Mathematics Commons^™

Cocyclic Hadamard Matrices: An Efficient Search Based Algorithm, Jonathan S. Turner

Theses and Dissertations

This dissertation serves as the culmination of three papers. “Counting the decimation classes of binary vectors with relatively prime fixed-density" presents the first non-exhaustive decimation class counting algorithm. “A Novel Approach to Relatively Prime Fixed Density Bracelet Generation in Constant Amortized Time" presents a novel lexicon for binary vectors based upon the Discrete Fourier Transform, and develops a bracelet generation method based upon the same. “A Novel Legendre Pair Generation Algorithm" expands upon the bracelet generation algorithm and includes additional constraints imposed by Legendre Pairs. It further presents an efficient sorting and comparison algorithm based upon symmetric functions, as well …

Mirror Symmetry For Non-Abelian Landau-Ginzburg Models, Matthew Michael Williams

Theses and Dissertations

We consider Landau-Ginzburg models stemming from non-abelian groups comprised of non-diagonal symmetries, and we describe a rule for the mirror LG model. In particular, we present the non-abelian dual group G*, which serves as the appropriate choice of group for the mirror LG model. We also describe an explicit mirror map between the A-model and the B-model state spaces for two examples. Further, we prove that this mirror map is an isomorphism between the untwisted broad sectors and the narrow diagonal sectors in general.

Secondary Preservice Mathematics Teachers' Curricular Reasoning, Kimber Anne Mathis

Theses and Dissertations

Researchers have found that teachers' decisions affect students' opportunity to learn. Prior researchers have investigated teachers' decisions while planning, implementing, or reflecting on lessons, but few researchers have studied teachers' decisions and their reasoning throughout the teaching process. It is important to study teachers' reasoning for why they make the decisions they do throughout the teaching process. Furthermore, because inservice and preservice teachers differ in experience and available resources that they draw on while making decisions, it is helpful to consider the resources PSTs' draw on while reasoning. Curricular reasoning is a framework that describes teachers' thinking processes when making …

Two-Stage Mixed Integer Stochastic Programming And Its Application To Bond Portfolio Optimization, Nasser Aedh Alreshidi

Theses and Dissertations

We consider a two-stage stochastic bond portfolio optimization problem, where an investor aims to optimize the cost of bond portfolio under different scenarios while ensuring predefined liabilities during a given planning horizon. The investor needs to optimally decide whether to buy, hold, or sell bonds based upon present market conditions under different scenarios and varying assumptions, where the scenarios are determined based on interest rates and buying prices of the bonds. Three stochastic integer programming models are proposed and applied to real-data from Saudi Sukuk (Bond) Market. The case-study results demonstrate the varying optimal decisions made to manage bond portfolio …

Existence And Classification Of Solutions To Nonlinear Elliptic Equations, Haseeb E. Ansari

Theses and Dissertations

The so-called Lane-Emden equation is a model in astrophysics, useful to problems in analysis and conformal geometry, and is closely related to the Yamabe Problem and the Uniformization Theorem. We discuss several important results for the equation, which include proving that the equation admits a distribution solution if and only if p is greater than the Serrin exponent, that classical solutions admit the form of a "bubble function" if p is equal to the Sobolev exponent, and no classical solutions exist for p less than the Sobolev exponent. A new proof of an extended result is also included.

Pm2.5 Data Reliability And Air Quality Improvement Trends In Beijing, Huimin Li

Theses and Dissertations

PM2.5 has been a main environmental concern due to its adverse effects on human health and society. We used data from two sources: monitoring station of the U.S. Embassy in Beijing, and several nearby monitoring stations of the Chinese Ministry of Environmental Protection. This study includes investigating (1) PM2.5 historical data reliability, (2) PM2.5 real-time data reliability, and (3) air quality improvement trends in Beijing over the past decade. We used graphical methods, descriptive statistics, correlation analysis, and inferential analyses including paired samples t-test, ANOVA, and Kruskal-Wallis test. We reported effect sizes to aid study on practical significance. Inferential procedures' …

Ensemble Correlation Coefficient For Variable Association Detection, Wejdan Deebani

Theses and Dissertations

Subjects in a population are represented by their characteristics, and the characteristics are represented by variables. Identifying the relationship between these variables is essential for prediction, hypothesis testing, and decision making. The relation between two variables is often quantified using a correlation factor. Once correlations between response and independent variables are known, they can be used to make predictions regarding response variables. That is, if two variables are correlated, by observing one, we can make predictions about the other one. A more accurate prediction can be made where there is a strong relationship between variables. Several correlation factors have been …

Parametric Methods For Analysis Of Survival Times With Applications To Organ Transplantation, Farag Hamad

Theses and Dissertations

In this dissertation, we have two main objectives. First, we introduce a hybrid method to model hazard function. Different approaches have been used for modeling survival times including parametric, semi-parametric, and non-parametric models. Non-parametric and semi-parametric models are commonly used for survival time analysis due to their flexibility. However, the parametric models are in high demand because of their predictive power. A challenging task is to extend semi-parametric methods and design full parametric models for analysis of survival times by estimating a set of unknown parameters. In the proposed method, the nonparametric estimate of the survival function by Kaplan Meier …

Weighted Aggregation Methods For Linear And Nonlinear Cluster Analysis With Applications To Cancer Research, Meshal Shutaywi

Theses and Dissertations

Due to advancements in data acquisition, large amount of data are collected on a daily basis. Analysis of the collected data is an important task to discover the patterns, extract the features, and make informed decisions. A vital step in data analysis is dividing the subjects (elements, individuals) in different groups based on their similarities. One way to group the subjects is clustering. Clustering methods can be divided into two categories, linear and non-linear. K-means is a commonly used linear clustering method, while Kernel K-means is a non-linear technique. Kernel K-means projects the elements to a new space using a …

Identification Of Parameters In Systems Biology, Roby Poteau

Theses and Dissertations

Systems Biology is an actively emerging interdisciplinary area between biology and applied mathematics, based on the idea of treating biological systems as a whole entity which is more than the sum of its interrelated components. One of the major goals of systems biology is to reveal, understand, and predict such properties through the development of mathematical models based on experimental data. In many cases, predictive models of systems biology are described by large systems of nonlinear differential equations. Quantitative identification of such systems requires the solution of inverse problems on the identification of parameters of the system. This dissertation explores …

Integrated Representation And Discrimination Models For Functional Data Classification, Rana Haber

Theses and Dissertations

The modus operandi for machine learning is to map functional data to numerical summaries, filter the data, and/or subject it to global signature extractions with the objecive of building robust feature vectors that uniquely characterize each function and then proceed with training algorithms that seek to optimally partition the feature space S ⊂ Rn into labeled regions. This holds true even when the original data are functional in nature, i.e. curves or surfaces that inherently vary over a continuum such as time or space. Functional data are often reduced to summary statistics, locally-sensitive features, and global signatures with the objective …

Multi-Class Logical Analysis Of Data With Relaxed Patterns And Its Extension To Survival Analysis, Travaughn Coren Bain

Theses and Dissertations

This dissertation builds on a previously successful optimization based linear program multi-class classification method, called Logical Analysis of Data (LAD), and improves its generalization capability by introducing relaxed constraint modifications and then further extends and applies it to Survival Analysis. First, we propose the relaxed modifications onto the constraints of the mixed integer linear program (MILP) in the pattern generation phase of LAD. Our modifications are aimed at minimizing the degree of over-fitting to noise, allowing for added flexibility to widen the solution space in hopes to discover more robust classification rules. The proposed method introduces relaxed homogeneity and minimum …

Classification Of Non-Singular Cubic Surfaces Up To E-Invariants, Mohammed Alabbood

Theses and Dissertations

In this thesis, we use the Clebsch map to construct cubic surfaces with twenty-seven lines in PG(3, q) from 6 points in general position in PG(2, q) for q = 17, 19, 23, 29, 31. We classify the cubic surfaces with twenty-seven lines in three dimensions (up to e- invariants) by introducing computational and geometrical procedures for the classi- fication. All elliptic and hyperbolic lines on a non-singular cubic surface in PG(3, q) for q = 17, 19, 23, 29 …

An Examination Of Kinetic Monte Carlo Methods With Application To A Model Of Epitaxial Growth, Dylana Ashton Wilhelm

Theses and Dissertations

Through the assembly of procedural information about physical processes, the kinetic Monte Carlo method offers a simple and efficient stochastic approach to model the temporal evolution of a system. While suitable for a variety of systems, the approach has found widespread use in the simulation of epitaxial growth. Motivated by chem- ically reacting systems, we discuss the developments and elaborations of the kinetic Monte Carlo method, highlighting the computational cost associated with realizing a given algorithm. We then formulate a solid-on-solid bond counting model of epitax- ial growth which permits surface atoms to advance the state of the system through …

On The Characteristic Polynomial Of A Hypergraph, Gregory J. Clark

Theses and Dissertations

We consider the computation of the adjacency characteristic polynomial of a uniform hypergraph. Computing the aforementioned polynomial is intractable, in general; however, we present two mechanisms for computing partial information about the spectrum of a hypergraph as well as a methodology (and in particular, an algo- rithm) for combining this information to determine complete information about said spectrum. The first mechanism is a generalization of the Harary-Sachs Theorem for hypergraphs which yields an explicit formula for each coefficient of the characteristic polynomial of a hypergraph as a weighted sum over a special family of its subgraphs. The second is a …

Successful Pressing Sequences In Simple Pseudo-Graphs, Hays Wimsatt Whitlatch

Theses and Dissertations

Motivated by the study of genomes evolving by reversals, the primary topic of this thesis is “successful pressing sequences” in simple pseudo-graphs. Pressing sequences where first introduced by Hannenhali and Pevzner in 1999 where they showed that sorting signed permutation problem can be solved in polynomial time, therefore demonstrating that the length of a most parsimonious solution to the genome in- version only rearrangement problem can be determined efficiently.

A signed permutation is an integer permutation where each entry is given a sign: plus or minus. A reversal in a signed permutation is the operation of reversing a subword and …

Dynamical Entropy Of Quantum Random Walks, Duncan Wright

Theses and Dissertations

In this manuscript, we study discrete-time dynamics of systems that arise in physics and information theory, and the measure of disorder in these systems known as dy- namical entropy. The study of dynamics in classical systems is done from two distinct viewpoints: random walks and dynamical systems. Random walks are probabilistic in nature and are described by stochastic processes. On the other hand, dynami- cal systems are described algebraically and deterministic in nature. The measure of disorder from either viewpoint is known as dynamical entropy.

Entropy is an essential notion in physics and information theory. Motivated by the study of …

On The Generators Of Quantum Dynamical Semigroups, Alexander Wiedemann

Theses and Dissertations

In recent years, digraph induced generators of quantum dynamical semigroups have been introduced and studied, particularly in the context of unique relaxation and invariance. We define the class of pair block diagonal generators, which allows for additional interaction coefficients but preserves the main structural properties. Namely, when the basis of the underlying Hilbert space is given by the eigenbasis of the Hamiltonian (for example the generic semigroups), then the action of the semigroup leaves invariant the diagonal and off-diagonal matrix spaces. In this case, we explicitly compute all invariant states of the semigroup.

In order to define this class we …

A New Characterization Of V-Posets, Peter Gartland

Theses and Dissertations

In 2016, Hasebe and Tsujie gave a recursive characterization of the set of induced N -free and bowtie-free posets; Misanantenaina and Wagner studied these orders fur- ther, naming them “V-posets”. Here we offer a new characterization of V-posets by introducing a property we refer to as autonomy. A poset P is said to be autonomous if there exists a directed acyclic graph D (with adjacency matrix U ) whose transitive closure is P, with the property that any total ordering of the vertices of D so that Gaussian elimination of UT U proceeds without row swaps is a …

A Development Of Transfer Entropy In Continuous-Time, Christopher David Edgar

Theses and Dissertations

The quantification of causal relationships between time series data is a fundamen- tal problem in fields including neuroscience, social networking, finance, and machine learning. Amongst the various means of measuring such relationships, information- theoretic approaches are a rapidly developing area in concert with other methods. One such approach is to make use of the notion of transfer entropy (TE). Broadly speaking, TE is an information-theoretic measure of information transfer between two stochastic processes. Schreiber’s 2001 definition of TE characterizes information transfer as an informational divergence between conditional probability mass func- tions. The original definition is native to discrete-time stochastic processes …

Exponential Stability Of Intrinsically Stable Dynamical Networks And Switched Networks With Time-Varying Time Delays, David Patrick Reber

Theses and Dissertations

Dynamic processes on real-world networks are time-delayed due to finite processing speeds and the need to transmit data over nonzero distances. These time-delays often destabilize the network's dynamics, but are difficult to analyze because they increase the dimension of the network.We present results outlining an alternative means of analyzing these networks, by focusing analysis on the Lipschitz matrix of the relatively low-dimensional undelayed network. The key criteria, intrinsic stability, is computationally efficient to verify by use of the power method. We demonstrate applications from control theory and neural networks.

Regular Fibrations Over The Hawaiian Earring, Stewart Mason Mcginnis

Theses and Dissertations

We present a family of fibrations over the Hawaiian earring that are inverse limits of regular covering spaces over the Hawaiian earring. These fibrations satisfy unique path lifting, and as such serve as a good extension of covering space theory in the case of nonsemi-locally simply connected spaces. We give a condition for when these fibrations are path-connected.

Piezoelectric Sensor Crack Detection On Airframe Systems, Kevin J. Lin

Theses and Dissertations

In 2008, the Department of Defense published a guidebook for a methodology named Condition-Based Maintenance Plus (CBM+) which capabilities include improving productivity, shortening maintenance cycles, lowering costs, and increasing availability and reliability. This push replaces existing inspection criteria, often conducted as non-destructive testing (NDT), with structural health monitoring (SHM) systems. The SHM system addressed utilizes guided Lamb waves generated by piezoelectric wafer active sensors (PWAS) to detect the existence, size, and location of damage from through-thickness cracks around a rivet hole. The SHM field lacks an experiment testing how small changes in receiver sensor distances affect damage detection. In addition, …

Analyzing A Method To Determine The Utility Of Adding A Classification System To A Sequence For Improved Accuracy, Kevin S. Pamilagas

Theses and Dissertations

Frequently, ensembles of classification systems are combined into a sequence in order to better enhance the accuracy in classifying objects of interest. However, there is a point in which adding an additional system to a sequence no longer enhances the system as either the increase in operational costs exceeds the benefit of improvements in classification or the addition of the system does not increase accuracy at all. This research will examine a utility measure to determine the valid or invalid nature of adding a classification system to a sequence of such systems based on the ratio of the change in …

Harmonic Equiangular Tight Frames Comprised Of Regular Simplices, Courtney A. Schmitt

Theses and Dissertations

An equiangular tight frame (ETF) is a sequence of equal-norm vectors in a Euclidean space whose coherence achieves equality in the Welch bound, and thus yields an optimal packing in a projective space. A regular simplex is a simple type of ETF in which the number of vectors is one more than the dimension of the underlying space. More sophisticated examples include harmonic ETFs, which are formed by restricting the characters of a finite abelian group to a difference set. Recently, it was shown that some harmonic ETFs are themselves comprised of regular simplices. In this thesis, we continue the …

Schlieren Imaging And Flow Analysis On A Cone/Flare Model In The Afrl Mach 6 Ludwieg Tube Facility, David A. Labuda

Theses and Dissertations

High-speed Schlieren photography was utilized to visualize flow in the Air Force Research Laboratory Mach 6 Ludwieg tube facility. A 7° half-angle cone/flare model with variable nosetip radius and flare angle options was used in the study. Testing was performed at two driver tube pressures, generating freestream Reynolds numbers of 10.0x10⁶ and 19.8x10⁶ per meter. The variable-angle flare portion of the model provided a method for adjusting the intensity of the adverse pressure gradient at the cone/flare junction. As expected from existing literature, boundary layer separation along the cone frustum occurred further upstream as the magnitude of the …

Wall Model Large Eddy Simulation Of A Diffusing Serpentine Inlet Duct, Ryan J. Thompson

Theses and Dissertations

The modeling focus on serpentine inlet ducts (S-duct), as with any inlet, is to quantify the total pressure recovery and ow distortion after the inlet, which directly impacts the performance of a turbine engine fed by the inlet. Accurate prediction of S-duct ow has yet to be achieved amongst the computational fluid dynamics (CFD) community to improve the reliance on modeling reducing costly testing. While direct numerical simulation of the turbulent ow in an S-duct is too cost prohibitive due to grid scaling with Reynolds number, wall-modeled large eddy simulation (WM-LES) serves as a tractable alternative. US3D, a hypersonic research …

Solving The Traveling Salesman Problem Using Ordered-Lists, Petar D. Jackovich

Theses and Dissertations

The arc-greedy heuristic is a constructive heuristic utilized to build an initial, quality tour for the Traveling Salesman Problem (TSP). There are two known sub-tour elimination methodologies utilized to ensure the resulting tours are viable. This thesis introduces a third novel methodology, the Greedy Tracker (GT), and compares it to both known methodologies. Computational results are generated across multiple TSP instances. The results demonstrate the GT is the fastest method for instances below 400 nodes while Bentley's Multi-Fragment maintains a computational advantage for larger instances. A novel concept called Ordered-Lists is also introduced which enables TSP instances to be explored …

Time Series Analysis Of Stochastic Networks With Correlated Random Arcs, Brendon T. Sands

Theses and Dissertations

While modern day weather forecasting is not perfect, there are many benefits given by the multitude and variety of predictive models. In the interest of routing airplanes, this paper uses time series analysis on successive weather forecasts to predict the optimal path and fuel burn of wind-based, fuel-burn networks with stochastic correlated arcs. Networks are populated with either deterministic or ensemble-based weather data, and the two data sources with and without time series analysis are compared. Methods were compared by fuel burn prediction accuracy and ability to predict a future optimal path. Of the four options, the ensemble-based methods were …

Schur Rings Over Infinite Groups, Cache Porter Dexter

Theses and Dissertations

A Schur ring is a subring of the group algebra with a basis that is formed by a partition of the group. These subrings were initially used to study finite permutation groups, and classifications of Schur rings over various finite groups have been studied. Here we investigate Schur rings over various infinite groups, including free groups. We classify Schur rings over the infinite cyclic group.