Physical Sciences and Mathematics Commons^™

Towards Constructing Vertex Algebroids, Nicholas J. Klecki

Theses and Dissertations

The notion of vertex algebroids were introduced in the late 1990's as a crucial tool for the study of chiral differential operators and chiral de Rham complex. Vertex algebroids play vital role in the study of N-graded vertex algebra. Also, they have deep connection with representation theory of Leibniz algebras. However, the classification of irreducible modules of vertex algebroids is not completed.

The aim of this thesis is to investigate the possibility of using the simple Lie algebra G_2 and its irreducible modules to construct vertex A-algebroids B that contain G_2 as their Levi factor. Under very mild and natural …

Lie Groups And Euler-Bernoulli Beam Equation, Medeu Amangeldi

Theses and Dissertations

Lie groups approach in differential equations was a breakthrough subject in the late nineteenth century. Sophus Lie, a Norwegian mathematician, introduced the systematic approach to study the solutions of differential equations. The main goal of this thesis is to study, using Lie's approach, the Euler-Bernoulli beam equation subject to swelling force, the fourth-order nonlinear differential equation used to describe the beam deflection under the swelling force. In particular, we will classify the symmetry groups of this equation, obtain several reductions, and demonstrate both analytical and numerical solutions.

Embedding Factorizations, Anna Johnsen

Theses and Dissertations

Let $V$ be a set of $n$ vertices for some $n\in\mathbb{N}$ and let $E$ be a collection of $h$-subsets of $V$. Then $\mathscr G = (V,E)$ is an $h$-unifrom hypergraph and we refer to $V$ as its vertex set and to $E$ as its edge set. We say that $\mathscr G$ is complete and denote it by $K_n^h$ if every $h$-subset of $V$ is contained in $E$. If every edge in $E$ is repeated $\lambda$ times, we say $G$ is $\lambda$-fold. Specifically, $\lambda K_n^h$ is the complete $\lambda$-fold $n$-vertex $h$-uniform hypergraph with an edge set containing $\lambda$ copies of every …

A Study Of The Efficacy Of Machine Learning For Diagnosing Obstructive Coronary Artery Disease In Non-Diabetic Patients, Demond Larae Handley

Theses and Dissertations

According to the Centers for Disease Control and Prevention, about 18.2 million adults age 20 and older have Coronary Artery Disease in the United States. Early diagnosis is therefore of crucial importance to help prevent debilitating consequences, and principally death for many patients. In this study we use data containing gene expression values from peripheral blood samples in 198 non-diabetic patients, with the goal of developing an age and sex gene expression model for diagnosis of Coronary Artery Disease. We employ machine learning methods to obtain a classification based on genetic information, age and sex. Our implementation uses feed forward …

Reliability Improvement On Feasibility Study For Selection Of Infrastructure Projects Using Data Mining And Machine Learning, Xi Hu

Theses and Dissertations

With the progressive development of infrastructure construction, conventional analytical methods such as correlation index, quantifying factors, and peer review are no longer satisfactory in support for decision-making of implementing an infrastructure project in the age of big data. This study proposes using a mathematical model named Fuzzy-Neural Comprehensive Evaluation Model (FNCEM) to improve the reliability of the feasibility study of infrastructure projects by using data mining and machine learning. Specifically, the data collection on time-series data, including traffic videos (278 Gigabytes) and historical weather data, uses transportation cameras and online searching, respectively. Meanwhile, the researcher sent out a questionnaire for …

Lattice-Gas Cellular Automata In Modeling Biological Pattern Formation, Gizem Yuce

Theses and Dissertations

There are several phenomena present in the physical world which can be defined or predicted by specific models. Cellular automata are basic mathematical models for characterization of natural systems by generating simple components and their local interactions. These models are specified on simple updating rules yet demonstrate complex behavior of physical phenomena. Besides this, lattice-gas cellular automata models go one step further and differ from cellular automata by having split updating rule into two parts as collision and propagation. In this study, the goal is to analyze hexagonal lattice-gas cellular automata with single cell type by using agent-based modeling and …

Clustering Biological Data With Self-Adjusting High-Dimensional Sieve, Josselyn Gonzalez

Theses and Dissertations

Data classification as a preprocessing technique is a crucial step in the analysis and understanding of numerical data. Cluster analysis, in particular, provides insight into the inherent patterns found in data which makes the interpretation of any follow-up analyses more meaningful. A clustering algorithm groups together data points according to a predefined similarity criterion. This allows the data set to be broken up into segments which, in turn, gives way for a more targeted statistical analysis. Cluster analysis has applications in numerous fields of study and, as a result, countless algorithms have been developed. However, the quantity of options makes …

Mathieu-Zhao Subspaces Of Vertex Algebras, Matthew Speck

Theses and Dissertations

A Mathieu-Zhao subspace is a generalization of an ideal of an associative ring-algebra, A, first formalized in 2010. A vertex algebra is an algebraic structure first developed in conjunction with string theory in the 1960s and later axiomatized by mathematicians in the 1990s. We formally introduce the definition of a Mathieu-Zhao subspace, M, of a vertex algebra, V. Building on natural connections to associative algebras, we classify an infinite set of non-trivial, non-ideal Mathieu-Zhao subspaces for simple and general vertex algebras by group action eigenspace decomposition. Finally, we state the locally nilpotent epsilon-derivation (LNED) conjecture for vertex algebras.

Modeling The Influence Of El Niño On Parasite Transmission In Sand Crab Populations And Seabird Abundance Along The Californian Coast, Aboubacar Dio Seck

Theses and Dissertations

Pacific mole crabs (Emerita analoga) are one of the most important and abundant

invertebrates in sandy beach environments. Consequently, they are a common food source

for seabirds and sea otters. Since the mole crab serves as the primary intermediate host for

acanthocephalan parasites, they have been linked to a number of mortality events. It is

currently estimated that 13-16% of deaths in the threatened California sea otter population

have been caused by infection. In addition, unusually high loads of acanthocephalan

parasites have been linked to episodic deaths of thousands of surf scoters. Studies suggest

that acanthocephalan development and transmission may …

On The Dynamics Of Boolean Gene Regulatory Networks With Stochasticity, Yuezhe Li

Theses and Dissertations

Genes are responsible for producing proteins that are essential to the construction of complex biological systems. The mechanisms by which this production is regulated have long been the center of wide spread research efforts. Deterministic Boolean gene regulatory models have been a particularly effective avenue of research in this field. However these models fall short of accounting for variations in the gene functionality due to the uncertain internal or external environmental conditions. One of the recent attempts to overcome this weakness is by (Murrugarra, 2012), in which a probabilistic component is introduced as the fixed activation/degradation propensities at the cellular …

P_4-Decomposability In Regular Graphs And Multigraphs, David Joshua Mendell

Theses and Dissertations

The main objective of this thesis is to review and expand the study of graph decomposability. An H-decomposition of a graph G=(V,E) is a partitioning of the edge set, $E$, into edge-disjoint isomorphic copies of a subgraph H. In particular we focus on the decompositions of graphs into paths. We prove that a 2,4 mutligraph with maximum multiplicity 2 admits a C_2,C_3-free Euler tour (and thus, a decomposition into paths of length 3 if it has size a multiple of 3) if and only if it avoids a set of 15 forbidden structures. We also prove that …

Identification Of Transcriptionally Quiescent Regions In The Neurospora Crassa Genome, Katie Marie Groskreutz

Theses and Dissertations

Sexual reproduction and genetic exchange via meiosis are important and highly conserved processes in many living organisms. Occasionally, complications occur during meiosis that can result in chromosome abnormalities. In humans, improper chromosome development can cause life altering disorders such as Down Syndrome, Edwards Syndrome, and Patau Syndrome. Unfortunately, despite its importance, gaps remain in our knowledge of how this process works. For instance, little is known about how homolog identification occurs and what proteins identify matching chromosomes during pairing. This fundamental process occurs early during meiosis and ensures proper development of gametes.

Understanding the proteins involved during homolog pairing may …

Examining Middle School Students' Statistical Thinking While Working In A Technological Environment, Melissa Arnold Scranton

Theses and Dissertations

Examining Middle School Students' Statistical Thinking

While Working in a Technological Environment

Melissa Arnold Scranton

The purpose of this study was to gain a better understanding of how students think in a technological environment. This was accomplished by exploring the differences in the thinking of students while they worked in a technological environment and comparing this to their work in a paper and pencil environment. The software program TinkerPlots: Dynamic Data Exploration (Konold & Miller, 2005), a construction tool that middle school students use for data analysis was the technological environment. In both environments, types of critical, creative, and statistical …