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.
Displaying 1 - 5 of 5
Filtering by
- All Subjects: Mathematics
- Creators: Barcelo, Helene
- Creators: Tepedelenlioğlu, Cihan
Description
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 ordering of the vertices, its back edges are all colored the same. I provide conjectures related to these results that ask if the result is also true for larger cycles and semi-cycles. A ruling class is a set of vertices in T so that every other vertex of T can reach a vertex of the ruling class along a monochromatic path. Every tournament contains a ruling class, although the ruling class may have a trivial size of the order of T. Sands, Sauer, and Woodrow asked (again in 1982) about the minimum size of ruling classes in T. In particular, in a 3-colored tournament, must there be a ruling class of size 3? I answer yes when it is required that all 2-colored cycles have an edge xy so that y has a monochromatic path to x. I conjecture that there is a ruling class of size 3 if there are no rainbow triangles in T. Finally, I present the new topic of alpha-step-chromatic sinks along with related results. I show that for certain values of alpha, a tournament is not guaranteed to have an alpha-step-chromatic sink. In fact, similar to the previous results in this thesis, alpha-step-chromatic sinks can only be demonstrated when additional restrictions are put on the coloring of the tournament's edges, such as excluding rainbow triangles. However, when proving the existence of alpha-step-chromatic sinks, it is only necessary to exclude special types of rainbow triangles.
ContributorsBland, Adam K (Author) / Kierstead, Henry A (Thesis advisor) / Czygrinow, Andrzej M (Committee member) / Hurlbert, Glenn H. (Committee member) / Barcelo, Helene (Committee member) / Aen, Arunabha (Committee member) / Arizona State University (Publisher)
Created2011
Description
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 $\Gal(F_\infty/F)$ has a $p$-adic analytic structure is to use the action of $\Gal(F_n/F)$ on $E(F_n)$ and the Galois cohomology groups attached to $E$, i.e. the Selmer and Tate-Shafarevich groups. As $n$ varies, these Galois actions fit into a coherent family, and taking a direct limit one obtains a short exact sequence of modules $$0 \longrightarrow E(F_\infty) \otimes(\mathbb{Q}_p/\mathbb{Z}_p) \longrightarrow \Sel_E(F_\infty)_p \longrightarrow \Sha_E(F_\infty)_p \longrightarrow 0 $$ over the profinite group algebra $\mathbb{Z}_p[[\Gal(F_\infty/F)]]$. When $\Gal(F_\infty/F) \cong \mathbb{Z}_p$, this ring is isomorphic to $\Lambda = \mathbb{Z}_p[[T]]$, and the $\Lambda$-module structure of $\Sel_E(F_\infty)_p$ and $\Sha_E(F_\infty)_p$ encode all the information about the curves $E(F_n)$ as $n$ varies. In this dissertation, it will be shown how one can classify certain finitely generated $\Lambda$-modules with fixed characteristic polynomial $f(T) \in \mathbb{Z}_p[T]$ up to isomorphism. The results yield explicit generators for each module up to isomorphism. As an application, it is shown how to identify the isomorphism class of $\Sel_E(\mathbb{Q_\infty})_p$ in this explicit form, where $\mathbb{Q}_\infty$ is the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$, and $E$ is an elliptic curve over $\mathbb{Q}$ with good ordinary reduction at $p$, and possessing the property that $E(\mathbb{Q})$ has no $p$-torsion.
ContributorsFranks, Chase (Author) / Childress, Nancy (Thesis advisor) / Barcelo, Helene (Committee member) / Bremner, Andrew (Committee member) / Jones, John (Committee member) / Spielberg, Jack (Committee member) / Arizona State University (Publisher)
Created2011
Description
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 which minimizes discontinuity. A framework for social choice methods based on grades is presented. It is based on the Balinski-Laraki framework, but doesn't require aggregation functions to be strictly monotone. By relaxing this restriction, strategy-proof aggregation functions can better handle a polarized electorate, can give a societal grade closer to the input grades, and can partially avoid certain voting paradoxes. A new cardinal voting method, called the linear median is presented, and is shown to have several very valuable properties. Range voting, the majority judgment, and the linear median are also simulated to compare their manipulability against that of the ordinal methods.
ContributorsJennings, Andrew (Author) / Hurlbert, Glenn (Thesis advisor) / Barcelo, Helene (Thesis advisor) / Balinski, Michel (Committee member) / Laraki, Rida (Committee member) / Jones, Don (Committee member) / Arizona State University (Publisher)
Created2010
Description
This dissertation centers on the development of Bayesian methods for learning differ- ent types of variation in switching nonlinear gene regulatory networks (GRNs). A new nonlinear and dynamic multivariate GRN model is introduced to account for different sources of variability in GRNs. The new model is aimed at more precisely capturing the complexity of GRN interactions through the introduction of time-varying kinetic order parameters, while allowing for variability in multiple model parameters. This model is used as the drift function in the development of several stochastic GRN mod- els based on Langevin dynamics. Six models are introduced which capture intrinsic and extrinsic noise in GRNs, thereby providing a full characterization of a stochastic regulatory system. A Bayesian hierarchical approach is developed for learning the Langevin model which best describes the noise dynamics at each time step. The trajectory of the state, which are the gene expression values, as well as the indicator corresponding to the correct noise model are estimated via sequential Monte Carlo (SMC) with a high degree of accuracy. To address the problem of time-varying regulatory interactions, a Bayesian hierarchical model is introduced for learning variation in switching GRN architectures with unknown measurement noise covariance. The trajectory of the state and the indicator corresponding to the network configuration at each time point are estimated using SMC. This work is extended to a fully Bayesian hierarchical model to account for uncertainty in the process noise covariance associated with each network architecture. An SMC algorithm with local Gibbs sampling is developed to estimate the trajectory of the state and the indicator correspond- ing to the network configuration at each time point with a high degree of accuracy. The results demonstrate the efficacy of Bayesian methods for learning information in switching nonlinear GRNs.
ContributorsVélez-Cruz, Nayely (Author) / Papandreou-Suppappola, Antonia (Thesis advisor) / Moraffah, Bahman (Committee member) / Tepedelenlioğlu, Cihan (Committee member) / Berisha, Visar (Committee member) / Arizona State University (Publisher)
Created2023
Description
In many real-world machine learning classification applications, well labeled training data can be difficult, expensive, or even impossible to obtain. In such situations, it is sometimes possible to label a small subset of data as belonging to the class of interest though it is impractical to manually label all data not of interest. The result is a small set of positive labeled data and a large set of unknown and unlabeled data. This is known as the Positive and Unlabeled learning (PU learning) problem, a type of semi-supervised learning. In this dissertation, the PU learning problem is rigorously defined, several common assumptions described, and a literature review of the field provided. A new family of effective PU learning algorithms, the MLR (Modified Logistic Regression) family of algorithms, is described. Theoretical and experimental justification for these algorithms is provided demonstrating their success and flexibility. Extensive experimentation and empirical evidence are provided comparing several new and existing PU learning evaluation estimation metrics in a wide variety of scenarios. The surprisingly clear advantage of a simple recall estimate as the best estimate for overall PU classifier performance is described. Finally, an application of PU learning to the field of solar fault detection, an area not previously explored in the field, demonstrates the advantage and potential of PU learning in new application domains.
ContributorsJaskie, Kristen P (Author) / Spanias, Andreas (Thesis advisor) / Blain-Christen, Jennifer (Committee member) / Tepedelenlioğlu, Cihan (Committee member) / Thiagarajan, Jayaraman (Committee member) / Arizona State University (Publisher)
Created2021