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Graduate Theses, Dissertations, and Problem Reports (ETD)

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Planar Semiconductor-Superconductor Topological Quantum Devices: Realistic Modeling Tools, Purna Prasad Paudel Jan 2024

Planar Semiconductor-Superconductor Topological Quantum Devices: Realistic Modeling Tools, Purna Prasad Paudel

Graduate Theses, Dissertations, and Problem Reports (ETD)

Planar semiconductor-superconductor (SM-SC) heterostructures hold significant promise for realizing topological superconductivity and hosting Majorana zero modes (MZMs) --- particle-hole symmetric quasiparticle excitations that emerge as localized zero-energy modes either at the edges of one-dimensional topological SCs or at the vortex cores of two-dimensional topological SCs. Due to their non-Abelian exchange statistics and topological protection, MZMs are prime candidates for constructing topological qubits and achieving fault-tolerant topological quantum computation. Despite notable progress, significant experimental and engineering challenges remain to realizing functional MZM-based qubits. One major challenge is the small topological gap achievable in these systems, rendering MZMs fragile against disorder. Additionally, …


Active Uncertainty Representation Learning: Toward More Label Efficiency In Deep Learning, Salman Mohamadi Jan 2024

Active Uncertainty Representation Learning: Toward More Label Efficiency In Deep Learning, Salman Mohamadi

Graduate Theses, Dissertations, and Problem Reports (ETD)

The primary goal of this dissertation is to investigate and improve the efficiency of deep learning algorithms, especially within computer vision problem domains, from the perspective of label-efficiency. This investigation showed that deep learning algorithms are mostly notorious for the lack of uncertainty representation. Accordingly, we aimed to develop an array of deep learning frameworks rich with uncertainty representation. These frameworks are mainly within two current pillars of machine learning, deep active learning and self-supervised learning. These frameworks include deep active ensemble sampling for efficient sample selection within deep active learning, a two-stage ensemble-based general self-training approach for existing visual …


The Relationship Between Social Justice Attitudes And Compassion In Preservice Teachers: A Critically Compassionate Intellectualism Framework, Megan Hut Jan 2024

The Relationship Between Social Justice Attitudes And Compassion In Preservice Teachers: A Critically Compassionate Intellectualism Framework, Megan Hut

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation aims to gain further knowledge about the implementation of the Critically Compassionate Intellectualism (CCI; Cammarota & Romero, 2003) framework in teacher education. This framework, originally developed to provide a better education for Latine students who were being silenced in their original schools, emphasizes authentic caring, critical pedagogy, and social justice content. CCI aims to provide students with an education that better equips them to be part of our democratic society and is supposed to lead to an increase in students’ critical consciousness through developing compassionate relationships and making content related to students’ experiences. Based on the success of …


Photoinduced Alpha-Hydroxy C–H Alkylation Of Mono-Alcohols Via Hydrogen Atom Transfer (Hat) Of An Activated Boron-Containing Complex, Courtney Deanna Glenn Jan 2024

Photoinduced Alpha-Hydroxy C–H Alkylation Of Mono-Alcohols Via Hydrogen Atom Transfer (Hat) Of An Activated Boron-Containing Complex, Courtney Deanna Glenn

Graduate Theses, Dissertations, and Problem Reports (ETD)

Hydroxy (-OH) groups are one of the most abundant functional groups found in natural products and pharmaceuticals with many of these compounds containing multiple alcohol classes. The ability to selectively functionalize a specific α-OH C–H bond in the presence of other competitive sites would provide straightforward access to new, potentially bioactive compounds. In recent literature, photoredox catalysis has been implemented to perform site and stereoselective α-OH C–H functionalization of cis-diol containing substrates. Incorporating an organoboron cocatalyst into these systems have proven to be crucial in decreasing the bond dissociation energy (BDE) and increasing hydricity of the α-OH C–H bond …


Implementing Unmanned Aerial Vehicles To Collect Human Gait Data At Distance And Altitude For Identification And Re-Identification, Donn E. Bartram Jan 2024

Implementing Unmanned Aerial Vehicles To Collect Human Gait Data At Distance And Altitude For Identification And Re-Identification, Donn E. Bartram

Graduate Theses, Dissertations, and Problem Reports (ETD)

Gait patterns are a class of biometric information pertaining to the way a person moves and poses. Gait information is unique to each person and can be used to identify and reidentify people. Historically, this task has been achieved through the use of multiple ground-based imaging sensors. However, as Unmanned Aerial Vehicles (UAVs) advance, they present the opportunity to evolve the process of persons identification and re-identification. Collecting human gait data using UAVs at distances ranging from 20m to 500m and altitudes ranging from 0m to 120m is a challenging task. The current biometric data collection methods, primarily designed for …


Limb Speed Perception Accuracy In Neurodegenerative Disease, Brandmeir Lynn Cheryl Jan 2024

Limb Speed Perception Accuracy In Neurodegenerative Disease, Brandmeir Lynn Cheryl

Graduate Theses, Dissertations, and Problem Reports (ETD)

Movement is a fundamental human activity, enabling us to engage with our surroundings. Consequently, a well-operating neuromuscular system is essential for maintaining quality of life. Motion is not only integral for the basic function of daily living, but also plays a significant role in enhancing our physical, mental, and emotional health. The importance of this system becomes abundantly clear when it is compromised, such as with neurodegenerative disease.

Alzheimer’s disease (AD), followed by Parkinson’s disease (PD) are the two most common neurodegenerative diseases that profoundly affect millions of individuals worldwide (Lamptey et al., 2022). Characterized by distinct but sometimes overlapping …


Quantifying Chemical Erosion In The Lithologically-Heterogenous Appalachian Valley And Ridge, Amelia Jayne Zanoni Jan 2024

Quantifying Chemical Erosion In The Lithologically-Heterogenous Appalachian Valley And Ridge, Amelia Jayne Zanoni

Graduate Theses, Dissertations, and Problem Reports (ETD)

Quantifying chemical erosion in the lithologically-heterogenous Appalachian Valley and Ridge

Amelia J. Zanoni

The interplay between physical and chemical erosion is well understood in landscapes underlain by a uniform rock type, but many regions are underlain by a mixture of rock types with varying erosion resistance and solubility. We used measurements of stream-water chemistry to estimate chemical erosion rates in the Appalachian Valley and Ridge, a region where the mechanisms of lithologic control over topography are poorly understood. Newly acquired stream water samples were collected from 51 locations across the research area during the Fall of 2023. The sampled waters …


Estimating Inorganic Carbon Flux From Coal Mining Discharge Portals In The Bituminous Coal Field Region Of Pennsylvania, Lauren J. Rockwell Jan 2024

Estimating Inorganic Carbon Flux From Coal Mining Discharge Portals In The Bituminous Coal Field Region Of Pennsylvania, Lauren J. Rockwell

Graduate Theses, Dissertations, and Problem Reports (ETD)

A fundamental driver of the adverse effects associated with coal mining is the interplay of water and oxygen within mined sites, leading to the creation of coal mine drainage (CMD). One often overlooked consequence of CMD is the release of geologically-bound carbon as carbon dioxide (CO2). The interaction of CMD with carbonate rocks, specifically the presence of sulfuric acid driving the dissolution of these rocks, leads to the release of dissolved inorganic carbon (DIC). This study examined 25 CMD locations in an approximately 2,370 km2 area within the bituminous coal field region of Pennsylvania (PA), specifically in …


Understanding Learners' Perception Of Virtual Reality-Assisted Learning In Engineering Education, Mohammad Samin Mansur Jan 2024

Understanding Learners' Perception Of Virtual Reality-Assisted Learning In Engineering Education, Mohammad Samin Mansur

Graduate Theses, Dissertations, and Problem Reports (ETD)

Virtual reality (VR)-assisted learning may facilitate an immersive and interactive learning environment and enable learners to explore and interact with learning content at their own pace and interest. However, it is still unknown how well VR is received in engineering learning while empowering autonomy and personalization. The objective of this study is to investigate learners' perceptions of VR-assisted learning in engineering education while allowing learners to learn at their own pace, driven by their personal preference. To this end, experiments were conducted, in which thirty engineering students were recruited and immersed in a VR setting designed to deliver an interactive …


Analyzing Viability Of Blue Indium Gallium Nitride Leds For Use In Space Missions Using A Low Earth Orbit Cubesa, Bertrand Edward Wieliczko Jan 2024

Analyzing Viability Of Blue Indium Gallium Nitride Leds For Use In Space Missions Using A Low Earth Orbit Cubesa, Bertrand Edward Wieliczko

Graduate Theses, Dissertations, and Problem Reports (ETD)

The payload capacity of spacecraft is constrained by the weight of the craft itself, including fuel and electronic systems. The protective measures used to shield onboard electronics from the harsh space environment, characterized by high-energy particles and significant temperature fluctuations, can further diminish the available payload capacity. This thesis explores the potential of naturally radiation-hard alternatives to commonly used electronic materials, such as Silicon, to reduce the need for shielding and other protective measures, thereby decreasing the weight and cost of space missions.

III-V semiconductor materials, such as Gallium Nitride (GaN), are known for their inherent resilience to temperature swings …


Investigation Of Deoxyfluorination Of Alkyl Alcohols Using Pentafluoropyridines Through A Covalent Intermediate, Christopher Allen Bias Jan 2024

Investigation Of Deoxyfluorination Of Alkyl Alcohols Using Pentafluoropyridines Through A Covalent Intermediate, Christopher Allen Bias

Graduate Theses, Dissertations, and Problem Reports (ETD)

Organofluorines are an omnipresent class of organic molecules, especially in pharmaceuticals. Selective fluorination of drug molecules allows for the influence of properties including metabolic activity, solubility, and intrinsic potency. Deoxyfluorinations are typically performed via generation of nucleophilic fluoride from a deoxyfluorination agent. Traditionally, diethylaminosulfur trifluoride (DAST) is the reagent of choice for these reactions, and it remains a popular reagent today. However, it has a propensity to form elimination side products and explode. Several research groups have recently developed new classes of deoxyfluorination agents including imidazole-based reagents (PhenoFluor) and sulfonyl fluorides (PyFluor) that exhibit better functional group tolerance and much …


Strategies For Process Systems Mapping And Control Based On Operability Analysis, Victor Manuel Cunha Alves Jan 2024

Strategies For Process Systems Mapping And Control Based On Operability Analysis, Victor Manuel Cunha Alves

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation aims to develop strategies for process systems engineering (PSE) mapping using models, emerging tools and algorithms motivated by process operability analysis research. Such strategies will be employed to ensure simultaneous design and control of large-scale industrial systems. The emerging tools and techniques in this research include supervised machine learning-based (ML-based) operability mapping, automatic differentiation (AD) for implicit mapping, and the development of a systematic mapping approach for control structure selection using operability analysis. Thus far, the developed operability algorithms either recur to nonlinear programming (NLP) solutions which are computationally expensive or to linearizing the underlying modeling task at …


Bridging Evolutionary And Bayesian Optimization For Enhanced Safety Verification In Control Systems, Joshua M. Yancosek Jan 2024

Bridging Evolutionary And Bayesian Optimization For Enhanced Safety Verification In Control Systems, Joshua M. Yancosek

Graduate Theses, Dissertations, and Problem Reports (ETD)

The rigorous safety verification of control systems in critical applications is essential, given their in creasing complexity and integration into everyday life. Simulation-based falsification approaches play a pivotal role in the safety verification of control systems, particularly within critical applications. These methods systematically explore the operational space of systems to identify configurations that result in violations of safety specifications. However, the effectiveness of traditional simulation based falsification is frequently limited by the high dimensionality of the search space and the sub stantial computational resources required for exhaustive exploration. This thesis presents Bayesian Evolutionary Approach for COuNterexample, or BEACON, a novel …


Joint Learning Of Unknown Safety Constraints And Control Policies In Reinforcement Learning, Lunet Abiye Yifru Jan 2024

Joint Learning Of Unknown Safety Constraints And Control Policies In Reinforcement Learning, Lunet Abiye Yifru

Graduate Theses, Dissertations, and Problem Reports (ETD)

Reinforcement learning (RL) has revolutionized decision-making across a wide range of domains over the past few decades. Yet, deploying RL policies in real-world scenarios presents the crucial challenge of ensuring safety. Traditional safe RL approaches have predominantly focused on incorporating predefined safety constraints into the policy learning process. However, this reliance on predefined safety constraints poses limitations in dynamic and unpredictable real-world settings where such constraints may not be available or sufficiently adaptable. Bridging this gap, we propose a novel approach that concurrently learns a safe RL control policy and identifies the unknown safety constraint parameters of a given environment. …


Using Critical Place-Based Pedagogy To Build A Bridge Between College Students’ Home Literacies And Their Academic Literacies In A Composition Class In West Virginia, Michael Vozniak Jan 2024

Using Critical Place-Based Pedagogy To Build A Bridge Between College Students’ Home Literacies And Their Academic Literacies In A Composition Class In West Virginia, Michael Vozniak

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation explores the use of place-based pedagogy as a tool for teaching for transfer in a college composition class in West Virginia. Although existing composition scholarship indicates that themed classes (such as a place-based class) are unlikely to facilitate transfer among the students, this is mostly due to instructors of themed classes not explicitly teaching for transfer. The literature suggests that the most effective way to facilitate transfer is to encourage students to reflect on how what they learned in one situation is similar to and different from what they need to learn in another situation. The aim of …


Machine Learning And Rna Bioinformatics, Jason Rafe Miller Jan 2024

Machine Learning And Rna Bioinformatics, Jason Rafe Miller

Graduate Theses, Dissertations, and Problem Reports (ETD)

The applied science of bioinformatics encompasses computational analysis of molecular biology data. Advances in genomics and DNA sequencing technology have enabled computational analysis of ribonucleic acids (RNAs), which play diverse and critical roles in most cells. To assist the study of human RNA, we trained machine learning models on RNA nucleotide sequences, devoid of domain knowledge. We built models that distinguish long non-coding lncRNA from protein-coding mRNA, and models that predict the cytoplasmic vs. nuclear preferences of lncRNAs. In a review of published lncRNA subcellular localization classifiers, we show that the commonly used validation protocol generates optimistic performance measures, and …


Exploring Crystal Polymorphism In Additive-Assisted Chemical Vapor-Deposited Transition Metal Chalcogenides And Oxides, Lawrence Kirimi Mubwika Jan 2024

Exploring Crystal Polymorphism In Additive-Assisted Chemical Vapor-Deposited Transition Metal Chalcogenides And Oxides, Lawrence Kirimi Mubwika

Graduate Theses, Dissertations, and Problem Reports (ETD)

Crystal polymorphism is a phenomenon in which compounds with the same chemical formula can be crystallized into different crystal structures. This phenomenon can be observed in elemental materials, such as diamond and graphite, as well as in compounds, such as the trigonal (1H) or octahedral (1T) prismatic MoS2. Crystals can also exhibit polytypism by stacking different polymorphs in a certain order, with the stacking sequence determining the variation between polytypes. Although all polymorphs and polytypes have the same chemical composition, each polymorph and polytype possesses unique electronic and physical properties.

This study explores the additive-assisted chemical vapor deposition …


Estimate Of The Random Match Frequency Of Acquired Characteristics In A Forensic Footwear Database, Alyssa N. Smale Jan 2023

Estimate Of The Random Match Frequency Of Acquired Characteristics In A Forensic Footwear Database, Alyssa N. Smale

Graduate Theses, Dissertations, and Problem Reports (ETD)

When analyzing footwear impression evidence, one of the goals of an examiner is to determine if an exemplar shoe could be the source of an impression found at a crime scene. This opinion is based on an assessment of the similarity of class characteristics and randomly acquired characteristics (RACs) between the known and questioned impressions, as well as the rarity of the observed characteristics. The primary aim of this research was to estimate the random match frequency of randomly acquired characteristics (RAC-RMF) within a forensic footwear database to determine the frequency of RACs with geometric similarity occurring in the same …


Advancing Carbon Sequestration Through Smart Proxy Modeling: Leveraging Domain Expertise And Machine Learning For Efficient Reservoir Simulation, Iman Oraki Kohshour Jan 2023

Advancing Carbon Sequestration Through Smart Proxy Modeling: Leveraging Domain Expertise And Machine Learning For Efficient Reservoir Simulation, Iman Oraki Kohshour

Graduate Theses, Dissertations, and Problem Reports (ETD)

Geological carbon sequestration (GCS) offers a promising solution to effectively manage extra carbon, mitigating the impact of climate change. This doctoral research introduces a cutting-edge Smart Proxy Modeling-based framework, integrating artificial neural networks (ANNs) and domain expertise, to re-engineer and empower numerical reservoir simulation for efficient modeling of CO2 sequestration and demonstrate predictive conformance and replicative capabilities of smart proxy modeling.

Creating well-performing proxy models requires extensive human intervention and trial-and-error processes. Additionally, a large training database is essential to ANN model for complex tasks such as deep saline aquifer CO2 sequestration since it is used as the …


Ai-Driven Security Constrained Unit Commitment Using Predictive Modeling And Eigen Decomposition, Talha Iqbal Jan 2023

Ai-Driven Security Constrained Unit Commitment Using Predictive Modeling And Eigen Decomposition, Talha Iqbal

Graduate Theses, Dissertations, and Problem Reports (ETD)

Security Constrained Unit Commitment (SC-UC) is a complex large scale mix integer constrained optimization problem solved by Independent System Operators (ISOs) in the daily planning of the electricity markets. After receiving offers and bids, ISOs have only few hours to clear the day-ahead electricity market. It requires a lot of computational effort and a reasonable time to solve a large-scale SC-UC problem. However, exploiting the fact that a UC problem is solved several times a day with only minor changes in the system data, the computational effort can be reduced by learning from the historical data and identifying the patterns …


Leveraging Data Science To Promote Sustainable Resource Recovery From Organic Waste Streams In Rural Regions, Mohammed Tamim Zaki Jan 2023

Leveraging Data Science To Promote Sustainable Resource Recovery From Organic Waste Streams In Rural Regions, Mohammed Tamim Zaki

Graduate Theses, Dissertations, and Problem Reports (ETD)

Conventional organic waste management practices such as landfilling contribute to global warming and degrade environmental and human health. Alternatively, organic waste can be treated to recover energy, nutrients, and carbon through resource recovery technologies. Data science could benefit such technologies by improving their efficiency through data-driven process modeling along with reducing environmental and economic burdens via life cycle assessment (LCA) and techno-economic analysis (TEA), respectively.

A critical review of 616 peer-reviewed articles published during 2002–2022 was conducted on the use of data science methods in resource recovery from organic waste. Although applications of machine learning (ML) methods have drastically increased …


A Test Of The Control Value Theory Of Achievement Emotions In An Instructional Communication Context, Katherine E. Armstrong Jan 2023

A Test Of The Control Value Theory Of Achievement Emotions In An Instructional Communication Context, Katherine E. Armstrong

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation tested the control-value theory of achievement emotions (CVTAE) in an instructional communication context. Based on the assumptions of CVTAE, the researcher predicted that when instructors were clearer, students would feel more confident in their abilities to perform well in their class and, in turn, experience positive achievement emotions (i.e., enjoyment and hope), ultimately becoming be more intrinsically motivated to learn. If instructors were less clear, however, students would experience decreased motivation to learn through negative appraisals of performance efficacy and negative achievement emotions (i.e., boredom, anxiety, and hopelessness). Additionally, the researcher hypothesized that when instructors made the course …


Strengthening Of Damaged Structural Members With External Frp, Krishna Tulasi Gadde Jan 2023

Strengthening Of Damaged Structural Members With External Frp, Krishna Tulasi Gadde

Graduate Theses, Dissertations, and Problem Reports (ETD)

Fiber reinforced polymer (FRP) composites are excellent alternatives to traditional materials for civil infrastructure. Several researchers have worked on the application of FRP composites for construction, repair, and rehabilitation of structures. This research aims at evaluating the use of carbon, glass, basalt, and hybrid FRPs with epoxy and polyurethane resin systems for rehabilitation of damaged structural components. Following evaluations were carried out in this research: (i) tension testing of FRP coupons, (ii) compression testing of concrete cylinders with and without damaged sections/FRP reinforcements, (iii) flexural testing of external-FRP reinforced RC beams with and without damages, (iv) pull-off tests on FRP …


Techno-Economic Analysis And Optimization Of Hydrogen And Mechanical Energy Storage Systems, Pavitra Senthamilselvan Sengalani Jan 2023

Techno-Economic Analysis And Optimization Of Hydrogen And Mechanical Energy Storage Systems, Pavitra Senthamilselvan Sengalani

Graduate Theses, Dissertations, and Problem Reports (ETD)

The increasing significance of renewable energy sources is thrusting the load cycling of fossil-fueled power plants (FFPP), designed to operate under nominal-load conditions. Integration of energy storage systems (ESS) with the FFPPs such as hydrogen energy storage (HES) and mechanical energy storage facility such as compressed air energy storage (CAES) shows the potential to minimize the levelized cost of electricity during high demand scenarios and also minimize the negative impacts of off-design FFPP operation. The deployment of energy storage facilities at the FFPP level have considerable potential advantages as they can be exploited within the existing equipment items and facilities …


Strengthening The Interpretation Of Glass And Paint Evidence Through The Study Of Random Frequency Of Occurrence And Analytical Information, Lauryn C. Alexander Jan 2023

Strengthening The Interpretation Of Glass And Paint Evidence Through The Study Of Random Frequency Of Occurrence And Analytical Information, Lauryn C. Alexander

Graduate Theses, Dissertations, and Problem Reports (ETD)

Glass and paint particles are frequently discovered at crime scenes as valuable trace evidence. Often, these fragments are transferred from a crime scene to a victim or person-of-interest, and can subsequently be evaluated, analyzed, and classified according to their physical and optical measurements, and chemical properties, each of which can provide important information to the analyst to assist in the determining if a recovered particle is distinguishable or indistinguishable from a known source. Moreover, these minute materials can provide information about how the events took place, leading to the reconstruction of crime scenes and the identification of valuable clues for …


Understanding Mentorship In Undergraduate Research: Three Perspectives On Experiencing, Conceptualizing, And Contextualizing Mentorship, Carinna F. Ferguson Jan 2023

Understanding Mentorship In Undergraduate Research: Three Perspectives On Experiencing, Conceptualizing, And Contextualizing Mentorship, Carinna F. Ferguson

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation aimed to explore mentorship in undergraduate research (UR) contexts. Specifically, the work aimed to provide three perspectives of mentorship from the perspectives of both mentors and mentees in undergraduate research. These three studies contributed to a greater understanding of the experiences, conceptualizations, and contextual factors that impact mentorship in the UR setting.

Highlighted in the first study were the storied experiences of eight faculty members who had served as a mentor to undergraduate students at a mid-Atlantic, research-intensive university from a range of research disciplines. Results of the first study highlighted the impact of faculty members’ initial and …


Emission Spectroscopy Of Ingaas Quantum Dots Via High-Resolution Fabry-Perot Interferometer, Raju Bhai Kc Jan 2023

Emission Spectroscopy Of Ingaas Quantum Dots Via High-Resolution Fabry-Perot Interferometer, Raju Bhai Kc

Graduate Theses, Dissertations, and Problem Reports (ETD)

Single photons emitted from self-assembled quantum dots have been widely studied to use as a promising qubit for quantum information processing. Therefore, it is critical to fully understand the emission spectra from the quantum dot's excitation if we want to use a single photon as a quantum bit. It is almost impossible to produce rotationally symmetric quantum dots due to various growth conditions and restrictions. So the real quantum dots do not have a perfectly symmetric structure. A broken rotational symmetry causes an asymmetric exchange interaction between electron and hole, leading to a fine structure splitting between two excited states. …


Effects Of Invasive Species On Ohio River Zooplankton, Samuel John Johnston Jan 2023

Effects Of Invasive Species On Ohio River Zooplankton, Samuel John Johnston

Graduate Theses, Dissertations, and Problem Reports (ETD)

Invasive species have the potential to dramatically change both aquatic and terrestrial ecosystems with rates of introduction only expected to increase across the Globe. In the Mississippi River basin filter feeding silver (Hypophthalmichthys molitrix) and bighead carp (Hypophthalmichthys nobilis) collectively known as invasive carp were introduced into aquaculture ponds where they subsequently escaped and spread to interconnected basins. Invasive carp have not yet completely established throughout the entire Ohio River. Managers recognize three distinct phases of carp invasion: establishment front, invasion front and presence front. In the Illinois River invasive carp are very well established and …


Longest Path And Cycle Transversal And Gallai Families, James A. Long Jr Jan 2023

Longest Path And Cycle Transversal And Gallai Families, James A. Long Jr

Graduate Theses, Dissertations, and Problem Reports (ETD)

A longest path transversal in a graph G is a set of vertices S of G such that every longest path in G has a vertex in S. The longest path transversal number of a graph G is the size of a smallest longest path transversal in G and is denoted lpt(G). Similarly, a longest cycle transversal is a set of vertices S in a graph G such that every longest cycle in G has a vertex in S. The longest cycle transversal number of a graph G is the size of a smallest longest cycle transversal in G and …


Flows On Signed Graphs, Chong Li Jan 2023

Flows On Signed Graphs, Chong Li

Graduate Theses, Dissertations, and Problem Reports (ETD)

This dissertation focuses on integer flow problems within specific signed graphs. The theory of integer flows, which serves as a dual problem to vertex coloring of planar graphs, was initially introduced by Tutte as a tool related to the Four-Color Theorem. This theory has been extended to signed graphs.

In 1983, Bouchet proposed a conjecture asserting that every flow-admissible signed graph admits a nowhere-zero 6-flow. To narrow dawn the focus, we investigate cubic signed graphs in Chapter 2. We prove that every flow-admissible 3-edge-colorable cubic signed graph admits a nowhere-zero 10-flow. This together with the 4-color theorem implies that every …