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- Creators: College of Liberal Arts and Sciences
Description
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, the original problem can be approximated via the sum of a series of simple functions with closed form solutions. A preconditioner for solving the block Toeplitz with Toeplitz block (BTTB) linear system is proposed to accelerate the computation. An in-depth discussion on the rate of convergence and the optimal parameter selection criteria is given. Numerical experiments are used to test the performance and the robustness of the proposed algorithm to a wide range of parameter values. Applications of the algorithm in magnetic resonance (MR) imaging and a comparison with other existing methods are included. The second part of this work is the application of the TV-$\ell_1$ model in source localization using sensor arrays. The array output is reformulated into a sparse waveform via an over-complete basis and study the $\ell_p$-norm properties in detecting the sparsity. An algorithm is proposed for minimizing a non-convex problem. According to the results of numerical experiments, the proposed algorithm with the aid of the $\ell_p$-norm can resolve closely distributed sources with higher accuracy than other existing methods.
ContributorsShen, Wei (Author) / Mittlemann, Hans D (Thesis advisor) / Renaut, Rosemary A. (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Gelb, Anne (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2011
Description
Meteorology is an uncommon term rarely resonating through elementary classrooms. However, it is a concept found in both fourth and sixth grade Arizona science standards. As issues involving the environment are becoming more pertinent, it is important to study and understand atmospheric processes along with fulfilling the standards for each grade level. This thesis project teaches the practical skills of weather map reading and weather forecasting through the creation and execution of an after school lesson with the aide of seven teen assistants.
ContributorsChoulet, Shayna (Author) / Walters, Debra (Thesis director) / Oliver, Jill (Committee member) / Balling, Robert (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
Description
Plants are essential to human life. They release oxygen into the atmosphere for us to breathe. They also provide shelter, medicine, clothing, tools, and food. For many people, the food that is on their tables and in their supermarkets isn't given much thought. Where did it come from? What part of the plant is it? How does it relate to others in the plant kingdom? How do other cultures use this plant? The most many of us know about them is that they are at the supermarket when we need them for dinner (Nabhan, 2009) (Vileisis, 2008).
ContributorsBarron, Kara (Author) / Landrum, Leslie (Thesis director) / Swanson, Tod (Committee member) / Pigg, Kathleen (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
DescriptionBased on previous research and findings it is proven that a non-profit class to create awareness will be beneficial in the prevention of eating disorders. This analysis will provide significant research to defend the proposed class.
ContributorsAllen, Brittany (Author) / Chung, Deborah (Author) / Fey, Richard (Thesis director) / Peck, Sidnee (Committee member) / Mazurkiewicz, Milena (Committee member) / Barrett, The Honors College (Contributor) / W. P. Carey School of Business (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
Description
Restraint stress is the most commonly used laboratory stressor. It is difficult to characterize as psychological or physical, because past studies show psychological features, but the nature of confinement adds a physical dimension. This was the first study to investigate how experience with restraint stress affects brain response to the next stress without a physical burden. Pair-housed adult male rats were transported to a novel context and restrained or left undisturbed (6hr). The next day, rats were returned to the same context and were either restrained or left undisturbed in the context (n=8/group). After 90min, rats were euthanized to determine functional activation in limbic structures using Fos immunohistochemistry and to measure HPA axis reactivity through blood serum corticosterone levels. Regardless of day 1 experience, context exposure on day 2 enhanced Fos expression in CA1 and CA3 of the hippocampus, basolateral amygdala, and central amygdala. Conversely, other regions and corticosterone levels demonstrated modulation from the previous day's experience. Specifically, rats that were placed back into the restraint context but not restrained on day 2 showed enhanced Fos expression in the dentate gyrus suprapyramidal blade (DGSup), and infralimbic cortex (IL). Also Fos expression was attenuated in rats that received two restraint exposures in the IL and medial amygdala (MEA), suggesting habituation. Only the DG infrapyramidal blade (DGInf) showed enhanced Fos expression to restraint on day 2 without influence of the previous day. While context predominately directed Fos activation, prior experience with restraint influenced Fos expression in the DGSup, IL, MEA and corticosterone levels to support restraint having psychological components.
ContributorsAnouti, P. Danya (Author) / Conrad, D. Cheryl (Thesis director) / Hammer, Ronald (Committee member) / Hoffman, N. Ann (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
Description
Rabies disease remains enzootic among raccoons, skunks, foxes and bats in the United States. It is of primary concern for public-health agencies to control spatial spread of rabies in wildlife and its potential spillover infection of domestic animals and humans. Rabies is invariably fatal in wildlife if untreated, with a non-negligible incubation period. Understanding how this latency affects spatial spread of rabies in wildlife is the concern of chapter 2 and 3. Chapter 1 deals with the background of mathematical models for rabies and lists main objectives. In chapter 2, a reaction-diffusion susceptible-exposed-infected (SEI) model and a delayed diffusive susceptible-infected (SI) model are constructed to describe the same epidemic process -- rabies spread in foxes. For the delayed diffusive model a non-local infection term with delay is resulted from modeling the dispersal during incubation stage. Comparison is made regarding minimum traveling wave speeds of the two models, which are verified using numerical experiments. In chapter 3, starting with two Kermack and McKendrick's models where infectivity, death rate and diffusion rate of infected individuals can depend on the age of infection, the asymptotic speed of spread $c^\ast$ for the cumulated force of infection can be analyzed. For the special case of fixed incubation period, the asymptotic speed of spread is governed by the same integral equation for both models. Although explicit solutions for $c^\ast$ are difficult to obtain, assuming that diffusion coefficient of incubating animals is small, $c^\ast$ can be estimated in terms of model parameter values. Chapter 4 considers the implementation of realistic landscape in simulation of rabies spread in skunks and bats in northeast Texas. The Finite Element Method (FEM) is adopted because the irregular shapes of realistic landscape naturally lead to unstructured grids in the spatial domain. This implementation leads to a more accurate description of skunk rabies cases distributions.
ContributorsLiu, Hao (Author) / Kuang, Yang (Thesis advisor) / Jackiewicz, Zdzislaw (Committee member) / Lanchier, Nicolas (Committee member) / Smith, Hal (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2013
Description
One explanation for membrane accommodation in response to a slowly rising current, and the phenomenon underlying the dynamics of elliptic bursting in nerves, is the mathematical problem of dynamic Hopf bifurcation. This problem has been studied extensively for linear (deterministic and stochastic) current ramps, nonlinear ramps, and elliptic bursting. These studies primarily investigated dynamic Hopf bifurcation in space-clamped excitable cells. In this study we introduce a new phenomenon associated with dynamic Hopf bifurcation. We show that for excitable spiny cables injected at one end with a slow current ramp, the generation of oscillations may occur an order one distance away from the current injection site. The phenomenon is significant since in the model the geometric and electrical parameters, as well as the ion channels, are uniformly distributed. In addition to demonstrating the phenomenon computationally, we analyze the problem using a singular perturbation method that provides a way to predict when and where the onset will occur in response to the input stimulus. We do not see this phenomenon for excitable cables in which the ion channels are embedded in the cable membrane itself, suggesting that it is essential for the channels to be isolated in the spines.
ContributorsBilinsky, Lydia M (Author) / Baer, Steven M. (Thesis advisor) / Crook, Sharon M (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Gardner, Carl L (Committee member) / Jung, Ranu (Committee member) / Arizona State University (Publisher)
Created2012
Description
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 infinite distributed delay terms based on some existing work is established. A rigorous analysis of the well-posedness of this model is provided, and it is proved that the susceptible bacteria persist. To study the persistence of phage species, a "Phage Reproduction Number" (PRN) is defined. The mathematical analysis shows phage persist if PRN > 1 and vanish if PRN < 1. A sufficient condition and a necessary condition for persistence of resistant bacteria are given. The persistence of the phage is essential for the persistence of resistant bacteria. Also, the resistant bacteria persist if its fitness is the same as the susceptible bacteria and if PRN > 1. A special case of the general model leads to a system of ordinary differential equations, for which numerical simulation results are presented.
ContributorsHan, Zhun (Author) / Smith, Hal (Thesis advisor) / Armbruster, Dieter (Committee member) / Kawski, Matthias (Committee member) / Kuang, Yang (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2012
Description
In vertebrate outer retina, changes in the membrane potential of horizontal cells affect the calcium influx and glutamate release of cone photoreceptors via a negative feedback. This feedback has a number of important physiological consequences. One is called background-induced flicker enhancement (BIFE) in which the onset of dim background enhances the center flicker response of horizontal cells. The underlying mechanism for the feedback is still unclear but competing hypotheses have been proposed. One is the GABA hypothesis, which states that the feedback is mediated by gamma-aminobutyric acid (GABA), an inhibitory neurotransmitter released from horizontal cells. Another is the ephaptic hypothesis, which contends that the feedback is non-GABAergic and is achieved through the modulation of electrical potential in the intersynaptic cleft between cones and horizontal cells. In this study, a continuum spine model of the cone-horizontal cell synaptic circuitry is formulated. This model, a partial differential equation system, incorporates both the GABA and ephaptic feedback mechanisms. Simulation results, in comparison with experiments, indicate that the ephaptic mechanism is necessary in order for the model to capture the major spatial and temporal dynamics of the BIFE effect. In addition, simulations indicate that the GABA mechanism may play some minor modulation role.
ContributorsChang, Shaojie (Author) / Baer, Steven M. (Thesis advisor) / Gardner, Carl L (Thesis advisor) / Crook, Sharon M (Committee member) / Kuang, Yang (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2012
Description
Through this creative project, I executed a Distracted Driving Awareness Campaign at Arizona State University to raise awareness about the dangers of distracted driving, specifically texting while driving. As an Undergraduate Student Government Senator, my priority is the safety and success of students, both in and out of the classroom. By partnering with State Farm and AT&T, we were able to raise awareness about the dangers of distracted driving and collected over 200 pledges from students to never text and drive.
ContributorsHibbs, Jordan Ashley (Author) / Miller, Clark (Thesis director) / Parmentier, Mary Jane (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor) / School of Politics and Global Studies (Contributor) / Department of Psychology (Contributor) / Graduate College (Contributor)
Created2014-05