## ASU Electronic Theses and Dissertations

This collection includes most of the ASU Theses and Dissertations from 2011 to present. ASU Theses and Dissertations are available in downloadable PDF format; however, a small percentage of items are under embargo. Information about the dissertations/theses includes degree information, committee members, an abstract, supporting data or media.

In addition to the electronic theses found in the ASU Digital Repository, ASU Theses and Dissertations can be found in the ASU Library Catalog.

Dissertations and Theses granted by Arizona State University are archived and made available through a joint effort of the ASU Graduate College and the ASU Libraries. For more information or questions about this collection contact or visit the Digital Repository ETD Library Guide or contact the ASU Graduate College at gradformat@asu.edu.

- 80 Arizona State University
- 17 Fishel, Susanna
- 14 Czygrinow, Andrzej
- 9 Jones, John
- 9 Spielberg, John
- 8 Bremner, Andrew
- 8 Childress, Nancy
- more
- 7 Colbourn, Charles
- 7 Hurlbert, Glenn
- 7 Quigg, John
- 5 Castillo-Chavez, Carlos
- 5 Kierstead, Henry
- 4 Kaliszewski, Steven
- 4 Kang, Yun
- 4 Kawski, Matthias
- 4 Kierstead, Henry A
- 4 Kuang, Yang
- 4 Paupert, Julien
- 4 Smith, Hal
- 4 Tang, Wenbo
- 4 Zambo, Ronald
- 3 Barcelo, Helene
- 3 Jones, Donald
- 3 Kotschwar, Brett
- 3 Middleton, James
- 3 Platte, Rodrigo
- 3 Sloane, Finbarr
- 3 Spielberg, Jack
- 2 Armbruster, Dieter
- 2 Baer, Steven
- 2 Battey, Daniel
- 2 Berman, Spring
- 2 Cochran, Douglas
- 2 Fainekos, Georgios
- 2 Flores, Alfinio
- 2 Gelb, Anne
- 2 Heck, Thomas
- 2 Herrmann, Marcus
- 2 Hurlbert, Glenn H
- 2 Jackiewicz, Zdzislaw
- 2 Kadell, Kevin W. J.
- 2 Kao, Ming-Hung
- 2 Kostelich, Eric
- 2 Lanchier, Nicolas
- 2 Mahalov, Alex
- 2 Middleton, James A
- 2 Milner, Fabio
- 2 Mubayi, Anuj
- 2 Reiser, Mark
- 2 Sen, Arunabha
- 2 Suslov, Sergei
- 2 Suslov, Sergei K
- 2 Taylor, Thomas
- 2 Thieme, Horst
- 2 Turaga, Pavan
- 2 Welfert, Bruno
- 2 Yang, Yezhou
- 1 AL-SULEIMAN, SULTAN
- 1 Abram, Christopher Robert
- 1 Aen, Arunabha
- 1 Alanazi, Khalaf Matar
- 1 Aldaco Lopez, Jesus
- 1 Anirudh, Rushil
- 1 Armbruster, Hans
- 1 Artemiadis, Panagiotis
- 1 Artemiadis, Panagiotis K.
- 1 Bacal, Emily Beth
- 1 Balasooriya, Janaka
- 1 Balasubramanian, Hari J
- 1 Balinski, Michel
- 1 Baral, Chitta
- 1 Barley, Kamal Kevin
- 1 Bazzi, Rida
- 1 Bell, Stephanie
- 1 Berliner, David
- 1 Berman, Spring M
- 1 Berman, Spring M.
- 1 Bland, Adam
- 1 Blumenfeld-Jones, Donald
- 1 Boggess, Albert
- 1 Bryan, Harvey J
- 1 Buss, Ray
- 1 Buss, Ray R
- 1 Byerley, Cameron O'Neill
- 1 Calhoun, Ronald
- 1 Camacho, Erika T.
- 1 Candan, Kasim
- 1 Caplan, Michael R
- 1 Carlson, Marilyn
- 1 Carlson, Marilyn P
- 1 Carrillo, Benjamin
- 1 Castillo_Chavez, Carlos
- 1 Caterino, Linda
- 1 Cavanagh, Mary C.
- 1 Chatha, Karamvir
- 1 Childress, Nancy E
- 1 Colbourn, Charles J.
- 1 Connor, Carol M.
- 1 Cruz-Aponte, Maytee
- 1 Cueva, Darren Luis

- 80 English

- 80 Public

- Mathematics
- 9 Computer science
- 9 Mathematics education
- 8 Applied mathematics
- 5 Statistics
- 4 Electrical engineering
- 4 Mechanical engineering
- more
- 3 Biology
- 3 Computer Science
- 3 Education
- 3 Teacher education
- 3 Theoretical mathematics
- 2 C*-algebras
- 2 Elementary education
- 2 Industrial engineering
- 2 Mathematics Education
- 2 Maximal Chains
- 2 Optimization
- 2 Physics
- 2 Polynomial optimization
- 2 Secondary education
- 2 Tamari Lattices
- 1 $\lambda$-invariant
- 1 2
- 1 4-hour block
- 1 AH1N1
- 1 Activated Carbon adsorption
- 1 Adsorption
- 1 Aerospace engineering
- 1 African American students
- 1 African American studies
- 1 Algebra
- 1 Algebraic reasoning
- 1 Anthroponotic Visceral Leishmaniasis
- 1 Applied Mathematics
- 1 Atmospheric sciences
- 1 Autonomous Systems
- 1 B-Splines
- 1 Battery Technologies
- 1 Bias Estimation
- 1 Bioinformatics
- 1 Biomedical engineering
- 1 Biophysics
- 1 Biostatistics
- 1 Blowup
- 1 Borodin-Kostochka
- 1 Boundary Coverage
- 1 Brooks
- 1 Butane adsorption
- 1 C*-correspondences
- 1 CGI
- 1 CHC theory
- 1 Cambrian Lattices
- 1 Catalan lattice
- 1 Chemotaxis
- 1 Circular arc graph
- 1 Cognitively Guided Instruction
- 1 Collective Transport
- 1 College
- 1 Combinatorics
- 1 Common Core
- 1 Communication Graph
- 1 Computational Fluid Dynamics
- 1 Computer engineering
- 1 Concentration Compactness
- 1 Condensed Matter Physics
- 1 Consecutive
- 1 Contact Mechanics
- 1 Content
- 1 Control systems
- 1 Convex optimization
- 1 Crossed products
- 1 Cumulative infectious force
- 1 Curriculum development
- 1 Data Assimilation
- 1 Data Mining
- 1 Degree
- 1 Depression
- 1 Developmental psychology
- 1 Differential-Drive Mobile Robot
- 1 Diophantine equations
- 1 Direct Method
- 1 Directed Graphs
- 1 Discrete Math
- 1 Divergence
- 1 Drosophila melanogaster
- 1 Drug Delivery
- 1 Dynamical System
- 1 Dynamical Systems
- 1 Dynamical systems
- 1 ELL
- 1 Early Childhood
- 1 Early childhood education
- 1 Earth-System Models
- 1 Education policy
- 1 Education, Community College
- 1 Educational Psychology
- 1 Educational Tests and Measurements
- 1 Energy
- 1 Engineering

- Microfluidic Models of Tumor-Stroma Interactions to Study the Interplay of Cancer Cells with their Surrounding Microenvironment
- Ain't She Sweet: A Critical Choreographic Study of Identity & Intersectionality
- Suppositions for Desert Modernism: An Architectural Framework Informed by Climate, Natural Light, and Topography
- Concurrent reduction of trichloroethylene and perchlorate in continuous flow-through soil columns
- Design and Fabrication of Fabric ReinforcedTextile Actuators forSoft Robotic Graspers

Bacteriophage (phage) are viruses that infect bacteria. Typical laboratory experiments show that in a chemostat containing phage and susceptible bacteria species, a mutant bacteria species will evolve. This mutant species is usually resistant to the phage infection and less competitive compared to the susceptible bacteria species. In some experiments, both susceptible and resistant bacteria species, as well as phage, can coexist at an equilibrium for hundreds of hours. The current research is inspired by these observations, and the goal is to establish a mathematical model and explore sufficient and necessary conditions for the coexistence. In this dissertation a model with ...

- Contributors
- Han, Zhun, Smith, Hal, Armbruster, Dieter, et al.
- Created Date
- 2012

This thesis focuses on sequencing questions in a way that provides students with manageable steps to understand some of the fundamental concepts in discrete mathematics. The questions are aimed at younger students (middle and high school aged) with the goal of helping young students, who have likely never seen discrete mathematics, to learn through guided discovery. Chapter 2 is the bulk of this thesis as it provides questions, hints, solutions, as well as a brief discussion of each question. In the discussions following the questions, I have attempted to illustrate some relationships between the current question and previous questions, explain ...

- Contributors
- Bell, Stephanie, Fishel, Susana, Hurlbert, Glenn, et al.
- Created Date
- 2014

Current trends in the Computer Aided Engineering (CAE) involve the integration of legacy mesh-based finite element software with newer solid-modeling kernels or full CAD systems in order to simplify laborious or highly specialized tasks in engineering analysis. In particular, mesh generation is becoming increasingly automated. In addition, emphasis is increasingly placed on full assembly (multi-part) models, which in turn necessitates an automated approach to contact analysis. This task is challenging due to increases in algebraic system size, as well as increases in the number of distorted elements - both of which necessitate manual intervention to maintain accuracy and conserve computer ...

- Contributors
- Grishin, Alexander, Shah, Jami J., Davidson, Joe, et al.
- Created Date
- 2010

Currently, one of the biggest limiting factors for long-term deployment of autonomous systems is the power constraints of a platform. In particular, for aerial robots such as unmanned aerial vehicles (UAVs), the energy resource is the main driver of mission planning and operation definitions, as everything revolved around flight time. The focus of this work is to develop a new method of energy storage and charging for autonomous UAV systems, for use during long-term deployments in a constrained environment. We developed a charging solution that allows pre-equipped UAV system to land on top of designated charging pads and rapidly replenish ...

- Contributors
- Mian, Sami, Panchanathan, Sethuraman, Berman, Spring, et al.
- Created Date
- 2018

Rabies is an infectious viral disease. It is usually fatal if a victim reaches the rabid stage, which starts after the appearance of disease symptoms. The disease virus attacks the central nervous system, and then it migrates from peripheral nerves to the spinal cord and brain. At the time when the rabies virus reaches the brain, the incubation period is over and the symptoms of clinical disease appear on the victim. From the brain, the virus travels via nerves to the salivary glands and saliva. A mathematical model is developed for the spread of rabies in a spatially distributed fox ...

- Contributors
- Alanazi, Khalaf Matar, Thieme, Horst R., Jackiewicz, Zdzislaw, et al.
- Created Date
- 2018

The theme for this work is the development of fast numerical algorithms for sparse optimization as well as their applications in medical imaging and source localization using sensor array processing. Due to the recently proposed theory of Compressive Sensing (CS), the $\ell_1$ minimization problem attracts more attention for its ability to exploit sparsity. Traditional interior point methods encounter difficulties in computation for solving the CS applications. In the first part of this work, a fast algorithm based on the augmented Lagrangian method for solving the large-scale TV-$\ell_1$ regularized inverse problem is proposed. Specifically, by taking advantage of the separable structure, ...

- Contributors
- Shen, Wei, Mittlemann, Hans D, Renaut, Rosemary A, et al.
- Created Date
- 2011

The close relationship between mathematics and music has been well documented in Western cultures since at least the time of the ancient Greeks. While many connections have been made between math and music over the centuries, it seems that many modern researchers have attempted to create interdisciplinary bridges between these disciplines by using mathematical principles to explain several essential aspects of music: harmony, melody, form, and rhythm. Using these established connections, in addition to several of my own, I have created an undergraduate level survey of Western music course for a population of mathematically inclined students. This approach makes music ...

- Contributors
- Cueva, Darren Luis, Norton, Kay, Wells, Christopher, et al.
- Created Date
- 2019

The principle purpose of this research was to compare two definitions and assessments of Mathematics Pedagogical Content Knowledge (PCK) and examine the development of that knowledge among pre-service and current math teachers. Seventy-eight current and future teachers took an online version of the Measures of Knowledge for Teaching (MKT) - Mathematics assessment and nine of them took the Cognitively Activating Instruction in Mathematics (COACTIV) assessment. Participants answered questions that demonstrated their understanding of students' challenges and misconceptions, ability to recognize and utilize multiple representations and methods of presenting content, and understanding of tasks and materials that they may be using ...

- Contributors
- Johnson, Jeffrey Ivan, Middleton, James A, Marsh, Josephine P, et al.
- Created Date
- 2016

Based on poor student performance in past studies, the incoherence present in the teaching of inverse functions, and teachers' own accounts of their struggles to teach this topic, it is apparent that the idea of function inverse deserves a closer look and an improved pedagogical approach. This improvement must enhance students' opportunity to construct a meaning for a function's inverse and, out of that meaning, produce ways to define a function's inverse without memorizing some procedure. This paper presents a proposed instructional sequence that promotes reflective abstraction in order to help students develop a process conception of function and further ...

- Contributors
- Fowler, Bethany Nicole, Carlson, Marilyn, Roh, Kyeong, et al.
- Created Date
- 2014

In this work, I present a Bayesian inference computational framework for the analysis of widefield microscopy data that addresses three challenges: (1) counting and localizing stationary fluorescent molecules; (2) inferring a spatially-dependent effective fluorescence profile that describes the spatially-varying rate at which fluorescent molecules emit subsequently-detected photons (due to different illumination intensities or different local environments); and (3) inferring the camera gain. My general theoretical framework utilizes the Bayesian nonparametric Gaussian and beta-Bernoulli processes with a Markov chain Monte Carlo sampling scheme, which I further specify and implement for Total Internal Reflection Fluorescence (TIRF) microscopy data, benchmarking the method on ...

- Contributors
- Wallgren, Ross Tod, Presse, Steve, Armbruster, Hans, et al.
- Created Date
- 2019

In this thesis, I investigate the C*-algebras and related constructions that arise from combinatorial structures such as directed graphs and their generalizations. I give a complete characterization of the C*-correspondences associated to directed graphs as well as results about obstructions to a similar characterization of these objects for generalizations of directed graphs. Viewing the higher-dimensional analogues of directed graphs through the lens of product systems, I give a rigorous proof that topological k-graphs are essentially product systems over N^k of topological graphs. I introduce a "compactly aligned" condition for such product systems of graphs and show that this coincides with ...

- Contributors
- Patani, Nura, Kaliszewski, Steven, Quigg, John, et al.
- Created Date
- 2011

In 1968, phycologist M.R. Droop published his famous discovery on the functional relationship between growth rate and internal nutrient status of algae in chemostat culture. The simple notion that growth is directly dependent on intracellular nutrient concentration is useful for understanding the dynamics in many ecological systems. The cell quota in particular lends itself to ecological stoichiometry, which is a powerful framework for mathematical ecology. Three models are developed based on the cell quota principal in order to demonstrate its applications beyond chemostat culture. First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to ...

- Contributors
- Packer, Aaron, Kuang, Yang, Nagy, John, et al.
- Created Date
- 2014

In Iwasawa theory, one studies how an arithmetic or geometric object grows as its field of definition varies over certain sequences of number fields. For example, let $F/\mathbb{Q}$ be a finite extension of fields, and let $E:y^2 = x^3 + Ax + B$ with $A,B \in F$ be an elliptic curve. If $F = F_0 \subseteq F_1 \subseteq F_2 \subseteq \cdots F_\infty = \bigcup_{i=0}^\infty F_i$, one may be interested in properties like the ranks and torsion subgroups of the increasing family of curves $E(F_0) \subseteq E(F_1) \subseteq \cdots \subseteq E(F_\infty)$. The main technique for studying this sequence of curves when ...

- Contributors
- Franks, Chase Leroyce, Childress, Nancy, Barcelo, Helene, et al.
- Created Date
- 2011

Every graph can be colored with one more color than its maximum degree. A well-known theorem of Brooks gives the precise conditions under which a graph can be colored with maximum degree colors. It is natural to ask for the required conditions on a graph to color with one less color than the maximum degree; in 1977 Borodin and Kostochka conjectured a solution for graphs with maximum degree at least 9: as long as the graph doesn't contain a maximum-degree-sized clique, it can be colored with one fewer than the maximum degree colors. This study attacks the conjecture on multiple ...

- Contributors
- Rabern, Landon, Kierstead, Henry, Colbourn, Charles, et al.
- Created Date
- 2013

Compressive sensing theory allows to sense and reconstruct signals/images with lower sampling rate than Nyquist rate. Applications in resource constrained environment stand to benefit from this theory, opening up many possibilities for new applications at the same time. The traditional inference pipeline for computer vision sequence reconstructing the image from compressive measurements. However,the reconstruction process is a computationally expensive step that also provides poor results at high compression rate. There have been several successful attempts to perform inference tasks directly on compressive measurements such as activity recognition. In this thesis, I am interested to tackle a more challenging vision problem ...

- Contributors
- Huang, Li-chi, Turaga, Pavan, Yang, Yezhou, et al.
- Created Date
- 2017

This study is a narrative inquiry into teachers' and instructional coaches' experiences of new curriculum policy implementation at the classroom and district levels. This study took place during the initial year of implementation of the third grade Common Core State Standards in Mathematics (CCSSM). Interviews were conducted with individuals directly involved in policy implementation at the classroom level, including several teachers and the school's instructional coach. Observations of the teachers' instruction and professional practice were also conducted. As an embedded researcher, I used this data to create a series of fictionalized narratives of the initial policy implementation experience. My analysis ...

- Contributors
- Frankiewicz, Megan, Powers, Jeanne, Fischman, Gustavo, et al.
- Created Date
- 2015

Modern software and hardware systems are composed of a large number of components. Often different components of a system interact with each other in unforeseen and undesired ways to cause failures. Covering arrays are a useful mathematical tool for testing all possible t-way interactions among the components of a system. The two major issues concerning covering arrays are explicit construction of a covering array, and exact or approximate determination of the covering array number---the minimum size of a covering array. Although these problems have been investigated extensively for the last couple of decades, in this thesis we present significant improvements ...

- Contributors
- Sarkar, Kaushik, Colbourn, Charles J., Czygrinow, Andrzej, et al.
- Created Date
- 2016

The Kuramoto model is an archetypal model for studying synchronization in groups of nonidentical oscillators where oscillators are imbued with their own frequency and coupled with other oscillators though a network of interactions. As the coupling strength increases, there is a bifurcation to complete synchronization where all oscillators move with the same frequency and show a collective rhythm. Kuramoto-like dynamics are considered a relevant model for instabilities of the AC-power grid which operates in synchrony under standard conditions but exhibits, in a state of failure, segmentation of the grid into desynchronized clusters. In this dissertation the minimum coupling strength required ...

- Contributors
- Gilg, Brady, Armbruster, Dieter, Mittelmann, Hans, et al.
- Created Date
- 2018

This dissertation contains three main results. First, a generalization of Ionescu's theorem is proven. Ionescu's theorem describes an unexpected connection between graph C*-algebras and fractal geometry. In this work, this theorem is extended from ordinary directed graphs to higher-rank graphs. Second, a characterization is given of the Cuntz-Pimsner algebra associated to a tensor product of C*-correspondences. This is a generalization of a result by Kumjian about graphs algebras. This second result is applied to several important special cases of Cuntz-Pimsner algebras including topological graph algebras, crossed products by the integers and crossed products by completely positive maps. The result has ...

- Contributors
- Morgan, Adam, Kaliszewski, Steven, Quigg, John, et al.
- Created Date
- 2016

Robotic technology is advancing to the point where it will soon be feasible to deploy massive populations, or swarms, of low-cost autonomous robots to collectively perform tasks over large domains and time scales. Many of these tasks will require the robots to allocate themselves around the boundaries of regions or features of interest and achieve target objectives that derive from their resulting spatial configurations, such as forming a connected communication network or acquiring sensor data around the entire boundary. We refer to this spatial allocation problem as boundary coverage. Possible swarm tasks that will involve boundary coverage include cooperative load ...

- Contributors
- Peruvemba Kumar, Ganesh, Berman, Spring M, Fainekos, Georgios, et al.
- Created Date
- 2016

Mathematical modeling of infectious diseases can help public health officials to make decisions related to the mitigation of epidemic outbreaks. However, over or under estimations of the morbidity of any infectious disease can be problematic. Therefore, public health officials can always make use of better models to study the potential implication of their decisions and strategies prior to their implementation. Previous work focuses on the mechanisms underlying the different epidemic waves observed in Mexico during the novel swine origin influenza H1N1 pandemic of 2009 and showed extensions of classical models in epidemiology by adding temporal variations in different parameters that ...

- Contributors
- Cruz-Aponte, Maytee, Wirkus, Stephen A., Castillo-Chavez, Carlos, et al.
- Created Date
- 2014

The primary focus of this dissertation lies in extremal combinatorics, in particular intersection theorems in finite set theory. A seminal result in the area is the theorem of Erdos, Ko and Rado which finds the upper bound on the size of an intersecting family of subsets of an n-element set and characterizes the structure of families which attain this upper bound. A major portion of this dissertation focuses on a recent generalization of the Erdos--Ko--Rado theorem which considers intersecting families of independent sets in graphs. An intersection theorem is proved for a large class of graphs, namely chordal graphs which ...

- Contributors
- Kamat, Vikram Mahendra, Hurlbert, Glenn, Colbourn, Charles, et al.
- Created Date
- 2011

Higher-rank graphs, or k-graphs, are higher-dimensional analogues of directed graphs, and as with ordinary directed graphs, there are various C*-algebraic objects that can be associated with them. This thesis adopts a functorial approach to study the relationship between k-graphs and their associated C*-algebras. In particular, two functors are given between appropriate categories of higher-rank graphs and the category of C*-algebras, one for Toeplitz algebras and one for Cuntz-Krieger algebras. Additionally, the Cayley graphs of finitely generated groups are used to define a class of k-graphs, and a functor is then given from a category of finitely generated groups to the ...

- Contributors
- Eikenberry, Keenan, Quigg, John, Kaliszewski, Steven, et al.
- Created Date
- 2016

Nonlinear dispersive equations model nonlinear waves in a wide range of physical and mathematics contexts. They reinforce or dissipate effects of linear dispersion and nonlinear interactions, and thus, may be of a focusing or defocusing nature. The nonlinear Schrödinger equation or NLS is an example of such equations. It appears as a model in hydrodynamics, nonlinear optics, quantum condensates, heat pulses in solids and various other nonlinear instability phenomena. In mathematics, one of the interests is to look at the wave interaction: waves propagation with different speeds and/or different directions produces either small perturbations comparable with linear behavior, or creates ...

- Contributors
- Guevara, Cristi Darley, Roudenko, Svetlana, Castillo_Chavez, Carlos, et al.
- Created Date
- 2011

A moving overlapping mesh methodology that achieves spectral accuracy in space and up to second-order accuracy in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The targeted applications are in aerospace and mechanical engineering domains and involve problems in turbomachinery, rotary aircrafts, wind turbines and others. The methodology is built within the dual-session communication framework initially developed for stationary overlapping meshes. The methodology employs semi-implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally-accurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet ...

- Contributors
- Merrill, Brandon Earl, Peet, Yulia, Herrmann, Marcus, et al.
- Created Date
- 2016

In the 1980's, Gromov and Piatetski-Shapiro introduced a technique called "hybridization'' which allowed them to produce non-arithmetic hyperbolic lattices from two non-commensurable arithmetic lattices. It has been asked whether an analogous hybridization technique exists for complex hyperbolic lattices, because certain geometric obstructions make it unclear how to adapt this technique. This thesis explores one possible construction (originally due to Hunt) in depth and uses it to produce arithmetic lattices, non-arithmetic lattices, and thin subgroups in SU(2,1). Dissertation/Thesis

- Contributors
- Wells, Joseph, Paupert, Julien, Kotschwar, Brett, et al.
- Created Date
- 2019

Toward the ambitious long-term goal of a fleet of cooperating Flexible Autonomous Machines operating in an uncertain Environment (FAME), this thesis addresses various control objectives for ground vehicles. There are two main objectives within this thesis, first is the use of visual information to control a Differential-Drive Thunder Tumbler (DDTT) mobile robot and second is the solution to a minimum time optimal control problem for the robot around a racetrack. One method to do the first objective is by using the Position Based Visual Servoing (PBVS) approach in which a camera looks at a target and the position of the ...

- Contributors
- Aldaco Lopez, Jesus, Rodriguez, Armando A., Artemiadis, Panagiotis K., et al.
- Created Date
- 2016

The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet ...

- Contributors
- Lopez, Raquel, Suslov, Sergei K, Radunskaya, Ami, et al.
- Created Date
- 2012

In 2007, Arizona voters passed House Bill (HB) 2064, a law that fundamentally restructured the Structured English Immersion (SEI) program, putting into place a 4-hour English language development (ELD) block for educating English language learners (ELLs). Under this new language policy, ELL students are segregated from their English-speaking peers to receive a minimum of four hours of instruction in discrete language skills with no contextual or native language support. Furthermore, ELD is separate from content-area instruction, meaning that language and mathematics are taught as two separate entities. While educators and researchers have begun to examine the organizational structure of the ...

- Contributors
- Llamas-Flores, Silvia, Middleton, James, Battey, Daniel, et al.
- Created Date
- 2013

In any instructional situation, the instructor's goal is to maximize the learning attained by students. Drawing on the adage, 'we learn best what we have taught,' this action research project was conducted to examine whether students, in fact, learned college algebra material better if they taught it to their peers. The teaching-to-learn process was conducted in the following way. The instructor-researcher met with individual students and taught a college algebra topic to a student who served as the leader of a group of four students. At the next step, the student who originally learned the material from the instructor met ...

- Contributors
- Nicoloff, Stephen James, Buss, Ray R, Zambo, Ronald, et al.
- Created Date
- 2011

Gray codes are perhaps the best known structures for listing sequences of combinatorial objects, such as binary strings. Simply defined as a minimal change listing, Gray codes vary greatly both in structure and in the types of objects that they list. More specific types of Gray codes are universal cycles and overlap sequences. Universal cycles are Gray codes on a set of strings of length n in which the first n-1 letters of one object are the same as the last n-1 letters of its predecessor in the listing. Overlap sequences allow this overlap to vary between 1 and n-1. ...

- Contributors
- Horan, Victoria E., Hurlbert, Glenn H, Czygrinow, Andrzej, et al.
- Created Date
- 2012

Earth-system models describe the interacting components of the climate system and technological systems that affect society, such as communication infrastructures. Data assimilation addresses the challenge of state specification by incorporating system observations into the model estimates. In this research, a particular data assimilation technique called the Local Ensemble Transform Kalman Filter (LETKF) is applied to the ionosphere, which is a domain of practical interest due to its effects on infrastructures that depend on satellite communication and remote sensing. This dissertation consists of three main studies that propose strategies to improve space- weather specification during ionospheric extreme events, but are generally ...

- Contributors
- Durazo, Juan Alberto, Kostelich, Eric J., Mahalov, Alex, et al.
- Created Date
- 2018

The need for improved mathematics education in many of America's schools that serve students from low income households has been extensively documented. This practical action research study, set in a suburban Title I school with a primarily Hispanic, non-native English speaking population, is designed to explore the effects of the progression through a set of problem solving solution strategies on the mathematics problem solving abilities of 2nd grade students. Students worked in class with partners to complete a Cognitively Guided Instruction-style (CGI) mathematics word problem using a dictated solution strategy five days a week for twelve weeks, three or four ...

- Contributors
- Spilde, Amy, Zambo, Ronald, Heck, Thomas, et al.
- Created Date
- 2013

Described is a study investigating the feasibility and predictive value of the Teacher Feedback Coding System, a novel observational measure of teachers’ feedback provided to students in third grade classrooms. This measure assessed individual feedback events across three domains: feedback type, level of specificity and affect of the teacher. Exploratory and confirmatory factor analysis revealed five factors indicating separate types of feedback: positive and negative academic-informative feedback, positive and negative behavioral-informative feedback, and an overall factor representing supportive feedback. Multilevel models revealed direct relations between teachers’ negative academic-informative feedback and students’ spring math achievement, as well as between teachers’ negative ...

- Contributors
- McLean, Leigh, Connor, Carol M., Lemery, Kathryn, et al.
- Created Date
- 2015

Borda's social choice method and Condorcet's social choice method are shown to satisfy different monotonicities and it is shown that it is impossible for any social choice method to satisfy them both. Results of a Monte Carlo simulation are presented which estimate the probability of each of the following social choice methods being manipulable: plurality (first past the post), Borda count, instant runoff, Kemeny-Young, Schulze, and majority Borda. The Kemeny-Young and Schulze methods exhibit the strongest resistance to random manipulability. Two variations of the majority judgment method, with different tie-breaking rules, are compared for continuity. A new variation is proposed ...

- Contributors
- Jennings, Andrew Blake, Hurlbert, Glenn, Barcelo, Helene, et al.
- Created Date
- 2010

Controlled release formulations for local, in vivo drug delivery are of growing interest to device manufacturers, research scientists, and clinicians; however, most research characterizing controlled release formulations occurs in vitro because the spatial and temporal distribution of drug delivery is difficult to measure in vivo. In this work, in vivo magnetic resonance imaging (MRI) of local drug delivery is performed to visualize and quantify the time resolved distribution of MRI contrast agents. I find it is possible to visualize contrast agent distributions in near real time from local delivery vehicles using MRI. Three dimensional T1 maps are processed to produce ...

- Contributors
- Giers, Morgan Boresi, Caplan, Michael R, Massia, Stephen P, et al.
- Created Date
- 2013

The Tamari lattice T(n) was originally defined on bracketings of a set of n+1 objects, with a cover relation based on the associativity rule in one direction. Since then it has been studied in various areas of mathematics including cluster algebras, discrete geometry, algebraic combinatorics, and Catalan theory. Although in several related lattices the number of maximal chains is known, the enumeration of these chains in Tamari lattices is still an open problem. This dissertation defines a partially-ordered set on equivalence classes of certain saturated chains of T(n) called the Tamari Block poset, TB(lambda). It further proves TB(lambda) is a ...

- Contributors
- Treat, Kevin, Fishel, Susanna, Czygrinow, Andrzej, et al.
- Created Date
- 2016

This dissertation will cover two topics. For the first, let $K$ be a number field. A $K$-derived polynomial $f(x) \in K[x]$ is a polynomial that factors into linear factors over $K$, as do all of its derivatives. Such a polynomial is said to be {\it proper} if its roots are distinct. An unresolved question in the literature is whether or not there exists a proper $\Q$-derived polynomial of degree 4. Some examples are known of proper $K$-derived quartics for a quadratic number field $K$, although other than $\Q(\sqrt{3})$, these fields have quite large discriminant. (The second known field is $\Q(\sqrt{3441})$.) ...

- Contributors
- Carrillo, Benjamin, Jones, John, Bremner, Andrew, et al.
- Created Date
- 2019

In 1959, Iwasawa proved that the size of the $p$-part of the class groups of a $\mathbb{Z}_p$-extension grows as a power of $p$ with exponent ${\mu}p^m+{\lambda}\,m+\nu$ for $m$ sufficiently large. Broadly, I construct conditions to verify if a given $m$ is indeed sufficiently large. More precisely, let $CG_m^i$ (class group) be the $\epsilon_i$-eigenspace component of the $p$-Sylow subgroup of the class group of the field at the $m$-th level in a $\mathbb{Z}_p$-extension; and let $IACG^i_m$ (Iwasawa analytic class group) be ${\mathbb{Z}_p[[T]]/((1+T)^{p^m}-1,f(T,\omega^{1-i}))}$, where $f$ is the associated Iwasawa power series. It is expected that $CG_m^i$ and $IACG^i_m$ be isomorphic, providing us ...

- Contributors
- Elledge, Shawn Michael, Childress, Nancy, Bremner, Andrew, et al.
- Created Date
- 2013

Extremal graph theory results often provide minimum degree conditions which guarantee a copy of one graph exists within another. A perfect $F$-tiling of a graph $G$ is a collection $\mathcal{F}$ of subgraphs of $G$ such that every element of $\mathcal{F}$ is isomorphic to $F$ and such that every vertex in $G$ is in exactly one element of $\mathcal{F}$. Let $C^{3}_{t}$ denote the loose cycle on $t = 2s$ vertices, the $3$-uniform hypergraph obtained by replacing the edges $e = \{u, v\}$ of a graph cycle $C$ on $s$ vertices with edge triples $\{u, x_e, v\}$, where $x_e$ is uniquely assigned ...

- Contributors
- Oursler, Roy, Czygrinow, Andrzej, Kierstead, Hal A, et al.
- Created Date
- 2019

The uncrossing partially ordered set $P_n$ is defined on the set of matchings on $2n$ points on a circle represented with wires. The order relation is $\tau'\leq \tau$ in $P_n$ if and only if $\tau'$ is obtained by resolving a crossing of $\tau$. %This partial order has been studied by Alman-Lian-Tran, Huang-Wen-Xie, Kenyon, and Lam. %The posets $P_n$ emerged from studies of circular planar electrical networks. Circular planar electrical networks are finite weighted undirected graphs embedded into a disk, with boundary vertices and interior vertices. By Curtis-Ingerman-Morrow and de Verdi\`ere-Gitler-Vertigan, the electrical networks can be encoded with response matrices. By ...

- Contributors
- Kim, Younghwan, Fishel, Susanna, Bremner, Andrew, et al.
- Created Date
- 2018

A tiling is a collection of vertex disjoint subgraphs called tiles. If the tiles are all isomorphic to a graph $H$ then the tiling is an $H$-tiling. If a graph $G$ has an $H$-tiling which covers all of the vertices of $G$ then the $H$-tiling is a perfect $H$-tiling or an $H$-factor. A goal of this study is to extend theorems on sufficient minimum degree conditions for perfect tilings in graphs to directed graphs. Corrádi and Hajnal proved that every graph $G$ on $3k$ vertices with minimum degree $delta(G)ge2k$ has a $K_3$-factor, where $K_s$ is the complete graph on $s$ ...

- Contributors
- Molla, Theodore, Kierstead, Henry A, Czygrinow, Andrzej, et al.
- Created Date
- 2013

In 1984, Sinnott used $p$-adic measures on $\mathbb{Z}_p$ to give a new proof of the Ferrero-Washington Theorem for abelian number fields by realizing $p$-adic $L$-functions as (essentially) the $Gamma$-transform of certain $p$-adic rational function measures. Shortly afterward, Gillard and Schneps independently adapted Sinnott's techniques to the case of $p$-adic $L$-functions associated to elliptic curves with complex multiplication (CM) by realizing these $p$-adic $L$-functions as $Gamma$-transforms of certain $p$-adic rational function measures. The results in the CM case give the vanishing of the Iwasawa $mu$-invariant for certain $mathbb{Z}_p$-extensions of imaginary quadratic fields constructed from torsion points of CM elliptic curves. In ...

- Contributors
- Zinzer, Scott, Childress, Nancy, Bremner, Andrew, et al.
- Created Date
- 2015

A central concept of combinatorics is partitioning structures with given constraints. Partitions of on-line posets and on-line graphs, which are dynamic versions of the more familiar static structures posets and graphs, are examined. In the on-line setting, vertices are continually added to a poset or graph while a chain partition or coloring (respectively) is maintained. %The optima of the static cases cannot be achieved in the on-line setting. Both upper and lower bounds for the optimum of the number of chains needed to partition a width $w$ on-line poset exist. Kierstead's upper bound of $\frac{5^w-1}{4}$ was improved to $w^{14 \lg ...

- Contributors
- Smith, Matthew Earl, Kierstead, Henry A, Colbourn, Charles, et al.
- Created Date
- 2012

Since Duffin and Schaeffer's introduction of frames in 1952, the concept of a frame has received much attention in the mathematical community and has inspired several generalizations. The focus of this thesis is on the concept of an operator-valued frame (OVF) and a more general concept called herein an operator-valued frame associated with a measure space (MS-OVF), which is sometimes called a continuous g-frame. The first of two main topics explored in this thesis is the relationship between MS-OVFs and objects prominent in quantum information theory called positive operator-valued measures (POVMs). It has been observed that every MS-OVF gives rise ...

- Contributors
- Robinson, Benjamin David, Cochran, Douglas, Moran, William, et al.
- Created Date
- 2014

In a large network (graph) it would be desirable to guarantee the existence of some local property based only on global knowledge of the network. Consider the following classical example: how many connections are necessary to guarantee that the network contains three nodes which are pairwise adjacent? It turns out that more than n^2/4 connections are needed, and no smaller number will suffice in general. Problems of this type fall into the category of ``extremal graph theory.'' Generally speaking, extremal graph theory is the study of how global parameters of a graph are related to local properties. This dissertation deals ...

- Contributors
- Debiasio, Louis, Kierstead, Henry A, Czygrinow, Andrzej, et al.
- Created Date
- 2011

Increasing interest in individualized treatment strategies for prevention and treatment of health disorders has created a new application domain for dynamic modeling and control. Standard population-level clinical trials, while useful, are not the most suitable vehicle for understanding the dynamics of dosage changes to patient response. A secondary analysis of intensive longitudinal data from a naltrexone intervention for fibromyalgia examined in this dissertation shows the promise of system identification and control. This includes datacentric identification methods such as Model-on-Demand, which are attractive techniques for estimating nonlinear dynamical systems from noisy data. These methods rely on generating a local function approximation ...

- Contributors
- Deshpande, Sunil, Rivera, Daniel E., Peet, Matthew M., et al.
- Created Date
- 2014

In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems - in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) - whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning ...

- Contributors
- Kamyar, Reza, Peet, Matthew, Berman, Spring, et al.
- Created Date
- 2016

The Visceral Leishmaniasis (VL) is primarily endemic in five countries, with India and Sudan having the highest burden. The risk factors associated with VL are either unknown in some regions or vary drastically among empirical studies. Here, a dynamical model, motivated and informed by field data from the literature, is analyzed and employed to identify and quantify the impact of region dependent risks on the VL transmission dynamics. Parameter estimation procedures were developed using model-derived quantities and empirical data from multiple resources. The dynamics of VL depend on the estimates of the control reproductive number, RC, interpreted as the average ...

- Contributors
- Barley, Kamal Kevin, Castillo-Chavez, Carlos, Mubayi, Anuj, et al.
- Created Date
- 2016

The dynamics of a fluid flow inside 2D square and 3D cubic cavities under various configurations were simulated and analyzed using a spectral code I developed. This code was validated against known studies in the 3D lid-driven cavity. It was then used to explore the various dynamical behaviors close to the onset of instability of the steady-state flow, and explain in the process the mechanism underlying an intermittent bursting previously observed. A fairly complete bifurcation picture emerged, using a combination of computational tools such as selective frequency damping, edge-state tracking and subspace restriction. The code was then used to investigate ...

- Contributors
- Wu, Ke, Lopez, Juan, Welfert, Bruno, et al.
- Created Date
- 2019

Persistence theory provides a mathematically rigorous answer to the question of population survival by establishing an initial-condition- independent positive lower bound for the long-term value of the population size. This study focuses on the persistence of discrete semiflows in infinite-dimensional state spaces that model the year-to-year dynamics of structured populations. The map which encapsulates the population development from one year to the next is approximated at the origin (the extinction state) by a linear or homogeneous map. The (cone) spectral radius of this approximating map is the threshold between extinction and persistence. General persistence results are applied to three particular ...

- Contributors
- Jin, Wen, Thieme, Horst, Milner, Fabio, et al.
- Created Date
- 2014

Bank institutions employ several marketing strategies to maximize new customer acquisition as well as current customer retention. Telemarketing is one such approach taken where individual customers are contacted by bank representatives with offers. These telemarketing strategies can be improved in combination with data mining techniques that allow predictability of customer information and interests. In this thesis, bank telemarketing data from a Portuguese banking institution were analyzed to determine predictability of several client demographic and financial attributes and find most contributing factors in each. Data were preprocessed to ensure quality, and then data mining models were generated for the attributes with ...

- Contributors
- Ejaz, Samira, Davulcu, Hasan, Balasooriya, Janaka, et al.
- Created Date
- 2016

Statistical Methods have been widely used in understanding factors for clinical and public health data. Statistical hypotheses are procedures for testing pre-stated hypotheses. The development and properties of these procedures as well as their performance are based upon certain assumptions. Desirable properties of statistical tests are to maintain validity and to perform well even if these assumptions are not met. A statistical test that maintains such desirable properties is called robust. Mathematical models are typically mechanistic framework, used to study dynamic interactions between components (mechanisms) of a system, and how these interactions give rise to the changes in behavior (patterns) ...

- Contributors
- Gonzalez, Beverly, Castillo-Chavez, Carlos, Mubayi, Anuj, et al.
- Created Date
- 2015

A fundamental motivation for this study was the underrepresentation of women in Science, Technology, Engineering and Mathematics careers. There is no doubt women and men can achieve at the same level in Mathematics, yet it is not clear why women are opting out. Adding race to the equation makes the underrepresentation more dramatic. Considering the important number of Latinos in the United States, especially in school age, it is relevant to find what reasons could be preventing them from participating in the careers mentioned. This study highlight the experiences young successful Latinas have in school Mathematics and how they shape ...

- Contributors
- Guerra Lombardi, Paula Patricia, Middleton, James, Battey, Daniel, et al.
- Created Date
- 2011

Let T be a tournament with edges colored with any number of colors. A rainbow triangle is a 3-colored 3-cycle. A monochromatic sink of T is a vertex which can be reached along a monochromatic path by every other vertex of T. In 1982, Sands, Sauer, and Woodrow asked if T has no rainbow triangles, then does T have a monochromatic sink? I answer yes in the following five scenarios: when all 4-cycles are monochromatic, all 4-semi-cycles are near-monochromatic, all 5-semi-cycles are near-monochromatic, all back-paths of an ordering of the vertices are vertex disjoint, and for any vertex in an ...

- Contributors
- Bland, Adam, Kierstead, Henry A, Czygrinow, Andrzej M, et al.
- Created Date
- 2011

The world is grappling with two serious issues related to energy and climate change. The use of solar energy is receiving much attention due to its potential as one of the solutions. Air conditioning is particularly attractive as a solar energy application because of the near coincidence of peak cooling loads with the available solar power. Recently, researchers have started serious discussions of using adsorptive processes for refrigeration and heat pumps. There is some success for the >100 ton adsorption systems but none exists in the <10 ton size range required for residential air conditioning. There are myriad reasons for ...

- Contributors
- Gupta, Yeshpal, Phelan, Patrick E, Bryan, Harvey J, et al.
- Created Date
- 2011

By the von Neumann min-max theorem, a two person zero sum game with finitely many pure strategies has a unique value for each player (summing to zero) and each player has a non-empty set of optimal mixed strategies. If the payoffs are independent, identically distributed (iid) uniform (0,1) random variables, then with probability one, both players have unique optimal mixed strategies utilizing the same number of pure strategies with positive probability (Jonasson 2004). The pure strategies with positive probability in the unique optimal mixed strategies are called saddle squares. In 1957, Goldman evaluated the probability of a saddle point (a ...

- Contributors
- Manley, Michael, Kadell, Kevin W. J., Kao, Ming-Hung, et al.
- Created Date
- 2011

ABSTRACT The early desire for and the pursuit of literacy are often mentioned in the teeming volumes devoted to African-American history. However, stories, facts, and figures about the acquisition of numeracy by African Americans have not been equally documented. The focus of this study was to search for the third R, this is the numeracy and mathematics experiences of African Americans who were born in, and before, 1933. The investigation of this generational cadre was pursued in order to develop oral histories and narratives going back to the early 1900s. This study examined formal and informal education and other relevant ...

- Contributors
- LaCount, Marilyn Ruth, Zambo, Ronald, Flores, Alfinio, et al.
- Created Date
- 2014

This dissertation reports three studies of students’ and teachers’ meanings for quotient, fraction, measure, rate, and rate of change functions. Each study investigated individual’s schemes (or meanings) for foundational mathematical ideas. Conceptual analysis of what constitutes strong meanings for fraction, measure, and rate of change is critical for each study. In particular, each study distinguishes additive and multiplicative meanings for fraction and rate of change. The first paper reports an investigation of 251 high school mathematics teachers’ meanings for slope, measurement, and rate of change. Most teachers conveyed primarily additive and formulaic meanings for slope and rate of change on ...

- Contributors
- Byerley, Cameron O'Neill, Thompson, Patrick W, Carlson, Marilyn P, et al.
- Created Date
- 2016

This research by studies the computational performance of four different mixed integer programming (MIP) formulations for single machine scheduling problems with varying complexity. These formulations are based on (1) start and completion time variables, (2) time index variables, (3) linear ordering variables and (4) assignment and positional date variables. The objective functions that are studied in this paper are total weighted completion time, maximum lateness, number of tardy jobs and total weighted tardiness. Based on the computational results, discussion and recommendations are made on which MIP formulation might work best for these problems. The performances of these formulations very much ...

- Contributors
- Khowala, Ketan, Fowler, John, Keha, Ahmet, et al.
- Created Date
- 2012

Diophantine arithmetic is one of the oldest branches of mathematics, the search for integer or rational solutions of algebraic equations. Pythagorean triangles are an early instance. Diophantus of Alexandria wrote the first related treatise in the fourth century; it was an area extensively studied by the great mathematicians of the seventeenth century, including Euler and Fermat. The modern approach is to treat the equations as defining geometric objects, curves, surfaces, etc. The theory of elliptic curves (or curves of genus 1, which are much used in modern cryptography) was developed extensively in the twentieth century, and has had great application ...

- Contributors
- Nguyen, Tho Xuan, Bremner, Andrew, Childress, Nancy, et al.
- Created Date
- 2019

Since the seminal work of Tur ́an, the forbidden subgraph problem has been among the central questions in extremal graph theory. Let ex(n;F) be the smallest number m such that any graph on n vertices with m edges contains F as a subgraph. Then the forbidden subgraph problem asks to find ex(n; F ) for various graphs F . The question can be further generalized by asking for the extreme values of other graph parameters like minimum degree, maximum degree, or connectivity. We call this type of question a Tura ́n-type problem. In this thesis, we will study Tura ́n-type ...

- Contributors
- Yie, Jangwon, Czygrinow, Andrzej, Kierstead, Henry, et al.
- Created Date
- 2018

Sparse learning is a technique in machine learning for feature selection and dimensionality reduction, to find a sparse set of the most relevant features. In any machine learning problem, there is a considerable amount of irrelevant information, and separating relevant information from the irrelevant information has been a topic of focus. In supervised learning like regression, the data consists of many features and only a subset of the features may be responsible for the result. Also, the features might require special structural requirements, which introduces additional complexity for feature selection. The sparse learning package, provides a set of algorithms for ...

- Contributors
- Thulasiram, Ramesh L., Ye, Jieping, Xue, Guoliang, et al.
- Created Date
- 2011

The data explosion in the past decade is in part due to the widespread use of rich sensors that measure various physical phenomenon -- gyroscopes that measure orientation in phones and fitness devices, the Microsoft Kinect which measures depth information, etc. A typical application requires inferring the underlying physical phenomenon from data, which is done using machine learning. A fundamental assumption in training models is that the data is Euclidean, i.e. the metric is the standard Euclidean distance governed by the L-2 norm. However in many cases this assumption is violated, when the data lies on non Euclidean spaces such ...

- Contributors
- Anirudh, Rushil, Turaga, Pavan, Cochran, Douglas, et al.
- Created Date
- 2016

There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. This fast growing theory provides new constraints and mechanisms that can be formulated into mathematical models. Stoichiometric models incorporate the effects of both food quantity and food quality into a single framework that produce rich dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insufficient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This ...

- Contributors
- Peace, Angela Lynn, Kuang, Yang, Elser, James J, et al.
- Created Date
- 2014

ABSTRACT This thesis attempts to answer two questions based upon the historical observation that 1^2 +2^2 +· · ·+24^2 = 70^2. The first question considers changing the starting number of the left hand side of the equation from 1 to any perfect square in the range 1 to 10000. On this question, I attempt to determine which perfect square to end the left hand side of the equation with so that the right hand side of the equation is a perfect square. Mathematically, Question #1 can be written as follows: Given a positive integer r with 1 less than or ...

- Contributors
- Roth, Sanford Gary, Bremner, Andrew, Childress, Nancy E, et al.
- Created Date
- 2010

The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. ...

- Contributors
- Sanborn, Barbara, Suslov, Sergei K, Suslov, Sergei, et al.
- Created Date
- 2011

Parallel Monte Carlo applications require the pseudorandom numbers used on each processor to be independent in a probabilistic sense. The TestU01 software package is the standard testing suite for detecting stream dependence and other properties that make certain pseudorandom generators ineffective in parallel (as well as serial) settings. TestU01 employs two basic schemes for testing parallel generated streams. The first applies serial tests to the individual streams and then tests the resulting P-values for uniformity. The second turns all the parallel generated streams into one long vector and then applies serial tests to the resulting concatenated stream. Various forms of ...

- Contributors
- Ismay, Chester Ivan, Eubank, Randall, Young, Dennis, et al.
- Created Date
- 2013

Reprising the work of Kolpakov and Martelli, a manifold is constructed by face pairings of a four dimensional polytope, the 24-cell. The resulting geometry is a single cusped hyperbolic 4-manifold of finite volume. A short discussion of its geometry and underlying topology is included. Dissertation/Thesis

- Contributors
- Abram, Christopher Robert, Paupert, Julien, Kawski, Mattias, et al.
- Created Date
- 2014

Presented is a study on the chemotaxis reaction process and its relation with flow topology. The effect of coherent structures in turbulent flows is characterized by studying nutrient uptake and the advantage that is received from motile bacteria over other non-motile bacteria. Variability is found to be dependent on the initial location of scalar impurity and can be tied to Lagrangian coherent structures through recent advances in the identification of finite-time transport barriers. Advantage is relatively small for initial nutrient found within high stretching regions of the flow, and nutrient within elliptic structures provide the greatest advantage for motile species. ...

- Contributors
- Jones, Kimberly, Tang, Wenbo, Kang, Yun, et al.
- Created Date
- 2015

Graph coloring is about allocating resources that can be shared except where there are certain pairwise conflicts between recipients. The simplest coloring algorithm that attempts to conserve resources is called first fit. Interval graphs are used in models for scheduling (in computer science and operations research) and in biochemistry for one-dimensional molecules such as genetic material. It is not known precisely how much waste in the worst case is due to the first-fit algorithm for coloring interval graphs. However, after decades of research the range is narrow. Kierstead proved that the performance ratio R is at most 40. Pemmaraju, Raman, ...

- Contributors
- Smith, David A., Kierstead, Henry A., Czygrinow, Andrzej, et al.
- Created Date
- 2010

This study investigated the link between the cognitive clusters from the Woodcock–Johnson III Tests of Cognitive Ability (WJ III COG) and Broad Math, Math Calculation Skills, and Math Reasoning clusters of the Woodcock–Johnson III Tests of Achievement (WJ III ACH) using data collected over seven years by a large elementary school district in the Southwest. The students in this study were all diagnosed with math learning disabilities. Multiple regression analyses were used to predict performance on the Broad Math, Math Calculation Skills, and Math Reasoning clusters from the WJ III ACH. Fluid Reasoning (Gf), Comprehension–Knowledge (Gc), Short–Term Memory (Gsm), and ...

- Contributors
- Bacal, Emily Beth, Caterino, Linda, Stamm, Jill, et al.
- Created Date
- 2011

Threshold logic has been studied by at least two independent group of researchers. One group of researchers studied threshold logic with the intention of building threshold logic circuits. The earliest research to this end was done in the 1960's. The major work at that time focused on studying mathematical properties of threshold logic as no efficient circuit implementations of threshold logic were available. Recently many post-CMOS (Complimentary Metal Oxide Semiconductor) technologies that implement threshold logic have been proposed along with efficient CMOS implementations. This has renewed the effort to develop efficient threshold logic design automation techniques. This work contributes to ...

- Contributors
- Linge Gowda, Tejaswi, Vrudhula, Sarma, Shrivastava, Aviral, et al.
- Created Date
- 2012

The Cambrian lattice corresponding to a Coxeter element c of An, denoted Camb(c), is the subposet of An induced by the c-sortable elements, and the m-eralized Cambrian lattice corresponding to c, denoted Cambm(c), is dened as a subposet of the braid group accompanied with the right weak ordering induced by the c-sortable elements under certain conditions. Both of these families generalize the well-studied Tamari lattice Tn rst introduced by D. Tamari in 1962. S. Fishel and L. Nelson enumerated the chains of maximum length of Tamari lattices. In this dissertation, I study the chains of maximum length of the Cambrian ...

- Contributors
- AL-SULEIMAN, SULTAN, Fishel, Susanna, Childress, Nancy, et al.
- Created Date
- 2017

The Tamari lattices have been intensely studied since they first appeared in Dov Tamari’s thesis around 1952. He defined the n-th Tamari lattice T(n) on bracketings of a set of n+1 objects, with a cover relation based on the associativity rule in one direction. Despite their interesting aspects and the attention they have received, a formula for the number of maximal chains in the Tamari lattices is still unknown. The purpose of this thesis is to convey my results on progress toward the solution of this problem and to discuss future work. A few years ago, Bergeron and Préville-Ratelle generalized ...

- Contributors
- Nelson, Luke Edwin, Fishel, Susanna, Czygrinow, Andrzej, et al.
- Created Date
- 2016

According to the Centers for Disease Control and Prevention (CDC), type 2 diabetes accounts for 90-95% of diabetes (29.1 million) cases and manifests in 15-30% of prediabetes (86 million) cases, where 9 out of 10 individuals do not know they have prediabetes. Obesity, observed in 56.9% of diabetes cases, arises from the interactions among genetic, biological, environmental, and behavioral factors that are not well understood. Assessing the strength of these links in conjunction with the identification and evaluation of intervention strategies in vulnerable populations is central to the study of chronic diseases. This research addresses three issues that loosely connect ...

- Contributors
- Murillo, Anarina, Castillo-Chavez, Carlos, Li, Jiaxu, et al.
- Created Date
- 2016

ABSTRACT There is a continuing emphasis in the United States to improve student's mathematical abilities and one approach is to better prepare teachers. This study investigated the effects of using lesson study with preservice secondary mathematics teachers to improve their proficiency at planning and implementing instruction. The participants were students (preservice teachers) in an undergraduate teacher preparation program at a private university who were enrolled in a mathematics methods course for secondary math teachers. This project used lesson study to engage preservice teachers in collaboratively creating lessons, field testing them, using feedback to revise the lessons, and re-teaching the revised ...

- Contributors
- Mostofo, Jameel (Jim) Richard, Zambo, Ronald, Elliott, Sherman, et al.
- Created Date
- 2013

Recently there has been an increase in the number of people calling for the incorporation of relevant mathematics in the mathematics classroom. Unfortunately, various researchers define the term relevant mathematics differently, establishing several ideas of how relevancy can be incorporated into the classroom. The differences between mathematics education researchers' definitions of relevant and the way they believe relevant math should be implemented in the classroom, leads one to conclude that a similarly varied set of perspectives probably exists between teachers and students as well. The purpose of this exploratory study focuses on how the student and teacher perspectives on relevant ...

- Contributors
- Redman, Alexandra, Middleton, James, Sloane, Finbarr, et al.
- Created Date
- 2012

In this dissertation I develop a deep theory of temporal planning well-suited to analyzing, understanding, and improving the state of the art implementations (as of 2012). At face-value the work is strictly theoretical; nonetheless its impact is entirely real and practical. The easiest portion of that impact to highlight concerns the notable improvements to the format of the temporal fragment of the International Planning Competitions (IPCs). Particularly: the theory I expound upon here is the primary cause of--and justification for--the altered (i) selection of benchmark problems, and (ii) notion of "winning temporal planner". For higher level motivation: robotics, web service ...

- Contributors
- Cushing, William Albemarle, Kambhampati, Subbarao, Weld, Daniel S, et al.
- Created Date
- 2012

The purpose of this study was to identify the algebraic reasoning abilities of young students prior to instruction. The goals of the study were to determine the influence of problem, problem type, question, grade level, and gender on: (a) young children’s abilities to predict the number of shapes in near and far positions in a “growing” pattern without assistance; (b) the nature and amount of assistance needed to solve the problems; and (c) reasoning methods employed by children. The 8-problem Growing Patterns and Functions Assessment (GPFA), with an accompanying interview protocol, were developed to respond to these goals. Each problem ...

- Contributors
- Cavanagh, Mary C., Greenes, Carole E, Buss, Ray, et al.
- Created Date
- 2016