Physical Sciences and Mathematics Commons^™

Parameter Estimation For Patient Enrollment In Clinical Trials, Junyan Liu

Undergraduate Honors Theses

In this paper, we study the Poisson-gamma model for recruitment time in clinical trials. We proved several properties of this model that match our intuitions from a reliability perspective, did simulations on this model, and used different optimization methods to estimate the parameters. Although the behaviors of the optimization methods were unfavorable and unstable, we identified certain conditions and provided potential explanations for this phenomenon and further insights into the Poisson-gamma model.

A Satellite Imagery Approach To Estimating Migratory Flows In Guatemala Using Convolutional Neural Networks, Sarah Larimer

Undergraduate Honors Theses

Being able to predict migratory flows is important in ensuring political, social, and economic stability. In the wake of violence, unrest, natural disasters, and social pressures, millions of mi- grants have fled Central America in search of a better life. However, due to the infrequent nature and high cost of census data, there is a need for a more remote and up to date approaches. Con- volutional Neural Networks offer a computer vision based approach that is cheaper and with significantly less lag. In this study, we seek to evaluate the effectiveness of different convolu- tional neural networks in predicting …

Considering The Accuracy Of Fiat Boundaries: Ontology And Quantification, Lydia Troup

Undergraduate Honors Theses

Administrative boundaries - i.e., states, counties, or districts - are fiat boundaries; they exist purely as defined by human interpretation. Because of this, and despite their critical importance to government functions, the accuracy of data products claiming to represent such boundaries is difficult to measure. Here, I explore this topic using three boundary data sets: the open source geoBoundaries data set, the humanitarian UN OCHA’s Common Operational Datasets (COD), and Esri’s commercial administrative divisions 0 and 1 data sets in the Living Atlas. The accuracy of each was quantified as the percent overlap between each data set and an authoritative …

Development Of A 780 Nm External Cavity Diode Laser For Rubidium Spectroscopy, Catherine Sturner

Undergraduate Honors Theses

This thesis describes the work done to improve an external cavity diode laser. These improvements consisted of constructing an insulated housing to stabilize the temperature of the laser, tuning the proportional-integral-derivative feedback of the temperature controller, achieving resonance frequencies of rubidium, and implementing and optimizing feed-forward scanning of the frequency of the laser. The laser was then successfully used to measure the linewidth of another laser in the laboratory to better understand how that laser could be best used. The knowledge gained in this thesis can also be used to change the frequency of the laser to achieve other resonances …

Black Hole Entropy In Ads/Cft And The Schwinger-Keldysh Formalism, Luke Mrini

Undergraduate Honors Theses

The Schwinger-Keldysh formalism for non-equilibrium field theory provides valuable tools for studying the black hole information loss paradox. In particular, there exists a Noether-like procedure to obtain the entropy density of a system by a discrete Kubo-Martin-Schwinger (KMS) variation of the action. Here, this Noether-like procedure is applied to the boundary action of an asymptotically anti-de Sitter (aAdS) black hole spacetime in maximally extended Kruskal coordinates. The result is the Kubo formula for shear viscosity, which is known in theories with an Einstein gravity dual to have a universal, constant ratio with the entropy density and is proportional to the …

Automorphisms Of A Generalized Quadrangle Of Order 6, Ryan Pesak

Undergraduate Honors Theses

In this thesis, we study the symmetries of the putative generalized quadrangle of order 6. Although it is unknown whether such a quadrangle Q can exist, we show that if it does, that Q cannot be transitive on either points or lines. We first cover the background necessary for studying this problem. Namely, the theory of groups and group actions, the theory of generalized quadrangles, and automorphisms of GQs. We then prove that a generalized quadrangle Q of order 6 cannot have a point- or line-transitive automorphism group, and we also prove that if a group G acts faithfully on …

Monoenergetic Neutrinos From Wimp Annihilations In Jupiter, George French

Undergraduate Honors Theses

Several important lines of evidence point to the existence of dark matter, but it has not yet been experimentally detected. There are several proposed candidates for what dark matter is like, the most popular being weakly interacting massive particles (WIMPs). It has been well-established in the literature that WIMPs would be captured by the Sun after scattering off of atomic nuclei to a velocity lower than the escape velocity. Over time, many WIMPs would be captured and begin to annihilate in the solar core; this would result in the production of kaons that decay at rest into monoenergetic 236 MeV …

Materials Characterization For Microwave Atom Chip Development, Jordan Shields

Undergraduate Honors Theses

This thesis describes research to characterize materials to be implemented on a microwave atom trap chip, which will be able to trap and spatially manipulate atoms using the spin-specific microwave AC Zeeman effect. Potential applications of this research include atom-based interferometry and quantum computing.

Namely, this thesis describes the characterization of the following: (1) the dielectric constant of a well-characterized substrate, Rogers RO4350B, in order to provide proof-of-concept for a method that can be applied to the chip’s substrate, aluminum nitride (AlN), (2) the maximum current that will be able to be applied to the chip, and (3) surface roughness …

Fecal Pellet Production By North Atlantic Zooplankton, Michael Gibson

Undergraduate Honors Theses

Fecal pellet carbon (FPC) production by zooplankton is a significant component of the ocean’s biological carbon pump: the suite of biological processes that mediate export of carbon to the deep ocean, ultimately leading to the sequestration of atmospheric carbon dioxide in the ocean. In this study, mesozooplankton (zooplankton 0.2 mm to ~2 cm) were collected from the epipelagic zone in the temperate North Atlantic Ocean during day and night in May 2021. Zooplankton were live separated into five size fractions and incubated on board ship in natural surface seawater to measure fecal pellet production rate of the mixed mesozooplankton community. …

Seeing What We Can't: Evaluating Implicit Biases In Deep Learning Satellite Imagery Models Trained For Poverty Prediction, Joseph O'Brien

Undergraduate Honors Theses

Previous studies have sought to use Convolutional Neural Networks for regional estimation of poverty levels. However, there is limited research into possible implicit biases in deep neural networks in the context of satellite imagery. In this work, we develop a deep learning model to predict the tertile of per-capita asset consumption, trained on satellite imagery and World Bank Living Standards Measurements Study data. Using satellite imagery collected via survey location data as inputs, we use transfer learning to train a VGG-16 Convolutional Neural Network to classify images based on per-capita consumption. The model achieves an $R^2$ of .74, using thousands …

A Study Of Reciprocal Underwater Motion And Its Use In Algae Harvesting, Marguerite Bright

Undergraduate Honors Theses

In 2009, many research groups at different companies and universities were funded by Statoil to study the use of algae as a potential biofuel. Combined with the Chesapeake Bay TMDL given by the EPA, a team at William & Mary and VIMS studied the growth and harvest of wild algae in the York River. This method also removed harmful nutrients such as nitrogen and phosphorus from the waterways. Other independent research projects stemmed from this. In 2014, a research team sought to commercialize and automate the IWAGS system, and found that a single oscillating blade was the most effective. This …

Identifying Social Media Users That Are Susceptible To Phishing Attacks, Zoe Metzger

Undergraduate Honors Theses

Phishing scams are a billion-dollar problem. According to Threatpost, in 2020, business email compromise phishing attacks cost the US economy $ 1.8 billion. Social media phishing scams are also on the rise with 74% of companies experiencing social media attacks in 2021 according to Proofpoint. Educating users about phishing scams is an effective strategy for reducing phishing attacks. Despite efforts to combat phishing, the number of attacks continues to rise, likely indicative of a reticence of users to change online behaviors. Existing research into predicting vulnerable social media users that are susceptible to phishing mostly focuses on content analysis of …

Examining Factors Using Standard Subspaces And Antiunitary Representations, Paul Anderson

Undergraduate Honors Theses

In an effort to provide an axiomization of quantum mechanics, John von Neumann and Francis Joseph Murray developed many tools in the theory of operator algebras. One of the many objects developed during the course of their work was the von Neumann algebra, originally called a ring of operators. The purpose of this thesis is to give an overview of the classification of elementary objects, called factors, and explore connections with other mathematical objects, namely standard subspaces in Hilbert spaces and antiunitary representations. The main results presented here illustrate instances of these interconnections that are relevant in Algebraic Quantum Field …

Spatial Variability Of Alkali-Metal Polarization, Lauren Vannell

Undergraduate Honors Theses

An experiment was conducted at William & Mary to study how alkali polarization varies spatially in a spherical cell during the process of optical pumping. Similar cells are used to study the neutron via electron scattering from polarized 3He nuclei, and those experiments could be improved if alkali polarization is maximized and uniformly distributed throughout the cell. The results of this experiment indicate that the alkali polarization is non-uniform and more heavily concentrated on the side of the cell facing the pump laser.

Kfactorvae: Self-Supervised Regularization For Better A.I. Disentanglement, Joseph S. Lee

Undergraduate Honors Theses

Obtaining disentangled representations is a goal sought after to make A.I. models more interpretable. Studies have proven the impossibility of obtaining these kinds of representations with just unsupervised learning, or in other words, without strong inductive biases. One strong inductive bias is a regularization term that encourages the invariance of factors of variations across an image and a carefully selected augmentation. In this thesis, we build upon the existing Variational Autoencoder (VAE)-based disentanglement literature by utilizing the aforementioned inductive bias. We evaluate our method on the dSprites dataset, a well-known benchmark, and demonstrate its ability to achieve comparable or higher …

Pion Detection For The Moller Parity-Violating Electron Scattering Experiment, Michael Tristan Hurst

Undergraduate Honors Theses

The MOLLER Experiment at Jefferson Lab intends to make a precise measurement of the weak charge of the electron through parity-violating electron scattering. To achieve the level of precision required for the experiment, background rates of events other than electron-electron scattering must be known. Working with data from Monte-Carlo simulations created using a GEANT4 simulation package, I show that the combined signal from two existing detector subsystems of the MOLLER experiment allow for particle identification between electron and pion events. I worked to optimize an additional ‘Pion Exit Scintillator’ which improves the ability to distinguish particle identity at the cost …

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 …