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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- All Subjects: Applied Mathematics
Description
Solving partial differential equations on surfaces has many applications including modeling chemical diffusion, pattern formation, geophysics and texture mapping. This dissertation presents two techniques for solving time dependent partial differential equations on various surfaces using the partition of unity method. A novel spectral cubed sphere method that utilizes the windowed Fourier technique is presented and used for both approximating functions on spherical domains and solving partial differential equations. The spectral cubed sphere method is applied to solve the transport equation as well as the diffusion equation on the unit sphere. The second approach is a partition of unity method with local radial basis function approximations. This technique is also used to explore the effect of the node distribution as it is well known that node choice plays an important role in the accuracy and stability of an approximation. A greedy algorithm is implemented to generate good interpolation nodes using the column pivoting QR factorization. The partition of unity radial basis function method is applied to solve the diffusion equation on the sphere as well as a system of reaction-diffusion equations on multiple surfaces including the surface of a red blood cell, a torus, and the Stanford bunny. Accuracy and stability of both methods are investigated.
ContributorsIslas, Genesis Juneiva (Author) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Espanol, Malena (Committee member) / Kao, Ming-Hung (Committee member) / Renaut, Rosemary (Committee member) / Arizona State University (Publisher)
Created2021
Description
This dissertation explores applications of machine learning methods in service of the design of screening tests, which are ubiquitous in applications from social work, to criminology, to healthcare. In the first part, a novel Bayesian decision theory framework is presented for designing tree-based adaptive tests. On an application to youth delinquency in Honduras, the method produces a 15-item instrument that is almost as accurate as a full-length 150+ item test. The framework includes specific considerations for the context in which the test will be administered, and provides uncertainty quantification around the trade-offs of shortening lengthy tests. In the second part, classification complexity is explored via theoretical and empirical results from statistical learning theory, information theory, and empirical data complexity measures. A simulation study that explicitly controls two key aspects of classification complexity is performed to relate the theoretical and empirical approaches. Throughout, a unified language and notation that formalizes classification complexity is developed; this same notation is used in subsequent chapters to discuss classification complexity in the context of a speech-based screening test. In the final part, the relative merits of task and feature engineering when designing a speech-based cognitive screening test are explored. Through an extensive classification analysis on a clinical speech dataset from patients with normal cognition and Alzheimer’s disease, the speech elicitation task is shown to have a large impact on test accuracy; carefully performed task and feature engineering are required for best results. A new framework for objectively quantifying speech elicitation tasks is introduced, and two methods are proposed for automatically extracting insights into the aspects of the speech elicitation task that are driving classification performance. The dissertation closes with recommendations for how to evaluate the obtained insights and use them to guide future design of speech-based screening tests.
ContributorsKrantsevich, Chelsea (Author) / Hahn, P. Richard (Thesis advisor) / Berisha, Visar (Committee member) / Lopes, Hedibert (Committee member) / Renaut, Rosemary (Committee member) / Zheng, Yi (Committee member) / Arizona State University (Publisher)
Created2023
Description
In the realm of discrete ill-posed problems, image deblurring is a challenging problem aimed at restoring clear and visually appealing images from their blurred counterparts. Over the years, various numerical techniques have been developed to solve this problem, each offering unique approaches to tackle blurring and noise.This thesis studies multilevel methods using Daubechies wavelets and Tikhonov regularization. The Daubechies wavelets are a family of orthogonal wavelets widely used in various fields because of their orthogonality and compact support. They have been widely applied in signal processing, image compression, and other applications. One key aspect of this investigation involves a comprehensive comparative analysis with Krylov methods, well-established iterative methods known for their efficiency and accuracy in solving large-scale inverse problems. The focus is on two well-known Krylov methods, namely hybrid LSQR and hybrid generalized minimal residual method \linebreak(GMRES). By contrasting the multilevel and Krylov methods, the aim is to discern their strengths and limitations, facilitating a deeper understanding of their applicability in diverse image-deblurring scenarios. Other critical comparison factors are the noise level adopted during the deblurring process and the amount of blur. To gauge their robustness and performance under different blurry and noisy conditions, this work explores how each method behaves with different noise levels from mild to severe and different amounts of blur from small to large. Moreover, this thesis combines multilevel and Krylov methods to test a new method for solving inverse problems.
This work aims to provide valuable insights into the strengths and weaknesses of these multilevel Krylov methods by shedding light on their efficacy. Ultimately, the findings could have implications across diverse domains, including medical imaging, remote sensing, and multimedia applications, where high-quality and noise-free images are indispensable for accurate analysis and interpretation.
ContributorsAmdouni, Bechir (Author) / Espanol, Malena (Thesis advisor) / Renaut, Rosemary (Committee member) / Platte, Rodrigo (Committee member) / Fricks, John (Committee member) / Moustaoui, Mohamed (Committee member) / Arizona State University (Publisher)
Created2024
Description
Gene expression models are key to understanding and predicting transcriptional dynamics. This thesis devises a computational method which can efficiently explore a large, highly correlated parameter space, ultimately allowing the author to accurately deduce the underlying gene network model using discrete, stochastic mRNA counts derived through the non-invasive imaging method of single molecule fluorescence in situ hybridization (smFISH). An underlying gene network model consists of the number of gene states (distinguished by distinct production rates) and all associated kinetic rate parameters. In this thesis, the author constructs an algorithm based on Bayesian parametric and nonparametric theory, expanding the traditional single gene network inference tools. This expansion starts by increasing the efficiency of classic Markov-Chain Monte Carlo (MCMC) sampling by combining three schemes known in the Bayesian statistical computing community: 1) Adaptive Metropolis-Hastings (AMH), 2) Hamiltonian Monte Carlo (HMC), and 3) Parallel Tempering (PT). The aggregation of these three methods decreases the autocorrelation between sequential MCMC samples, reducing the number of samples required to gain an accurate representation of the posterior probability distribution. Second, by employing Bayesian nonparametric methods, the author is able to simultaneously evaluate discrete and continuous parameters, enabling the method to devise the structure of the gene network and all kinetic parameters, respectively. Due to the nature of Bayesian theory, uncertainty is evaluated for the gene network model in combination with the kinetic parameters. Tools brought from Bayesian nonparametric theory equip the method with an ability to sample from the posterior distribution of all possible gene network models without pre-defining the gene network structure, i.e. the number of gene states. The author verifies the method’s robustness through the use of synthetic snapshot data, designed to closely represent experimental smFISH data sets, across a range of gene network model structures, parameters and experimental settings (number of probed cells and timepoints).
ContributorsMoyer, Camille (Author) / Armbruster, Dieter (Thesis advisor) / Fricks, John (Committee member) / Hahn, Richard (Committee member) / Renaut, Rosemary (Committee member) / Crook, Sharon (Committee member) / Kilic, Zeliha (Committee member) / Arizona State University (Publisher)
Created2024
Description
I focus on algorithms that generate good sampling points for function approximation. In 1D, it is well known that polynomial interpolation using equispaced points is unstable. On the other hand, using Chebyshev nodes provides both stable and highly accurate points for polynomial interpolation. In higher dimensional complex regions, optimal sampling points are not known explicitly. This work presents robust algorithms that find good sampling points in complex regions for polynomial interpolation, least-squares, and radial basis function (RBF) methods. The quality of these nodes is measured using the Lebesgue constant. I will also consider optimal sampling for constrained optimization, used to solve PDEs, where boundary conditions must be imposed. Furthermore, I extend the scope of the problem to include finding near-optimal sampling points for high-order finite difference methods. These high-order finite difference methods can be implemented using either piecewise polynomials or RBFs.
ContributorsLiu, Tony (Author) / Platte, Rodrigo B (Thesis advisor) / Renaut, Rosemary (Committee member) / Kaspar, David (Committee member) / Moustaoui, Mohamed (Committee member) / Motsch, Sebastien (Committee member) / Arizona State University (Publisher)
Created2019
Description
Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.
ContributorsIlkturk, Utku (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Renaut, Rosemary (Committee member) / Armbruster, Dieter (Committee member) / Arizona State University (Publisher)
Created2015
Description
Divergence-free vector field interpolants properties are explored on uniform and scattered nodes, and also their application to fluid flow problems. These interpolants may be applied to physical problems that require the approximant to have zero divergence, such as the velocity field in the incompressible Navier-Stokes equations and the magnetic and electric fields in the Maxwell's equations. In addition, the methods studied here are meshfree, and are suitable for problems defined on complex domains, where mesh generation is computationally expensive or inaccurate, or for problems where the data is only available at scattered locations.
The contributions of this work include a detailed comparison between standard and divergence-free radial basis approximations, a study of the Lebesgue constants for divergence-free approximations and their dependence on node placement, and an investigation of the flat limit of divergence-free interpolants. Finally, numerical solvers for the incompressible Navier-Stokes equations in primitive variables are implemented using discretizations based on traditional and divergence-free kernels. The numerical results are compared to reference solutions obtained with a spectral
method.
The contributions of this work include a detailed comparison between standard and divergence-free radial basis approximations, a study of the Lebesgue constants for divergence-free approximations and their dependence on node placement, and an investigation of the flat limit of divergence-free interpolants. Finally, numerical solvers for the incompressible Navier-Stokes equations in primitive variables are implemented using discretizations based on traditional and divergence-free kernels. The numerical results are compared to reference solutions obtained with a spectral
method.
ContributorsAraujo Mitrano, Arthur (Author) / Platte, Rodrigo (Thesis advisor) / Wright, Grady (Committee member) / Welfert, Bruno (Committee member) / Gelb, Anne (Committee member) / Renaut, Rosemary (Committee member) / Arizona State University (Publisher)
Created2016
Description
Global optimization (programming) has been attracting the attention of researchers for almost a century. Since linear programming (LP) and mixed integer linear programming (MILP) had been well studied in early stages, MILP methods and software tools had improved in their efficiency in the past few years. They are now fast and robust even for problems with millions of variables. Therefore, it is desirable to use MILP software to solve mixed integer nonlinear programming (MINLP) problems. For an MINLP problem to be solved by an MILP solver, its nonlinear functions must be transformed to linear ones. The most common method to do the transformation is the piecewise linear approximation (PLA). This dissertation will summarize the types of optimization and the most important tools and methods, and will discuss in depth the PLA tool. PLA will be done using nonuniform partitioning of the domain of the variables involved in the function that will be approximated. Also partial PLA models that approximate only parts of a complicated optimization problem will be introduced. Computational experiments will be done and the results will show that nonuniform partitioning and partial PLA can be beneficial.
ContributorsAlkhalifa, Loay (Author) / Mittelmann, Hans (Thesis advisor) / Armbruster, Hans (Committee member) / Escobedo, Adolfo (Committee member) / Renaut, Rosemary (Committee member) / Sefair, Jorge (Committee member) / Arizona State University (Publisher)
Created2020