Physical Sciences and Mathematics Commons^™

Voting Rules And Properties, Zhuorong Mao

Undergraduate Honors Theses

This thesis composes of two chapters. Chapter one considers the higher order of Borda Rules (Bp) and the Perron Rule (P) as extensions of the classic Borda Rule. We study the properties of those vector-valued voting rules and compare them with Simple Majority Voting (SMV). Using simulation, we found that SMV can yield different results from B1, B2, and P even when it is transitive. We also give a new condition that forces SMV to be transitive, and then quantify the frequency of transitivity when it fails.

In chapter two, we study the `protocol paradox' of approval voting. In approval …

Quantum Federated Learning: Training Hybrid Neural Networks Collaboratively, Anneliese Brei

Undergraduate Honors Theses

This thesis explores basic concepts of machine learning, neural networks, federated learning, and quantum computing in an effort to better understand Quantum Machine Learning, an emerging field of research. We propose Quantum Federated Learning (QFL), a schema for collaborative distributed learning that maintains privacy and low communication costs. We demonstrate the QFL framework and local and global update algorithms with implementations that utilize TensorFlow Quantum libraries. Our experiments test the effectiveness of frameworks of different sizes. We also test the effect of changing the number of training cycles and changing distribution of training data. This thesis serves as a synoptic …

Modern Theory Of Copositive Matrices, Yuqiao Li

Undergraduate Honors Theses

Copositivity is a generalization of positive semidefiniteness. It has applications in theoretical economics, operations research, and statistics. An $n$-by-$n$ real, symmetric matrix $A$ is copositive (CoP) if $x^T Ax \ge 0$ for any nonnegative vector $x \ge 0.$ The set of all CoP matrices forms a convex cone. A CoP matrix is ordinary if it can be written as the sum of a positive semidefinite (PSD) matrix and a symmetric nonnegative (sN) matrix. When $n < 5,$ all CoP matrices are ordinary. However, recognizing whether a given CoP matrix is ordinary and determining an ordinary decomposition (PSD + sN) is still an unsolved problem. Here, we give an overview on modern theory of CoP matrices, talk about our progress on the ordinary recognition and decomposition problem, and emphasis the graph theory aspect of ordinary CoP matrices.

Development Of A Vector Magnetometer Based On Electromagnetically Induced Transparency In 87rb Atomic Vapor, Alexander Toyryla

Undergraduate Honors Theses

We present progress towards the development of an atomic magnetometer capable of accurate scalar and vector magnetic field measurements with high sensitivity and no need for external calibration. The proposed device will use the interaction between a bi-chromatic laser field and rubidium vapor to derive magnetic field magnitude and direction from measured amplitudes of Electromagnetically Induced Transparency (EIT) resonances. Since the proposed method requires precision control of light polarization, we observe the performance capabilities of a liquid crystal device to dynamically rotate the polarization of the laser field. Another goal in this project is to establish a polarization locking mechanism …

Alkali Linewidths Under High Temperatures And Pressures Of 3he, Michael Parker

Undergraduate Honors Theses

Current research at Thomas Jefferson National Accelerator Facility is being conducted to study the spin structure of the neutron through collisions with polarized 3He nuclei. The helium is contained in high pressure glass vessels (called cells) along with nitrogen, rubidium, and potassium. To deduce the spin structure from collisions, we need to know the precise number density of 3He in the cell. The process of polarizing 3He through spin-exchange optical pumping requires nitrogen and alkali metal. We can use the absorption linewidths of rubidium and potassium to more accurately determine the density of helium. Throughout my research, I collected absorption …

Enumerating Switching Isomorphism Classes Of Signed Graphs, Nathaniel Healy

Undergraduate Honors Theses

Let Γ be a simple connected graph, and let {+,−}^E(Γ) be the set of signatures of Γ. For σ a signature of Γ, we call the pair Σ = (Γ,σ) a signed graph of Γ. We may define switching functions ζ_X ∈ {+, −}^V (Γ) that negate the sign of every edge {u, v} incident with exactly one vertex in the fiber X = ζ^{−1}(−). The group Sw(Γ) of switching functions acts X on the set of signed graphs of Γ and induces an equivalence relation of switching classes in its orbits; there are 2^{|E(Γ)|−|V (Γ)|+1} such classes. More interestingly, …

Climate Change And Conservation Of Milkweed: Evidence Of Extensive Admixture Between Common Milkweed And Poke Milkweed, Elizabeth Davies

Undergraduate Honors Theses

Global climate change can drive many changes in species interactions. One primary way it affects species is by changing climates, causing species to expand their ranges and allowing them to interact with species from whom they were previously isolated. In plants, new species interactions can result in hybridization – the creation of hybrid offspring between two separate species. This hybridization can increase gene flow between the species and lead to introgression, the transfer of genetic material from one species to another through hybrid backcrossing with the parent species. My thesis investigates hybridization in the model system Asclepias (milkweed) by analyzing …

Chemical Analysis Of Organic Compounds In Dew Water, Monica Dibley

Undergraduate Honors Theses

Water films on outdoor surfaces, such as dew, can act as a reservoir for organic molecules deposited from the atmosphere and they present a potential reactive medium for chemical transformations. To better understand the flux of volatile organic compounds from evaporating films, the composition and reactivity of the complex mixture of dissolved organic material (DOM) found in these films need to be characterized. Previous studies have measured the salts and the small organic molecules in dew collected on clean Teflon surfaces or condensers. Here, we expand on this by probing the organic chemicals found on natural outdoor surfaces covered in …

Using Deep Learning With Satellite Imagery To Estimate Deforestation Rates, Maeve Naughton-Rockwell

Undergraduate Honors Theses

Previous studies have used Convolutional Neural Networks for regional detection of deforestation breaks. However, there is limited research into the capability of deep neural networks to identify sudden shifts in global forest cover from satellite imagery. Additionally, many deforestation detection models are trained on region specific data and need manual input thresholds. In this work, we develop a deep learning model to predict the percent of deforestation in a region between two points in time, trained on globally sourced data. Using the before and after satellite images of a deforestation event as inputs, we implemented a two input Convolutional Neural …

Differential Protein Expression In Bacteriophages Crimd And Larva, Daria Moody

Undergraduate Honors Theses

Proteomics studies allow us to answer questions about differential protein expression across different systems. Mass spectrometry is a powerful tool in these studies due to the distinct masses of the amino acids that compose proteins. In our experiment, we used a bottom-up approach and focused on two bacteriophages found on the William & Mary campus, CrimD and Larva. The infection of Mycobacterium smegmatis, a nonpathogenic model for tuberculosis, by these two bacteriophages was frozen at five different timepoints, and our goal was to compare the differential protein expression across the samples in order to gain a greater understanding of …

Using A Machine Learning Model To Predict Plant Inflorescences Based Upon Its Soil Microbiome, Luke Denoncourt

Undergraduate Honors Theses

The UN estimates that the global population could reach 9.7 billion by 2050 (United Nations). As a result, the amount of food required to feed humanity is thought to double by 2050 (Ray et al., 2012). Humanity must find a way to increase crop production without increasing fertilizer usage and eutrophication, which can be done using the soil microbiome. Using potted plants with soils inoculated with Pseudomonas alcaligenes, Pseudomonas denitrificans, Bacillus polymyxa, and Mycobacterium phlei, both the shoot and root growth of pea and cotton plants was significantly increased (Egamberdieva & Höflich, 2004). In this study, utilizing a random forest …

An Atomic Magnetometer Based On Nonlinear Magneto-Optical Polarization Rotation, Jiahui Li

Undergraduate Honors Theses

Magnetometers with high precision and accuracy have wide applications across various areas. We are developing an atomic magnetometer based on nonlinear magneto-optical rotation (NMOR). The magnetometer measures the polarization rotation of a light field, which is proportional to the magnetic field strength. However, such a magnetometer usually has a limited operation range and stops working for fields stronger than the Earth's magnetic field. To overcome this shortage, we implement frequency and amplitude modulation that induces side frequencies in the Fourier space which allows us to measure strong magnetic fields, up to 200 mG. We have achieved 60 pT sensitivity for …

Bayesian Spatial Model Development Of Soil Core Organic Matter As A Proxy For Blue Carbon Stocks Within The Chesapeake Bay, Christian Longo

Undergraduate Honors Theses

Blue carbon is carbon captured and stored within bodies of water and their ecosystems. Blue carbon stocks are very important due to their ability to store carbon away from the atmosphere. The destruction of these stocks can accelerate climate change. In particular, we wish to assess blue carbon stock within the Chesapeake Bay. Previous studies have only used geographical features to predict blue carbon stock levels. The big picture question this thesis was meant to answer is: What is the best approach for building a statistical model that factors in both spatial parameters and geographical features to predict blue carbon …

Co-Planar Waveguides For Microwave Atom Chips, Morgan Logsdon

Undergraduate Honors Theses

This thesis describes research to develop co-planar waveguides (CPW) for coupling microwaves from mm-scale coaxial cables into 50 μm-scale microstrip transmission lines of a microwave atom chip. This new atom chip confines and manipulates atoms using spin-specific microwave AC Zeeman potentials and is particularly well suited for trapped atom interferometry. The coaxial-to-microstrip coupler scheme uses a focused CPW (FCPW) that shrinks the microwave field mode while maintaining a constant 50 Ω impedance for optimal power coupling. The FCPW development includes the simulation, design, fabrication, and testing of multiple CPW and microstrip prototypes using aluminum nitride substrates. Notably, the FCPW approach …

Investigation Of Tertiary Impact Cratering And Relation To Impact Physics Theory, Mikayla Huffman

Undergraduate Honors Theses

Extraterrestrial impact crater formation is important in many subfields of planetary science, including geochronology, planetary formation, and dynamic fragmentation theory. Current dynamic fragmentation theory lacks scale dependence and relies heavily on terrestrial data. Exploring a range of impact and ejecta velocities as is produced by cratering events on the Moon may bridge the gap between heavily terrestrial-based theory and planetary data. The secondary craters of secondary craters deemed “tertiary craters,” have been theorized, but planetary images have not been of sufficient resolution to effectively search for them until recently. Tertiary craters are formed by relatively low-velocity fragments ejected by nearby …

Gas-Phase Proton Affinities For Twenty Of The Proline-Containing Dipeptides, Henry Cardwell

Undergraduate Honors Theses

Peptide fragmentation plays a crucial role in the analysis of proteins through mass spectrometry-based proteomics. Most proteomics experiments take place in the low-energy regime and are governed by the mobile proton model which predicts random cleavages along the peptide backbone; however, there sometimes arise circumstances where the mobile proton model fails causing sequencing algorithms to misidentify peptides. One such example is noted in the “proline effect” wherein proline-containing peptides preferentially fragment N-terminal. While it has been established that the “proline effect” is due to the rigidity and basicity of the proline N-terminus, a further understanding of the factors influencing the …

Period Doubling Cascades From Data, Alexander Berliner

Undergraduate Honors Theses

Orbit diagrams of period doubling cascades represent systems going from periodicity to chaos. Here, we investigate whether a Gaussian process regression can be used to approximate a system from data and recover asymptotic dynamics in the orbit diagrams for period doubling cascades. To compare the orbits of a system to the approximation, we compute the Wasserstein metric between the point clouds of their obits for varying bifurcation parameter values. Visually comparing the period doubling cascades, we note that the exact bifurcation values may shift, which is confirmed in the plots of the Wasserstein distance. This has implications for studying dynamics …

Machine Learning In Healthcare: Improving The Diagnosis Of Pulmonary Embolism In Covid-19 Patients, Soheb Osmani

Undergraduate Honors Theses

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has created new challenges for clinicians diagnosing pulmonary embolism (PE). Clinicians currently rely on D-Dimer levels in conjunction with clinical prediction scores to rule out and diagnose PE. However, patients with COVID-19 (the disease caused by SARS-CoV-2) often present with elevated D-Dimer levels. D-Dimer levels in COVID-19 patients have been found to be positively correlated with the severity of disease. Symptoms of COVID-19 also often align with symptoms of PE. Therefore, it becomes more difficult for clinicians to identify which COVID-19 positive patients should undergo further testing for PE. This study evaluates …

Modeling And Analyses Of Mechanisms Underlying Network Synaptic Dynamics In Two Neural Circuits, Linda Ma

Undergraduate Honors Theses

In systems neuroscience, circuit models of cortical structures can be used to deconstruct mechanisms responsible for spike patterns that generate a variety of behaviors observed in the brain. In particular, mathematical simulations of these circuits can replicate complex dynamical behaviors that mirror not only macroscopically patterns observed in the brain, but also a significant amount of experimentally characterized minutiae. These models are capable of analyzing neural mechanisms by explicitly deconstructing connectivities between populations of neurons in ways that tend to be empirically inaccessible. This work presents two such models; one in the rat somatosensory barrel cortex, responsible for processing sensory …

Analysis Of Edna To Assess Effects Of Water Quality On Freshwater Fungal Diversity In A Virginia Coastal Watershed, Lauren French

Undergraduate Honors Theses

Freshwater fungi comprise a phylogenetically and functionally diverse group which contributes to wide-ranging ecosystem processes in aquatic systems. Saprotrophic fungi convert detritus into nutrient-rich food sources for fish and invertebrates, whereas pathogenic and parasitic fungi can cause disease and population declines of other aquatic organisms. With their diverse and important roles, changes in freshwater fungal community structure may have far-reaching impacts on ecosystems. To understand how natural and anthropogenic stressors to freshwater systems impact fungal-mediated ecosystem processes, a greater understanding of the taxonomic and functional composition of freshwater fungal communities is needed. We assessed relationships among freshwater habitat types, water …

The Enumeration Of Minimum Path Covers Of Trees, Merielyn Sher

Undergraduate Honors Theses

A path cover of a tree T is a collection of induced paths of T that are vertex disjoint and cover all the vertices of T. A minimum path cover (MPC) of T is a path cover with the minimum possible number of paths, and that minimum number is called the path cover number of T. A tree can have just one or several MPC's. Prior results have established equality between the path cover number of a tree T and the largest possible multiplicity of an eigenvalue that can occur in a symmetric matrix whose graph is that tree. We …

The Pandemic From Above: Estimating Covid-19 Cases Using Deep Learning And Satellite Imagery, John Hennin

Undergraduate Honors Theses

Monitoring the spread of an outbreak of disease (such as COVID-19) is an important component of any coordinated pandemic response. Across the globe, our ability to conduct such monitoring - especially at early stages of the COVID- 19 pandemic - was highly limited due to a lack of public reporting mechanisms. Today, the process of case data collection remains expensive and, in some regions, is subject to political considerations. Researchers have turned to some techniques leveraging Google Trends and Twitter data to overcome limitations in public data sources. Here, we provide another approach which leverages satellite information to provide estimates …

Honey As A Biomonitor For Air Pollutant Deposition In The Eastern United States Using Ion Chromatography And Scanning Electron Microscopy, Cole Cochran

Undergraduate Honors Theses

Anthropogenic activities generate metal, acid, and particulate air pollutants which negatively impact human and ecological health. In the United States, power plant, industrial, and vehicle emissions are leading causes of air pollution, however, the measurement of air pollution at high-resolution spatial regimes remains a challenge. Honey has emerged as a powerful biomonitoring tool to effectively quantify contaminants without the need for a large array of monitoring instruments. I hypothesized that honey could be used to effectively measure and map modern air pollutant spatiotemporal relationships over the Eastern U.S. Using ion chromatography with sulfate as an indicator for air pollution and …

Geologic Controls On 137cs Cycling By Terrestrial Vegetation In The Eastern U.S., Kathleen Chellman

Undergraduate Honors Theses

¹³⁷Cs is a radioactive trace metal (T_1/2 = 30 y) that was dispersed globally by nuclear weapons testing in the 1950s-1960s. Prevailing winds and precipitation systems caused some areas far from the test sites to receive significant fallout, which is still easily measured in soils, sediments and even some vegetation in the Eastern United States. Recent work near Chernobyl and Fukushima indicates that trace levels of ¹³⁷Cs can harm insects, pollination services, and other ecological functions. In areas with low soil potassium, ¹³⁷Cs is cycled in vegetation; however, soil potassium alone doesn't consistently predict the ^{137 …}

Roles Of Hydrodynamics And Topographies On The Transport Of Dissolved Material, Particulates, And Harmful Algae In Chesapeake Bay, Jilian Xiong

Dissertations, Theses, and Masters Projects

Estuaries are highly productive and characterized by complex shoreline geometry and topography. Multiple materials produced within or transported into estuaries include non-living dissolved/particulate materials and living organisms. Estuarine circulation determines material transport and distributions, which further impact estuarine ecosystem to support abundant fauna/flora and their vulnerability to escalated anthropogenic inputs. Short-term material transport process in Chesapeake Bay (CB) has been studied for years, yet its long-term characteristics and the transport of materials with settling and biological behaviors that interact with physical transport have not been fully studied. This study aims to understand the transport of non-living and non-motile dissolved/particulate materials, …

Investigation Of Stripes, Spin Density Waves And Superconductivity In The Ground State Of The Two-Dimensional Hubbard Model, Hao Xu

Dissertations, Theses, and Masters Projects

The Hubbard model is a "paradigmatic" model in the realm of condensed matter physics. Recently a work with various state-or-art methods established the ground state stripe order near 1/8 doping and strong on-site interaction. Therefore, in this thesis, we determine the spin and charge order of ground state of 2D doped Hubbard model in its simplest form (with only on site repulsion and nearest-neighbor hoping) with various doping and small to medium interaction. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. …

Importance Of Muddy Bed Aggregate Processes In Cohesive Sediment Dynamics Associated With Sediment Management Projects, David Perkey

Dissertations, Theses, and Masters Projects

The erosion and transport processes of fine sediment is largely impacted by the aggregation state. Understanding fine sediment transport processes is a key component to managing the nation’s navigation channels, ports, and reservoirs. To improve its ability to apply management strategies related to fine sediments, the USACE has undertaken research that focusses on the aggregation state of fine sediment. Of particular interest is the ability to expand the use of fine-grained sediment in projects that seek to beneficially use dredge material. In this study, a newly developed camera system was used to evaluate the aggregation state of eroded sediment from …

Feedbacks Among Benthic Metabolism, Nitrogen Cycling, And Intense Phytoplankton Blooms In The York River Estuary, Michelle H. Woods

Dissertations, Theses, and Masters Projects

Benthic-pelagic coupling is defined as the deposition of organic matter from the water column to the sediments, and the subsequent remineralization of this organic matter and release of inorganic nutrients back to the water column. This process plays an important role in determining the magnitude of benthic net community production (NCP), a metric that reflects the balance between gross primary production and respiration. Environmental factors, such as the presence or absence of intense phytoplankton blooms can influence the direction and magnitude of benthic-pelagic coupling and determine if benthic NCP is net autotrophic or heterotrophic. The objective this thesis was to …

Partial Wave Analysis Of Strange Mesons Decaying To K + Π − Π + In The Reaction Γp → K + Π + Π − Λ(1520) And The Commissioning Of The Gluex Dirc Detector, Andrew Hurley

Dissertations, Theses, and Masters Projects

Hadron spectroscopy is a cornerstone of our understanding of the strong nuclear interac-tions. Studying the hadron spectrum led to the postulation of quarks and gluons, and the development of Quantum Chromodynamics (QCD), the theory of the strong nuclear force. Today hadron spectroscopy provides an important test of QCD, particularly in the non-perturbative energy regime. One such test is the existence of hybrid hadrons that have gluonic degrees of freedom, e.g. qq̄g states, that are allowed by QCD but have remained elusive in experimental searches. The GlueX experiment located at Thomas Jefferson National Accelerator Facility, is designed to map the light …

Exploring The Photophysics Of Brown Carbon Chromophores Using Laser-Based Spectroscopy And Computational Methods, Megan Elizabeth Alfieri

Dissertations, Theses, and Masters Projects

Atmospheric aerosols are made up of suspended liquids and solids in the atmosphere. These aerosols play a very important role in the solar energy exchange in Earth’s atmosphere as well have dramatic impact on human health. Different aerosols have different effects on the atmosphere depending on the physical properties of the aerosols.

The purpose of this research project is to understand how the structure of molecular chromophores impacts the solar absorption properties of aerosols. We propose a series of laboratory studies to investigate the outcomes from solar absorption of brown carbon chromophores: 1-phenylpyrrole, 2-phenyl-1-H-pyrrole, 2-phenylimadazole, as well as water complexes. …