Mathematics Commons^™

On Toroidal Knots, Chirality, And Molecules, Ramiro Garza

Theses and Dissertations - UTB/UTPA

The inspiration for this thesis came from two sources: the book When topology meets chemistry: a topological look at molecular chirality, by Erica Flapan [7], which discusses topologically interesting molecules; and the paper All toroidal embeddings of polyhedral graphs in 3-space are chiral, by T. Castle et al., which proves that toroidal embeddings of polyhedra are chiral. Their proof is examined in detail. A possible application of this work, as discussed by the team, would be in molecules which have the structure of a toroidal polyhedral embedding. Various methods of seeking such an example are attempted and discussed.

On The Dynamic Coloring Of Cartesian Product Graphs., Saieed Akbari, Maryam Ghanbari, S. Jahanbekam

Faculty Publications

No abstract provided.

One-Parameter Families Of Supersymmetric Isospectral Potentials From Riccati Solutions In Function Composition Form, Haret C. Rosu, S.C. Mancas, Pisin Chen

Publications

In the context of supersymmetric quantum mechanics, we define a potential through a particular Riccati solution of the composition form (F∘f)(x)=F(f(x)) and obtain a generalized Mielnik construction of one-parameter isospectral potentials when we use the general Riccati solution. Some examples for special cases of F and f are given to illustrate the method. An interesting result is obtained in the case of a parametric double well potential generated by this method, for which it is shown that the parameter of the potential controls the heights of the localization probability in the two wells, and for certain values of the parameter …

Ray- And Wave-Theoretic Approach To Electromagnetic Scattering From Radially Inhomogeneous Spheres And Cylinders, Michael A. Pohrivchak

Mathematics & Statistics Theses & Dissertations

With applications in the areas of chemistry, physics, microbiology, meteorology, radar, astronomy, and many other fields, electromagnetic scattering is an important area of research. Many everyday phenomena that we experience are a result of the scattering of electromagnetic and acoustic waves. In this dissertation, the scattering of plane electromagnetic waves from radially inhomogeneous spheres and cylinders using both ray- and wave-theoretic principles is considered. Chapters 2 and 3 examine the use of the ray approach. The deviation undergone by an incident ray from its original direction is related to the angle through which the radius vector turns from the point …

An Analysis Of The Practical Dpg Method, Jay Gopalakrishnan, Weifeng Qiu

Mathematics and Statistics Faculty Publications and Presentations

We give a complete error analysis of the Discontinuous Petrov Galerkin (DPG) method, accounting for all the approximations made in its practical implementation. Specifically, we consider the DPG method that uses a trial space consisting of polynomials of degree p on each mesh element. Earlier works showed that there is a "trial-to-test" operator T, which when applied to the trial space, defines a test space that guarantees stability. In DPG formulations, this operator T is local: it can be applied element-by-element. However, an infinite dimensional problem on each mesh element needed to be solved to apply T. In practical computations, …

Reducing The Size And Number Of Linear Programs In A Dynamic Gröbner Basis Algorithm, Massimo Caboara, John Edward Perry Iii

Faculty Publications

The goal of the Dynamic Buchberger Algorithm is to compute a Gröbner basis quickly by adjusting the term ordering as the computation proceeds. A known problem concerns the size and number of linear progams to be solved when refining the ordering. This paper describes two methods for reducing both their size and number.

Euler-Poincar´E Equations For G-Strands, Darryl Holm, Rossen Ivanov

Conference papers

The G-strand equations for a map R×R into a Lie group G are associated to a G-invariant Lagrangian. The Lie group manifold is also the configuration space for the Lagrangian. The G-strand itself is the map g(t,s):R×R→G, where t and s are the independent variables of the G-strand equations. The Euler-Poincar'e reduction of the variational principle leads to a formulation where the dependent variables of the G-strand equations take values in the corresponding Lie algebra g and its co-algebra, g^∗ with respect to the pairing provided by the variational derivatives of the Lagrangian. We review examples of different G-strand …

Greedy Signal Space Methods For Incoherence And Beyond, Raja Giryes, Deanna Needell

CMC Faculty Publications and Research

Compressive sampling (CoSa) has provided many methods for signal recovery of signals compressible with respect to an orthonormal basis. However, modern applications have sparked the emergence of approaches for signals not sparse in an orthonormal basis but in some arbitrary, perhaps highly overcomplete, dictionary. Recently, several "signal-space" greedy methods have been proposed to address signal recovery in this setting. However, such methods inherently rely on the existence of fast and accurate projections which allow one to identify the most relevant atoms in a dictionary for any given signal, up to a very strict accuracy. When the dictionary is highly overcomplete, …

Identification Of Transcriptionally Quiescent Regions In The Neurospora Crassa Genome, Katie Marie Groskreutz

Theses and Dissertations

Sexual reproduction and genetic exchange via meiosis are important and highly conserved processes in many living organisms. Occasionally, complications occur during meiosis that can result in chromosome abnormalities. In humans, improper chromosome development can cause life altering disorders such as Down Syndrome, Edwards Syndrome, and Patau Syndrome. Unfortunately, despite its importance, gaps remain in our knowledge of how this process works. For instance, little is known about how homolog identification occurs and what proteins identify matching chromosomes during pairing. This fundamental process occurs early during meiosis and ensures proper development of gametes.

Understanding the proteins involved during homolog pairing may …

Fearless Friday: Kirsten Crear, Kirsten Crear

SURGE

Even in her last semester here at Gettysburg, Kirsten Crear ’14 is fearlessly working to make changes for the future of the campus community. This semester, Kirsten introduced a STEMinists club on campus that will give female students who are STEM (an acronym for Science-Technology-Engineering-Mathematics) majors the opportunity to come together and create a community, share and discuss the difficulties they face as women in their fields of study, and support and mentor each other as they prepare to enter their fields.

Kirsten is passionate, driven, and determined, taking the initiative to bring this group of women together on campus …

On The Classification Of Groups Generated By Automata With 4 States Over A 2-Letter Alphabet, Louis Caponi

USF Tampa Graduate Theses and Dissertations

The class of groups generated by automata have been a source of many counterexamples in group theory. At the same time it is connected to other branches of mathematics, such as analysis, holomorphic dynamics, combinatorics, etc. A question that naturally arises is finding the ways to classify these groups. The task of a complete classification and understanding at the moment seems to be too ambitious, but it is reasonable to concentrate on some smaller subclasses of this class. One approach is to consider groups generated by small automata: the automata with k states over d-letter alphabet (so called, (k,d)-automata) with …

What Makes A ‘Good’ Definition: Analyzing Students’ Conceptions Of Mathematical Definitions And The Pedagogy Of Definitions In Math Education, Jesse Aston

Seaver College Research And Scholarly Achievement Symposium

What are the key differences between how students view mathematical definitions and how their professors think they do? In this study we follow students during a guided reconstruction exercise in which they create a definition for, in this case, the convergence of a sequence and we record the process on film. Several theoretical frameworks including RME are then used to analyze student responses and behavior throughout the process and determine the difference in perceptions between student and teacher; these differences inform the best method to present definitions to students.

Review: The Relationships Among Multiplicities Of A J-Self-Adjoint Differential Operator's Eigenvalue, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Properties Of Graphs Used To Model Dna Recombination, Ryan Arredondo

USF Tampa Graduate Theses and Dissertations

A model for DNA recombination uses 4-valent rigid vertex graphs,

called assembly graphs. An assembly graph,

similarly to the projection of knots, can be associated with an

unsigned Gauss code, or double occurrence word.

We define biologically motivated reductions that act on double

occurrence words and, in turn, on their associated assembly graphs. For

every double occurrence word w there is a sequence of reduction

operations that may be applied to w so that what remains is the

empty word, [epsilon]. Then the nesting index of a word w,

denoted by NI(w), is defined to to be …

Stochastic Gradient Descent, Weighted Sampling, And The Randomized Kaczmarz Algorithm, Deanna Needell, Nathan Srebro, Rachel Ward

CMC Faculty Publications and Research

We obtain an improved finite-sample guarantee on the linear convergence of stochastic gradient descent for smooth and strongly convex objectives, improving from a quadratic dependence on the conditioning (L/µ) 2 (where L is a bound on the smoothness and µ on the strong convexity) to a linear dependence on L/µ. Furthermore, we show how reweighting the sampling distribution (i.e. importance sampling) is necessary in order to further improve convergence, and obtain a linear dependence in the average smoothness, dominating previous results. We also discuss importance sampling for SGD more broadly and show how it can improve convergence also in other …

Equivariant Quantum Schubert Polynomials, D. Anderson, Linda Chen

Mathematics & Statistics Faculty Works

We establish an equivariant quantum Giambelli formula for partial flag varieties. The answer is given in terms of a specialization of universal double Schubert polynomials. Along the way, we give new proofs of the presentation of the equivariant quantum cohomology ring, as well as Graham-positivity of the structure constants in equivariant quantum Schubert calculus. (C) 2013 Elsevier Inc. All rights reserved.

Randomized Block Kaczmarz Method With Projection For Solving Least Squares, Deanna Needell, Ran Zhao, Anastasios Zouzias

CMC Faculty Publications and Research

The Kaczmarz method is an iterative method for solving overcomplete linear systems of equations Ax = b. The randomized version of the Kaczmarz method put forth by Strohmer and Vershynin iteratively projects onto a randomly chosen solution space given by a single row of the matrix A and converges exponentially in expectation to the solution of a consistent system. In this paper we analyze two block versions of the method each with a randomized projection, that converge in expectation to the least squares solution of inconsistent systems. Our approach utilizes a paving of the matrix A to guarantee exponential convergence, …

A Generalization Of Aztec Diamond Theorem, Part I, Tri Lai

Department of Mathematics: Faculty Publications

We consider a new family of 4-vertex regions with zigzag boundary on the square lattice with diagonals drawn in. By proving that the number of tilings of the new regions is given by a power 2, we generalize both Aztec diamond theorem and Douglas’ theorem. The proof extends an idea of Eu and Fu for Aztec diamonds, by using a bijection between domino tilings and non-intersecting Schr¨oder paths, then applying Lindstr¨om-Gessel-Viennot methodology.

Plasma Ceruloplasmin, A Regulator Of Nitric Oxide Activity, And Incident Cardiovascular Risk In Patients With Ckd, David J. Kennedy, Yiying Fan, Yuping Wu, Michael Pepoy, Stanley L. Hazen, W.H. Wilson Tang

Mathematics and Statistics Faculty Publications

Background and objectives: Increased serum levels of the acute-phase reactant ceruloplasmin predict adverse clinical outcomes in the setting of acute coronary syndromes and heart failure, but their role in patients with CKD is unclear. This study investigated the relationship of ceruloplasmin with clinical outcomes in CKD, especially with regard to traditional cardiac biomarkers. Design, setting, participants, & measurements: Serum ceruloplasmin levels in consecutive study participants with CKD (n=654; estimated GFR<60 ml/min per 1.73 m2) as well as a control group of non-CKD participants matched for age and sex (n=250) were measured. Study participants were enrolled during 2001–2006 from a population of patients presenting for elective diagnostic coronary angiography and prospectively followed for 3 years (median follow-up=1095 days) to determine incident major adverse cardiac events (defined as a composite of death, nonfatal myocardial infarction, and stroke). Results: Serum ceruloplasmin levels in CKD patients were elevated versus controls (median [interquartile range]; 25.5 [21.8–29.6] versus 22.7 [19.7–26.5] mg/dl; P<0.001) and associated with increased risk of future major adverse cardiac events (hazard ratio, 1.35; 95% confidence interval, 1.0 to 1.82; P=0.04). After adjusting for traditional risk factors, higher serum ceruloplasmin was still associated with higher risk of major adverse cardiac events at 3 years (hazard ratio, 1.61; 95% confidence interval, 1.15 to 2.25; P=0.01). Conclusion: In CKD patients, increased serum ceruloplasmin, a regulator of nitric oxide activity, is associated with increased risk of long-term adverse cardiovascular events, even after multivariable model adjustment for traditional clinical and biologic risk factors.

Self-Adjoint Extension And Spectral Theory Of A Linear Relation In A Hilbert Space, Keshav R. Acharya

Publications

The aim of this paper is to develop the conditions for a symmetric relation in a Hilbert space ℋ to have self-adjoint extensions in terms of defect indices and discuss some spectral theory of such linear relation.