Physical Sciences and Mathematics Commons^™

Computer-Assisted Coloring-Graph Generation And Structural Analysis, Wesley Su

Honors Theses

Graphs are a well studied construction in discrete math, with one of the most common areas of study being graph coloring. The graph coloring problem asks for a color to be assigned to each vertex in a graph such that no two adjacent vertices share a color. An assignment of k colors that meets these criteria is called a k-coloring. The coloring graph Ck(G) is defined as the graph where every vertex represents a valid k-coloring of graph G and edges exist between colorings that di↵er by one vertex. We call graph G the base graph of the k-coloring graph …

Using 3-Dimensional Ffts To Simulate Cmb Maps On A Spherical Cap, Eric Goetz

Honors Theses

The current methods of simulating the Cosmic Microwave Background (CMB) involve either simulating the entire sky using spherical transforms or simulating a at patch with fast Fourier transforms (FFTs). For patches that are too large to be considered at but much less than the full sky, the former method is inecient and the latter is inaccurate. One alternative method of CMB simulation is to simulate the random processes behind the CMB in a 3-dimensional box that contains the part of the sphere that we want to measure. Then, we can select the points we want from the box. This method …

Polychromatic Map-Making With Asymmetric Antenna Patterns, Connor Mooney

Honors Theses

Imaging telescopes with asymmetric antenna patterns that vary with wavelength can create time-ordered data that may be processed into multiple images corresponding to different bands of wavelengths from just a single set of scans. The imaging telescope named QUBIC has this property and is the inspiration behind this project. Our goal is to quantify, both statistically and analytically, the ability of these telescopes to perform such a reconstruction given different cases. In the case that the telescope is observing the full sky, we reconstruct our maps via a spherical harmonic basis. In this way, the reconstructed images are described as …

Structural Investigations Using Theoretical Approaches : A Study Of Metal Halides, Borylenes, Phenalenyl Complexes And Σ-Hole Interactions, Supreeth Prasad

Honors Theses

The anomalous bending in the group 2 binary dihalides and the absence of this behavior in group 12 systems is well established. Their structuralpreferences contradict simple bonding models, yet they have received little to no attention in the literature. In this work, for the first time, the gas phase structuralpreferences of the groups 2 and 12 mixed (ternary) dihalides MXY (M=Be, Mg, Ca, Sr, Ba, Ra, Zn, Cd and Hg,and X, Y=F, Cl, Br, I, At) are investigated at high levels of theory. I extend a previously established softness criterion for bending to the mixed systems and I find that …

Waveband Luminosity Correlations In Flux-Limited Multiwavelength Data And The Schwinger Effect In Minkowski & De Sitter Space-Times, Syed Jibran Haider

Honors Theses

The first part of the thesis explores key findings determined from plotting multiple waveband luminosity and redshift correlations in quasar data binned in redshift. The second part of the thesis concerns itself with applying Picard-Lefschetz theory to pair particle production in de Sitter space-time (with or without a constant electric field).

Analysis Of A Custom Support Vector Machine For Photometric Redshift Estimation And The Inclusion Of Galaxy Shape Information, Evan Jones, J. Singal

Honors Theses

Aims. We present a custom support vector machine classification package for photometric redshift estimation, including comparisons with other methods. We also explore the efficacy of including galaxy shape information in redshift estimation. Support vector machines, a type of machine learning, utilize optimization theory and supervised learning algorithms to construct predictive models based on the information content of data in a way that can treat different input features symmetrically, which can be a useful estimator of the information contained in additional features beyond photometry, such as those describing the morphology of galaxies.

Methods. The custom support vector machine package we have …

Differential Equations Models Of Pathogen-Induced Single- And Multi-Organ Tissue Damage, Fiona Lynch

Honors Theses

The rise of antibiotic resistance has created a significant burden on healthcare systems around the world. Antibiotic resistance arises from the increased use of antibiotic drugs and antimicrobial agents, which kill susceptible bacterial strains, but have little effect on strains that have a mutation allowing them to survive antibiotic treatment, defined as “resistant” strains. With no non-resistant bacteria to compete for resources, the resistant bacteria thrives in this environment, continuing to reproduce and infect the host with an infection that does not respond to traditional antibiotic treatment.

A number of strategies have been proposed to tackle the problem of antibiotic …

Investigating Medicinally Important Portein-Protein And Protein-Ligand Interactions : A Computational Approach, Cooper Ashley Taylor

Honors Theses

Molecular dynamics (MD) simulations and computational chemistry allow for an atomistic understanding of protein-protein and protein-ligand binding motifs. Through the use of MD, medicinally relevant complexes can be examined in detail unattainable by experimental methods. Within this work, systems pertinent to both Alzheimer’s Disease and HIV-1 are probed and thoroughly sampled to help elucidate potential therapeutic pathways. We used molecular dynamics and free energy estimations to gauge the affinity for the binary and ternary complexes of KLC1, APP and JIP1, three proteins all believed to be involved in the propagation of Alzheimer’s Disease. Two areas of thought exist suggesting that …

A New Almost Difference Set Construction, David Clayton

Honors Theses

This paper considers the appearance of almost difference sets in non-abelian groups. While numerous construction methods for these structures are known in abelian groups, little is known about ADSs in the case where the group elements do not commute. This paper presents a construction method for combining abelian difference sets into nonabelian almost difference sets, while also showing that at least one known almost difference set construction can be generalized to the nonabelian case.

Toward A Scientific Investigation Of Convolutional Neural Networks, Anh Tran

Honors Theses

This thesis does not assume the reader is familiar with artificial neural networks. However, to keep the thesis concise, it assumes the reader is familiar with the standard Machine Learning concepts of training set, validation set, and test set [1]. Their usage is intended to help ensure that the Machine Learning system can generalize its training from input examples used during its training to “similar” kinds of examples never used during its training.

The concept of a Convolutional Neural Network (CNN) is one of the most successful computational concepts today for solving image classification problems. However, CNNs are difficult and …

Study Of The Neutron Detection Efficiency Of The Clas12 Detector, Keegan Sherman

Honors Theses

One of the central physics goals of Jefferson Lab is to understand how quarks and gluons form nuclei. The 12 GeV upgrade is nearing completion and a new detector, CLAS12, is being built in Hall B. One of the approved experiments will measure the magnetic form factor of the neutron (Gn ). To make this measurement, the ratio of electron-neutron (e-n) to electron-proton (e-p) scattering events will be extracted from deuterium in quasi-elastic kinematics. A major source of systematic uncertainty is the neutron detection efficiency (NDE) of CLAS12. To better understand the NDE I used the Monte Carlo …

Quantum Groups And Knot Invariants, Greg A. Hamilton

Honors Theses

Knot theory arguably holds claim to the title of the mathematical discipline with the most unusually diverse applications. A knot can be defined topologically as an embedding of S1 in R3. Naturally, two knots are topologically equivalent if one cannot be smoothly deformed into the other. The question of whether two knots are equivalent is highly non-trivial, and so the question of knot invariants used to distinguish knots has occupied knot theorists for over a century. Knot theory has found application in statistical mechanics [1], symbolic logic and set theory [2], quantum fi theory [3], quantum computing [4], etc. …

Differential Privacy For Growing Databases, Gi Heung (Robin) Kim

Honors Theses

Differential privacy [DMNS06] is a strong definition of database privacy that provides indi- viduals in a database with the guarantee that any particular person’s information has very little effect on the output of any analysis of the overall database. In order for this type of analysis to be practical, it must simultaneously preserve privacy and utility, where utility refers to how well the analysis describes the contents of the database.

An analyst may additionally wish to evaluate how a database’s composition changes over time. Consider a company, for example, that accumulates data from a growing base of customers. This company …

Nonexistence Of Nonquadratic Kerdock Sets In Six Variables, John Clikeman

Honors Theses

Kerdock sets are maximally sized sets of boolean functions such that the sum of any two functions in the set is bent. This paper modifies the methodology of a paper by Phelps (2015) to the problem of finding Kerdock sets in six variables containing non-quadratic elements. Using a computer search, we demonstrate that no Kerdock sets exist containing non-quadratic six- variable bent functions, and that the largest bent set containing such functions has size 8.

Partitioning Groups With Difference Sets, Rebecca Funke

Honors Theses

This thesis explores the use of difference sets to partition algebraic groups. Difference sets are a tool belonging to both group theory and combinatorics that provide symmetric properties that can be map into over mathematical fields such as design theory or coding theory. In my work, I will be taking algebraic groups and partitioning them into a subgroup and multiple McFarland difference sets. This partitioning can then be mapped to an association scheme. This bridge between difference sets and association schemes have important contributions to coding theory.

Synthetic Flexibility Of A Bromopyrrole Ester Intermediate : Toward Novel Biologically Active Compounds, Scott Cameron Yeudall

Honors Theses

Compounds containing the pyrrole ring as a core structural motif continue to show significant biological activity, and both natural product derivatives and novel chemical scaffolds show potential for use as pharmaceuticals in treating a variety of cancers, infections, and inflammation. Given the widespread and important applications of compounds containing this motif, novel, rapid, and selective methods for the synthesis of multifunctional pyrroles is of some importance. Previous work in our group has utilized palladium-mediated Suzuki cross-coupling as a powerful tool for functionalizing activated bromopyrrole esters, generating structural analogues of bioactive natural products. We have also used a similar approach to …

Cameron-Liebler Line Classes And Partial Difference Sets, Uthaipon Tantipongipat

Honors Theses

The work consists of three parts. The first is a study of Cameron-Liebler line classes which receive much attention recently. We studied a new construction of infinite family of Cameron-Liebler line classes presented in the paper by Tao Feng, Koji Momihara, and Qing Xiang (rst introduced in 2014), and summarized our attempts to generalize this construction to discover any new Cameron-Liebler line classes or partial difference sets (PDSs) resulting from the Cameron-Liebler line classes. The second is our approach to finding PDS in non-elementary abelian groups. Our attempt eventually led to the same general construction of PDS presented in John …

An Examination Of The Cmb Large-Angle Suppression, Ellis Herman

Honors Theses

As shown by COBE­DMR and then by the Wilkinson Anisotropy Probe (WMAP), there exists an anomaly in the correlation function of the cosmic microwave background (CMB) radiation, namely that said correlation function is suppressed to zero on large angular scales. This observation conflicts with the prediction made by Lambda­CDM, the standard model of cosmology, indicating either necessary changes to the standard model or that our universe is a rare fluke within LCDM ­ such suppressions are seen in only about 0.3% of universes predicted by LCDM. To differentiate into which of these categories our universe falls, we have attempted to …

Real-Time Translation Of American Sign Language Using Wearable Technology, Jackson Taylor

Honors Theses

The goal of this work is to implement a real-time system using wearable technology for translating American Sign Language (ASL) gestures into audible form. This system could be used to facilitate conversations between individuals who do and do not communicate using ASL. We use as our source of input the Myo armband, an affordable commercially-available wearable technology equipped with on-board accelerometer, gyroscope, and electromyography sensors. We investigate the performance of two different classification algorithms in this context: linear discriminant analysis and k-Nearest Neighbors (k-NN) using various distance metrics. Using the k-NN classifier and windowed dynamic time …

Structure-Function Relationships Affecting The Sensing Mechanism Of Monolayer-Protected Cluster Doped Xerogel Amperometric Glucose Biosensors, Luke T. Dipasquale

Honors Theses

The research conducted in the Leopold Bioanalytical and Nanomaterials Analytical Chemistry Lab prior to the summer of 2013 focused on the synthesis of a functional biosensor equipped with a nanoparticle network embedded in a xerogel film for the detection of glucose. Xerogel-based films featuring embedded glucose oxidase enzyme and doped with alkanethiolate-protected gold NPs, known as monolayer protected clusters (MPCs), exhibit significantly enhanced performance compared to analogous systems without NPs including higher sensitivity, faster response time, and extended linear/dynamic ranges.

The following presented research is a systematic study of the structure-function relationships critical to understanding the sensing mechanism of the …

The Application Of Formyl Group Activation Of Brompyrrole Esters To A Formal Synthesis Of Lycogarubin C, Jon Patteson

Honors Theses

Lycogarubln C is a member of an interesting family of marine natural products, which contains two indole groups appended to a pyrrole scaffold at the 3 and 4 positions. Such compounds are proposed to be biosynthetically related to the important antitumor agent, Staurosporine. Recent work in our lab involving the use of Suzuki cross-coupling reactions of an ortho activated bromoformylpyrrole ester has provided key intermediates for the synthesis of pyrrole natural products and pyrolle-based analogues.

A Computational Investigation Of Halogen Bonding With Halomethanes And Their Group 14 Analogues, William Kretz

Honors Theses

It is known that halogen bonding is supported by so-called sigma holes on halides that interact with bases, but what are the limits of that interaction? How does the interaction depend on the group to which the halogen atom is bonded? To answer these questions, complexes of the form MH3X---Y (where M=C, Si, Ge, Sn, Pb; X= F, Cl, Br, I and Y are Lewis bases) were optimized and their energetics and relative stability were assessed. The Lewis bases range from NH3 to the more complicated pentafluroropyridine (F-py). Calculations were performed entirely at the MP2(full) level of theory, including frequency …

The Effects Of Coal Mining On Health In Appalachia : Global Context And Social Justice Implications, Adrienne Schmidt

Honors Theses

The purpose of this report is to investigate the environmental and health effects of coal mining in the Appalachian region of the United States in the context of global natural resource extraction, explore existing regulation for the reduction of negative environmental health effects of mining in Appalachia, and explore the social justice implications of current mining practices. The research for this report was limited to literature published in English. It was found that there are widespread negative health effects of mining in Appalachia due to environmental toxins, a toxic social environment of limited economic opportunity, and occupational health hazards. The …

Statistical Analysis Of The Variability And Reliability Of Eye-Tracking Test In Measuring Mild Traumatic Brain Injury, Xi He

Honors Theses

Saccadic eye-tracking tests have been advocated as a useful tool to distinguish mTBI patients from healthy people. However, intra-individual variances sometimes interfere with the interpretation of eye-tracking results, especially in experiments when group size is restricted. This study analyzes eye-tracking results of 14 mTBI patients taking the test twice with no medical administration in between. Using more accurate models to fit each individual's result, variables such as asymptote (of the fit func­tions) and hypothetical values for peak velocity, peak acceleration, and duration are derived for variability analysis. We conclude that the asymptotes for peak velocity and peak acceleration are the …

Power Distribution In The European Union, Dayton Steele

Honors Theses

The Treaty of Lisbon, the latest treaty governing law-making in the European Union (EU), was ratified in 2009 and goes fully into effect in 2014. This treaty, with its change to voting procedures in the Council of Ministers, claims to make decision-making in the EU more democratic and more efficient. Since the EU serves as an economic and political entity, we will assess these claims by comparing each member state's GDP and population to its power as modeled using the concept of a power index from the game theory literature. We will utilize the normalized Banzhaf index, the Shapley-Shubik index, …

Difference Sets In Non-Abelian Groups Of Order 256, Taylor Applebaum

Honors Theses

This paper considers the problem of determining which of the 56092 groups of order 256 contain (256; 120; 56; 64) difference sets. John Dillon at the National Security Agency communicated 724 groups which were still open as of August 2012. In this paper, we present a construction method for groups containing a normal subgroup isomorphic to Z4 Z4 Z2 . This construction method was able to produce difference sets in 643 of the 649 unsolved groups with the correct normal subgroup. These constructions elimated approximately 90% of the open cases, leaving 81 remaining unsolved groups.

One-Pot Reactions Of Ethyl Propiolate, Ana Maria Neferu

Honors Theses

Through an efficient one-pot reaction sequence, ethyl propiolate can be transformed into a complex, usefully functionalized bicyclic product. Thioconjugate addition yielding Z-selective enoates has been developed for both aromatic thiols (trialkylamine-catalyzed) and aliphatic thiols (KOt-Bu-catalyzed). The oxidation of the thioenoates thus generated is followed by Li-catalyzed oxidation to sulfones using mCPBA, and Li-catalyzed Diels–Alder addition of cyclopentadiene. These subsequent steps are performed in situ, without any purification of intermediates. The yields obtained using the described synthesis are acceptable for a one-pot three-step sequence. Preliminary conjugate addition results with alcohols and amines as nucleophiles are also presented.

Mapping Of Stochastic Matrices Into Polynomial Form In The Complex Plane, Jordan Emile Cates

Honors Theses

This thesis originated from a specific problem from biology. Namely we need to study probabilistic models that represent molecular interactions that take place inside living cells, such as the number of molecular heat-shock proteins present in a cell. Because of the intrinsic discrete nature of the number of molecules present in cells, the fundamental mathematical models are based on Markov processes. For such processes a transition probability matrix describes the evolution of the state of the cell, whereas the state itself, i.e. the number of molecules present at a specific time, is described by a vector. The components of this …

Rank One Perturbations Of Self-Adjoint Operators, Haoxuan Zheng

Honors Theses

No abstract provided.

Synthesis Of Indole Containing Pyrimidines, Kara Finzel

Honors Theses

No abstract provided.