UNT Theses and Dissertations - 59 Matching Results

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Fundamental Issues in Support Vector Machines

Description: This dissertation considers certain issues in support vector machines (SVMs), including a description of their construction, aspects of certain exponential kernels used in some SVMs, and a presentation of an algorithm that computes the necessary elements of their operation with proof of convergence. In its first section, this dissertation provides a reasonably complete description of SVMs and their theoretical basis, along with a few motivating examples and counterexamples. This section may be … more
Date: May 2014
Creator: McWhorter, Samuel P.
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A General Approach to Buhlmann Credibility Theory

Description: Credibility theory is widely used in insurance. It is included in the examination of the Society of Actuaries and in the construction and evaluation of actuarial models. In particular, the Buhlmann credibility model has played a fundamental role in both actuarial theory and practice. It provides a mathematical rigorous procedure for deciding how much credibility should be given to the actual experience rating of an individual risk relative to the manual rating common to a particular class of ri… more
Date: August 2017
Creator: Yan, Yujie yy
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Gibbs/Equilibrium Measures for Functions of Multidimensional Shifts with Countable Alphabets

Description: Consider a multidimensional shift space with a countably infinite alphabet, which serves in mathematical physics as a classical lattice gas or lattice spin system. A new definition of a Gibbs measure is introduced for suitable real-valued functions of the configuration space, which play the physical role of specific internal energy. The variational principle is proved for a large class of functions, and then a more restrictive modulus of continuity condition is provided that guarantees a functi… more
Date: May 2011
Creator: Muir, Stephen R.
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A Global Spatial Model for Loop Pattern Fingerprints and Its Spectral Analysis

Description: The use of fingerprints for personal identification has been around for thousands of years (first established in ancient China and India). Fingerprint identification is based on two basic premises that the fingerprint is unique to an individual and the basic characteristics such as ridge pattern do not change over time. Despite extensive research, there are still mathematical challenges in characterization of fingerprints, matching and compression. We develop a new mathematical model in the spa… more
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Date: August 2019
Creator: Wu, Di
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Graev Metrics and Isometry Groups of Polish Ultrametric Spaces

Description: This dissertation presents results about computations of Graev metrics on free groups and characterizes isometry groups of countable noncompact Heine-Borel Polish ultrametric spaces. In Chapter 2, computations of Graev metrics are performed on free groups. One of the related results answers an open question of Van Den Dries and Gao. In Chapter 3, isometry groups of countable noncompact Heine-Borel Polish ultrametric spaces are characterized. The notion of generalized tree is defined and a corre… more
Date: May 2013
Creator: Shi, Xiaohui
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Hausdorff Dimension of Shrinking-Target Sets Under Non-Autonomous Systems

Description: For a dynamical system on a metric space a shrinking-target set consists of those points whose orbit hit a given ball of shrinking radius infinitely often. Historically such sets originate in Diophantine approximation, in which case they describe the set of well-approximable numbers. One aspect of such sets that is often studied is their Hausdorff dimension. We will show that an analogue of Bowen's dimension formula holds for such sets when they are generated by conformal non-autonomous iterate… more
Date: August 2018
Creator: Lopez, Marco Antonio
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Hermitian Jacobi Forms and Congruences

Description: In this thesis, we introduce a new space of Hermitian Jacobi forms, and we determine its structure. As an application, we study heat cycles of Hermitian Jacobi forms, and we establish a criterion for the existence of U(p) congruences of Hermitian Jacobi forms. We demonstrate that criterion with some explicit examples. Finally, in the appendix we give tables of Fourier series coefficients of several Hermitian Jacobi forms.
Date: August 2014
Creator: Senadheera, Jayantha
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Hochschild Cohomology and Complex Reflection Groups

Description: A concrete description of Hochschild cohomology is the first step toward exploring associative deformations of algebras. In this dissertation, deformation theory, geometry, combinatorics, invariant theory, representation theory, and homological algebra merge in an investigation of Hochschild cohomology of skew group algebras arising from complex reflection groups. Given a linear action of a finite group on a finite dimensional vector space, the skew group algebra under consideration is the se… more
Date: August 2012
Creator: Foster-Greenwood, Briana A.
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Infinitary Combinatorics and the Spreading Models of Banach Spaces

Description: Spreading models have become fundamental to the study of asymptotic geometry in Banach spaces. The existence of spreading models in every Banach space, and the so-called good sequences which generate them, was one of the first applications of Ramsey theory in Banach space theory. We use Ramsey theory and other techniques from infinitary combinatorics to examine some old and new questions concerning spreading models and good sequences. First, we consider the lp spreading model problem which asks… more
Date: May 2019
Creator: Krause, Cory A.
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Infinitely Many Solutions of Semilinear Equations on Exterior Domains

Description: We prove the existence and nonexistence of solutions for the semilinear problem ∆u + K(r)f(u) = 0 with various boundary conditions on the exterior of the ball in R^N such that lim r→∞u(r) = 0. Here f : R → R is an odd locally lipschitz non-linear function such that there exists a β > 0 with f < 0 on (0, β), f > 0 on (β, ∞), and K(r) \equiv r^−α for some α > 0.
Date: August 2018
Creator: Joshi, Janak R
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Irreducible Modules for Yokonuma-Type Hecke Algebras

Description: Yokonuma-type Hecke algebras are a class of Hecke algebras built from a Type A construction. In this thesis, I construct the irreducible representations for a class of generic Yokonuma-type Hecke algebras which specialize to group algebras of the complex reflection groups and to endomorphism rings of certain permutation characters of finite general linear groups.
Date: August 2016
Creator: Dave, Ojas
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Kleinian Groups in Hilbert Spaces

Description: The theory of discrete groups acting on finite dimensional Euclidean open balls by hyperbolic isometries was borne around the end of 19th century within the works of Fuchs, Klein and Poincaré. We develop the theory of discrete groups acting by hyperbolic isometries on the open unit ball of an infinite dimensional separable Hilbert space. We present our investigations on the geometry of limit sets at the sphere at infinity with an attempt to highlight the differences between the finite and infin… more
Date: August 2012
Creator: Das, Tushar
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Maximum Likelihood Estimation of Logistic Sinusoidal Regression Models

Description: We consider the problem of maximum likelihood estimation of logistic sinusoidal regression models and develop some asymptotic theory including the consistency and joint rates of convergence for the maximum likelihood estimators. The key techniques build upon a synthesis of the results of Walker and Song and Li for the widely studied sinusoidal regression model and on making a connection to a result of Radchenko. Monte Carlo simulations are also presented to demonstrate the finite-sample perform… more
Date: December 2013
Creator: Weng, Yu
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Mycielski-Regular Measures

Description: Let μ be a Radon probability measure on M, the d-dimensional Real Euclidean space (where d is a positive integer), and f a measurable function. Let P be the space of sequences whose coordinates are elements in M. Then, for any point x in M, define a function ƒn on M and P that looks at the first n terms of an element of P and evaluates f at the first of those n terms that minimizes the distance to x in M. The measures for which such sequences converge in measure to f for almost every sequence a… more
Date: August 2011
Creator: Bass, Jeremiah Joseph
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Non-Resonant Uniserial Representations of Vec(R)

Description: The non-resonant bounded uniserial representations of Vec(R) form a certain class of extensions composed of tensor density modules, all of whose subquotients are indecomposable. The problem of classifying the extensions with a given composition series is reduced via cohomological methods to computing the solution of a certain system of polynomial equations in several variables derived from the cup equations for the extension. Using this method, we classify all non-resonant bounded uniserial ext… more
Date: May 2018
Creator: O'Dell, Connor
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Nonparametric Estimation of Receiver Operating Characteristic Surfaces Via Bernstein Polynomials

Description: Receiver operating characteristic (ROC) analysis is one of the most widely used methods in evaluating the accuracy of a classification method. It is used in many areas of decision making such as radiology, cardiology, machine learning as well as many other areas of medical sciences. The dissertation proposes a novel nonparametric estimation method of the ROC surface for the three-class classification problem via Bernstein polynomials. The… more
Date: December 2012
Creator: Herath, Dushanthi N.
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A Novel Two-Stage Adaptive Method for Estimating Large Covariance and Precision Matrices

Description: Estimating large covariance and precision (inverse covariance) matrices has become increasingly important in high dimensional statistics because of its wide applications. The estimation problem is challenging not only theoretically due to the constraint of its positive definiteness, but also computationally because of the curse of dimensionality. Many types of estimators have been proposed such as thresholding under the sparsity assumption of the target matrix, banding and tapering the sample c… more
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Date: August 2019
Creator: Rajendran, Rajanikanth
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Numerical Values of the Hausdorff and Packing Measures for Limit Sets of Iterated Function Systems

Description: In the context of fractal geometry, the natural extension of volume in Euclidean space is given by Hausdorff and packing measures. These measures arise naturally in the context of iterated function systems (IFS). For example, if the IFS is finite and conformal, then the Hausdorff and packing dimensions of the limit sets agree and the corresponding Hausdorff and packing measures are positive and finite. Moreover, the map which takes the IFS to its dimension is continuous. Developing on previous … more
Date: August 2017
Creator: Reid, James Edward
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On Factors of Rank One Subshifts

Description: Rank one subshifts are dynamical systems generated by a regular combinatorial process based on sequences of positive integers called the cut and spacer parameters. Despite the simple process that generates them, rank one subshifts comprise a generic set and are the source of many counterexamples. As a result, measure theoretic rank one subshifts, called rank one transformations, have been extensively studied and investigations into rank one subshifts been the basis of much recent work. We will … more
Date: May 2018
Creator: Ziegler, Caleb
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On Steinhaus Sets, Orbit Trees and Universal Properties of Various Subgroups in the Permutation Group of Natural Numbers

Description: In the first chapter, we define Steinhaus set as a set that meets every isometric copy of another set at exactly one point. We show that there is no Steinhaus set for any four-point subset in a plane.In the second chapter, we define the orbit tree of a permutation group of natural numbers, and further introduce compressed orbit trees. We show that any rooted finite tree can be realized as a compressed orbit tree of some permutation group. In the third chapter, we investigate certain classes of … more
Date: August 2012
Creator: Xuan, Mingzhi
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Optimal Strategies for Stopping Near the Top of a Sequence

Description: In Chapter 1 the classical secretary problem is introduced. Chapters 2 and 3 are variations of this problem. Chapter 2, discusses the problem of maximizing the probability of stopping with one of the two highest values in a Bernoulli random walk with arbitrary parameter p and finite time horizon n. The optimal strategy (continue or stop) depends on a sequence of threshold values (critical probabilities) which has an oscillating pattern. Several properties of this sequence have been proved by Dr… more
Date: December 2015
Creator: Islas Anguiano, Jose Angel
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Partition Properties for Non-Ordinal Sets under the Axiom of Determinacy

Description: In this paper we explore coloring theorems for the reals, its quotients, cardinals, and their combinations. This work is done under the scope of the axiom of determinacy. We also explore generalizations of Mycielski's theorem and show how these can be used to establish coloring theorems. To finish, we discuss the strange realm of long unions.
Date: May 2017
Creator: Holshouser, Jared
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Prophet Inequalities for Multivariate Random Variables with Cost for Observations

Description: In prophet problems, two players with different levels of information make decisions to optimize their return from an underlying optimal stopping problem. The player with more information is called the "prophet" while the player with less information is known as the "gambler." In this thesis, as in the majority of the literature on such problems, we assume that the prophet is omniscient, and the gambler does not know future outcomes when making his decisions. Certainly, the prophet will get a b… more
Date: August 2019
Creator: Brophy, Edmond M.
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Quantum Drinfeld Hecke Algebras

Description: Quantum Drinfeld Hecke algebras extend both Lusztig's graded Hecke algebras and the symplectic reflection algebras of Etingof and Ginzburg to the quantum setting. A quantum (or skew) polynomial ring is generated by variables which commute only up to a set of quantum parameters. Certain finite groups may act by graded automorphisms on a quantum polynomial ring and quantum Drinfeld Hecke algebras deform the natural semi-direct product. We classify these algebras for the infinite family of complex… more
Date: August 2016
Creator: Uhl, Christine
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