Physical Sciences and Mathematics Commons^™

Emergence And Complexity In Music, Zoe Tucker

HMC Senior Theses

How can we apply mathematical notions of complexity and emergence to music, and how can these mathematical ideas then inspire new musical works? Using Steve Reich's Clapping Music as a starting point, we look for emergent patterns in music by considering cases where a piece's complexity is significantly different from the total complexity of each of the individual parts. Definitions of complexity inspired by information theory, data compression, and musical practice are considered. We also consider the number of distinct musical pieces that could be composed in the same manner as Clapping Music. Finally, we present a new musical …

Classifying The Jacobian Groups Of Adinkras, Aaron R. Bagheri

HMC Senior Theses

Supersymmetry is a theoretical model of particle physics that posits a symmetry between bosons and fermions. Supersymmetry proposes the existence of particles that we have not yet observed and through them, offers a more unified view of the universe. In the same way Feynman Diagrams represent Feynman Integrals describing subatomic particle behaviour, supersymmetry algebras can be represented by graphs called adinkras. In addition to being motivated by physics, these graphs are highly structured and mathematically interesting. No one has looked at the Jacobians of these graphs before, so we attempt to characterize them in this thesis. We compute Jacobians through …

Sudoku Variants On The Torus, Kira A. Wyld

HMC Senior Theses

This paper examines the mathematical properties of Sudoku puzzles defined on a Torus. We seek to answer the questions for these variants that have been explored for the traditional Sudoku. We do this process with two such embeddings. The end result of this paper is a deeper mathematical understanding of logic puzzles of this type, as well as a fun new puzzle which could be played.

Tropical Derivation Of Cohomology Ring Of Heavy/Light Hassett Spaces, Shiyue Li

HMC Senior Theses

The cohomology of moduli spaces of curves has been extensively studied in classical algebraic geometry. The emergent field of tropical geometry gives new views and combinatorial tools for treating these classical problems. In particular, we study the cohomology of heavy/light Hassett spaces, moduli spaces of heavy/light weighted stable curves, denoted as $\calm_{g, w}$ for a particular genus $g$ and a weight vector $w \in (0, 1]^n$ using tropical geometry. We survey and build on the work of \citet{Cavalieri2014}, which proved that tropical compactification is a \textit{wonderful} compactification of the complement of hyperplane arrangement for these heavy/light Hassett spaces. For $g …

Pattern Recognition In Stock Data, Kathryn Dover

HMC Senior Theses

Finding patterns in high dimensional data can be difficult because it cannot be easily visualized. There are many different machine learning methods to fit data in order to predict and classify future data but there is typically a large expense on having the machine learn the fit for a certain part of a dataset. We propose a geometric way of defining different patterns in data that is invariant under size and rotation. Using a Gaussian Process, we find that pattern within stock datasets and make predictions from it.

Toric Ideals, Polytopes, And Convex Neural Codes, Caitlin Lienkaemper

HMC Senior Theses

How does the brain encode the spatial structure of the external world?

A partial answer comes through place cells, hippocampal neurons which

become associated to approximately convex regions of the world known

as their place fields. When an organism is in the place field of some place

cell, that cell will fire at an increased rate. A neural code describes the set

of firing patterns observed in a set of neurons in terms of which subsets

fire together and which do not. If the neurons the code describes are place

cells, then the neural code gives some information about the …

Maximal Lelm Distinguishability Of Qubit And Qutrit Bell States Using Projective And Non-Projective Measurements, Nathaniel Leslie

HMC Senior Theses

Many quantum information tasks require measurements to distinguish between different quantum-mechanically entangled states (Bell states) of a particle pair. In practice, measurements are often limited to linear evolution and local measurement (LELM) of the particles. We investigate LELM distinguishability of the Bell states of two qubits (two-state particles) and qutrits (three-state particles), via standard projective measurement and via generalized measurement, which allows detection channels beyond the number of orthogonal single-particle states. Projective LELM can only distinguish 3 of 4 qubit Bell states; we show that generalized measurement does no better. We show that projective LELM can distinguish only 3 of …

Combinatorial Polynomial Hirsch Conjecture, Sam Miller

HMC Senior Theses

The Hirsch Conjecture states that for a d-dimensional polytope with n facets, the diameter of the graph of the polytope is at most n-d. This conjecture was disproven in 2010 by Francisco Santos Leal. However, a polynomial bound in n and d on the diameter of a polytope may still exist. Finding a polynomial bound would provide a worst-case scenario runtime for the Simplex Method of Linear Programming. However working only with polytopes in higher dimensions can prove challenging, so other approaches are welcome. There are many equivalent formulations of the Hirsch Conjecture, one of which is the …

Machine Learning On Statistical Manifold, Bo Zhang

HMC Senior Theses

This senior thesis project explores and generalizes some fundamental machine learning algorithms from the Euclidean space to the statistical manifold, an abstract space in which each point is a probability distribution. In this thesis, we adapt the optimal separating hyperplane, the k-means clustering method, and the hierarchical clustering method for classifying and clustering probability distributions. In these modifications, we use the statistical distances as a measure of the dissimilarity between objects. We describe a situation where the clustering of probability distributions is needed and useful. We present many interesting and promising empirical clustering results, which demonstrate the statistical-distance-based clustering algorithms …

Incorporating The Centers For Disease Control And Prevention Into Vaccine Pricing Models, Dina Sinclair

HMC Senior Theses

The American vaccine pricing market has many actors, making it a complex system to model. Because of this, previous papers have chosen to model only vaccine manufacturers while leaving out the government. However, the government is also an important actor in the market, since it buys over half of vaccines produced. In this work, we aim to introduce the government into vaccine pricing models to better recommend pricing strategies to the Centers for Disease Control and Prevention.

Quantum Foundations With Astronomical Photons, Calvin Leung

HMC Senior Theses

Bell's inequalities impose an upper limit on correlations between measurements of two-photon states under the assumption that the photons play by a set of local rules rather than by quantum mechanics. Quantum theory and decades of experiments both violate this limit.

Recent theoretical work in quantum foundations has demonstrated that a local realist model can explain the non-local correlations observed in experimental tests of Bell's inequality if the underlying probability distribution of the local hidden variable depends on the choice of measurement basis, or ``setting choice''. By using setting choices determined by astrophysical events in the distant past, it is …

Shallow Shear-Wave Seismic Analysis Of Point Bar Deposits Of False River, Louisiana, Martial James Morrison

LSU Master's Theses

Current point-bar complex models do not include subsurface unit bars as a normal feature. This study provides evidence for a potential buried unit bar amongst point-bar sediments of the large-scale, modern-day False River point-bar complex of the Mississippi River. We collect, process and interpret a two-dimensional, 150-m-long CMP seismic reflection profile that cuts perpendicularly across a major discontinuity surface in the False River point bar complex. The seismic source consists of a ground recoil device that fires a shotgun shell horizontally, producing shear waves. Multiple field experiments demonstrated which type of source and receiver provided the least amount of noise, …

Analyzing User Comments On Youtube Coding Tutorial Videos, Elizabeth Heidi Poche

LSU Master's Theses

Video coding tutorials enable expert and novice programmers to visually observe real developers write, debug, and execute code. Previous research in this domain has focused on helping programmers find relevant content in coding tutorial videos as well as understanding the motivation and needs of content creators. In this thesis, we focus on the link connecting programmers creating coding videos with their audience. More specifically, we analyze user comments on YouTube coding tutorial videos. Our main objective is to help content creators to effectively understand the needs and concerns of their viewers, thus respond faster to these concerns and deliver higher-quality …

Interactive Web-Based Visualization Of Atomic Position-Time Series Data, Simron Thapa

LSU Master's Theses

Extracting and interpreting the information contained in large sets of time-varying three dimensional positional data for the constituent atoms of simulated material system is a challenging task. This thesis work reports our initial implementation of a web-based visualization system and its use-case study. The system allows the users to perform the desired visualization task on a web browser for the position-time series data extracted from the local or remote hosts. It involves a pre-processing step for data reduction, which involves skipping uninteresting parts of the data uniformly (at full atomic configuration level) or non-uniformly (at atomic species level or individual …

Microseismic Event Characteristics Associated With The Spatial And Temporal Stages Of Hydraulic Fracture Growth In Laboratory Experiments, Abigail Arielle Maxwell

LSU Master's Theses

There are uncertainties in the exact mechanisms that occur during hydraulic fracture growth and the interactions of hydraulic fractures with pre-existing fractures. In some cases fracture growth is seen to be purely tensile and in others a combination of tensile and shear mechanisms. In order to develop a seismic model to explain fracture propagation, there is a need for a complete classification of the microseismic events occurring during fracturing using waveform characteristics such as frequency, duration and magnitude. This classification would allow for more accurate prediction of the behavior of the hydraulic fracture from its initiation to when it intersects …

The Effectiveness Of Isco Injection Methods For Remediation Of Groundwater, Matthew Ryan Vidrine

LSU Master's Theses

In-Situ Chemical Oxidation (ISCO) injections were performed at Petro Stopping Centers # 10 (Petro) in December 2013 and June 2015. The methodology was direct injection of a heavy oxidizer, RegenOx®, followed by a time-release oxygen compound, ORC Advanced®, into a plume of gasoline sitting on top of the water in the aquifer in hope that this remediate the aquifer. Both chemicals are registered trademarks of the Regenesis® Company. The levels of contaminates have dropped considerably. However, Petro has not achieved closure criteria according to RECAP standards. The site is classified as a GW-1B, subject to the most stringent of remediation …

Pesticide Concentrations In Water From A Southern Louisiana Marsh Influenced By The Mississippi River, Kara Leigh Callicott

LSU Master's Theses

The pesticides atrazine, chlorothalonil, and fipronil are common surface water contaminants due to their high rates of application and their chemical properties. This study investigates the introduction of contaminants into coastal wetlands via the Bayou Lamoque Mississippi River control structure in Plaquemines Parish, Louisiana. A protocol for environmental sampling using Continuous Low-level Aquatic Monitoring (C.L.A.M.) C-18 disks is described, along with effective solid phase extraction (SPE) and gas chromatography mass spectrometry (GC/MS) methodology for the determination of atrazine, chlorothalonil, and fipronil in surface water. Average concentrations of atrazine and chlorothalonil inside the Bayou Lamoque freshwater diversion structure for the months …

The Anticancer Effects Of The Different Analogs Of Cysteine Deleted Tachyplesin On A549 Lung Cancer Cells, Nathan Riley Hendrickson

Master's Theses and Doctoral Dissertations

It has been previously shown that cysteine-deleted tachyplesin (CDT) and its many analogs display antibacterial effects. However, little has been said about its possible anticancer effects and which analogs serve as the best inhibitors of the growing cancer cells. This research focused on CDT and four of its analogs: All D-CDT, Reverse DCDT, Reverse CDT, and Serine-Control CDT. MTT assays against the A549 adenocarcinoma lung cancer cell line showed All D-CDT to be the most effective analog in preventing cancer cell growth. Hyaluronidase and apoptosis assays were performed to better understand the mechanism by which the All D-CDT is preventing …

Enzymatically Active Microspheres For Self-Propelled Colloidal Engines, Jungeun Park

Dissertations and Theses

Micro- and nano-motors have attracted numerous attentions from various scientific areas due to their potential applications. Most studies on self-propelled colloidal engines have exploited catalytic decomposition of hydrogen peroxide to drive the motor. Since the hydrogen peroxide is caustic, it is not suitable to use in biological applications, encouraging people to develop “greener” fuels. The aim of this research is to study a new transduction mechanism for self-propulsion not tied to hydrogen peroxide, and which can in particular be used with biological molecules as fuels. In this study, we focus on making particles with enzymatic activity which can effectively decompose …

Temporal Variability Of Fluorescent Dissolved Organic Matter At A Brackish, Tidal Marsh-Estuary Interface, Alana B. Menendez

Dissertations and Theses

Marshes are both terrestrial and aqueous, sitting as an intermediate between land and water. Studies over constrained numbers of tidal cycles have demonstrated that these marshes are net exporters of dissolved organic carbon (DOC) to adjoining estuaries, however, there is need for continuous monitoring to better understand the temporal variability of this flux: tidally, seasonally, and during episodic rain events. Through use of a YSI EXO2 sonde, an in situ optical sensor at the interface of the brackish, tidal Kirkpatrick Marsh and Rhode River sub-estuary in Edgewater, Maryland (located on the northwestern shore of the Chesapeake Bay), we were able …

2d Vector Map And Database Design For Indoor Assisted Navigation, Luciano Caraciolo Albuquerque

Dissertations and Theses

In this paper we implemented a 2D Vector Map, map editor and Database design intended to provide an efficient way to convert cad files from indoor environments to a set of vectors representing hallways, doors, exits, elevators, and other entities embedded in a floor plan, and save them in a database for use by other applications, such as assisted navigation for blind people.

A graphical application as developed in C++ to allow the user to input a CAD DXF file, process the file to automatically obtain nodes and edges, and save the nodes and edges to a database for posterior …

Marsh-Exported Dissolved Organic Matter Fate In Estuaries, Laura Ann Logozzo

Dissertations and Theses

Dissolved organic matter (DOM) is a significant driver of estuarine productivity and nutrient cycling. The colored component of DOM, chromophoric dissolved organic matter (CDOM), impacts coastal optical properties, ocean color, and light attenuation. While marshes are largely considered sinks for carbon due to their high productivity and low soil carbon degradation rates, laterally they are sources of carbon as optically and chemically distinct DOM to surrounding aquatic ecosystems; these inputs are often essential in sustaining a net heterotrophic system. However, the photoreactivity and bioavailability of marsh-exported DOM is largely uncategorized, thus making it difficult to quantify its impacts on estuarine …

Synthesis Of Multifunctional Polyacrylates And A Binding Group To Hemoglobin For The Treatment Of Traumatic Brain Injuries, Marina Michaud

Honors College Theses

Hemoglobin based oxygen carriers (HBOCs) hold promise as an effective emergency treatment of severe traumatic brain injuries (TBI). In the latest generation of HBOCs, polynitroxyl-pegylated hemoglobin (PNPH), cell-free hemoglobin is modified with TEMPO and PEG which reduce the toxicities associated with earlier generations of HBOCs. In our efforts to optimize the economic and therapeutic impacts of PNPH’s we have synthesized polydimethylaminoethyl methacrylate (poly-DMAEMA) under controlled living conditions via reverse addition-fragmentation chain transfer (RAFT) polymerization. The poly-DMAEMA was then successfully functionalized via quaternization of its NMe₂ groups using chloroacetate derivatives of the TEMPO and PEG. This process was quantitative and …

Assessment Of Critical Habitats For Recovering The Chesapeake Bay Atlantic Sturgeon Distinct Population Segment, Bob Greenlee, David H. Secor, Greg C. Garman, Matthew Balazak, Eric J. Hilton, Matthew T. Fisher

Reports

The states of Virginia and Maryland along with Virginia Commonwealth University (VCU), Virginia Institute of Marine Science (VIMS) and University of Maryland Center for Environmental Science (UMCES) partnered to assess critical habitat for recovering the Chesapeake Bay Atlantic sturgeon (Acipenser oxyrinchus oxyrinchus) distinct population segment. The primary objectives were to assess reproductive habitat in the James River, nursery habitat in the James and York Rivers and the degree of dependence of those populations to habitat in the Chesapeake Bay.

Isle Of Wight County, Virginia - Shoreline Inventory Report: Methods And Guidelines, Marcia Berman, Karinna Nunez, Tamia Rudnicky, Julie G. Bradshaw, Karen Duhring, Kallie Brown, Jessica Hendricks, David Stanhope, Kory Angstadt, Christine Tombleson, David Weiss, Carl Hershner

Reports

The 2017 Inventory for the Isle of Wight County was generated using on-screen, digitizing techniques in ArcGIS® -ArcMap v10.4.1while viewing conditions observed in Bing high resolution oblique imagery, Google Earth, and2013imagery from the Virginia Base Mapping Program (VBMP). Four GIS shapefiles are developed. The first describes land use and bank conditions (IsleofWight_lubc_2017). The second portrays the presence of beaches (IsleofWight_beaches_2017). The third reports shoreline structures that are described as arcs or lines(e.g. riprap)(IsleofWight_sstru_2017). The final shapefile includes all structures that are represented as points(e.g. piers)(IsleofWight_astru_2017).The metadata file accompanies the shapefiles and defines attribute accuracy, data development, and any use restrictions …

On The Equivalence Between Bayesian And Frequentist Nonparametric Hypothesis Testing, Qiuchen Hai

Dissertations, Master's Theses and Master's Reports

Testing of hypotheses about the population parameter is one of the most fundamental tasks in the empirical sciences and is often conducted by using parametric tests (e.g., the t-test and F-test), in which they assume that the samples are from populations that are normally distributed. When the normality assumption is violated, nonparametric tests are employed as alternatives for making statistical inference. In recent years, the Bayesian versions of parametric tests have been well studied in the literature, whereas in contrast, the Bayesian versions of nonparametric tests are quite scant (for exception, Yuan and Johnson (2008) ) in the literature, mainly …

Musical Exercise For People With Visual Impairments, Ridwan Ahmed Khan

Dissertations, Master's Theses and Master's Reports

However, it is hard specifically for people with visual impairments to do exercise without proper guidance. They have accessibility issues and thus, without others ’ help, they cannot be sure if they are doing exercise in a consistent form. To address this problem, I have developed a Musical Exercise platform for people with visual impairments . With the help of audio feedback of Musical Exercise, people with visual impairments can perform exercises in a good form consistently. To assess usability of the system and compare different audio profiles of the system, I designed six different con ditions, including blindfolded or …

Quantum Inspired Symmetries In Laser Engineering, Mohammad Hosain Teimourpour

Dissertations, Master's Theses and Master's Reports

In this thesis, quantum inspired symmetries including Parity-Time (PT) symmetry and Supersymmetry (SUSY) have been studied in the context of non-Hermitian engineered laser systems. This thesis starts with a short review of semiconductor lasers theory in second chapter, followed by an introduction to quantum inspired symmetries: PT symmetry and SUSY in optics and photonics in chapter three.

In chapter four, we have studied the robustness and mode selectivity in PT symmetric lasers. We investigate two important aspects of PT symmetric photonic molecule lasers, namely the robustness of their single longitudinal mode operation against instabilities triggered by spectral hole burning effects, …

Using Lidar To Map The Geology And Morphology Of Alluvial Fans: Salton Sea Area, California, Eric Alexander Macleod

Dissertations, Master's Theses and Master's Reports

The main result of this study has been to show that detailed maps of the geology and morphology of alluvial fans can be generated from high spatial resolution (1-meter) DEM’s (Digital Elevation Models) obtained from LiDAR (Light Detection and Ranging) data. DEMs with spatial resolutions of 1-meter, 10-meters and 30-meters were all examined but it was determined that only the 1-meter LiDAR data had sufficient spatial resolution to produce satisfactory maps of the geology and morphology. A case study on an alluvial fan in the Santa Rosa mountains northeast of the Salton Sea (California) showed that 1-meter spatial resolution LiDAR …

Investigating The Utility Of Rapid Assessment Process For Environmental Development Work Of Peace Corps Master’S International Students, Mariah Maggio

Dissertations, Master's Theses and Master's Reports

Peace Corps Master’s International (PCMI) students engage in international development when they assume the role of Volunteer and graduate researcher. Michigan Technological University had the largest PCMI program in the country, with many Volunteer assignments involving environmental problem solving opportunities. Unfortunately some PCMI students have experienced “failed projects,” something not un-common to international development approaches. This research design supports institutional interdisciplinary efforts aimed at preparing PCMI students to engage in productive community development that avoids historic pitfalls of international development efforts. In order to contribute to this effort, the Rapid Assessment Process (RAP) approach was identified as a potential tool …