Browsing Mathematics by Title
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Absolutely Continuous Spectrum for Parabolic Flows/Maps
(2016)This work is devoted to creating an abstract framework for the study of certain spectral properties of parabolic systems. Specifically, we determine under which general conditions to expect the presence of absolutely ... 
Abstract Elementary Classes with LowenheimSkolem Number Cofinal with Omega
(20080803)An abstract elementary class is a class $\aec$ of structures for some vocabulary $L$ together with a ``strong substructure'' relation $\prec_{\aec}$ on $\aec$ satisfying certain axioms. Abstract elementary classes include ... 
Abundance of escaping orbitsin a family of antiintegrable limitsof the standard map
(2009)We give quantitative results about the abundance of escaping orbits in a family of exact twist maps preserving Lebesgue measure on the cylinder <bold>T</bold> × <bold>R</bold>; geometrical features of maps of this family ... 
Adapting Swarm Intelligence For The SelfAssembly And Optimization Of Networks
(2011)While selfassembly is a fairly active area of research in swarm intelligence and robotics, relatively little attention has been paid to the issues surrounding the construction of network structures. Here, methods developed ... 
Adaptive Finite Element Methods for Variational Inequalities: Theory and Applications in Finance
(20070529)We consider variational inequalities (VIs) in a bounded open domain Omega subset IR^d with a piecewise smooth obstacle constraint. To solve VIs, we formulate a fullydiscrete adaptive algorithm by using the backward Euler ... 
The Adelic Differential Graded Algebra for Surfaces
(2017)For any variety X/k, we consider the Beilinson–Huber adeles AX as a differ ential graded kalgebra and examine the category Moddg of differential graded Amodules. We characterize the modules associated to certain ... 
Adiabatic quantum computation: Noise in the adiabatic theorem and using the JordanWigner transform to find effective Hamiltonians
(20080422)This thesis explores two mathematical aspects of adiabatic quantum computation. Adiabatic quantum computation depends on the adiabatic theorem of quantum mechanics, and (a) we provide a rigorous formulation of the adiabatic ... 
ADJUSTMENT FOR DENSITY METHOD TO ESTIMATE RANDOM EFFECTS IN HIERARCHICAL BAYES MODELS
(2018)The Adjustment for Density Method (ADM) has received considerable attention in recent years. The method was proposed about thirty years back in approximating a complex univariate density by a density from the Pearson family ... 
Adversarial Robustness and Robust MetaLearning for Neural Networks
(2020)Despite the overwhelming success of neural networks for pattern recognition, these models behave categorically different from humans. Adversarial examples, small perturbations which are often undetectable to the human ... 
Affine Pavings of Hessenberg Ideal Fibers
(2020)We define certain closed subvarieties of the flag variety, Hessenberg ideal fibers, and prove that they are paved by affines. Hessenberg ideal fibers are a natural generalization of Springer fibers. In type $G_2$, we give ... 
An AgentBased Modeling Approach to Reducing Pathogenic Transmission in Medical Facilities and Community Populations
(2012)The spread of infectious diseases is a significant and ongoing problem in human populations. In hospitals, the cost of patients acquiring infections causes many downstream effects, including longer lengths of stay for ... 
Algorithm Development for Hyperspectral Anomaly Detection
(20080812)This dissertation proposes and evaluates a novel anomaly detection algorithm suite for groundtoground, or airtoground, applications requiring automatic target detection using hyperspectral (HS) data. Targets are manmade ... 
An Algorithmic Approach to Invariant Rational Functions
(2014)For any field K and group A acting on K(x0, x1,..., xn1), the fixed field consists of the elements fixed under the action of A, and is denoted K(x0, x1,..., xn1)^A. Noether's problem seeks to answer whether K(x0, x1,..., ... 
Algorithms and Generalizations for the Lovasz Local Lemma
(2015)The Lovasz Local Lemma (LLL) is a cornerstone principle of the probabilistic method for combinatorics. This shows that one can avoid a large of set of “badevents” (forbidden configurations of variables), provided the local ... 
Algorithms for Solving Linear and Polynomial Systems of Equations over Finite Fields with Applications to Cryptanalysis
(20070607)This dissertation contains algorithms for solving linear and polynomial systems of equations over GF(2). The objective is to provide fast and exact tools for algebraic cryptanalysis and other applications. Accordingly, it ... 
ALGORITHMS FOR THE ALIGNMENT AND VISUALIZATION OF GENOME MAPPING DATA WITH APPLICATIONS TO STRUCTURAL VARIANT DETECTION
(2015)Optical mapping and nanocoding are single molecule restriction mapping systems for interrogating genomic structure at a scale that cannot currently be achieved using DNA sequencing methods. In these mapping experiments, ... 
Analysis and correction of compositional bias in sparse sequencing count data
(Springer Nature, 20181106)Count data derived from highthroughput deoxyribonucliec acid (DNA) sequencing is frequently used in quantitative molecular assays. Due to properties inherent to the sequencing process, unnormalized count data is ... 
Analysis and Extension of NonCommutative NTRU
(20070806)We discuss the ring based publickey cryptosystem known as noncommutative NTRU. The original system is defined over the group ring R = Z[D_N] (where D_N is the dihedral group of order 2N) and uses a commutative subring ... 
An Analysis of Chaum's VoterVerifiable Election Scheme
(20050503)Chaum's VoterVerifiable election scheme introduces a new direction for electronic voting. The scheme eliminates the need to trust any machinery or authority, and instead relies on mathematical proof to certify the ... 
Analysis of Data Security Vulnerabilities in Deep Learning
(2022)As deep learning systems become more integrated into important application areas, the security of such systems becomes a paramount concern. Specifically, as modern networks require an increasing amount of data on which to ...