Mathematics Commons^™

Rows Vs. Columns: Randomized Kaczmarz Or Gauss-Seidel For Ridge Regression, Ahmed Hefny, Deanna Needell, Aaditya Ramdas

CMC Faculty Publications and Research

The Kaczmarz and Gauss-Seidel methods aim to solve a linear m × n system Xβ = y by iteratively refining the solution estimate; the former uses random rows of X to update β given the corresponding equations and the latter uses random columns of X to update corresponding coordinates in β. Interest in these methods was recently revitalized by a proof of Strohmer and Vershynin showing linear convergence in expectation for a randomized Kaczmarz method variant (RK), and a similar result for the randomized Gauss-Seidel algorithm (RGS) was later proved by Lewis and Leventhal. Recent work unified the analysis of …

Modelling The Links Between Inflation, Output Growth, Inflation Uncertainty And Output Growth Uncertainty In The Frameworks Of Regime-Switching And Multiple Structural Breaks: Evidence From The G7 Countries., Kushal Banik Chowdhury Dr.

Doctoral Theses

One of the long-standing and most investigated issues in macroeconomics is the nature of the relationship between inflation and output growth. Given this relationship as a central point of intense interest, one strand of studies has focused on the levels of the two series, while, more recently, an overgrowing body of research has highlighted the importance of the effects which are due to both the levels and the uncertainties associated with these two variables. These studies raise a number of interesting issues regarding the relationship between inflation and output growth. First, is there any direct effect of inflation on output …

What You Gotta Know To Play Good In The Iterated Prisoner’S Dilemma, Ethan Akin

Mathematics and Statistics Faculty Research & Creative Works

For the iterated Prisoner's Dilemma there exist good strategies which solve the problem when we restrict attention to the long-term average payoff. When used by both players, these assure the cooperative payoff for each of them. Neither player can benefit by moving unilaterally to any other strategy, i.e., these provide Nash equilibria. In addition, if a player uses instead an alternative which decreases the opponent's payoff below the cooperative level, then his own payoff is decreased as well. Thus, if we limit attention to the long-term payoff, these strategies effectively stabilize cooperative behavior. The existence of such strategies follows from …

Characterizing The Properties Of Specific Binomial Coefficients In Congruence Relations, Tyler Robert Russ

Master's Theses and Doctoral Dissertations

The number theoretic conjecture we examine in this paper originates when trying to construct a characterizable generating set for the complex cobordism polynomial ring. To date there is no efficient, universal method for characterizing such a generating set. Wilfong conjectures that smooth projective toric varieties can act as these generators [7]. Toric varieties are related to polytopes by a bijective correspondence. Studying the combinatorial structure of these polytopes is much more manageable than studying properties of toric varieties directly. This gives rise to the number theoretic conjecture considered here. A proof of this number theoretic conjecture would in turn prove …

Prevalence And Prediction Of Obstructive Coronary Artery Disease In Patients Referred For Valvular Heart Surgery, Jason M. Lappe, Justin L. Grodin, Yuping Wu, Corinne Bott Silverman, Leslie Cho

Mathematics and Statistics Faculty Publications

Current guidelines recommend a coronary evaluation before valvular heart surgery (VHS). Diagnostic coronary angiography is recommended in patients with known coronary artery disease (CAD) and those with high pretest probability of CAD. In patients with low or intermediate pretest probability of CAD, the guidelines recommend coronary computed tomographic angiography. However, there are no tools available to objectively assess a patient’s risk for obstructive CAD before VHS. To address this deficit, 5,360 patients without histories of CAD who underwent diagnostic coronary angiography as part of preoperative evaluation for VHS were identified. Obstructive CAD was defined as ≥50% stenosis in ≥1 artery. …

Undiagnosed Diabetes And Pre-Diabetes In Health Disparities, Susan P. Fisher-Hoch, Kristina Vatcheva, Mohammad H. Rahbar, Joseph B. Mccormick

School of Mathematical & Statistical Sciences Faculty Publications

Globally half of all diabetes mellitus is undiagnosed. We sought to determine the extent and characteristics of undiagnosed type 2 diabetes mellitus and pre-diabetes in Mexican Americans residing in the United States. This disadvantaged population with 50% lifetime risk of diabetes is a microcosm of the current pandemic. We accessed baseline data between 2004 and 2014 from 2,838 adults recruited to our Cameron County Hispanic Cohort (CCHC); a two-stage randomly selected 'Framingham-like' cohort of Mexican Americans on the US Mexico border with severe health disparities. We examined prevalence, risk factors and metabolic health in diagnosed and undiagnosed diabetes and pre-diabetes. …

Review: Nevanlinna-Pick Spaces With Hyponormal Multiplication Operators, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Mathematician's Apology, Tom Clark

Faculty Work Comprehensive List

"Better standards may help all math teachers to shape our classes to better reflect the creativity and play at the heart of mathematics."

Posting about ways to improve math's negative image­­­­­­­­ from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world.

http://inallthings.org/a-mathematicians-apology/

Tame Filling Functions And Closure Properties, Anisah Nu'man

Department of Mathematics: Dissertations, Theses, and Student Research

Let G be a group with a finite presentation P = such that A is inverse- closed. Let f : N[1/4] → N[1/4] be a nondecreasing function. Loosely, f is an intrinsic tame filling function for (G;P) if for every word w over A* that represents the identity element in G, there exists a van Kampen diagram Δ for w over P and a continuous choice of paths from the basepoint * of Δ to points on the boundary of Δ such that the paths are steadily moving outward as measured by f. The isodiametric function (or intrinsic diameter function) …

On The Generalized Linear And Non-Linear Dfc In Non-Linear Dynamics, Dmitriy Dmitrishin, Anna Khamitova, Alexander M. Stokolos

Mathematical Sciences: Faculty Publications

The article is devoted to investigation of robust stability of the generalized linear control of the discrete autonomous dynamical systems. Sharp necessary conditions on the size of the set of multipliers that guaranty robust stabilization of the equilibrium of the system are provided. Surprisingly enough it turns out that the generalized linear delayed feedback control has same limitation as the classical Pyragas DFC. This generalized Ushio 1996 DFC limitation statement. Note that in scalar case a generalized non-linear control can robustly stabilize an equilibrium for any admissible range of multipliers. In the current article similar result is obtained in the …

Introduction To Functions And Generality Of Logic. Reflections On Frege's And Dedekind's Logicisms, Hourya Benis Sinaceur, Marco Panza, Gabriel Sandu

MPP Published Research

This book examines three connected aspects of Frege’s logicism: the differences between Dedekind’s and Frege’s interpretation of the term ‘logic’ and related terms and reflects on Frege’s notion of function, comparing its understanding and the role it played in Frege’s and Lagrange’s foundational programs. It concludes with an examination of the notion of arbitrary function, taking into account Frege’s, Ramsey’s and Russell’s view on the subject. Composed of three chapters, this book sheds light on important aspects of Dedekind’s and Frege’s logicisms. The first chapter explains how, although he shares Frege’s aim at substituting logical standards of rigor to intuitive …

Reproducing Kernel Hilbert Space Vs. Frame Estimates, Palle E. T. Jorgensen, Myung-Sin Song

SIUE Faculty Research, Scholarship, and Creative Activity

We consider conditions on a given system F of vectors in Hilbert space H, forming a frame, which turn Hinto a reproducing kernel Hilbert space. It is assumed that the vectors in F are functions on some set Ω . We then identify conditions on these functions which automatically give H the structure of a reproducing kernel Hilbert space of functions on Ω. We further give an explicit formula for the kernel, and for the corresponding isometric isomorphism. Applications are given to Hilbert spaces associated to families of Gaussian processes.

Review Of Developing Quantitative Literacy Skills In History And The Social Sciences: A Web-Based Common Core Approach By Kathleen W. Craver, Victor J. Ricchezza, H L. Vacher

Numeracy

Kathleen W. Craver. Developing Quantitative Literacy Skills in History and Social Sciences: A Web-Based Common Core Standards Approach (Lantham MD: Rowman & Littlefield Publishing Group, Inc., 2014). 191 pp.
ISBN 978-1-4758-1050-9 (cloth); ISBN …-1051-6 (pbk); ISBN…-1052-3 (electronic).

This book could be a breakthrough for teachers in the trenches who are interested in or need to know about quantitative literacy (QL). It is a resource providing 85 topical pieces, averaging 1.5 pages, in which a featured Web site is presented, described, and accompanied by 2-4 critical-thinking questions purposefully drawing on data from the Web site. The featured Web sites range from …

Mathematics And Humor: John Allen Paulos And The Numeracy Crusade, Paul H. Grawe

Numeracy

John Allen Paulos at minimum gave the Numeracy movement a name through his book Innumeracy: Mathematical Illiteracy and Its Consequences. What may not be so obvious was Paulos’ strong interest in the relationship between mathematics and mathematicians on the one hand and humor and stand-up-comedian joke structures on the other. Innumeracy itself could be seen as a typically mathematical Gotcha joke on American culture generally. In this perspective, a Minnesotan acculturated to Minnesota-Nice Humor of Self-Immolation Proclivities (SImP) looks at the more raw-boned, take-no-prisoners humor style Paulos outlined in Mathematics and Humor and implemented in Innumeracy.

Despite the …

The Math You Need, When You Need It (Tmyn): Leveling The Playing Field, Jennifer M. Wenner, Eric M. D. Baer

Numeracy

The Math You Need, When You Need It (TMYN) is a set of online tutorials designed to help students develop and review mathematical skills that are applied in undergraduate geoscience courses. We present results of a three-year study of more than 4000 students in 106 geoscience courses at a variety of post-secondary schools who were assigned TMYN tutorials as supplemental mathematics instruction. Changes in student scores from pre- to post-test suggest that the support provided by programs such as TMYN can begin to reduce the gap between mathematically well-prepared and underprepared students; in essence, TMYN levels the quantitative playing field …

Why Linear (And Piecewise Linear) Models Often Successfully Describe Complex Non-Linear Economic And Financial Phenomena: A Fuzzy-Based Explanation, Hung T. Nguyen, Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta

Departmental Technical Reports (CS)

Economic and financial phenomena are highly complex and non-linear. However, surprisingly, in many cases, these phenomena are accurately described by linear models -- or, sometimes, by piecewise linear ones. In this paper, we show that fuzzy techniques can explain the unexpected efficiency of linear and piecewise linear models: namely, we show that a natural fuzzy-based precisiation of imprecise ("fuzzy") expert knowledge often leads to linear and piecewise linear models.

We also discuss which expert-motivated nonlinear models should be used to get a more accurate description of economic and financial phenomena.

New Lower Bounds For The Topological Complexity Of Aspherical Spaces, Mark Grant, Gregory Lupton, John Oprea

Mathematics and Statistics Faculty Publications

We show that the topological complexity of an aspherical space X is bounded below by the cohomological dimension of the direct product A×BA×B, whenever A and B are subgroups of π1(X)π1(X) whose conjugates intersect trivially. For instance, this assumption is satisfied whenever A and B are complementary subgroups of π1(X)π1(X). This gives computable lower bounds for the topological complexity of many groups of interest (including semidirect products, pure braid groups, certain link groups, and Higman's acyclic four-generator group), which in some cases improve upon the standard lower bounds in terms of zero-divisors cup-length. Our results illustrate an intimate relationship between …

Why Political Scientists Are Wrong 15% Of The Time, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

An experimental study has shown that among situations when political scientists claimed that a political outcome was impossible, this outcome actually occurred in 15% of the cases. In this paper, we provide a possible explanation for this empirical fact.

Al-Sijistani's And Maimonides's Double Negation Theology Explained By Constructive Logic, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Famous medieval philosophers Al-Sijistani and Maimonides argued that the use of double negation helps us to better understand issues related to theology. To a modern reader, however, their arguments are somewhat obscure and unclear. We show that these arguments can be drastically clarified if we take into account the 20 century use of double negation in constructive logic.

Course Proposal For A Mathematical Modeling Course In A High School Curriculum, Thomas P. Marlowe

Masters Essays

In the winter of 2015, I will be piloting a course on mathematical modeling at Hawken School, an independent high school in Gates Mills, OH. As I develop all elements of this course, such as lesson plans, assessments, and rubrics, I will be mindful of factors such as the newly adopted Common Core mathematics standards, the variety of student backgrounds in such a course, and how various mathematical societies and organizations such as SIAM, MAA, and COMAP can help in implementing it. However, there is one basic question driving my interest in and design of this course: “when am I …