Mathematics Commons^™

Density Of Gallai Multigraphs, Colton Magnant

Department of Mathematical Sciences Faculty Publications

Diwan and Mubayi asked how many edges of each color could be included in a 33-edge-colored multigraph containing no rainbow triangle. We answer this question under the modest assumption that the multigraphs in question contain at least one edge between every pair of vertices. We also conjecture that this assumption is, in fact, without loss of generality.

Transition To Higher Mathematics: Structure And Proof (Second Edition), Bob A. Dumas, John E. Mccarthy

Books and Monographs

This book is written for students who have taken calculus and want to learn what “real mathematics" is. We hope you will find the material engaging and interesting, and that you will be encouraged to learn more advanced mathematics. This is the second edition of our text. It is intended for students who have taken a calculus course, and are interested in learning what higher mathematics is all about. It can be used as a textbook for an "Introduction to Proofs" course, or for self-study. Chapter 1: Preliminaries, Chapter 2: Relations, Chapter 3: Proofs, Chapter 4: Principles of Induction, Chapter …

Boundedness In Functional Dynamic Equations On Time Scales, Elvan Akin, Youssef N. Raffoul

Youssef N. Raffoul

Using nonnegative definite Lyapunov functionals, we prove general theorems for the boundedness of all solutions of a functional dynamic equation on time scales. We apply our obtained results to linear and nonlinear Volterra integro-dynamic equations on time scales by displaying suitable Lyapunov functionals.

Exponential Stability In Functional Dynamic Equations On Time Scales, Elvan Akin, Youssef Raffoul, Christopher Tisdell

Youssef N. Raffoul

We are interested in the exponential stability of the zero solution of a functional dynamic equation on a time scale, a nonempty closed subset of real numbers. The approach is based on suitable Lyapunov functionals and certain inequalities. We apply our results to obtain exponential stability in Volterra integrodynamic equations on time scales.

Ascent Sequences Avoiding Pairs Of Patterns, Andrew M. Baxter, Lara Pudwell

Mathematics and Statistics Faculty Publications

Ascent sequences were introduced by Bousquet-Melou et al. in connection with (2+2)-avoiding posets and their pattern avoidance properties were first considered by Duncan and Steingrímsson. In this paper, we consider ascent sequences of length n" role="presentation" style="display: inline; font-size: 11.2px; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; font-family: Verdana, Arial, Helvetica, sans-serif; position: relative;">nn avoiding two patterns of length 3, and we determine an exact enumeration for 16 different pairs of patterns. Methods include simple recurrences, bijections to other combinatorial objects (including Dyck paths …

Solutions To A Partial Integro-Differential Parabolic System Arising In The Pricing Of Financial Options In Regime- Switching Jump Diffusion Models, Ionut Florescu, Ruihua Liu, Maria Mariani

Ruihua Liu

No abstract provided.

K-Theory And Pseudospectra For Topological Insulators [Dataset], Terry A. Loring

Math and Statistics Datasets

We derive formulas and algorithms for Kitaev's invariants in the periodic table for topological insulators and superconductors for finite disordered systems on lattices with boundaries. We find that K-theory arises as an obstruction to perturbing approximately compatible observables into compatible observables. We derive formulas in all symmetry classes up to dimension two, and in one symmetry class in dimension three, that can be computed with sparse matrix algorithms. We present algorithms in two symmetry classes in 2D and one in 3D and provide illustrative studies regarding how these algorithms can detect the scaling properties of phase transitions.

A Unified And Preserved Dirichlet Boundary Treatment For The Cell-Centered Finite Volume Discrete Boltzmann Method, Leitao Chen, Laura A. Schaefer

Publications

A new boundary treatment is proposed for the finite volume discrete Boltzmann method (FVDBM) that can be used for accurate simulations of curved boundaries and complicated flow conditions. First, a brief review of different boundary treatments for the general Boltzmann simulations is made in order to primarily explain what type of boundary treatment will be developed in this paper for the cell-centered FVDBM. After that, the new boundary treatment along with the cell-centered FVDBM model is developed in detail. Next, the proposed boundary treatment is applied to a series of numerical tests with a detailed discussion of its qualitative and …

Identifying Locations Of Active Corrosion Growth From Successive In-Line Inspections, Tom Bubenik, William V. Harper, Pam Moreno, Steven Polasik

Mathematics Faculty Scholarship

The integrated approach covered by this paper identifies corrosion activity using a combination of statistics, inspection-signal comparisons, and engineering analyses. The approach relies on an understanding of ILI and the mechanisms that cause corrosion and its growth. Pipeline operators can use the approach to calculate remaining lives, prioritize repairs and mitigation, and extend reassessment intervals. This process is collectively known as statistically-active corrosion.

Biological Control Via "Ecological" Damping: An Approach That Attenuates Non-Target Effects, Rana D. Parshad, Kelly Black, Emmanuel Quansah, Matthew Beauregard

Faculty Publications

In this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population in a three-species food chain. We allow for finite time blowup in the model as a mathematical construct to mimic the explosive increase in population, enabling the species to reach “disastrous” levels, in a finite time. We next propose various controls to drive down the invasive population growth and, in certain cases, eliminate blow-up. The controls avoid chemical treatments and/or natural enemy introduction, thus eliminating various non-target effects associated with such classical methods. We refer …

Comparing Skew Schur Functions: A Quasisymmetric Perspective, Peter R. W. Mcnamara

Peter R. W. McNamara

Reiner, Shaw and van Willigenburg showed that if two skew Schur functions s_A and s_B are equal, then the skew shapes $A$ and $B$ must have the same "row overlap partitions." Here we show that these row overlap equalities are also implied by a much weaker condition than Schur equality: that s_A and s_B have the same support when expanded in the fundamental quasisymmetric basis F. Surprisingly, there is significant evidence supporting a conjecture that the converse is also true.

In fact, we work in terms of inequalities, showing that if the F-support of s_{A …}

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 …

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 …

Dark-Bright Solitons And Their Lattices In Atomic Bose-Einstein Condensates, D. Yan, F. Tsitoura, Panos Kevrekidis, D. J. Frantzeskakis

Panos Kevrekidis

In the present contribution, we explore a host of different stationary states, namely dark-bright solitons and their lattices, that arise in the context of multicomponent atomic Bose-Einstein condensates. The latter are modeled by systems of coupled Gross-Pitaevskii equations with general interaction (nonlinearity) coefficients gij. It is found that in some particular parameter ranges such solutions can be obtained in analytical form, however, numerically they are computed as existing in a far wider parametric range. Many features of the solutions under study, such as their analytical form without the trap or the stability and dynamical properties of one dark-bright soliton even …

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 …

A Mathematician's Villanelle, Gizem Karaali

Pomona Faculty Publications and Research

No abstract provided.

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 …

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 …

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}, …