Physical Sciences and Mathematics Commons^™

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 …