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.
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Description
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 phenomenon, known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, needs to be incorporated into mathematical models. Here we present Lotka-Volterra type models to investigate the growth response of Daphnia to algae of varying P:C ratios. Using a nonsmooth system of two ordinary differential equations (ODEs), we formulate the first model to incorporate the phenomenon of the stoichiometric knife edge. We then extend this stoichiometric model by mechanistically deriving and tracking free P in the environment. This resulting full knife edge model is a nonsmooth system of three ODEs. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, leads to quantitatively different predictions than previous models that neglect to track free nutrients. The full model shows that the grazer population is sensitive to excess nutrient concentrations as a dynamical free nutrient pool induces extreme grazer population density changes. These modeling efforts provide insight on the effects of excess nutrient content on grazer dynamics and deepen our understanding of the effects of stoichiometry on the mechanisms governing population dynamics and the interactions between trophic levels.
ContributorsPeace, Angela (Author) / Kuang, Yang (Thesis advisor) / Elser, James J (Committee member) / Baer, Steven (Committee member) / Tang, Wenbo (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
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 this thesis, I develop the theory of $p$-adic measures on $mathbb{Z}_p^d$, with particular interest given to the case of $d>1$. Although I introduce these measures within the context of $p$-adic integration, this study includes a strong emphasis on the interpretation of $p$-adic measures as $p$-adic power series. With this dual perspective, I describe $p$-adic analytic operations as maps on power series; the most important of these operations is the multivariate $Gamma$-transform on $p$-adic measures.
This thesis gives new significance to product measures, and in particular to the use of product measures to construct measures on $mathbb{Z}_p^2$ from measures on $mathbb{Z}_p$. I introduce a subring of pseudo-polynomial measures on $mathbb{Z}_p^2$ which is closed under the standard operations on measures, including the $Gamma$-transform. I obtain results on the Iwasawa-invariants of such pseudo-polynomial measures, and use these results to deduce certain continuity results for the $Gamma$-transform. As an application, I establish the vanishing of the Iwasawa $mu$-invariant of Yager's two-variable $p$-adic $L$-function from measure theoretic considerations.
In this thesis, I develop the theory of $p$-adic measures on $mathbb{Z}_p^d$, with particular interest given to the case of $d>1$. Although I introduce these measures within the context of $p$-adic integration, this study includes a strong emphasis on the interpretation of $p$-adic measures as $p$-adic power series. With this dual perspective, I describe $p$-adic analytic operations as maps on power series; the most important of these operations is the multivariate $Gamma$-transform on $p$-adic measures.
This thesis gives new significance to product measures, and in particular to the use of product measures to construct measures on $mathbb{Z}_p^2$ from measures on $mathbb{Z}_p$. I introduce a subring of pseudo-polynomial measures on $mathbb{Z}_p^2$ which is closed under the standard operations on measures, including the $Gamma$-transform. I obtain results on the Iwasawa-invariants of such pseudo-polynomial measures, and use these results to deduce certain continuity results for the $Gamma$-transform. As an application, I establish the vanishing of the Iwasawa $mu$-invariant of Yager's two-variable $p$-adic $L$-function from measure theoretic considerations.
ContributorsZinzer, Scott Michael (Author) / Childress, Nancy (Thesis advisor) / Bremner, Andrew (Committee member) / Fishel, Susanna (Committee member) / Jones, John (Committee member) / Spielberg, John (Committee member) / Arizona State University (Publisher)
Created2015
DescriptionReprising 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.
ContributorsAbram, Christopher (Author) / Paupert, Julien (Thesis advisor) / Kawski, Mattias (Committee member) / Kotschwar, Brett (Committee member) / Arizona State University (Publisher)
Created2014
Description
The State of Arizona mandates that students with superior intellect or abilities, or identified gifted students, receive appropriate gifted education and services in order to achieve at levels commensurate with their intellect and abilities. Additionally, the State of Arizona adopted the Arizona College and Career Ready Standards (AZCCRS) initiative. This investigation explores if, according to the perceptions of gifted educators, the AZCCRS support a gifted mathematic curriculum and pedagogy at the elementary level which is commensurate with academic abilities, potential, and intellect of these mathematically gifted students, what the relationships are between exemplary gifted curriculum and pedagogy and the AZCCRS, and exactly how the gifted education specialists charged with meeting the academic and intellectual needs and potential of their gifted students interpret, negotiate, and implement the AZCCRS.
This study utilized a qualitative approach and a variety of instruments to gather data, including: profile questionnaires, semi-structured pre-interviews, reflective journals, three group discussion sessions, and semi-structured post interviews. The pre- and post interviews as well as the group discussion sessions were audiotape recorded and transcribed. A three stage coding process was utilized on the questionnaires, interviews, discussion sessions, and journal entries.
The results and findings demonstrated that AZCCRS clearly support exemplary gifted mathematic curriculum and practices at the elementary level, that there are at least nine distinct relationships between the AZCCRS and gifted pedagogy, and that the gifted education specialists interpret, negotiate, and implement the AZCCRS uniquely in at least four distinct ways, in their mathematically gifted pullout classes.
This study utilized a qualitative approach and a variety of instruments to gather data, including: profile questionnaires, semi-structured pre-interviews, reflective journals, three group discussion sessions, and semi-structured post interviews. The pre- and post interviews as well as the group discussion sessions were audiotape recorded and transcribed. A three stage coding process was utilized on the questionnaires, interviews, discussion sessions, and journal entries.
The results and findings demonstrated that AZCCRS clearly support exemplary gifted mathematic curriculum and practices at the elementary level, that there are at least nine distinct relationships between the AZCCRS and gifted pedagogy, and that the gifted education specialists interpret, negotiate, and implement the AZCCRS uniquely in at least four distinct ways, in their mathematically gifted pullout classes.
ContributorsDohm, Dianna (Author) / Carlson, David L. (Thesis advisor) / Barnard, Wendy (Committee member) / Moses, Lindsey (Committee member) / Arizona State University (Publisher)
Created2014
Description
The most recent reauthorizations of No Child Left Behind and the Individuals with Disabilities Education Act served to usher in an age of results and accountability within American education. States were charged with developing more rigorous systems to specifically address areas such as critical academic skill proficiency, empirically validated instruction and intervention, and overall student performance as measured on annual statewide achievement tests. Educational practice has shown that foundational math ability can be easily assessed through student performance on Curriculum-Based Measurements of Math Computational Fluency (CBM-M). Research on the application of CBM-M's predictive validity across specific academic math abilities as measured by state standardized tests is currently limited. In addition, little research is available on the differential effects of ethnic subgroups and gender in this area. This study investigated the effectiveness of using CBM-M measures to predict achievement on high stakes tests, as well as whether or not there are significant differential effects of ethnic subgroups and gender. Study participants included 358 students across six elementary schools in a large suburban school district in Arizona that utilizes the Response to Intervention (RTI) model. Participants' CBM-M scores from the first through third grade years and their third grade standardized achievement test scores were collected. Pearson product-moment and Spearman correlations were used to determine how well CBM-M scores and specific math skills are related. The predictive validity of CBM-M scores from the third-grade school year was also assessed to determine whether the fall, winter, or spring screening was most related to third-grade high-stakes test scores.
ContributorsGambrel, Thomas J (Author) / Caterino, Linda (Thesis advisor) / Stamm, Jill (Committee member) / DiGangi, Samuel (Committee member) / Arizona State University (Publisher)
Created2014
Description
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 to a POVM with invertible total variation in a natural way. The first main result of this thesis is a characterization of which POVMs arise in this way, a result obtained by extending certain existing Radon-Nikodym theorems for POVMs. The second main topic investigated in this thesis is the role of the theory of unitary representations of a Lie group G in the construction of OVFs for the L^2-space of a relatively compact subset of G. For G=R, Duffin and Schaeffer have given general conditions that ensure a sequence of (one-dimensional) representations of G, restricted to (-1/2,1/2), forms a frame for L^{2}(-1/2,1/2), and similar conditions exist for G=R^n. The second main result of this thesis expresses conditions related to Duffin and Schaeffer's for two more particular Lie groups: the Euclidean motion group on R^2 and the (2n+1)-dimensional Heisenberg group. This proceeds in two steps. First, for a Lie group admitting a uniform lattice and an appropriate relatively compact subset E of G, the Selberg Trace Formula is used to obtain a Parseval OVF for L^{2}(E) that is expressed in terms of irreducible representations of G. Second, for the two particular Lie groups an appropriate set E is found, and it is shown that for each of these groups, with suitably parametrized unitary duals, the Parseval OVF remains an OVF when perturbations are made to the parameters of the included representations.
ContributorsRobinson, Benjamin (Author) / Cochran, Douglas (Thesis advisor) / Moran, William (Thesis advisor) / Boggess, Albert (Committee member) / Milner, Fabio (Committee member) / Spielberg, John (Committee member) / Arizona State University (Publisher)
Created2014
Description
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 models: a size-structured plant population model, a diffusion model (with both Neumann and Dirichlet boundary conditions) for a dispersing population of males and females that only mate and reproduce once during a very short season, and a rank-structured model for a population of males and females.
ContributorsJin, Wen (Author) / Thieme, Horst (Thesis advisor) / Milner, Fabio (Committee member) / Quigg, John (Committee member) / Smith, Hal (Committee member) / Spielberg, John (Committee member) / Arizona State University (Publisher)
Created2014
Description
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 of the narratives suggests that accountability structures shaped individual's sense-making of the original policy. This sense-making process consequently influenced individuals' actions during implementation by directing them towards certain policy actions and ultimately altered how the policy unfolded in this school and district. In particular, accountability structures directed participants' attention to the technical instructional `forms' of the reform, such as the presence of written responses on assessments and how standards were distributed between grade levels, rather than the overall principled shifts in practice intended by the policy's creators.
ContributorsFrankiewicz, Megan Marie (Author) / Powers, Jeanne (Thesis advisor) / Fischman, Gustavo (Committee member) / Berliner, David (Committee member) / Arizona State University (Publisher)
Created2015
Description
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 nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
ContributorsPacker, Aaron (Author) / Kuang, Yang (Thesis advisor) / Nagy, John (Committee member) / Smith, Hal (Committee member) / Kostelich, Eric (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Improving Arizona English language learners' mathematics achievement using curriculum-based measures
Description
ABSTRACT
This study was an investigation of the effectiveness of curriculum-based measures (CBMs) on the math achievement of first and second grade English Language Learners (ELL). The No Child Left Behind Act (NCLB) of 2001 led to a new educational reform, which identifies and provides services to students in need of academic support based on English language proficiency. Students are from certain demographics: minorities, low-income families, students with disabilities, and students with limited English proficiency. NCLB intended to lead as to improvement in the quality of the United States educational system.
Four classes from the community of Kayenta, Arizona in the Navajo Nation were randomly assigned to control and experimental groups, one each per grade. All four classes used the state-approved, core math curriculum, but one class in each grade was provided with weekly CBMs for an entire school year that included sample questions developed from the Arizona Department of Education performance standards. The CBMs contained at least one question from each of the five math strands: number and operations, algebra, geometry, measurement, and data and probability.
The NorthWest Evaluation Assessment (NWEA) served as the pretest and posttest for all four groups. The SAT 10 (RIT scores) math test, administered near the time of the pretest, served as the covariate in the analysis. Two analysis of covariance tests revealed no statistically significant treatment effects, subject gender effects, or interactions for either Grade 1 or Grade 2. Achievement levels were relatively constant across both genders and the two grade levels.
Despite increasing emphasis on assessment and accountability, the achievement gaps between these subpopulations and the general population of students continues to widen. It appears that other variables are responsible for the different achievement levels found among students. Researchers have found that teachers with math certification, degrees related to math, and advanced course work in math leads to improved math performance over students of teachers who lack those qualifications. The design of the current study did not permit analyses of teacher or school effects.
This study was an investigation of the effectiveness of curriculum-based measures (CBMs) on the math achievement of first and second grade English Language Learners (ELL). The No Child Left Behind Act (NCLB) of 2001 led to a new educational reform, which identifies and provides services to students in need of academic support based on English language proficiency. Students are from certain demographics: minorities, low-income families, students with disabilities, and students with limited English proficiency. NCLB intended to lead as to improvement in the quality of the United States educational system.
Four classes from the community of Kayenta, Arizona in the Navajo Nation were randomly assigned to control and experimental groups, one each per grade. All four classes used the state-approved, core math curriculum, but one class in each grade was provided with weekly CBMs for an entire school year that included sample questions developed from the Arizona Department of Education performance standards. The CBMs contained at least one question from each of the five math strands: number and operations, algebra, geometry, measurement, and data and probability.
The NorthWest Evaluation Assessment (NWEA) served as the pretest and posttest for all four groups. The SAT 10 (RIT scores) math test, administered near the time of the pretest, served as the covariate in the analysis. Two analysis of covariance tests revealed no statistically significant treatment effects, subject gender effects, or interactions for either Grade 1 or Grade 2. Achievement levels were relatively constant across both genders and the two grade levels.
Despite increasing emphasis on assessment and accountability, the achievement gaps between these subpopulations and the general population of students continues to widen. It appears that other variables are responsible for the different achievement levels found among students. Researchers have found that teachers with math certification, degrees related to math, and advanced course work in math leads to improved math performance over students of teachers who lack those qualifications. The design of the current study did not permit analyses of teacher or school effects.
ContributorsBenally, Jacqueline (Author) / Humphreys, Jere (Thesis advisor) / Spencer, Dee (Committee member) / Nicholas, Appleton (Committee member) / Arizona State University (Publisher)
Created2014