Mathematics Commons^™

A Mathematician's Villanelle, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

Order-Preserving Derivative Approximation With Periodic Radial Basis Functions, Edward Fuselier, Grady B. Wright

Mathematics Faculty Publications and Presentations

In this exploratory paper we study the convergence rates of an iterated method for approximating derivatives of periodic functions using radial basis function (RBF) interpolation. Given a target function sampled on some node set, an approximation of the m ^th derivative is obtained by m successive applications of the operator “interpolate, then differentiate”- this process is known in the spline community as successive splines or iterated splines. For uniformly spaced nodes on the circle, we give a sufficient condition on the RBF kernel to guarantee that, when the error is measured only at the nodes, this iterated method approximates …

Material Hardship In Families With Children With Health Conditions: Implications For Practice, Patricia Stoddard Dare, Leaanne Derigne, Linda M. Quinn, Christopher Mallett

Mathematics and Statistics Faculty Publications

Cross-sectional data from the third wave of a ten-year data collection initiative were used to assess the odds of experiencing four material hardships between families who have a child member with a limiting health condition, and families with children who do not have a child member with a limiting health condition. The odds of experiencing material hardship in families with more than one child with a limiting health condition were also assessed. In the multivariable models, having a child in the household with a limiting health condition increases the odds the household will be unable to pay bills, and have …

A Novel Scoring Based Distributed Protein Docking Application To Improve Enrichment, Prachi Pradeep, Craig Struble, Terrence Neumann, Daniel S. Sem, Stephen Merrill

Mathematics, Statistics and Computer Science Faculty Research and Publications

Molecular docking is a computational technique which predicts the binding energy and the preferred binding mode of a ligand to a protein target. Virtual screening is a tool which uses docking to investigate large chemical libraries to identify ligands that bind favorably to a protein target. We have developed a novel scoring based distributed protein docking application to improve enrichment in virtual screening. The application addresses the issue of time and cost of screening in contrast to conventional systematic parallel virtual screening methods in two ways. Firstly, it automates the process of creating and launching multiple independent dockings on a …

Intestinal Microbiota-Dependent Phosphatidylcholine Metabolites, Diastolic Dysfunction, And Adverse Clinical Outcomes In Chronic Systolic Heart Failure, W.H. Wilson Tang, Zeneng Wang, Kevin Shrestha, Allen G. Borowski, Yuping Wu, Richard W. Troughton, Allan L. Klein, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

Background: Trimethylamine-N-oxide (TMAO) has been linked to increased cardiovascular risk. We aimed to determine the prognostic value of TMAO and its dietary precursors, choline and betaine, in heart failure (HF). Methods and Results: In 112 patients with chronic systolic HF with comprehensive echocardiographic evaluation, we measured plasma TMAO, choline, and betaine by mass spectrometry. Median (interquartile range) TMAO levels, choline, and betaine levels were 5.8 (3.6–12.1) μmol/L, 10.9 (8.4–14.0) μmol/L, and 43.8 (37.1–53.0) μmol/L, respectively, and were correlated with each other (all P < .0001 for both). TMAO levels were significantly higher in patients with diabetes mellitus (9.4 [4.9–13.2] vs 4.8 [3.4–9.8] μmol/L; P = .005) and in subjects with New York Heart Association functional class III or greater (7.0 [4.7–14.8] vs 4.7 [3.4–11.3] μmol/L; P = .02). Elevated TMAO, choline, and betaine levels were each associated with higher plasma N-terminal pro–B-type natriuretic peptide (NT-proBNP) levels and more advanced left ventricular diastolic dysfunction, but not systolic dysfunction or inflammatory and endothelial biomarkers. Higher choline (hazard ratio [HR] 1.64, 95% CI 1.22–2.20; P = .001), betaine (HR 1.51, 95% CI 1.10–2.08; P = .01), and TMAO (HR 1.48, 95% CI 1.10–1.96; P = .01) predicted increased risk for 5-year adverse clinical events (death/transplantation). Only higher TMAO levels predicted incident adverse clinical events independently from age, estimated glomerular filtration rate, mitral E/septal Ea, and NT-proBNP levels (HR 1.46, 95% CI 1.03–2.14; P = .03). Conclusion: Elevated plasma TMAO, choline, and betaine levels are each associated with more advanced left ventricular diastolic dysfunction and portend poorer long-term adverse clinical outcomes in chronic systolic HF. However, only higher plasma TMAO was associated with poor prognosis after adjustment for cardiorenal indices.

E-Esas: Evolution Of A Participatory Design-Based Solution For Breast Cancer (Bc) Patients In Rural Bangladesh, Mohammad Munirul Haque, Ferdaus Kawsar, Mohammad Adibuzzaman, Md Miftah Uddin, Sheikh Iqbal Ahamed, Richard Love, Ragib Hasan, Rumana Dowla, Tahmina Ferdousy, Reza Salim

Mathematics, Statistics and Computer Science Faculty Research and Publications

Healthcare facility is scarce for rural women in the developing world. The situation is worse for patients who are suffering from diseases that require long-term feedback-oriented monitoring such as breast cancer. Lack of motivation to go to the health centers on patients’ side due to sociocultural barriers, financial restrictions and transportation hazards results in inadequate data for proper assessment. Fortunately, mobile phones have penetrated the masses even in rural communities of the developing countries. In this scenario, a mobile phone-based remote symptom monitoring system (RSMS) with inspirational videos can serve the purpose of both patients and doctors. Here, we present …

Activin-A And Bmp4 Levels Modulate Cell Type Specification During Chir-Induced Cardiomyogenesis, Min-Su Kim, Audrey Horst, Steven Blinka, Karl D. Stamm, Donna K. Mahnke, James Schuman, Rebekah Gundry, Aoy Tomita-Mitchell, John Lough

Mathematics, Statistics and Computer Science Faculty Research and Publications

The use of human pluripotent cell progeny for cardiac disease modeling, drug testing and therapeutics requires the ability to efficiently induce pluripotent cells into the cardiomyogenic lineage. Although direct activation of the Activin-A and/or Bmp pathways with growth factors yields context-dependent success, recent studies have shown that induction of Wnt signaling using low molecular weight molecules such as CHIR, which in turn induces the Activin-A and Bmp pathways, is widely effective. To further enhance the reproducibility of CHIR-induced cardiomyogenesis, and to ultimately promote myocyte maturation, we are using exogenous growth factors to optimize cardiomyogenic signaling downstream of CHIR induction. As …

On Polynomial Roots Approximation Via Dominant Eigenspaces And Isolation Of Real Roots, Omar Ivan Retamoso Urbano

Dissertations, Theses, and Capstone Projects

Finding the roots of a given polynomial is a very old and noble problem in mathematics and computational mathematics. For about 4,000 years, various approaches had been proposed to solve this problem (see cite{FC99}). In 1824, Niels Abel showed that there existed polynomials of degree five, whose roots could not be expressed using radicals and arithmetic operations through their coefficients. Here is an example of such polynomials:$$x^5-4x-2.$$

Thus we must resort to iterative methods to approximate the roots of a polynomial given with its coefficients.

There are many algorithms that approximate the roots of a polynomial(see cite{B40}, cite{B68}, cite{MN93}, cite{MN97}, …

Explicit Solutions Of Imaginary Quadratic Norm Equations, Sandra Sze

Dissertations, Theses, and Capstone Projects

Let $K=\mathbb{Q}(\sqrt{-d})$ be an imaginary quadratic extension of $\mathbb{Q}$. Let $h$ be the class number and $D$ be the discriminant of the field $K$. Assume $p$ is a prime such that $\displaystyle\left(\frac{D}{p}\right)=1$. Then $p$ splits in $K$. The elements of the ring of integers $\mathcal{O}_K$ are of the form $x+\sqrt{-d}y$ if $d\equiv1,2\pmod{4}$ and $\displaystyle x+\frac{1+\sqrt{-d}}{2}y$ if $d\equiv3\pmod{4}$, where $x$ and $y\in \mathbb{Z}$. The norm \\$N_{K/\mathbb{Q}}(x+\sqrt{-d}y)=x^2+dy^2$ and $N_{K/\mathbb{Q}}\left(\displaystyle x+\frac{1+\sqrt{-d}}{2}y\right)=\displaystyle\frac{(2x+y)^2}{4}+\frac{dy^2}{4}$. In this thesis, we find the elements of norm $p^h$ explicitly. We also prove certain congruences for solutions of norm equations.

My Finite Field, Matthew Schroeder

Journal of Humanistic Mathematics

A love poem written in the language of mathematics.

Prisoner's Dilemma, Raymond N. Greenwell

Journal of Humanistic Mathematics

No abstract provided.

Abscissas And Ordinates, David Pierce

Journal of Humanistic Mathematics

In the manner of Apollonius of Perga, but hardly any modern book, we investigate conic sections as such. We thus discover why Apollonius calls a conic section a parabola, an hyperbola, or an ellipse; and we discover the meanings of the terms abscissa and ordinate. In an education that is liberating and not simply indoctrinating, the student of mathematics will learn these things.

The Symbolic And Mathematical Influence Of Diophantus's Arithmetica, Cyrus Hettle

Journal of Humanistic Mathematics

Though it was written in Greek in a center of ancient Greek learning, Diophantus's Arithmetica is a curious synthesis of Greek, Egyptian, and Mesopotamian mathematics. It was not only one of the first purely number-theoretic and algebraic texts, but the first to use the blend of rhetorical and symbolic exposition known as syncopated mathematics. The text was influential in the development of Arabic algebra and European number theory and notation, and its development of the theory of indeterminate, or Diophantine, equations inspired modern work in both abstract algebra and computer science. We present, in this article, a selection of problems …

Love Games: A Game-Theory Approach To Compatibility, Kerstin Bever, Julie Rowlett

Journal of Humanistic Mathematics

In this note, we present a compatibility test with a rigorous mathematical foundation in game theory. The test must be taken separately by both partners, making it difficult for either partner alone to control the outcome. To introduce basic notions of game theory we investigate a scene from the film "A Beautiful Mind" based on John Nash's life and Nobel-prize-winning theorem. We recall this result and reveal the mathematics behind our test. Readers may customize and modify the test for more accurate results or to evaluate interpersonal relationships in other settings, not only romantic. Finally, we apply Dyson's and Press's …

On The Persistence And Attrition Of Women In Mathematics, Katrina Piatek-Jimenez

Journal of Humanistic Mathematics

The purpose of this study was to investigate what motivates women to choose mathematics as an undergraduate major and to further explore what shapes their future career goals, paying particular attention to their undergraduate experiences and their perceptions of the role of gender in these decisions. A series of semi-structured, individual interviews were conducted with twelve undergraduate women mathematics majors who were attending either a large public university or a small liberal arts college. This study found that strong mathematical identities and enjoyment of mathematics heavily influenced their decisions to major in mathematics. At the career selection stage, these women …

Gut Microbiota-Dependent Trimethylamine N-Oxide (Tmao) Pathway Contributes To Both Development Of Renal Insufficiency And Mortality Risk In Chronic Kidney Disease, W.H. Wilson Tang, Zeneng Wang, David J. Kennedy, Yuping Wu, Jennifer A. Buffa, Brendan Agatisa Boyle, Xinmin S. Li, Bruce S. Levison, Stanley L. Hazen

Mathematics and Statistics Faculty Publications

RATIONALE: Trimethylamine-N-oxide (TMAO), a gut microbial-dependent metabolite of dietary choline, phosphatidylcholine (lecithin), and l-carnitine, is elevated in chronic kidney diseases (CKD) and associated with coronary artery disease pathogenesis. OBJECTIVE: To both investigate the clinical prognostic value of TMAO in subjects with versus without CKD, and test the hypothesis that TMAO plays a direct contributory role in the development and progression of renal dysfunction. METHODS AND RESULTS: We first examined the relationship between fasting plasma TMAO and all-cause mortality over 5-year follow-up in 521 stable subjects with CKD (estimated glomerular filtration rate, <60 mL/min per 1.73 m(2)). Median TMAO level among CKD subjects was 7.9 μmol/L (interquartile range, 5.2-12.4 μmol/L), which was markedly higher (P<0.001) than in non-CKD subjects (n=3166). Within CKD subjects, higher (fourth versus first quartile) plasma TMAO level was associated with a 2.8-fold increased mortality risk. After adjustments for traditional risk factors, high-sensitivity C-reactive protein, estimated glomerular filtration rate, elevated TMAO levels remained predictive of 5-year mortality risk (hazard ratio, 1.93; 95% confidence interval, 1.13-3.29; P<0.05). TMAO provided significant incremental prognostic value (net reclassification index, 17.26%; P<0.001 and differences in area under receiver operator characteristic curve, 63.26% versus 65.95%; P=0.036). Among non-CKD subjects, elevated TMAO levels portend poorer prognosis within cohorts of high and low cystatin C. In animal models, elevated dietary choline or TMAO directly led to progressive renal tubulointerstitial fibrosis and dysfunction. CONCLUSIONS: Plasma TMAO levels are both elevated in patients with CKD and portend poorer long-term survival. Chronic dietary exposures that increase TMAO directly contributes to progressive renal fibrosis and dysfunction in animal models.

The Game Of Thrones: A Study Of Power Networks And How They Change, Trevor Williams

Research on Capitol Hill

No abstract provided.

A Compactness Theorem For The Dual Gromov-Hausdorff Propinquity, Frédéric Latrémolière

Mathematics Preprint Series

We prove a compactness theorem for the dual Gromov-Hausdorff propinquity as a noncommutative analogue of the Gromov compactness theorem for the Gromov-Hausdorff distance. Our theorem is valid for subclasses of quasi-Leibniz quantum compact metric spaces of the closure of finite dimensional quasi-Leibniz quantum compact metric spaces for the dual propinquity. While finding characterizations of this class proves delicate, we show that all nuclear, quasi-diagonal quasi-Leibniz quantum compact metric spaces are limits of finite dimensional quasi-Leibniz quantum compact metric spaces. This result involves a mild extension of the definition of the dual propinquity to quasi-Leibniz quantum compact metric spaces, which is …

Probing The Inverted Classroom: A Study Of Teaching And Learning Outcomes In Engineering And Mathematics, Nancy K. Lape, Rachel Levy, Darryl Yong

All HMC Faculty Publications and Research

Flipped classrooms have started to become commonplace on university campuses. Despite the growing number of flipped courses, however, quantitative information on their effectiveness remains sparse. Active learning is a mode of instruction that focuses the responsibility of learning on learners. Multiple studies have shown that active learning leads to better student outcomes. Given that instructors in flipped classrooms are generally able to create more opportunities for students to apply or practice course material, we hypothesized that students in a flipped classroom would exhibit more learning compared to students in an unflipped class. This case study describes our research comparing …

Periodic Body-And-Bar Frameworks, Ciprian Borcea, Ileana Streinu, Shin-Ichi Tanigawa

Computer Science: Faculty Publications

Periodic body-and-bar frameworks are abstractions of crystalline structures made of rigid bodies connected by fixed-length bars and subject to the action of a lattice of translations. We give a Maxwell–Laman characterization for minimally rigid periodic body-and-bar frameworks in terms of their quotient graphs. As a consequence we obtain efficient polynomial time algorithms for their recognition based on matroid partition and pebble games.