Mathematics Commons^™

The Use Of Variable-Bagging And The Cross-Validation Selector In The Prediction Of Alzheimer’S Using The Adni Database., Michael Wayne Godbey

Electronic Theses and Dissertations

Dimensionality plays a huge part in the modeling process. If there are more elements in a data set than variables in each element then there are very few restrictions in selection of an algorithm. Bagging, bootstrap aggregating (Breiman, 1994), may also be used to improve a model’s prediction capability. On the other hand, if there more variables in each observation than the number of observations in the dataset, the number of usable algorithms is greatly reduced. The recently developed algorithm, support vector machines, was designed for such situations, in comparison to algorithms such as logistic regression which have instability issues …

Truckload Shipment Planning And Procurement, Neo Nguyen

Graduate Theses and Dissertations

This dissertation presents three issues encountered by a shipper in the context of truckload transportation. In all of the studies, we utilize optimization techniques to model and solve the problems. Each study is inspired from the real world and much of the data used in the experiments is real data or representative of real data.

The first topic is about the freight consolidation in truckload transportation. We integrate it with a purchase incentive program to increase truckload utilization and maximize profit. The second topic is about supporting decision making collaboration among departments of a manufacturer. It is a bi-objective optimization …

Radio Number For Fourth Power Paths, Linda V. Alegria

Electronic Theses, Projects, and Dissertations

A path on n vertices, denoted by Pn, is a simple graph whose vertices can be ordered so that two vertices are adjacent if and only if they are consecutive in the order. A fourth power path, Pn4, is obtained from Pn by adding edges between any two vertices, u and v, whose distance in Pn, denoted by dPn(u,v), is less than or equal to four. The diameter of a graph G, denoted diam(G) is the greatest distance between any two distinct vertices of G. A radio labeling of a graph G is a function f that assigns to each …

Mixed Variational Formulation For The Wellposedness And Numerical Approximation Of A Pde Model Arising In A 3-D Fluid-Structure Interaction, George Avalos, Tom Clark

Faculty Work Comprehensive List

We present qualitative and numerical results on a partial differential equation (PDE) system which models a certain fluid-structure dynamics. Wellposedness is established by constructing for it a nonstandard semigroup generator representation; this representation is accomplished by an appropriate elimination of the pressure. This coupled PDE model involves the Stokes system which evolves on a three dimensional domain O coupled to a fourth order plate equation, possibly with rotational inertia parameter ρ>0. This plate PDE evolves on a flat portion Ω of the boundary of O. The coupling on Ω is implemented via the Dirichlet trace of the Stokes system …

Pro-Covering Fibrations Of The Hawaiian Earring, Nickolas Brenten Callor

Theses and Dissertations

Let H be the Hawaiian Earring, and let H denote its fundamental group. Assume (Bi) is an inverse system of bouquets of circles whose inverse limit is H. We give an explicit bijection between finite normal covering spaces of H and finite normal covering spaces of Bi. This bijection induces a correspondence between a certain family of inverse sequences of these covering spaces. The correspondence preserves the inverse limit of these sequences, thus offering two methods of constructing the same limit. Finally, we characterize all spaces that can be obtained in this fashion as a particular type of fibrations of …

Mathematical Modeling Of Immune Responses To Hepatitis C Virus Infection, Ivan Ramirez

Electronic Theses and Dissertations

An existing mathematical model of ordinary differential equations was studied to better understand the interactions between hepatitis C virus (HCV) and the immune system cells in the human body. Three possible qualitative scenarios were explored: dominant CTL response, dominant antibody response, and coexistence. Additionally, a sensitivity analysis was carried out to rank model parameters for each of these scenarios. Therapy was addressed as an optimal control problem. Numerical solutions of optimal controls were computed using a forward-backward sweep scheme for each scenario. Model parameters were estimated using ordinary least squares fitting from longitudinal data (serum HCV RNA measurements) given in …

Two Dimensional Mathematical Model Of Fluid Flow In A Growing Solid Tumor, Adriana Gracia

Theses and Dissertations - UTB/UTPA

We investigate the problem of steady and unsteady fluid flow in a growing solid tumor. We develop a mathematical model for the two dimensional fluid flow in a spherical tumor where the spatial variations of the interstitial velocity, interstitial pressure and the drug concentration within the tumor are, in general, with respect to the radial distance and the latitudinal angle in the spherical coordinates. The expressions for radial and latitudinal variations of the interstitial velocity, interstitial pressure, and the two investigated drug concentrations were determined analytically. We calculated these quantities in the tumor as well as in a corresponding normal …

Gradient-Based Compressive Sensing For Noise Image And Video Reconstruction, Huihuang Zhao, Yaonan Wang, Xiaojiang Peng, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

In this study, a fast gradient-based compressive sensing (FGB-CS) for noise image and video is proposed. Given a noise image or video, the authors first make it sparse by orthogonal transformation, and then reconstruct it by solving a convex optimisation problem with a novel gradient-based method. The main contribution is twofold. Firstly, they deal with the noise signal reconstruction as a convex minimisation problem, and propose a new compressive sensing based on gradient-based method for noise image and video. Secondly, to improve the computational efficiency of gradient-based compressive sensing, they formulate the convex optimisation of noise signal reconstruction under Lipschitz …

Connections Of Zero Curvature And Applications To Nonlinear Partial Differential Equations, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

A general formulation of zero curvature connections in a principle bundle is presented and some applications are discussed. It is proved that a related connection based on a prolongation in an associated bundle remains zero curvature as well. It is also shown that the connection coefficients can be defined so that the partial differential equation to be studied appears as the curvature term in the structure equations. It is discussed how Lax pairs and Bäcklund tranformations can be formulated for such equations that occur as zero curvature terms.

Hybrid Meshless Method For Numerical Solution Of Partial Differential Equations, Jeanette Marie Monroe

Dissertations

A meshless method for solving partial differential equations (PDEs) which combines the method of fundamental solutions (MFS) and the method of particular solutions (MPS) is formulated and tested. The hybrid method finds a numerical approximation by solving only one system of equations as opposed to the two-stage method of fundamental solutions and method of particular solutions. This new approach, denoted MFS-MPS, one-stage MFS-MPS, or hybrid method, can be applied to a wide variety of PDEs including PDEs with variable coefficients. The MFS-MPS can simplify Helmholtz-type differential operators to Laplacian-type differential operators providing flexibility and simplification to calculating particular solutions and …

Modeling And Analysis Of Pedestrian Flows, Romesh Khaddar

UNLV Theses, Dissertations, Professional Papers, and Capstones

According to the Traveler Opinion and Perception Survey of 2005, about 107.4 million Americans regularly use walking as a mode of transport during their commute, which amounts for 51% of the total American population. In 2009, 4092 pedestrian fatalities were reported nationwide, out of 59,000 pedestrian crashes. This amounts for 12% of the fatalities in the total traffic accidents recorded, and shows an over-representation of pedestrians incidents. Thus, it is imperative to understand the causes behind such statistics, and conduct a comprehensive research on pedestrian walking behavior and their interaction with surroundings.

A lot of researches on pedestrian flows have …

A Survey Of Ekeland's Variational Principle And Related Theorems And Applications, Jessica Robinson

UNLV Theses, Dissertations, Professional Papers, and Capstones

Ekeland's Variational Principle has been a key result used in various areas of analysis such as fixed point analysis, optimization, and optimal control theory. In this paper, the application of Ekeland's Variational Principle to Caristi's Fixed Point Theorem, Clarke's Fixed Point Theorem, and Takahashi's Minimization theorem is the focus. In addition, Ekeland produced a version of the classical Pontryagin Mini- mum Principle where his variational principle can be applied. A further look at this proof and discussion of his approach will be contrasted with the classical method of Pontryagin. With an understanding of how Ekeland's Variational Princple is used in …

Empirical Studies On Interest Rate Derivatives, Xudong Sun

UNLV Theses, Dissertations, Professional Papers, and Capstones

Interest rate models are the building blocks of financial market and the interest rate derivatives market is the largest derivatives market in the world. In this dissertation, we shall focus on numerical pricing of interest rate derivatives, estimating model parameters by Kalman filter, and studying various models empirically. We shall propose a front-fixing finite element method to price the American put option under the quadratic term structure framework and compare it with a trinomial tree method and common finite element method. Numerical test results show the superiority of our front-fixing finite element method in the aspects of computing the option …

A Study Of Graphical Permutations, Jessica Thune

UNLV Theses, Dissertations, Professional Papers, and Capstones

A permutation π on a set of positive integers {a_1,a_2,...,a_n} is said to be graphical if there exists a graph containing exactly a_i vertices of degree (a_i) for each i. It has been shown that for positive integers with a_1

Exact Controllability Of The Lazer-Mckenna Suspension Bridge Equation, Lanxuan Yu

UNLV Theses, Dissertations, Professional Papers, and Capstones

It is well known that suspension bridges may display certain oscillations under external aerodynamic forces. Since the collapse of the Tacoma Narrows suspension bridge in 1940, suspension bridge models have been studied by many researchers. Based upon the fundamental nonlinearity in suspension bridges that the stays connecting the supporting cables and the roadbed resist expansion, but do not resist compression, new models describing oscillations in suspension bridges have been developed by Lazer and McKenna [Lazer and McKenna (1990)]. Except for a paper by Leiva [Leiva (2005)], there have been very few work on controls of the Lazer-McKenna suspension bridge models …

Bures Distance For Completely Positive Maps And Cp-H-Extendable Maps Between Hilbert C*- Modules., Sumesh K Dr.

Doctoral Theses

Completely positive (CP-) maps are special kinds of positivity preserving maps on C ∗ -algebras. W.F. Stinespring [Sti55] obtained a structure theorem for CP-maps showing that they are closely connected with ∗-homomorphisms. W. Arveson and other operator algebraists quickly realized the importance of these maps. Presently the role of the theory of CP-maps in our understanding of C ∗ -algebras and von Neumann algebras is well recognised. It has been argued by physicists that CPmaps are physically more meaningful than just positive maps due to their stability under ampliations. From quantum probabilistic point of view CP-maps are quantum analogues of …

Enumeration Of Tilings Of Quartered Aztec Rectangles, Tri Lai

Department of Mathematics: Faculty Publications

We generalize a theorem of W. Jockusch and J. Propp on quartered Aztec diamonds by enumerating the tilings of quartered Aztec rectangles. We use subgraph replacement method to transform the dual graph of a quartered Aztec rectangle to the dual graph of a quartered lozenge hexagon, and then use Lindstr¨om-Gessel- Viennot methodology to find the number of tilings of a quartered lozenge hexagon.

Von Neumann Algebras And Extensions Of Inverse Semigroups, Allan P. Donsig, Adam H. Fuller, David R. Pitts

Department of Mathematics: Faculty Publications

In the 1970s, Feldman and Moore classified separably acting von Neumann algebras containing Cartan MASAs using measured equivalence re- lations and 2-cocycles on such equivalence relations. In this paper, we give a new classification in terms of extensions of inverse semigroups. Our approach is more algebraic in character and less point-based than that of Feldman-Moore. As an application, we give a restatement of the spectral theorem for bimodules in terms of subsets of inverse semigroups. We also show how our viewpoint leads naturally to a description of maximal subdiagonal algebras.

The Number Of Framings Of A Knot In A 3-Manifold, Patricia Cahn, Vladimir Chernov, Rustam Sadykov

Mathematics Sciences: Faculty Publications

In view of the self-linking invariant, the number |K| of framed knots in S3 with given underlying knot K is infinite. In fact, the second author previously defined affine self-linking invariants and used them to show that |K| is infinite for every knot in an orientable manifold unless the manifold contains a connected sum factor of S1 × S2; the knot K need not be zero-homologous and the manifold is not required to be compact. We show that when M is orientable, the number |K| is infinite unless K intersects a nonseparating sphere at exactly one point, in which case …

Oscillation Of Second-Order Emden–Fowler Neutral Delay Differential Equations, Ravi P. Agarwal, Martin Bohner, Tongxing Li, Chenghui Zhang

Mathematics and Statistics Faculty Research & Creative Works

We establish some new criteria for the oscillation of second-order Emden–Fowler neutral delay differential equations. We study the case of super linear and the case of sublinear equations subject to various conditions. The results obtained show that the presence of a neutral term in a differential equation can cause or destroy oscillatory properties. Several examples are provided to illustrate the relevance of new theorems.

Quantum States Localized On Lagrangian Submanifolds, François Ziegler

Mathematical Sciences: Faculty Presentations (1991-2022)

Let X be a symplectic manifold and Aut(L) the automorphism group of a Kostant-Souriau line bundle on X. *Quantum states for X*, as defined by J.-M. Souriau in the 1990s, are certain positive-definite functions on Aut(L) or, less ambitiously, on any “large enough” subgroup G of Aut(L). This definition has two major drawbacks: when G = Aut(L) there are no known examples; and when G is a Lie subgroup the notion is far from selective enough. In this talk I’ll introduce the concept of a quantum state *localized at Y *, where Y is a coadjoint orbit of a subgroup …

Prognostic Value Of Elevated Levels Of Intestinal Microbe-Generated Metabolite Trimethylamine-N-Oxide In Patients With Heart Failure: Refining The Gut Hypothesis, W.H. Wilson Tang, Zeneng Wang, Yiying Fan, Bruce Levison, Jennie E. Hazen, Lillian M. Donahue, Yuping Wu, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Background: Altered intestinal function is prevalent in patients with heart failure (HF), but its role in adverse outcomes is unclear. Objectives: This study investigated the potential pathophysiological contributions of intestinal microbiota in HF. Methods: We examined the relationship between fasting plasma trimethylamine-N-oxide (TMAO) and all-cause mortality over a 5-year follow-up in 720 patients with stable HF. Results:The median TMAO level was 5.0 μM, which was higher than in subjects without HF (3.5 μM; p < 0.001). There was modest but significant correlation between TMAO concentrations and B-type natriuretic peptide (BNP) levels (r = 0.23; p < 0.001). Higher plasma TMAO levels were associated with a 3.4-fold increased mortality risk. Following adjustments for traditional risk factors and BNP levels, elevated TMAO levels remained predictive of 5-year mortality risk (hazard ratio [HR]: 2.2; 95% CI: 1.42 to 3.43; p < 0.001), as well as following the addition of estimated glomerular filtration rate to the model (HR: 1.75; 95% CI: 1.07 to 2.86; p < 0.001). Conclusions: High TMAO levels were observed in patients with HF, and elevated TMAO levels portended higher long-term mortality risk independent of traditional risk factors and cardiorenal indexes.

Γ-Butyrobetaine Is A Proatherogenic Intermediate In Gut Microbial Metabolism Of L-Carnitine To Tmao, Robert A. Koeth, Bruce S. Levison, Miranda K. Culley, Jennifer A. Buffa, Zeneng Wang, Jill C. Gregory, Elin Org, Yuping Wu, Lin Li, Jonathan D. Smith, W.H. Wilson Tang, Joseph A. Didonato, Aldons J. Lusis, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

L-carnitine, a nutrient in red meat, was recently reported to accelerate atherosclerosis via a metaorganismal pathway involving gut microbial trimethylamine (TMA) formation and host hepatic conversion into trimethylamine-N-oxide (TMAO). Herein, we show that following L-carnitine ingestion, γ-butyrobetaine (γBB) is produced as an intermediary metabolite by gut microbes at a site anatomically proximal to and at a rate ∼1,000-fold higher than the formation of TMA. Moreover, we show that γBB is the major gut microbial metabolite formed from dietary L-carnitine in mice, is converted into TMA and TMAO in a gut microbiota-dependent manner (like dietary L-carnitine), and accelerates atherosclerosis. Gut microbial …

A Potential Foundation For Emergent Space-Time, Kevin H. Knuth, Newshaw Bahreyni

Physics Faculty Scholarship

We present a novel derivation of both the Minkowski metric and Lorentz transformations from the consistent quantification of a causally ordered set of events with respect to an embedded observer. Unlike past derivations, which have relied on assumptions such as the existence of a 4-dimensional manifold, symmetries of space-time, or the constant speed of light, we demonstrate that these now familiar mathematics can be derived as the unique means to consistently quantify a network of events. This suggests that space-time need not be physical, but instead the mathematics of space and time emerges as the unique way in which an …

The Lp Relaxation Orthogonal Array Polytope And Its Permutation Symmetries, Andrew J. Geyer, Dursun A. Bulutoglu, Steven J. Rosenberg

Faculty Publications

Symmetry plays a fundamental role in design of experiments. In particular, symmetries of factorial designs that preserve their statistical properties are exploited to find designs with the best statistical properties. By using a result proved by Rosenberg [6], the concept of the LP relaxation orthogonal array polytope is developed and studied. A complete characterization of the permutation symmetry group of this polytope is made. Also, this characterization is verified computationally for many cases. Finally, a proof is provided.

Learning Style Relationship To Motivation And Success In The Flipped Vs Non-Flipped Classroom, Shannon Seaver

Mathematics Graduate Theses

This research paper will provide a brief overview of what a “flipped classroom” is and the variations of it. It will address whether a flipped classroom is a possible way of addressing students of all learning styles and if all learning styles are motivated in a flipped classroom. The VARK learning style inventory will be given to all students in four College Algebra Prep classes. Two classes will be the flipped “inverted” style of classroom and the other two will be the traditional (control) style of classroom. All students in both formats will also be given a periodic survey to …

A Quasi-Classical Logic For Classical Mathematics, Henry Nikogosyan

Honors College Theses

Classical mathematics is a form of mathematics that has a large range of application; however, its application has boundaries. In this paper, I show that Sperber and Wilson’s concept of relevance can demarcate classical mathematics’ range of applicability by demarcating classical logic’s range of applicability. Furthermore, I introduce how to systematize Sperber and Wilson’s concept of relevance into a quasi-classical logic that can explain classical logic’s and classical mathematics’ range of applicability.

Correction To “Master Regulators, Regulatory Networks, And Pathways Of Glioblastoma Subtypes”, Serdar Bozdag, Aiguo Li, Mehmet Baysan, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Remarks On Characterizations Of Malinowska And Szynal, Gholamhossein Hamedani, Z. Javanshiri, Mehdi Maadooliat, A. Yazdani

Mathematics, Statistics and Computer Science Faculty Research and Publications

The problem of characterizing a distribution is an important problem which has recently attracted the attention of many researchers. Thus, various characterizations have been established in many different directions. An investigator will be vitally interested to know if their model fits the requirements of a particular distribution. To this end, one will depend on the characterizations of this distribution which provide conditions under which the underlying distribution is indeed that particular distribution. In this work, several characterizations of Malinowska and Szynal (2008) for certain general classes of distributions are revisited and simpler proofs of them are presented. These characterizations are …

Quantification Of The Statistical Effects Of Spatiotemporal Processing Of Nontask Fmri Data, M. Muge Karaman, Andrew S. Nencka, Iain P. Bruce, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

Nontask functional magnetic resonance imaging (fMRI) has become one of the most popular noninvasive areas of brain mapping research for neuroscientists. In nontask fMRI, various sources of “noise” corrupt the measured blood oxygenation level-dependent signal. Many studies have aimed to attenuate the noise in reconstructed voxel measurements through spatial and temporal processing operations. While these solutions make the data more “appealing,” many commonly used processing operations induce artificial correlations in the acquired data. As such, it becomes increasingly more difficult to derive the true underlying covariance structure once the data have been processed. As the goal of nontask fMRI studies …