consequences Of Winter Foraging For Northern Temperate Fish Species, Benjamin David Block Jan 2020

The Energetic Consequences Of Winter Foraging For Northern Temperate Fish Species, Benjamin David Block

Graduate College Dissertations and Theses

The seasonal energy dynamics of temperate fishes will likely be affected by climate change, especially during the winter. To date, freshwater fish are understudied in winter compared to other aquatic organisms, and additional winter-focused studies are urgently needed. Recent research has demonstrated that some fish species are more active in winter than previously thought, therefore, an inquiry into the energetic contributions of winter foraging to the annual growth of freshwater fishes is needed prior to imminent changes in winter conditions. Here I have empirically shown that winter foraging behavior and seasonal energy dynamics likely depend on the thermal preference of …


Effects Of Winter Ticks And Internal Parasites On Moose Survival And Fecundity In Vermont, Usa, Jacob Richard Debow Jan 2020

Effects Of Winter Ticks And Internal Parasites On Moose Survival And Fecundity In Vermont, Usa, Jacob Richard Debow

Graduate College Dissertations and Theses

Moose (Alces alces) have experienced considerable declines along the periphery of their range in the northeastern United States. In Vermont, the population declined by approximately 44% from 2010 to 2017 despite minimal hunter harvest and adequate habitat. Populations in New Hampshire and Maine have shown similar declines, associated primarily with the impacts of winter ticks (Dermacentor albipictus). However, uncertainty exists about the effects of environmental and other parasite related conditions on moose survival and reproduction. I examined patterns of moose survival and productivity among a radio-collared population (n = 127) in Vermont from 2017 to 2019. In terms of productivity, …


Using Chirality-Assisted Synthesis To Construct Light-Responsive, Freeform Helical Foldamers And Shape-Defined Polymers, Jessica Leigh Bocanegra Jan 2020

Using Chirality-Assisted Synthesis To Construct Light-Responsive, Freeform Helical Foldamers And Shape-Defined Polymers, Jessica Leigh Bocanegra

Graduate College Dissertations and Theses

Foldamers (i.e. polymers which fold into well-defined shapes) are able to imitate arrangements of proteins, nucleic acids, and polysaccharides. However, previously reported foldamers are limiting in their ability to bind a multitude of guests—mainly due to very rigid conformational skeletal structures. Additionally, these structures commonly rely on π-π stacking and hydrogen bonding to dictate their shapes. We now report a helical foldamer that has (i) the capacity to bind selectively around a myriad of molecules while (ii) still embodying a well-defined, synthetically-controlled shape. We were able to create such structures as single-handed helices with chirality-assisted synthesis (CAS, see: Angew. Chem. …


Investigation Of The Intramolecular 1,3-Diaza-Claisen Rearrangement In The Ring Expansion Reactions Of Vinyl Pyrrolidines And Vinyl Piperidines, Teruki Watanabe Jan 2020

Investigation Of The Intramolecular 1,3-Diaza-Claisen Rearrangement In The Ring Expansion Reactions Of Vinyl Pyrrolidines And Vinyl Piperidines, Teruki Watanabe

Graduate College Dissertations and Theses

The 1,3-diaza-Claisen rearrangement was discovered and developed in the Madalengoitia group since 2004. The rearrangement is initiated by the desulfurization of the electron deficient thiourea and isothiourea to obtain the highly electrophilic carbodiimide which can be reacted with an allylic tertiary amine to form the zwitterionic intermediate which then undergoes [3,3]-sigmatropic rearrangement. Previous investigation includes multiple examples of successful formation of complex guanidines through intermolecular and intramolecular variants. Providing an easy access to guanidine which is one of the most prevalent functional groups in the biologically relevant system, the rearrangement can be a valuable tool in the organic synthesis.

The …


On The Dynamics And Structure Of Multiple Strain Epidemic Models And Genotype Networks, Blake Joseph Mitchell Williams Jan 2020

On The Dynamics And Structure Of Multiple Strain Epidemic Models And Genotype Networks, Blake Joseph Mitchell Williams

Graduate College Dissertations and Theses

Mathematical disease modeling has long operated under the assumption that any one infectious disease is caused by one transmissible pathogen. This paradigm has been useful in simplifying the biological reality of epidemics and has allowed the modeling community to focus on the complexity of other factors such as contact structure and interventions. However, there is an increasing amount of evidence that the strain diversity of pathogens, and their interplay with the host immune system, can play a large role in shaping the dynamics of epidemics.

This body of work first explores the role of strain-transcending immunity in mathematical disease models, …


Bottom-Up Synthesis Of Macromolecules And Their Selective Catalytic Performance At The Nanoscale, Mona Sharafi Jan 2020

Bottom-Up Synthesis Of Macromolecules And Their Selective Catalytic Performance At The Nanoscale, Mona Sharafi

Graduate College Dissertations and Theses

Finding sustainable ways to create complex, sequence-defined polymers is

essential for future advances in the fields of medicine, electronics, and energy. Thus,

inspired by how nature builds functional macromolecules, this account aims to discover

catalysts, which will facilitate the accurate replication of synthetic nanoscale structures. In

this regard, the comprehensive sight of the work described within this dissertation is to

resolve the following fundamental questions: i) How to generate large, preorganized

macromolecules which can behave as supramolecular hosts to tune the properties of

molecules present in the vicinity of them? ii) What shapes do sequence-defined

oligomers/polymers adopt in solution under …


Some Results On A Set Of Data Driven Stochastic Wildfire Models, Maxfield E. Green Jan 2020

Some Results On A Set Of Data Driven Stochastic Wildfire Models, Maxfield E. Green

Graduate College Dissertations and Theses

Across the globe, the frequency and size of wildfire events are increasing. Research focused on minimizing wildfire is critically needed to mitigate impending humanitarian and environmental crises. Real-time wildfire response is dependent on timely and accurate prediction of dynamic wildfire fronts. Current models used to inform decisions made by the U.S. Forest Service, such as Farsite, FlamMap and Behave do not incorporate modern remotely sensed wildfire records and are typically deterministic, making uncertainty calculations difficult. In this research, we tested two methods that combine artificial intelligence with remote sensing data. First, a stochastic cellular automata that learns algebraic expressions was …


Model-Based Machine Learning To Identify Clinical Relevance In A High-Resolution Simulation Of Sepsis And Trauma, Zachary H. Silberman Md, Robert Chase Cockrell Phd, Gary An Md Jan 2020

Model-Based Machine Learning To Identify Clinical Relevance In A High-Resolution Simulation Of Sepsis And Trauma, Zachary H. Silberman Md, Robert Chase Cockrell Phd, Gary An Md

Larner College of Medicine Fourth Year Advanced Integration Teaching/Scholarly Projects

Introduction: Sepsis is a devastating, costly, and complicated disease. It represents the summation of varied host immune responses in a clinical and physiological diagnosis. Despite extensive research, there is no current mediator-directed therapy, nor a biomarker panel able to categorize disease severity or reliably predict outcome. Although still distant from direct clinical translation, dynamic computational and mathematical models of acute systemic inflammation and sepsis are being developed. Although computationally intensive to run and calibrate, agent-based models (ABMs) are one type of model well suited for this. New analytical methods to efficiently extract knowledge from ABMs are needed. Specifically, machine-learning …


Water Use Governance In A Temperate Region: Implications For Agricultural Climate Change Adaptation In The Northeastern United States, Rachel E. Schattman, Meredith T. Niles, Hannah M. Aitken Jan 2020

Water Use Governance In A Temperate Region: Implications For Agricultural Climate Change Adaptation In The Northeastern United States, Rachel E. Schattman, Meredith T. Niles, Hannah M. Aitken

College of Agriculture and Life Sciences Faculty Publications

Climate change and access to water are interrelated concerns for agriculture and other sectors, even in temperate regions. Governance approaches and regulatory frameworks determine who has access to water, for what purpose, and when. In the northeastern United States, water governance has historically been conducted by states through a combination of statutory guidance and common law. However, it is unclear what effect if current governance approaches will be sufficient for achieving resource conservation and equitable allocation in a changing climate. To provide insight into these issues, we conducted the first review of freshwater governance in the 12 states that comprise …


Visualizing Climate Change Adaptation: An Effective Tool For Agricultural Outreach?, Rachel E. Schattman, Stephanie E. Hurley, Holly L. Greenleaf, Meredith T. Niles, Martha Caswell Jan 2020

Visualizing Climate Change Adaptation: An Effective Tool For Agricultural Outreach?, Rachel E. Schattman, Stephanie E. Hurley, Holly L. Greenleaf, Meredith T. Niles, Martha Caswell

College of Agriculture and Life Sciences Faculty Publications

Landscape photovisualizations (PVZs) are digitally altered photographs that show existing landscapes altered to include a simulated future scenario. They are commonly used to support dialogue and decision-making in multistakeholder contexts. In agricultural sectors, stakeholders increasingly must contend with pressures to adapt to climatic changes and shifts in weather patterns. This study examines the potential of PVZs to engage agricultural stakeholders about climate change adaptation, specifically around best management practices (BMPs). In 2015, survey data were collected (n 5 133) at six agricultural confer-ences Vermont. Participants were asked about their climate change knowledge, perceptions of adaptation, and their intentions to adopt …


Why We Publish Where We Do: Faculty Publishing Values And Their Relationship To Review, Promotion And Tenure Expectations, Meredith T. Niles, Lesley A. Schimanski, Erin C. Mckiernan, Juan Pablo Alperin Jan 2020

Why We Publish Where We Do: Faculty Publishing Values And Their Relationship To Review, Promotion And Tenure Expectations, Meredith T. Niles, Lesley A. Schimanski, Erin C. Mckiernan, Juan Pablo Alperin

College of Agriculture and Life Sciences Faculty Publications

Using an online survey of academics at 55 randomly selected institutions across the US and Canada, we explore priorities for publishing decisions and their perceived importance within review, promotion, and tenure (RPT). We find that respondents most value journal readership, while they believe their peers most value prestige and related metrics such as impact factor when submitting their work for publication. Respondents indicated that total number of publications, number of publications per year, and journal name recognition were the most valued factors in RPT. Older and tenured respondents (most likely to serve on RPT committees) were less likely to value …


Evaluating Water Quality Regulation As A Driver Of Farmer Behavior: A Social-Ecological Systems Approach, Courtney R.Hammond Wagner, Suzie Greenhalgh, Meredith T. Niles, Asim Zia, William B. Bowden Jan 2020

Evaluating Water Quality Regulation As A Driver Of Farmer Behavior: A Social-Ecological Systems Approach, Courtney R.Hammond Wagner, Suzie Greenhalgh, Meredith T. Niles, Asim Zia, William B. Bowden

College of Agriculture and Life Sciences Faculty Publications

Water quality policy for agricultural lands seeks to improve water quality by changing farmer behavior. We investigate farmer behavior in three water quality regimes that differ by rule structure to examine the fit and interplay of each policy within its social-ecological context, important aspects for improving water quality. Vermont, USA’s practice-based policy requires the adoption of specific practices, whereas New Zealand’s Lake Taupo and Lake Rotorua performance-based policies require farmers to meet a numeric limit for nutrient loss on their farm. Across the three regions we interviewed 38 farmers to elicit mental models of nutrient management changes. We utilized the …


Using Experimental Gaming Simulations To Elicit Risk Mitigation Behavioral Strategies For Agricultural Disease Management, Eric M. Clark, Scott C. Merrill, Luke Trinity, Gabriela Bucini, Nicholas Cheney, Ollin Langle-Chimal, Trisha Shrum, Christopher Koliba, Asim Zia, Julia M. Smith Jan 2020

Using Experimental Gaming Simulations To Elicit Risk Mitigation Behavioral Strategies For Agricultural Disease Management, Eric M. Clark, Scott C. Merrill, Luke Trinity, Gabriela Bucini, Nicholas Cheney, Ollin Langle-Chimal, Trisha Shrum, Christopher Koliba, Asim Zia, Julia M. Smith

College of Agriculture and Life Sciences Faculty Publications

Failing to mitigate propagation of disease spread can result in dire economic consequences for agricultural networks. Pathogens like Porcine Epidemic Diarrhea virus, can quickly spread among producers. Biosecurity is designed to prevent infection transmission. When considering biosecurity investments, management must balance the cost of protection versus the consequences of contracting an infection. Thus, an examination of the decision making processes associated with investment in biosecurity is important for enhancing system wide biosecurity. Data gathered from experimental gaming simulations can provide insights into behavioral strategies and inform the development of decision support systems. We created an online digital experiment to simulate …


Utilizing Machine Learning For Respiratory Rate Detection Via Radar Sensor, Anwar Elhadad Jan 2020

Utilizing Machine Learning For Respiratory Rate Detection Via Radar Sensor, Anwar Elhadad

Graduate College Dissertations and Theses

In this research, we investigate a data processing method to capture the respiratory rate of a person by utilizing a doppler radar to monitor their body movement during respiration. We utilize a machine learning algorithm with a radar sensor to capture the chest movement of a person while breathing and determine the respiratory rate according to that movement. We are using a Random Forest classifier to distinguish between different classes of pulses. After that, the algorithm constructs a sinusoidal signal representing the breathing rate of the sample. By applying this technique, we can detect the breathing rate accurately for different …


Factors Affecting The Adoption Of Automated Wood Pellet Heating Systems In The Northeastern Us And Implications For The Transition To Renewable Energy, Laura Edling Jan 2020

Factors Affecting The Adoption Of Automated Wood Pellet Heating Systems In The Northeastern Us And Implications For The Transition To Renewable Energy, Laura Edling

Graduate College Dissertations and Theses

Public and private incentive programs have encouraged conversions to high efficiency, low emissions wood heating systems as a strategy to promote renewable energy and support local economies in the Northeastern US. Despite these efforts, the adoption of these systems remains slow. The study that is the subject of this dissertation examines several social, economic, policy and environmental factors that affect the decisions of individuals and small-scale institutions (local business and community facilities) to transition to automated wood pellet boilers and furnaces (AWPH) utilizing local fuel sources. Due to the complexity and risk associated with conversion, the transition to these systems …


Exciton Coherence In 1d Phthalocyanine Based Organic Crystalline Thin Films, Kimngan Burrill Jan 2020

Exciton Coherence In 1d Phthalocyanine Based Organic Crystalline Thin Films, Kimngan Burrill

Graduate College Dissertations and Theses

Quantum coherence plays a vital role in the excitonic properties of organic semiconductors. Several theoretical and experimental studies have shown an unprecedented role of coherence in charge transfer and transport processes, which in turn can improve the performance of electronic devices. Specifically, an enhancement of exciton coherence size can result in fast energy transport and efficient charge separation. The ability to tailor the design and performance of organic electronics based on exciton coherence effects represents the possibility of ultrafast electronic applications in communication and information technology.

The objective of this thesis is the excitonic coherence studies of 1D crystalline thin …


The Environmental Microbiome In A Changing World: Microbial Processes And Biogeochemistry, Stephanie Juice Jan 2020

The Environmental Microbiome In A Changing World: Microbial Processes And Biogeochemistry, Stephanie Juice

Graduate College Dissertations and Theses

Climate change can alter ecosystem processes and organismal phenology through both long-term, gradual changes and alteration of disturbance regimes. Because microbes mediate decomposition, and therefore the initial stages of nutrient cycling, soil biogeochemical responses to climate change will be driven by microbial responses to changes in temperature, precipitation, and pulsed climatic events. Improving projections of soil ecological and biogeochemical responses to climate change effects therefore requires greater knowledge of microbial contributions to decomposition. This dissertation examines soil microbial and biogeochemical responses to the long-term and punctuated effects of climate change, as well as improvement to decomposition models following addition of …


Seasonal Water Column Dynamics Exert Strong Control On The Chemical Partitioning Of Benthic Phosphorus Pools Of Shallow Eutrophic Freshwater Systems, Meagan Leduc Jan 2020

Seasonal Water Column Dynamics Exert Strong Control On The Chemical Partitioning Of Benthic Phosphorus Pools Of Shallow Eutrophic Freshwater Systems, Meagan Leduc

Graduate College Dissertations and Theses

In shallow lake systems, phosphorus (P) availability to cyanobacteria populations is often controlled by the release (internal loading) or sequestration of sediment P. This study provides novel insight into the feedbacks between the water column and benthic P pools across multiple time scales and explain how these dynamics influence chemical partitioning of P in lake sediment. Phosphorus partitioning in seasonal sediment core time series collected from a shallow eutrophic bay of Lake Champlain were quantified with SEDEX and enzyme hydrolysis selective extraction schemes. Time series extraction data were interpreted with concurrent water column physical and biogeochemical monitoring data to examine …


Essays On Modeling And Analysis Of Dynamic Sociotechnical Systems, David Rushing Dewhurst Jan 2020

Essays On Modeling And Analysis Of Dynamic Sociotechnical Systems, David Rushing Dewhurst

Graduate College Dissertations and Theses

A sociotechnical system is a collection of humans and algorithms that interact under the partial supervision of a decentralized controller. These systems often display in- tricate dynamics and can be characterized by their unique emergent behavior. In this work, we describe, analyze, and model aspects of three distinct classes of sociotech- nical systems: financial markets, social media platforms, and elections. Though our work is diverse in subject matter content, it is unified though the study of evolution- and adaptation-driven change in social systems and the development of methods used to infer this change.

We first analyze evolutionary financial market microstructure …


Planning For People In Communities And Outdoor Recreation Places: Fostering Community Cohesion, Shaping Place Meanings, And Exploring Imaginaries, Yumiko Jakobcic Jan 2020

Planning For People In Communities And Outdoor Recreation Places: Fostering Community Cohesion, Shaping Place Meanings, And Exploring Imaginaries, Yumiko Jakobcic

Graduate College Dissertations and Theses

This dissertation examines people’s relationships to place and community. The papers are linked by three broad themes: 1) place meanings, 2) community connections to resource places, and 3) innovative qualitative research methodologies.

The first paper used ethnographic methods in a case study of Vermont’s Winooski Valley Park District to examine how regional park districts can strengthen community relationships. It explored how the district serves visitors and communities, stimulates community interactions and cohesion, and perceives the outcomes of these efforts. Results showed that regional park districts connect people with nature and with others across neighborhoods, communities, and regions. These unique places …


Chirality-Assisted Synthesis Of Single-Handed Freeform Helical Ladder Polymers, Kyle Everett Murphy Jan 2020

Chirality-Assisted Synthesis Of Single-Handed Freeform Helical Ladder Polymers, Kyle Everett Murphy

Graduate College Dissertations and Theses

In nature, shape defines function, and as such scientists have long since attempted to mimic nature in a pursuit to reach a similar level of fidelity. Complex macromolecular structures and shapes have been developed with interesting and unique functionalities—such as the design and synthesis of molecular machines. However, macromolecular structures such as these are difficult to synthesize. My work in the Schneebeli group builds upon this challenge, where I have developed a strategy to precisely control the shape of macromolecules to generate well-defined structures. This was accomplished with stereoisomerically pure triptycene-like derivatives as the building block pieces which have an …


Growth Evaluation And Standardized Assessment Of Juvenile Lake Trout In Lake Champlain, Pascal Dylan Wilkins Jan 2020

Growth Evaluation And Standardized Assessment Of Juvenile Lake Trout In Lake Champlain, Pascal Dylan Wilkins

Graduate College Dissertations and Theses

Restoration and recovery of lake trout (Salvelinus namaycush) has been the focus of research and management in the Great Lakes and Lake Champlain since populations collapsed in the late 19th and 20th centuries. Wild juvenile lake trout recruitment was discovered in Lake Champlain in 2015 after 42 years of stocking efforts. Intensive biweekly bottom trawl sampling during the ice-free season was conducted from 2015 to 2018 to assess the extent of wild recruitment at three different sampling areas (north, central, south) of the Main Lake. The collection of wild and stocked lake trout in bottom trawls enabled analysis and comparison …


The Development And Expansion Of A Cationic 1,3-Diaza Claisen Rearrangement That Affords Guanidines, Jordan Tocher Jan 2020

The Development And Expansion Of A Cationic 1,3-Diaza Claisen Rearrangement That Affords Guanidines, Jordan Tocher

Graduate College Dissertations and Theses

Guanidines are found readily in many natural product scaffolds and biological systems. However, the chemical makeup of the guanidines is such that synthesis of guanidine-containing molecules remains challenging. In 2004, the Madalengoitia group first reported a zwitterionic 1,3-diaza Claisen rearrangement that affords complex guanidines. This was later expanded from the initial strained-bridged bicyclic systems to systems that encompassed more linear precursors, positively charged intermediates, and compounds with ring-expansion applications.

Due to the historical precedent that introduction of a positive charge into a rearranging system can benefit the kinetics and thermodynamics of a reaction, experiments were designed in order to probe …


Investigations Of Pnictogen And Boron-Group Compounds Towards The Synthesis Of Group Iii/V Pre-Ceramic Molecules, Brandon James Ackley Jan 2020

Investigations Of Pnictogen And Boron-Group Compounds Towards The Synthesis Of Group Iii/V Pre-Ceramic Molecules, Brandon James Ackley

Graduate College Dissertations and Theses

Semiconductor ceramics have been the subject of study for many years due to their usefulness in applications ranging from LED devices to computer chips. Despite the ubiquity of semiconductor ceramics in daily life, the synthesis and manufacturing of such devices is tedious, energy intensive, or have a high potential for danger. Manufacturing methods such as deposition require the use of toxic or pyrophoric gases as well as requiring the temperatures often exceeding 1,000 °C. One way to address the issues of toxicity and high thermal barriers can be found in the implementation of pre-ceramic materials; materials which are either molecular …


Co-Optimization Of A Robot's Body And Brain Via Evolution And Reinforcement Learning, Jack Felag Jan 2020

Co-Optimization Of A Robot's Body And Brain Via Evolution And Reinforcement Learning, Jack Felag

Graduate College Dissertations and Theses

Agents are often trained to perform a task via optimization algorithms. One class of algorithms used is evolution, which is ``survival of the fitness'' used to pick the best agents for the objective, and slowly changing the best over time to find a good solution. Evolution, or evolutionary algorithms, have been commonly used to automatically select for a better body of the agent, which can outperform hand-designed models. Another class of algorithms used is reinforcement learning. Through this strategy, agents learn from prior experiences in order to maximize some reward. Generally, this reward is how close the objective is to …


Extremal/Saturation Numbers For Guessing Numbers Of Undirected Graphs, Jo Ryder Martin Jan 2020

Extremal/Saturation Numbers For Guessing Numbers Of Undirected Graphs, Jo Ryder Martin

Graduate College Dissertations and Theses

Hat guessing games—logic puzzles where a group of players must try to guess the color of their own hat—have been a fun party game for decades but have become of academic interest to mathematicians and computer scientists in the past 20 years. In 2006, Søren Riis, a computer scientist, introduced a new variant of the hat guessing game as well as an associated graph invariant, the guessing number, that has applications to network coding and circuit complexity. In this thesis, to better understand the nature of the guessing number of undirected graphs we apply the concept of saturation to guessing …


The Circuit And Cocircuit Lattices Of A Regular Matroid, Patrick Mullins Jan 2020

The Circuit And Cocircuit Lattices Of A Regular Matroid, Patrick Mullins

Graduate College Dissertations and Theses

A matroid abstracts the notions of dependence common to linear algebra, graph theory, and geometry. We show the equivalence of some of the various axiom systems which define a matroid and examine the concepts of matroid minors and duality before moving on to those matroids which can be represented by a matrix over any field, known as regular matroids. Placing an orientation on a regular matroid allows us to define certain lattices (discrete groups) associated to the matroid. These allow us to construct the Jacobian group of a regular matroid analogous to the Jacobian group of a graph. We then …