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Articles 91 - 120 of 129
Full-Text Articles in Applied Mathematics
Source Optimization In Abstract Function Spaces For Maximizing Distinguishability: Applications To The Optical Tomography Inverse Problem, Bonnie Jacob
All Dissertations
The focus of this thesis is to formulate an optimal source problem for the medical imaging technique of optical tomography by maximizing certain distinguishability criteria. We extend the concept of distinguishability in electrical impedance tomography to the frequency-domain diffusion approximation model used in optical tomography.
We consider the dependence of the optimal source on the choice of appropriate function spaces, which can be chosen from certain Sobolev or Lp spaces. All of the spaces we consider are Hilbert spaces; we therefore exploit the inner product in several ways. First, we define and use throughout an inner product on the Sobolev …
Improved Accuracy For Fluid Flow Problems Via Enhanced Physics, Michael Case
Improved Accuracy For Fluid Flow Problems Via Enhanced Physics, Michael Case
All Dissertations
This thesis is an investigation of numerical methods for approximating solutions to fluid flow problems, specifically the Navier-Stokes equations (NSE) and magnetohydrodynamic equations (MHD), with an overriding theme of enforcing more physical behavior in discrete solutions. It is well documented that numerical methods with more physical accuracy exhibit better long-time behavior than comparable methods that enforce less physics in their solutions. This work develops, analyzes and tests finite element methods that better enforce mass conservation in discrete velocity solutions to the NSE and MHD, helicity conservation for NSE, cross-helicity conservation in MHD, and magnetic field incompressibility in MHD.
Some New Problems In Changepoint Analysis, Jonathan Woody
Some New Problems In Changepoint Analysis, Jonathan Woody
All Dissertations
Climatological studies have often neglected changepoint effects when modeling
various physical phenomena. Here, changepoints are plausible whenever a station location moves or its instruments are changed. There is frequently meta-data to
perform sound statistical inferences that account for changepoint
information. This dissertation focuses on two such problems in changepoint analysis.
The first problem we investigate involves assessing trends
in daily snow depth series. Here, we introduce a stochastic storage model. The model allows for seasonal features, which permits the
analysis of daily data. Changepoint times are shown to greatly influence estimated trends in one snow depth series and are accounted …
Decoding Of Multipoint Algebraic Geometry Codes Via Lists, Nathan Drake
Decoding Of Multipoint Algebraic Geometry Codes Via Lists, Nathan Drake
All Dissertations
Algebraic geometry codes have been studied greatly since their introduction by Goppa . Early study had focused on algebraic geometry codes CL(D;G) where G was taken to be a multiple of a single point. However, it has been shown that if we allow G to be supported by more points, then the associated code may have better parameters. We call such a code a multipoint code and if G is supported by m points, then we call it an m-point code. In this dissertation, we wish to develop a decoding algorithm for multipoint codes. We show how we can embed …
Portfolio Selection Problem Under Uncertainty And Risk, Dimitri Nowak
Portfolio Selection Problem Under Uncertainty And Risk, Dimitri Nowak
All Theses
The purpose of this research is the investigation of a portfolio problem in an uncertain environment. Given possible investments with random performance depending on uncertain environmental settings the objective is to establish a methodology for construction of a portfolio which is non-dominated with respect to second order stochastic dominance and whose return distribution is preferable for a least risk decision maker.
Change-Point Analysis: Asymptotic Theory And Applications, Michael Robbins
Change-Point Analysis: Asymptotic Theory And Applications, Michael Robbins
All Dissertations
The problem of undocumented change-points in data sets appears in many areas of science. Mathematical fundamentals of asymptotic methods used in change-point analysis are discussed, and several important maximally selected change-point statistics are introduced. First, the likelihood ratio method is applied to abstract data models within the setting of precipitation series. Basic inference as to the legitimacy and effectiveness of asymptotic methods at detecting undocumented change-points is provided. Next, maximally selected chi-square statistics are discussed in detail and applied to data on tropical cyclone behavior, where a widely available and widely analyzed data set on Atlantic basin cyclones is studied. …
Multiobjective Optimization For Complex Systems, Melissa Gardenghi
Multiobjective Optimization For Complex Systems, Melissa Gardenghi
All Dissertations
Complex systems are becoming more and more apparent in a variety of disciplines, making solution methods for these systems valuable tools. The solution of complex systems requires two significant skills. The first challenge of developing mathematical models for these systems is followed by the difficulty of solving these models to produce preferred solutions for the overall systems. Both issues are addressed by this research.
This study of complex systems focuses on two distinct aspects. First, models of complex systems with multiobjective formulations and a variety of structures are proposed. Using multiobjective optimization theory, relationships between the efficient solutions of the …
Discrete Dynamics Over Finite Fields, Jang-Woo Park
Discrete Dynamics Over Finite Fields, Jang-Woo Park
All Dissertations
A dynamical system consists of a set V and a map f : V → V . The primary goal is to characterize points in V according to their limiting behaviors under iteration of the map f . Especially understanding dynamics of nonlinear maps is an important but difficult problem, and there are not many methods available. This work concentrates on dynamics of certain nonlinear maps over finite fields. First we study monomial dynamics over finite fields. We show that determining the number of fixed points of a boolean monomial dynamics is #P–complete problem and consider various cases in which …
Local Adaptive Smoothing In Kernel Regression Estimation, Qi Zheng
Local Adaptive Smoothing In Kernel Regression Estimation, Qi Zheng
All Theses
We consider nonparametric estimation of a smooth regression function of one variable. In practice it is quite popular to use the data to select one global smoothing parameter. Such global selection procedures cannot sufficiently account for local sparseness of the covariate nor can they adapt to local curvature of the regression function. We propose a new method to select local smoothing parameters which takes into account sparseness and adapts to local curvature of the regression function. A Bayesian method allows the smoothing parameter to adapt to the local sparseness of the covariate and provides the basis for a local cross …
Sparse Representations In Power Systems Signals, Jack Cooper
Sparse Representations In Power Systems Signals, Jack Cooper
All Theses
This thesis seeks to detect transient disturbances in power system signals in a sparse framework. To this end, an overcomplete wavelet packet dictionary and damped sinusoid dictionary are considered, and for each dictionary Matching Pursuit is compared with Basis Pursuit. Previous work in developing waveform dictionary theory and sparse representation is reviewed, and simulations are run on a test signal in both noisy and noiseless environments. The solutions are viewed as time-frequency plane tilings to compare the accuracy and sparsity of these algorithms in properly resolving optimal representations of the disturbances. The advantages and disadvantages of each combination of dictionary …
Optimization Models For Designing Spatially Compact Ecological Reserve Systems, Lakmali Weerasena
Optimization Models For Designing Spatially Compact Ecological Reserve Systems, Lakmali Weerasena
All Theses
Over the past decades, a number of mathematical models and solution techniques have been developed to preserve reserve sites for species and their natural habitats. Two optimization models for designing spatially compact ecological reserve systems are addressed here as zero-one integer programming problems. These formulations have a bicriteria objective function that is a combination of both boundary length and distance. The two formulations cluster the sites into a relatively small number of compact groups while preserving a required number of sites that contain a certain species using a given amount of resources. Two general types of approaches have been developed …
Variations On Graph Products And Vertex Partitions, Jobby Jacob
Variations On Graph Products And Vertex Partitions, Jobby Jacob
All Dissertations
In this thesis we investigate two graph products called double vertex graphs and complete double vertex graphs, and two vertex partitions called dominator partitions and rankings.
We introduce a new graph product called the complete double vertex graph and study its properties. The complete double vertex graph is a natural extension of the Cartesian product and a generalization of the double vertex graph.
We establish many properties of complete double vertex graphs, including results involving the chromatic number of a complete double vertex graph and the characterization of planar complete double vertex graphs. We also investigate the important problem of …
Asymptotics Of Families Of Polynomials And Sums Of Hurwitz Class Numbers, Timothy Flowers
Asymptotics Of Families Of Polynomials And Sums Of Hurwitz Class Numbers, Timothy Flowers
All Dissertations
In a note in the American Mathematical Monthly in 1960, Strodt mentions a way to prove both the Euler-Maclaurin summation formula and the Boole summation formula using operators. In a 2009 article in the Monthly, Borwein, Calkin, and Manna expand on this idea. Therein, they define Strodt operators and Strodt polynomials and show that the classical Bernoulli polynomials and Euler polynomials are examples of Strodt polynomials.
It is well known that both Bernoulli polynomials and Euler polynomials on a fixed interval are asymptotically sinusoidal. Borwein, Calkin, and Manna show that a similar result holds for the uniform Strodt polynomials. We …
Quality Representation In Multiobjective Programming, Stacey Faulkenberg
Quality Representation In Multiobjective Programming, Stacey Faulkenberg
All Dissertations
In recent years, emphasis has been placed on generating quality representations of the nondominated set of multiobjective programming problems. This manuscript presents two methods for generating discrete representations with equidistant points for multiobjective programs with solution sets determined by convex cones. The Bilevel Controlled Spacing (BCS) method has a bilevel structure with the lower-level generating the nondominated points and the upper-level controlling the spacing. The Constraint Controlled Spacing (CCS) method is based on the epsilon-constraint method with an additional constraint to control the spacing of generated points. Both methods (under certain assumptions) are proven to produce (weakly) nondominated points. Along …
Factoring Polynomials And Groebner Bases, Genhua (Yinhua) Guan
Factoring Polynomials And Groebner Bases, Genhua (Yinhua) Guan
All Dissertations
Factoring polynomials is a central problem in computational algebra and number theory and is a basic routine in most
computer algebra systems (e.g. Maple, Mathematica, Magma, etc). It has been extensively studied
in the last few decades by many mathematicians and computer scientists. The main approaches include Berlekamp's method
(1967) based on the kernel of Frobenius map, Niederreiter's method (1993) via an ordinary differential equation,
Zassenhaus's modular approach (1969), Lenstra, Lenstra and Lovasz's lattice reduction (1982), and Gao's method via a partial differential equation (2003). These methods and their recent improvements due to van Hoeij (2002) and
Lecerf et al …
Binary Quadratic Forms Over F[T] And Principal Ideal Domains, Jeff Beyerl
Binary Quadratic Forms Over F[T] And Principal Ideal Domains, Jeff Beyerl
All Theses
This paper concerns binary quadratic forms over F[T]. It develops theory analogous to the theory of binary quadratic forms over the integers. Most although not all of the results are almost identical, while some of the proofs require different techniques.
In particular, the form class group is determined when the form takes values in a principal ideal domain, and the ideal class group (and class group isomorphism) is determined when the form takes values in F[T].
A Dual Algorithm For The Weighted Euclidean Distance Min-Max Location Problem In R^2 And R^3, Andrea Smith
A Dual Algorithm For The Weighted Euclidean Distance Min-Max Location Problem In R^2 And R^3, Andrea Smith
All Theses
A dual approach algorithm is given for the solution of the weighted min-max location problem with Euclidean distance in R^2 and R^3. Each subproblem is solved using a directional search procedure and by taking advantage of its geometric structure. An algebraic replacement rule is employed to update the subproblem.
On Elliptic Curves, Modular Forms, And The Distribution Of Primes, Ethan Smith
On Elliptic Curves, Modular Forms, And The Distribution Of Primes, Ethan Smith
All Dissertations
In this thesis, we present four problems related to elliptic curves, modular forms, the distribution of primes, or some combination of the three. The first chapter surveys the relevant background material necessary for understanding the remainder of the thesis. The four following chapters present our problems of interest and their solutions. In the final chapter, we present our conclusions as well as a few possible directions for future research.
Hurwitz class numbers are known to have connections to many areas of number theory. In particular, they are intimately connected to the theory of binary quadratic forms, the structure of imaginary …
Construction Of A Dimension Two Rank One Drinfeld Module, Catherine Trentacoste
Construction Of A Dimension Two Rank One Drinfeld Module, Catherine Trentacoste
All Theses
Consider Fr[t] where r = pm for some prime p and m in the natural numbers. Let f(t) be an irreducible square-free polynomial with even degree in Fr[t] so that the leading coeffcient is not a square
mod Fr. Let A = L = Fr[t][\sqrt{f(t)}].
We will examine the basic set-up required for a dimension two rank one Drinfeld module over L along with an explanation of our choice of f(t). In addition we will show the construction for the exponential function.
Intersections And Representations Of Graphs, John Light
Intersections And Representations Of Graphs, John Light
All Dissertations
Given two graphs G and H sharing the same vertex set, the edge-intersection spectrum of G and H is the set of possible
sizes of the intersection of the edge sets of both graphs. For example,
the spectrum of two copies of the cycle C5 is {0, 2, 3, 5}, and the spectrum of two copies of the star K1,r is {1, r}. The intersection spectrum was initially studied for designs by Lindner and Fu and others and was originally extended to graphs by Eric Mendelsohn. Several examples are studied, both when G and H are isomorphic and …
New Directions In Multivariate Public Key Cryptography, Raymond Heindl
New Directions In Multivariate Public Key Cryptography, Raymond Heindl
All Dissertations
Most public key cryptosystems used in practice are based on integer factorization or discrete logarithms (in finite fields or elliptic curves). However, these systems suffer from two potential drawbacks. First, they must use large keys to maintain security, resulting in decreased efficiency. Second, if large enough quantum computers can be built, Shor's algorithm will render them completely insecure.
Multivariate public key cryptosystems (MPKC) are one possible alternative. MPKC makes use of the fact that solving multivariate polynomial systems over a finite field is an NP-complete problem, for which it is not known whether there is a polynomial algorithm on quantum …
Modeling Hiv Drug Resistance, Mingfu Zhu
Modeling Hiv Drug Resistance, Mingfu Zhu
All Dissertations
Despite the development of antiviral drugs and the optimization of therapies, the emergence of drug resistance remains one of the most challenging issues for successful treatments of HIV-infected patients. The availability of massive HIV drug resistance data provides us not only exciting opportunities for HIV research, but also the curse of high dimensionality.
We provide several statistical learning methods in this thesis to analyze sequence data from different perspectives. We propose a hierarchical random graph approach to identify possible covariation among residue-specific mutations. Viral progression pathways were inferred using an EM-like algorithm in literature, and we present a normalization method …
Fast Fourier Transform Algorithms With Applications, Todd Mateer
Fast Fourier Transform Algorithms With Applications, Todd Mateer
All Dissertations
This manuscript describes a number of algorithms that can be used to quickly evaluate a polynomial over a collection of points and interpolate these evaluations back into a polynomial. Engineers define the 'Fast Fourier Transform' as a method of solving the interpolation problem where the coefficient ring used to construct the polynomials has a special multiplicative structure. Mathematicians define the 'Fast Fourier Transform' as a method of solving the evaluation problem. One purpose of the document is to provide a mathematical treatment of the topic of the 'Fast Fourier Transform' that can also be understood by someone who has an …
Numerical Analysis Of A Fractional Step Theta-Method For Fluid Flow Problems, John Chrispell
Numerical Analysis Of A Fractional Step Theta-Method For Fluid Flow Problems, John Chrispell
All Dissertations
The accurate numerical approximation of viscoelastic fluid flow poses two difficulties: the large number of unknowns in the approximating algebraic system (corresponding to velocity, pressure, and stress), and the different mathematical types of the modeling equations. Specifically, the viscoelastic modeling equations have a hyperbolic constitutive equation coupled to a parabolic conservation of momentum equation. An appealing approximation approach is to use a fractional step $\theta$-method. The $\theta$-method is an operator splitting technique that may be used to decouple mathematical equations of different types as well as separate the updates of distinct modeling equation variables when modeling mixed systems of partial …
Homomorphisms Of Graphs, Samuel Lyle
Homomorphisms Of Graphs, Samuel Lyle
All Dissertations
Understanding the structure of graphs is fundamental to advances in many areas of graph theory, as well as in many applications. In many cases, an analysis of the structure of graphs follows one of two approaches; either many structural properties are considered over a restricted class of graphs, or a particular structural property is considered over many classes of graphs. Both approaches will be considered in this dissertation.
Graphs which do not contain a clique of size r, i.e., Kr-free graphs, are of fundamental importance in the area of extremal graph theory. Many results have been obtained …
Portfolio Selection Under Various Risk Measures, Hariharan Kandasamy
Portfolio Selection Under Various Risk Measures, Hariharan Kandasamy
All Dissertations
Portfolio selection has been a major area of study after Markowitz's ground-breaking paper. Risk quantification for portfolio selection is studied in the literature extensively and many risk measures have been proposed.
In this dissertation we study portfolio selection under various risk measures. After exploring important risk measures currently available we propose a new risk measure, Unequal Prioritized Downside Risk (UPDR). We illustrate the formulation of UPDR for portfolio selection as a mixed-integer program. We establish conditions under which UPDR can be formulated as a linear program.
We study single-period portfolio selection using two risk measures simultaneously. We propose four alternate …
The Square Threshold Problem In Number Fields, Matt Lafferty
The Square Threshold Problem In Number Fields, Matt Lafferty
All Theses
Let K be a degree n extension of Q, and let O_K be the ring of algebraic integers in K. Let x >= 2. Suppose we were to generate an ideal sequence by choosing ideals with norm at most x from O_K, independently and with uniform probability. How long would our sequence of ideals need to be before we obtain a subsequence whose terms have a product that is a square ideal in O_K? We show that the answer is about exp((2\ln(x)\ln\ln(x))^(1/2)).
Ordered Matrices Of Prescribed Row And Column Sum, Janine Janoski
Ordered Matrices Of Prescribed Row And Column Sum, Janine Janoski
All Theses
Let M(n,s) be the number of nxn matrices with binary entries, row and column sum s, and whose rows are in lexicographical order. Let S(n) be the number of nxn matrices with entries from {0,1,2}, symmetric, with trace 0, and row sum 2. (The sequence S(n) appears as A002137 in N.J.A. Sloane's Online Encyclopedia of Integer Sequences.)
We give two proofs to show that M(n,2)=S(n). First, we show they satisfy the same recurrence. Second, we give an explicit bijection between the two sets. We also show that the bijection maintains the cycle structure of our matrices.
Let M_s(n,2) be the …
Dow Jones Index, Garch(1,1) And Change-Points, Tharanga Wickramarachchi
Dow Jones Index, Garch(1,1) And Change-Points, Tharanga Wickramarachchi
All Theses
Many econometric time series data sets, such as log returns of stocks, exhibit evidence of the so called stylized facts. Namely it is generally observed that the data itself is uncorrelated with heavy tails, but the squared data has signicant autocorrelation. For such data sets, there appears to be little or no linear information in the past about the future values of the series. Thus the class of Autoregressive Integrated moving average models (ARIMA) are not appropriate. However, there does in general appear to be information in past values of the squared data about future values of the squared data. …
Issues In Model Selection, Minimax Estimation, And Censored Data Analysis, Meng Zhao
Issues In Model Selection, Minimax Estimation, And Censored Data Analysis, Meng Zhao
All Dissertations
In this dissertation, we address several research problems in statistical inference. We obtain results in the following four directions: linear model selection, minimax estimation of linear functionals, Bayes type estimators for the survival functions based on right censored data, and estimation of survival functions based on doubly censored data.