Physical Sciences and Mathematics Commons^™

On Properties Of Matroid Connectivity, Simon Pfeil

LSU Doctoral Dissertations

Highly connected matroids are consistently useful in the analysis of matroid structure. Round matroids, in particular, were instrumental in the proof of Rota's conjecture. Chapter 2 concerns a class of matroids with similar properties to those of round matroids. We provide many useful characterizations of these matroids, and determine explicitly their regular members. Tutte proved that a 3-connected matroid with every element in a 3-element circuit and a 3-element cocircuit is either a whirl or the cycle matroid of a wheel. This result led to the proof of the 3-connected splitter theorem. More recently, Miller proved that matroids of sufficient …

The Sea Is Rising… But Not Onto The Policy Agenda: A Multiple Streams Approach To Understanding Sea Level Rise Policies, Juita-Elena (Wie) Yusuf, Katharine Neill, Burton St. John Iii, Ivan K. Ash, Kaitrin Mahar

School of Public Service Faculty Publications

There has been little policy effort to address sea level rise in coastal states in the US. It is important to examine, at the state level, how the multitude of different (and changing) actors with different preferences and perspectives contribute to such inertia. This study examines state-level legislative inaction with regards to sea level rise. Using Kingdon's multiple streams framework, we draw a picture of the policy landscape in Virginia as one where the problem of sea level rise is perceived as a low priority, with little consensus on achievable policy solutions, and is politically controversial. We find that policy …

Excluding A Weakly 4-Connected Minor, Kimberly Sevin D'Souza

LSU Doctoral Dissertations

A 3-connected graph $G$ is called weakly 4-connected if min $(|E(G_1)|, |E(G_2)|) \leq 4$ holds for all 3-separations $(G_1,G_2)$ of $G$. A 3-connected graph $G$ is called quasi 4-connected if min $(|V(G_1)|, |V(G_2)|) \leq 4$. We first discuss how to decompose a 3-connected graph into quasi 4-connected components. We will establish a chain theorem which will allow us to easily generate the set of all quasi 4-connected graphs. Finally, we will apply these results to characterizing all graphs which do not contain the Pyramid as a minor, where the Pyramid is the weakly 4-connected graph obtained by performing a $\Delta …

Biomedical Applications Of Thiol-Acrylate Polymers, Leah Alyce Garber

LSU Doctoral Dissertations

The development of biocompatible polymers using thiol-acrylate Michael addition reactions between not only acrylates and thiols but also between amines and acrylates were demonstrated. The synthesis of an in situ tertiary amine catalyst initiates the propagation steps of the polymerization process by subsequently reacting with trimethylolpropane tris (3-mercaptopropionate) (TMPTMP). A few notable characteristics of this reaction are tunable gel times, the capability of reaching high polymer conversion and suitable mechanical strength. With addition of hydroxyapatite to the polymeric phase and foaming, a porous bone composite was produced. Further osteogenisis and in vivo work using the PETA-co-TMPTMP (HA) composite material was …

Towards Structural Determination Of Human Α1-Glycine Receptor Allostery, Rathna Jyothi Veeramachaneni

Electronic Theses and Dissertations

Recent advances in technology have led to the determination of numerous notable structures of membrane proteins. While they provide valuable information about the structure of membrane proteins these studies often provide static images with potentially limited dynamics, and structural determination often requires truncation of flexible regions, and often utilizes bacterial homologs given the need for stable, heterologous overexpression. In order to better understand allostery at a molecular level, state-dependent crosslinking studies coupled with multidimensional mass spectrometry (MS) were conducted on glycine receptor (GlyR) stabilized in different allosteric states. Predominant allosteric states were stabilized using wild type or mutated receptor in …

Properties Of Polynomial Identity Quantized Weyl Algebras, Jesse S. F. Levitt

LSU Doctoral Dissertations

In this work on Polynomial Identity (PI) quantized Weyl algebras we begin with a brief survey of Poisson geometry and quantum cluster algebras, before using these as tools to classify the possible centers of such algebras in two different ways. In doing so we explicitly calculate the formulas of the discriminants of these algebras in terms of a general class of central polynomial subalgebras. From this we can classify all members of this family of algebras free over their centers while proving that their discriminants have the properties of effectiveness and local domination. Applying these results to the family of …

Biomass Gasification For Electricity Generation: An Integrated Approach For Development Of Forest Residue-Based Projects In Rural India, Anand Mishra

LSU Doctoral Dissertations

Biomass gasification is generally regarded as a promising technology for various advanced application in energy production. Biomass is the only carbon-based sustainable option among the renewable energy sources. This study is focused on fostering biomass gasification for electricity generation sector in India. The study addresses four broad aspects of biomass gasification for electricity generation - feedstock properties and gasification technology, policy and regulatory framework governing the sector, financial evaluation of electricity generation from biomass gasification, and feedstock supply. The study is divided in four chapters, each of which addresses one aspect of electricity generation through biomass gasification. Based on literature, …

Probabilistic And Deep Learning Algorithms For The Analysis Of Imagery Data, Saikat Basu

LSU Doctoral Dissertations

Accurate object classification is a challenging problem for various low to high resolution imagery data. This applies to both natural as well as synthetic image datasets. However, each object recognition dataset poses its own distinct set of domain-specific problems. In order to address these issues, we need to devise intelligent learning algorithms which require a deep understanding and careful analysis of the feature space. In this thesis, we introduce three new learning frameworks for the analysis of both airborne images (NAIP dataset) and handwritten digit datasets without and with noise (MNIST and n-MNIST respectively). First, we propose a probabilistic framework …

Spectral Properties Of Photonic Crystals: Bloch Waves And Band Gaps, Robert Paul Viator Jr

LSU Doctoral Dissertations

The author of this dissertation studies the spectral properties of high-contrast photonic crystals, i.e. periodic electromagnetic waveguides made of two materials (a connected phase and included phase) whose electromagnetic material properties are in large contrast. A spectral analysis of 2nd-order divergence-form partial differential operators (with a coupling constant k) is provided. A result of this analysis is a uniformly convergent power series representation of Bloch-wave eigenvalues in terms of the coupling constant k in the high-contrast limit k -> infinity. An explicit radius of convergence for this power series is obtained, and can be written explicitly in terms of the …

Visible Light And Electron Transfer Chemistry For O-Glycosylation And Remote Hydroxylation, Mark Louis Spell

LSU Doctoral Dissertations

This dissertation focuses on the synthesis of dauer pheromone analogs for biological evaluation, the development of visible light promoted O-glycosylation methods and the development of an Ir(ppy)3 catalyzed C-H hydroxylation method. Chapter 1 describes the synthesis of dauer pheromone analogs. C.elegans is a small nematode that enters a dauer stage when encountering unfavorable environmental conditions. The dauer stage is initiated by the nematodes chemosensation of the dauer pheromone caused by the down regulation biochemical pathways TGF-â and IGF-1. These biochemical pathways are also seen in Homo Sapiens and play a role in a number of biological processes. Understanding how these …

Synthesis Of Functional Polypeptides And Development Of New Synthetic Strategies Toward Polypeptides, Jinbao Cao

LSU Doctoral Dissertations

The objective of this work is to develop a new synthetic strategy for synthesizing advanced functional polypeptides or polypeptides in general. Polypeptides are amino acids based polymers with appealing properties for different applications. One of the key challenges in polypeptide research is the synthesis of functional polypeptides under mild conditions. We developed a system based on ring-opening polymerization (ROP) of N-thiocarboxyanhydrosulfides (NTAs) to synthesize polypeptides with wide range of molecular weights under mild conditions. Owing to NTAs’ good stability, our system serves as an excellent alternative to the traditional ROP of N-carboxyanhydrides (NCA). In Chapter 1, the fundamental knowledge and …

A Direct Study Of 20ne(Alpha,P)23na With The Helical Orbit Spectrometer (Helios), Jianping Lai

LSU Doctoral Dissertations

Type Ia Supernovae are thermonuclear explosions that occur on CO white dwarfs in binary systems, completely disrupting the system. While the exact progenitor of these events is unclear, there have been several studies exploring the nucleosynthesis that drives these stellar explosions. These studies have shown that a handful of reactions have a significant effect on Type Ia Supernova nucleosynthesis, specifically 12C(alpha, gamma), 12C+12C, 20Ne(alpha, p), 20Ne(alpha, gamma), and 30Si(p, gamma). While the 20Ne(alpha,p)23Na reaction has been shown to be one of the five most influential reactions, it has not been directly been measured at astrophysically relevant energies. We performed direct …

Dynamic Resonant Scattering Of Near-Monochromatic Fields, Gayan Shanaka Abeynanda

LSU Doctoral Dissertations

Certain universal features of photonic resonant scattering systems are encapsulated in a simple model which is a resonant modification of the famous Lamb Model for free vibrations of a nucleus in an extended medium. We analyze this "resonant Lamb model" to garner information on dynamic resonant scattering of near-monochromatic fields when an extended system is weakly coupled to a resonator. The transmitted field in a resonant scattering process consists of two distinct pathways: an initial pulse (direct transmission) and a tail of slow decay (resonant transmission). The resonant Lamb model incorporates a two-part scatterer attached to an infinite string with …

Minimizing Decoherence In Optical Fiber For Long Distance Quantum Communication, Manish Kumar Gupta

LSU Doctoral Dissertations

In this research work, I have derived analytical models for decoherence of quantum states of light and developed techniques based on Dynamical Decoupling (DD) to preserve the quantum state of polarization qubit and Orbital Angular Momentum (OAM) qudit in single-mode, multi-mode and specialized optical fibers. In subsequent work, I have derived the analytical model for decoherence of an entangled state in an optical fiber to show that such a decoherence causes loss of entanglement. I also showed that such states can be preserved with DD. In Chapter 1, I have introduced the subject of a quantum computer and its relation …

Twisted Reflection Positivity, Mostafa Ahmad Hayajneh

LSU Doctoral Dissertations

Reflection positivity has several applications in both mathematics and physics. For example, reflection positivity induces a duality between group representations. In this thesis, we coin a new definition for a new kind of reflection positivity, namely, twisted reflection positive representation on a vector space. We show that all of the non-compactly causal symmetric spaces give rise to twisted reflection positive representations. We discover examples of twisted reflection positive representations on the sphere and on the Grassmannian manifold which are not unitary, namely, the generalized principle series with the Cosine transform as an intertwining operator. We give a direct proof for …

Tip-Enhanced Laser Ablation Sample Transfer For Mass Spectrometry, Chinthaka Aravinda Seneviratne

LSU Doctoral Dissertations

In this research, atomic force microscope tip-enhanced laser ablation mass spectrometry (AFM TELA-MS), an ambient sub-micrometer scale sampling method for offline MS was developed. AFM TELA was used to transfer molecules from thin films to a suspended silver wire for off-line mass spectrometry using laser desorption ionization (LDI) and matrix-assisted laser desorption ionization (MALDI). An AFM with a 30 nm radius gold-coated silicon tip was used to image the sample and to hold the tip 15 nm from the surface for material removal using a pulsed Nd:YAG laser, which provides output at wavelengths of 532 nm in the visible, 1064 …

Using Mathematical Research Methods To Solve A Problem In Music Theory Instruction, Specifically, The Teaching Of Secondary Dominant Chords, Angela Ulrich

Williams Honors College, Honors Research Projects

The mathematical method for research is used to find a solution to a problem in music theory: understanding and identifying secondary dominant chords. By reviewing and assessing the teaching methods of university professors and theory textbooks, and comparing those findings with student reviews, a new method for teaching the concept is developed. The proposed system incorporates aural, visual, and kinetic exercises to serve every learner. The literature review and sample unit plan are followed by a possible procedure for testing the effectiveness of the new method.

Microstructure And Deformation Mechanism Analysis Of Carbonate Rock Located In An Anticline, Natalie R. Zidd

Williams Honors College, Honors Research Projects

Rock samples were collected from the Tensleep formation in the Seminoe Mountains located in Carbon County, Wyoming. These samples were analyzed to determine the deformation mechanisms operating during small scale displacement faulting. There are three distinct zones included in the sample which includes the undeformed Tensleep, fine grained layers with grain size variation, and porous layers with grain size variation. The microstructures in the fine grained layer were consistent with deformation by crystal plastic deformation mechanisms; whereas, the microstructures in the porous layer were consistent with brittle deformation mechanisms. The microstructures in these rocks are nearly identical to those observed …

The Diameter Of A Rouquier Block, Andrew Mayer

Williams Honors College, Honors Research Projects

For my Honors Research Project, I will be researching special properties of Rouquier blocks that represent the partitions of integers. This problem is motivated by ongoing work in representation theory of the symmetric group. For each integer n and each prime p, there is an object called a Rouquier block; this block can be visualized as a collection of points in a plane, each corresponding to a partition. In this group of points, we say a pair of points is “connected” if certain conditions on the partitions are met. We compare each partition with each other partition, add edges when …

Galvanically Induced/Accelerated Crevice Corrosion, Zachary R. Roland

Williams Honors College, Honors Research Projects

In this thesis, a one dimensional model is developed to investigate the initial stages of corrosion in a fastener assembly consisting of a stainless steel fastener and aluminum 7075 as the plate. Differential equations are formulated and solved to determine the profiles for the potential, the oxygen concentration, and the aluminum ion concentration in the crevice, and also the potential in the bulk electrolyte. This fastener system exhibits galvanic corrosion, pitting corrosion, and crevice corrosion. It is found that the potential decreases monotonically down the length of the crevice, the oxygen concentration decreases exponentially down the length of the crevice, …

Effects Of Invasion Timing In A One-Dimensional Model Of Competing Species With An Infectious Disease, Eliza Jacops

Williams Honors College, Honors Research Projects

In combining two classes of models, we are able to analyze the dynamics of two species that compete for the same resources while fighting a disease. The native species is the disease host and the invasive species enters their habitat and encounters the disease for the first time. Their natural response is to evolve resistance to the disease, and this can assist in their invasion of the natives' habitat. We find conditions for coexistence of the two species, conditions under which an invasion would succeed and wipe out all native individuals, and conditions under which the invasion fails. We explore …

Diversification And Market Neutral Portfolios In S&P500, Alan S. Agnew

Williams Honors College, Honors Research Projects

Our goal is to investigate strategies to deal with the risks associated with holding asset in the stock market. We first deal with risk of holding a specific stock, by the use of diversification. Later, we’ll attempt to deal with the market risk, which is the risk of entire market going up and down. Data used in this project comes from daily adjusted closing price of stocks listed in the S&P500 index ranging from January 3^rd, 2000 to December 31^st, 2015 and the data is processed using statistical software R.

Sections 2 through 4 of this …

Comparison Of Option Price From Black-Scholes Model To Actual Values, Matthew J. Krznaric

Williams Honors College, Honors Research Projects

The Black-Scholes model is a widely used method for pricing European-style options in a straightforward way, through the use of calculations and ideal market assumptions. Due to certain unrealistic ideal conditions exercised by the model, The Black-Scholes technique of pricing options may not be entirely accurate in implementation. This paper addresses these problems due to the model limitations, determining how The Black-Scholes method compares to the results when using the actual data. Using a mix of historical S&P500 data and generated normal distributions, we first calculated and graphed option prices through the Black-Scholes formulas. With the help of R, we …

Illustrating Pit Initiation And Evolution In Aluminum Alloys According To A 3-Dimensional Cellular Automata Based Model, Kathryn Stalker

Williams Honors College, Honors Research Projects

The objective of this work is to develop a cellular automata based model of pitting initiation and subsequent three-dimensional evolution of pit shapes. Here, a cellular automaton is a collection of cells, each of which may be in one of two states, metallic or electrolyte, arranged over a grid. Pit initiation is implemented over a 2-dimensional grid representative of the metal surface while pit propagation is resolved over a 3-dimensional grid which describes a subsection of the bulk metal. The size of the bulk metal will be on the order of millimeters, and a layer of electrolyte, in which chloride …

Identification And Quantification Of Zooplankton In Ne Ohio Drinking Water Reservoirs, Michael Vigorito

Williams Honors College, Honors Research Projects

Cyanobacteria, or blue-green algae, are present in most freshwater ecosystems and are usually harmless. When these algae swell in numbers, they release harmful toxins that can be detrimental to animal and human health, and can destroy ecosystems. For this reason, many scientists and engineers have studied these harmful algal blooms in an attempt to predict, prevent, or control them to keep people and ecosystems safe. One of the variables in this investigation is the presence and quantity of zooplankton. These animals could play an important role in the prevalence of cyanobacteria, but more information is needed to determine what that …

New Facets Of The Balanced Minimal Evolution Polytope, Logan Keefe

Williams Honors College, Honors Research Projects

The balanced minimal evolution (BME) polytope arises from the study of phylogenetic trees in biology. It is a geometric structure which has a variant for each natural number n. The main application of this polytope is that we can use linear programming with it in order to determine the most likely phylogenetic tree for a given genetic data set. In this paper, we explore the geometric and combinatorial structure of the BME polytope. Background information will be covered, highlighting some points from previous research, and a new result on the structure of the BME polytope will be given.

Optimizing Solvent Blends For A Quinary System, Thomas L. Hoy

Williams Honors College, Honors Research Projects

The Department of Polymer Engineering had received a grant from the Keck foundation to produce a process in which hundreds of copolymers can be formulated, synthesized, analyzed and then extrapolated to produce the optimal polymer for the desired material property. This process involves synthesizing approximately fifty polymers in a custom apparatus, none of which necessarily have the same monomer components. This leads to issue of which solvent or blend of solvents to use that would sufficiently dissolve both monomers and the resulting copolymer. If the monomers are not completely dissolved, a homogenous reaction will be impossible and if the copolymer …

Fine-Scale Change Detection Using Unmanned Aircraft Systems (Uas) To Inform Reproductive Biology In Nesting Waterbirds, Sharon Dulava

Cal Poly Humboldt theses and projects

Aerial photographic surveys from manned aircraft are commonly used to estimate the size of bird breeding colonies but are rarely used to evaluate reproductive success. Recent technological advances have spurred interest in the use of unmanned aircraft systems (UAS) for monitoring wildlife. The ability to repeatedly sample and collect imagery at fine-scale spatial and temporal resolutions while minimizing disturbance and safety risks make UAS particularly appealing for monitoring colonial nesting waterbirds. In addition, advances in photogrammetric and GIS software have allowed for more streamlined data processing and analysis. Using UAS imagery collected at Anaho Island National Wildlife Refuge during the …

Simulation Of Nuclear Fusion Using A One Dimensional Particle In Cell Method, Steven T. Margell

Cal Poly Humboldt theses and projects

In this thesis several novel techniques are developed to simulate fusion events in an isotropic, electrostatic three-dimensional Deuterium-Tritium plasma. These techniques allow us to accurately predict three-dimensional collision events with a one-dimensional model while simultaneously reducing compute time via a nearest neighbor algorithm. Furthermore, a fusion model based on first principles is developed that yields an average fusion reactivity which correlates well with empirical results.

Price Signaling In A Two-Market Duopoly, Matthew Hughes

Williams Honors College, Honors Research Projects

Within any industry, firms typically produce related products over multiple subsequent periods in an attempt to build consumer loyalty and achieve continued sales. Apple releases new iPhones and car companies produce new models every year, relying on consumers believing each new product is of high quality. Firms rely on the spillover effects from previous markets, where firms are able to more easily demonstrate their product's quality to the consumers before purchase. The goal is to find a range of prices which allows the high quality firm to distinguish its type to consumers via the price pH and if spillover effects …