Mathematics Commons^™

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 …

Weyl Groups And The Nil-Hecke Algebra, Arta Holaj

Mathematics and Statistics

We begin this paper with a short survey on finite reflection groups. First we establish what a reflection in Euclidean space is. Then we introduce a root system, which is then partitioned into two sets: one of positive roots and one with negative roots. Th is articulates our understanding of groups generated by simple reflections. Furthermore, we develop our insight to Weyl groups and crystallographic groups before exploring crystallographic root systems. The section section of this paper examines the twisted group algebra along with the Demazure element Xi and the Demazure-Lusztig element Ti. Lastly, the third section of this paper …

Phase-Only Digital Encryption, Jonathan Blackledge, Western Govere, Dumisani Sibanda

Articles

Abstract—We study then-dimensional deconvolution prob-lem associated with an impulse response function and an(additive) noise function that are both characterised by thesame phase-only stochastic spectrum. In this case, it is shownthat the deconvolution problem becomes well-posed and has ageneral solution that is both exact and unique, subject to are-normalisation condition relating to the scale of the solution.While the phase-only spectral model considered is of limitedvalue in general (in particular, problems arising in the fieldsof digital signal processing and communications engineering,specifically with regard to the retrieval of information fromnoise), its application to digital cryptography has potential.One of the reasons for this (as …

Methods For Meta–Analyses Of Rare Events, Sparse Data, And Heterogeneity, Brinley Zabriskie

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The vast and complex wealth of information available to researchers often leads to a systematic review, which involves a detailed and comprehensive plan and search strategy with the goal of identifying, appraising, and synthesizing all relevant studies on a particular topic. A meta–analysis, conducted ideally as part of a comprehensive systematic review, statistically synthesizes evidence from multiple independent studies to produce one overall conclusion. The increasingly widespread use of meta–analysis has led to growing interest in meta–analytic methods for rare events and sparse data. Conventional approaches tend to perform very poorly in such settings. Recent work in this area has …

Contributions To Mcmc Methods In Constrained Domains With Applications To Neuroimaging, Sharang Chaudhry

UNLV Theses, Dissertations, Professional Papers, and Capstones

Markov chain Monte Carlo (MCMC) methods form a rich class of computational techniques that help its user ascertain samples from target distributions when direct sampling is not possible or when their closed forms are intractable. Over the years, MCMC methods have been used in innumerable situations due to their flexibility and generalizability, even in situations involving nonlinear and/or highly parametrized models. In this dissertation, two major works relating to MCMC methods are presented.

The first involves the development of a method to identify the number and directions of nerve fibers using diffusion-weighted MRI measurements. For this, the biological problem is …

Numerical Analysis And Fluid Flow Modeling Of Incompressible Navier-Stokes Equations, Tahj Hill

UNLV Theses, Dissertations, Professional Papers, and Capstones

The Navier-Stokes equations (NSE) are an essential set of partial differential equations for governing the motion of fluids. In this paper, we will study the NSE for an incompressible flow, one which density ρ = ρ0 is constant.

First, we will present the derivation of the NSE and discuss solutions and boundary conditions for the equations. We will then discuss the Reynolds number, a dimensionless number that is important in the observations of fluid flow patterns. We will study the NSE at various Reynolds numbers, and use the Reynolds number to write the NSE in a nondimensional form.

We will …

A Monolithic Arbitrary Lagrangian-Eulerian Finite Element Method For An Unsteady Stokes/Parabolic Interface Problem, Ian Kesler

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis, a non-conservative arbitrary Lagrangian-Eulerian (ALE) method is developed

and analyzed for a type of linearized Fluid-Structure Interaction (FSI) problem in a

time dependent domain with a moving interface - an unsteady Stokes/parabolic interface

problem with jump coefficients. The corresponding mixed finite element approximation is

analyzed for both semi- and full discretization based upon the so-called non-conservative

ALE scheme. The stability and optimal convergence properties in the energy norm are

obtained for both schemes.

Generalized And Higher Dimensional Apollonian Packings, Daniel Lautzenheiser

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this thesis, we show that circle, sphere, and higher dimensional sphere packings may

be realized as subsets of the boundary of hyperbolic space, subject to certain symmetry

conditions based on a discrete group of motions of the hyperbolic space. This leads to

developing and applying counting methods which admit rigorous upper and lower bounds on

the Hausdorff (or Besikovitch) dimension of the residual set of several generalized Apollonian

circle packings. We find that this dimension (which also coincides with the critical exponent

of a zeta-type function) of each packing is strictly greater than that of the Apollonian

packing, supporting …

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 …

Admissibility Of C*-Covers And Crossed Products Of Operator Algebras, Mitchell A. Hamidi

Department of Mathematics: Dissertations, Theses, and Student Research

In 2015, E. Katsoulis and C. Ramsey introduced the construction of a non-self-adjoint crossed product that encodes the action of a group of automorphisms on an operator algebra. They did so by realizing a non-self-adjoint crossed product as the subalgebra of a C*-crossed product when dynamics of a group acting on an operator algebra by completely isometric automorphisms can be extended to self-adjoint dynamics of the group acting on a C*-algebra by ∗-automorphisms. We show that this extension of dynamics is highly dependent on the representation of the given algebra and we define a lattice structure for an operator algebra's …

Direct Detection Of Relic Neutrino Background Remains Impossible: A Review Of More Recent Arguments, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The existence of big bang relic neutrinos—exact analogues of the big bang relic photons comprising the cosmic microwave background radiation—is a basic prediction of standard cosmology. The standard big bang theory predicts the existence of 1087 neutrinos per flavour in the visible universe. This is an enormous abundance unrivalled by any other known form of matter, falling second only to the cosmic microwave background (CMB) photon. Yet, unlike the CMB photon which boasts its first (serendipitous) detection in the 1960s and which has since been observed and its properties measured to a high degree of accuracy in a series of …

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 …

Understanding The Impact Of Peer-Led Workshops On Student Learning, Afolabi Ibitoye, Nadia Kennedy, Armando Cosme

Publications and Research

As students we often wonder why some subjects are easy to understand and requires not much effort in terms of re-reading the material, for us to grasp what it entails. One subject seems to remain elusive and uneasy for a vast majority of learners at all levels of education; that subject is Mathematics, it is one subject that most learners finds difficult even after doubling the amount of time spent on studying the material. My intention is to explore ways to make Mathematics easier for other students using feedback from students enrolled in NSF mathematics peer leading workshops, and use …

A Comparative Study Of Incidence Of Domestic Violence Between Immigrant And Non-Immigrant Women In The United States Of America, Nadia A. Gordon, Urmi Ghosh-Dastidar, Janet Liou-Mark, Shamita Dasgupta

Publications and Research

Immigrant women in the USA come from various socio-economic, cultural, and religious backgrounds. Some of these women suffer from domestic violence; however, due to their strict cultural or social structure, they often stay quiet and rarely report these incidents to the authorities. Additionally, since these immigrant women face more challenges than their non-immigrant peers, they are more reluctant or unlikely to leave their abusive partners. An analysis was completed using published data as an attempt to establish if any statistically significant differences exist between reported incidences among immigrant women and non-immigrant women. A chi-square analysis (χ² = 14.53; p-value …

Simulation As A Predictor In Probability, Xiaona Zhou

Publications and Research

In this study, we simulate bivariate normal data. We gain intuition about the bivariate normal distribution by comparing the generated data to the associated bivariate normal density surface. We also get results about covariance and correlation. We will use tools from linear algebra to discuss transformations of random normal vectors, and the use of contours.

On The Complexity Of Computing Galois Groups Of Differential Equations, Mengxiao Sun

Dissertations, Theses, and Capstone Projects

The differential Galois group is an analogue for a linear differential equation of the classical Galois group for a polynomial equation. An important application of the differential Galois group is that a linear differential equation can be solved by integrals, exponentials and algebraic functions if and only if the connected component of its differential Galois group is solvable. Computing the differential Galois groups would help us determine the existence of the solutions expressed in terms of elementary functions (integrals, exponentials and algebraic functions) and understand the algebraic relations among the solutions.

Hrushovski first proposed an algorithm for computing the differential …

A Differential Algebra Approach To Commuting Polynomial Vector Fields And To Parameter Identifiability In Ode Models, Peter Thompson

Dissertations, Theses, and Capstone Projects

In the first part, we study the problem of characterizing polynomial vector fields that commute with a given polynomial vector field. One motivating factor is that we can write down solution formulas for an ODE that corresponds to a planar vector field that possesses a linearly independent commuting vector field. This problem is also central to the question of linearizability of vector fields. We first show that a linear vector field admits a full complement of commuting vector fields. Then we study a type of planar vector field for which there exists an upper bound on the degree of a …

Analysis Of A Group Of Automorphisms Of A Free Group As A Platform For Conjugacy-Based Group Cryptography, Pavel Shostak

Dissertations, Theses, and Capstone Projects

Let F be a finitely generated free group and Aut(F) its group of automorphisms.

In this monograph we discuss potential uses of Aut(F) in group-based cryptography.

Our main focus is on using Aut(F) as a platform group for the Anshel-Anshel-Goldfeld protocol, Ko-Lee protocol, and other protocols based on different versions of the conjugacy search problem or decomposition problem, such as Shpilrain-Ushakov protocol.

We attack the Anshel-Anshel-Goldfeld and Ko-Lee protocols by adapting the existing types of the length-based attack to the specifics of Aut(F). We also present our own version of the length-based attack that significantly increases the attack' success …

Formation Of Radial Patterns Via Mixed Attractive And Repulsive Interactions For Schrödinger Systems, Jaeyoung Byeon, Youngae Lee, Zhi-Qiang Wang

Mathematics and Statistics Faculty Publications

This paper is concerned with the asymptotic behavior of least energy vector solutions for nonlinear Schrödinger systems with mixed couplings of attractive and repulsive forces. We focus here on the radially symmetric case while the general studies were already conducted in our earlier work [J. Byeon, Y. Sato, and Z.-Q. Wang, J. Math. Pures Appl. (9), 106 (2016), pp. 477--511], [J. Byeon, Y. Sato, and Z.-Q. Wang, J. Fixed Point Theory Appl., 19 (2017), pp. 559--583]. Though there is still the general phenomenon of component-wise pattern formation with co-existence of partial synchronization and segregation for positive least energy …

Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer

Undergraduate Theses and Capstone Projects

This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic models. …

Orbit Spaces Of Unimodular Rows Over Smooth Real Affine Algebras., Soumi Tikader Dr.

Doctoral Theses

Let R be a commutative, Noetherian ring of (Krull) dimension d. It is well known that the set of isomorphism classes of (oriented, if d is even) stably free R-modules of rank d carries the structure of an abelian group. This group can be identified with the orbit space of unimodular rows namely, Umd+1(R)/SLd+1(R). The prime objective of this thesis is to provide the complete computation of this group, when X = Spec(R) be a smooth real affine variety of dimension d ≥ 2 (with the assumption that the set of real points of X is non-empty and orientable). In …

Improving Bertini 2.0: Classifying Singular Polynomials With Machine Learning, Riley Anderson

Departmental Honors & Graduate Capstone Projects

The purpose of this research is to decrease the run time of Bertini, a program that approximates solutions of polynomial systems. Bertini can be run more efficiently if it is known whether a polynomial is singular or non-singular. In this research, we focus on polynomials in one variable. We use a machine learning algorithm to classify polynomials into these two categories. To do so, we create and use a set of polynomials to train a neural network and create a model. Then, we create and use a test set to assess the accuracy of the model. By changing the hyper-parameters …

Analysis Of Deterministic And Stochastic Hiv Models, Emily Macindoe

Departmental Honors & Graduate Capstone Projects

In this research paper, I apply the Susceptible-Infected-Virus (SIV) model to the Human Immunodeficiency Virus (HIV). The SIV model is a compartmental model describing within-host dynamics of viral infections; I analyze it in both its deterministic (in which constants are assumed to be known exactly) and stochastic (in which the death rate of the healthy cells is represented by a random variable) forms. First, I give analytical solutions to two simplified versions of the deterministic model. Next, I apply numerical methods to the full deterministic and stochastic systems. The results give an illustrative picture of HIV in-host population dynamics in …

Knot Groups Of Torus Knots, Alexander H. Galindo

Undergraduate Research Symposium

For this project, an expository approach was taking insofar as examining knots groups goes, specifically for torus knots. As such, the first set of materials examined covered the concept of knot groups and the general tenets of knot theory itself. The rest of the time was spent gaining acquaintance with group theory, specifically relating to free groups, and the basics of abstract algebra. The last portion of work spent on the project was examining how all of these theories work together to define the knot groups of torus knots.

Series-Parallel Operations With Alpha-Graphs, Christian Barrientos, Sarah Minion

Theory & Applications of Graphs

Among difference vertex labelings of graphs, α-labelings are the most restrictive one. A graph is an α-graph if it admits an α-labeling. In this work, we study a new alternative to construct α-graphs using, the well-known, series-parallel operations on smaller α-graphs. As an application of the series operation, we show that all members of a subfamily of all trees with maximum degree 4, obtained using vertex amalgamation of copies of the path Ρ₁₁}, are α-graphs. We also show that the one-point union of up to four copies of Κ_n,n is an …

A Gene-Based Recessive Diplotype Exome Scan Discovers Fgf6, A Novel Hepcidin-Regulating Iron-Metabolism Gene, Shicheng Guo, Shuai Jiang, Narendranath Epperla, Yanyun Ma, Mehdi Maadooliat, Zhan Ye, Brent Olson, Minghua Wang, Terrie Kitchner, Jeffrey Joyce, Peng An, Fudi Wang, Robert Strenn, Joseph J. Mazza, Jennifer K. Meece, Wenyu Wu, Li Jin, Judith A. Smith, Jiucan Wang, Steven J. Schrodi

Mathematical and Statistical Science Faculty Research and Publications

Standard analyses applied to genome-wide association data are well designed to detect additive effects of moderate strength. However, the power for standard genome-wide association study (GWAS) analyses to identify effects from recessive diplotypes is not typically high. We proposed and conducted a gene-based compound heterozygosity test to reveal additional genes underlying complex diseases. With this approach applied to iron overload, a strong association signal was identified between the fibroblast growth factor–encoding gene, FGF6, and hemochromatosis in the central Wisconsin population. Functional validation showed that fibroblast growth factor 6 protein (FGF-6) regulates iron homeostasis and induces transcriptional regulation of hepcidin. …

Predicting Parameters For Bertini Using Neural Networks, Makenzie Clower

Departmental Honors & Graduate Capstone Projects

The purpose of this research is to use machine learning algorithms to predict the fastest settings for a program called Bertini. Bertini is a computer program that approximates solutions to systems of polynomial equations. Settings for this program can be changed by the user, but the user may not necessarily know the best settings to use to optimize the run time for a particular system of polynomial equations. The settings that were focused on were the differential equation predictor methods when tracking the homotopy to the solution of the system. A neural network was used on a training set of …