Browsing by Department "Mathematics"
Now showing items 120 of 47

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 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 ... 
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 ... 
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 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 ... 
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 ... 
Global Existence of solutions to ReactionDiffusion Systems with Mass Transport type Boundary Conditions
(201308)We consider coupled reactiondiffusion models, where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. ... 
HighOrder Numerical Methods for TimeDependent Problems with Applications
(201508)In this dissertation, several highorder numerical methods for solving time dependent problems are studied. In the first part, a maximum principle preserving (MPP) finitevolume (FV) weighted essentially nonoscillatory ... 
Image Analysis Using Directional Multiscale Representations and Applications for Characterization of Neuronal Morphology
(201512)Recent advances in highresolution fluorescence microscopy have enabled the system atic study of morphological changes in large populations of cells induced by chemical and genetic perturbations, facilitating the discovery ... 
Large Deviations Approach for Stochastic Genetic Evolution
(201308)Theoretical ecologists have long strived to explain how the persistence of populations depends on biotic and abiotic factors and have proposed various models to predict the long time behavior of biological populations. We ... 
Large Time Step and Overlapping Grids for Conservation Laws
(201405)One focus of this dissertation is to construct a large time step Finite Volume Method for computing numerical solutions to hyperbolic systems of conservation laws. We also consider a method of overlapping spatial grids for ... 
Mass spectrometry data mining for cancer detection
(201312)Early detection of cancer is crucial for successful intervention strategies. Mass spectrometrybased high throughput proteomics is recognized as a major breakthrough in cancer detection. Many machine learning methods have ...