Browsing by Department "Mathematics, Department of"
Now showing items 120 of 70

A Comprehensive Method for Integrated (Realized) Volatility Estimation
(December 2)In this dissertation, a comprehensive kernelbased estimator, PCA Kernel (PK), is studied to estimate the integrated (realized) volatility under the effect of a more realistic and complex market microstructure noise. ... 
A COMPREHENSIVE OVERVIEW OF MINIMALSURFACE THEORY, WITH A THOROUGH MATHEMATICAL TREATMENT OF BERNSTEIN'S THEOREM, THE WEIERSTRASSENNEPER REPRESENTATIONS, AND PROPERTIES OF THE GAUSS MAP
(201408)Notable results in minimalsurface theory include Bernstein's Theorem, the WeierstrassEnneper representations, and properties of the Gauss map of a minimal surface. For a solution f(x_1, x_2) of the minimalsurface ... 
A FLUIDSTRUCTURE INTERACTION MODEL CAPTURING LONGITUDINAL DISPLACEMENT IN ARTERIES: MODELING, COMPUTATIONAL METHOD, AND COMPARISON WITH EXPERIMENTAL DATA
(201205)The focus of this thesis is on numerical modeling of fluidstructure interaction (FSI) problems with application to hemodynamics. Recent in vivo studies, utilizing ultrasound contour and speckle tracking methods, have ... 
A General Defect Relation and Height Inequality for Divisors in Subgeneral Position
(August 201)In this dissertation, we describe a paper that improves on the conditions that imply holomorphic curves and integral points are degenerate or not Zariskidense. Specifically, we show that for a holomorphic curve into a ... 
A Hidden Markov Renewal Model
(December 2)Hidden semiMarkov models (HSMMs) are a powerful class of statistical model that have been applied to a wide range of areas such as speech recognition, protein structure prediction, Internettraffic modeling, financial ... 
A PrimalDual ActiveSet Method and Algorithm for Chemical Equilibrium Problem Related To Modeling of Atmospheric Inorganic Aerosols
(201412)In this dissertation, we studied a general equilibrium model for multiphase multicomponent inorganic atmospheric aerosols. We developed the thermodynamic model to predict the phase transition and multistage growth phenomena ... 
A Second Order Variational Approach For Diffeomorphic Matching Of 3D Surfaces
(201308)In medical 3Dimaging, one of the main goals of image registration is to accurately compare two observed 3Dshapes. In this dissertation, we consider optimal matching of surfaces by a variational approach based on Hilbert ... 
Active Manipulation of Acoustic Fields and Applications
(December 2)In this thesis we present the research performed in the last three and a half years concerning frequency domain control of acoustic and electromagnetic fields through secondary exterior sources or arrays. We will discuss ... 
CLASSIFICATION OF LEAVITT PATH ALGEBRAS USING ALGEBRAIC KTHEORY
(201505)We show that the long exact sequence for the $K$theory of Leavitt path algebras over rowfinite graphs, discovered by Ara, Brustenga, and Corti{\~n}as, extends to Leavitt path algebras of arbitrary countable graphs. Using ... 
Combining Diffeomorphic Matching with Image Sequence Intensity Registration
(201405)This thesis presents the research work completed over the past 4 years in the context of a collaborative project between The Methodist Hospital (TMH) and the University of Houston. We have developed and implemented novel ... 
Datadriven Techniques For Estimation And Stochastic Reduction Of Multiscale Systems
(201212)Parametric estimation of stochastic processes is one of the most widely used techniques for obtaining effective models, given a discrete dataset. Often, the experimental or observational datasets are not explicitly generated ... 
Decision Making in Social Networks
(December 2)We investigate how the network topology of social networks impacts decision making. First we look at sequential models of decision making with feedforward network toplogies. We see how rational agents incorporate knowledge ... 
Determining Coherent Sets in 2D Fluid Flows by Transfer Operator Methods
(2017)Coherent sets are areas of the flow which are closed or nearly closed from the rest of the fluid (e.g. ocean garbage patches, Jupiter’s red spot). Our goal is to identify such set; this is useful for other areas of research ... 
DIRECTIONAL MULTISCALE ANALYSIS USING SHEARLET THEORY AND APPLICATIONS
(201208)Shearlets emerged in recent years in applied harmonic analysis as a general framework to provide sparse representations of multidimensional data. This construction was motivated by the need to provide more efficient ... 
Extensions of Approximately Unital Operator Algebras
(201308)Extension theory in the study of C*algebras has been important in many aspects. For that reason, a theory of extensions of operator algebras, with as direct a link as possible to the C*algebras theory, will be developed. ... 
EXTERIOR REGULARIZED HARMONIC AND HARMONIC FUNCTIONS
(201208)This thesis mainly studies harmonic functions on exterior regions, having compact, Lipschitz boundaries, in our new finite energy function space, via the sequence of exterior harmonic Steklov eigenvalues and associated ... 
Fast and Stable Algorithms for Deep Learning
(2018)Brain tumors are the leading cause of cancerrelated deaths among multiple age groups. An important step in clinical management of patients diagnosed with tumors is tumor segmentation, which separates abnormal (cancerous) ... 
Fast Illumination Normalization for Face Recognition
(2017)Many applications of computer vision, security and surveillance require an accurate and realtime method for illumination neutralization and contrast enhancement. We present a new mathematical framework, with a real time ... 
Following the Crowd: How Herding May Affect Binary Decisions
(2018)“Network”, referring to the concept information flow among agents, is ubiquitous today. The networks we looked at consist of individuals tasked with making a binary decision based on partial information about the true ... 
FRAMES AS CODES FOR STRUCTURED ERASURES
(201212)This dissertation studies the role of frames as codes. Frames are families of vectors that give rise to embeddings of Hilbert spaces. These embeddings can be interpreted as codes, because possible linear dependencies among ...