Mathematics Commons^™

Asymptotic Spectral Distributions Of Distance-K Graphs Of Hamming Graphs, Yuji Hibino

Communications on Stochastic Analysis

No abstract provided.

Dynamics Of The Fitzhugh-Nagumo Neuron Model, Zechariah Thurman

Physics

In this paper, the dynamical behavior of the Fitzhugh-Nagumo model is examined. The relationship between neuron input current and the firing frequency of the neuron is characterized. Various coupling schemes are also examined, and their effects on the dynamics of the system is discussed. The phenomenon of stochastic resonance is studied for a single uncoupled Fitzhugh-Nagumo neuron.

Partially Gaussian Stationary Stochastic Processes In Discrete Time, K R Parthasarathy

Communications on Stochastic Analysis

No abstract provided.

Linear Stochastic Differential Equations With Anticipating Initial Conditions, Narjess Khalifa, Hui-Hsiung Kuo, Habib Ouerdiane, Benedykt Szozda

Communications on Stochastic Analysis

No abstract provided.

Crra Utility Maximization Under Dynamic Risk Constraints, Santiago Moreno-Bromberg, Traian A Pirvu, Anthony Reveillac

Communications on Stochastic Analysis

No abstract provided.

Anticipated Backward Stochastic Differential Equations With Continuous Coefficients, Zhe Yang, Robert J Elliott

Communications on Stochastic Analysis

No abstract provided.

Asymptotic And Geometric Properties Of Compactly Perturbed Wiener Process And Self-Intersection Local Time, Andrey A Dorogovtsev, Olga L Izyumtseva

Communications on Stochastic Analysis

No abstract provided.

Nonparametric Regression With Non-Gaussian Long Memory, Mariela Sued, Soledad Torres, Ciprian A. Tudor

Communications on Stochastic Analysis

No abstract provided.

Projected Surface Finite Elements For Elliptic Equations, Necibe Tuncer

Applications and Applied Mathematics: An International Journal (AAM)

In this article, we define a new finite element method for numerically approximating solutions of elliptic partial differential equations defined on “arbitrary” smooth surfaces S in RN+1. By “arbitrary” smooth surfaces, we mean surfaces that can be implicitly represented as level sets of smooth functions. The key idea is to first approximate the surface S by a polyhedral surface Sh, which is a union of planar triangles whose vertices lie on S; then to project Sh onto S. With this method, we can also approximate the eigenvalues and eigenfunctions of th Laplace-Beltrami operator on these “arbitrary” surfaces.

A New Implementation Of Gmres Using Generalized Purcell Method, Morteza Rahmani, Sayed H. Momeni-Masuleh

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a new method based on the generalized Purcell method is proposed to solve the usual least-squares problem arising in the GMRES method. The theoretical aspects and computational results of the method are provided. For the popular iterative method GMRES, the decomposition matrices of the Hessenberg matrix is obtained by using a simple recursive relation instead of Givens rotations. The other advantages of the proposed method are low computational cost and no need for orthogonal decomposition of the Hessenberg matrix or pivoting. The comparisons for ill-conditioned sparse standard matrices are made. They show a good agreement with available …

Tetrathiomolybdate-Associated Copper Depletion Decreases Circulating Endothelial Progenitor Cells In Women With Breast Cancer At High Risk Of Relapse, S. Jain, J. Cohen, M. M. Ward, N. Kornhauser, E. Chuang, T. Cigler, A. Moore, D. Donovan, C. Lam, M. V. Cobham, S. Schneider, Sandra M. Hurtado Rua, S. Benkert, C. Mathijsen Greenwood, R. Zelkowitz, J. D. Warren, M. E. Lane, V. Mittal, S. Rafii, L. T. Vahdat

Mathematics and Statistics Faculty Publications

Background: Bone marrow-derived endothelial progenitor cells (EPCs) are critical for metastatic progression. This study explores the effect of tetrathiomolybdate (TM), an anti-angiogenic copper chelator, on EPCs in patients at high risk for breast cancer recurrence. Patients and methods: This phase 2 study enrolled breast cancer patients with stage 3 and stage 4 without evidence of disease (NED), and stage 2 if triple-negative. TM 100 mg orally was administered to maintain ceruloplasmin <17 mg/dl for 2 years or until relapse. The primary end point was change in EPCs. Results: Forty patients (28 stage 2/3, 12 stage 4 NED) were enrolled. Seventy-five percent patients achieved the copper depletion target by 1 month. Ninety-one percent of triple-negative patients copper-depleted compared with 41% luminal subtypes. In copper-depleted patients only, there was a significant reduction in EPCs/ml by 27 (P = 0.04). Six patients relapsed while on study, of which only one patient had EPCs maintained below baseline. The 10-month relapse-free survival was 85.0% (95% CI 74.6%–96.8%). Only grade 3/4 toxicity was hematologic: neutropenia (3.1% of cycles), febrile neutropenia (0.2%), and anemia (0.2%). Conclusions: TM is safe and appears to maintain EPCs below baseline in copper-depleted patients. TM may promote tumor dormancy and ultimately prevent relapse.

Explore Global Opportunities For Mathematics Scholarship, Teaching, And Service, Ron Benbow

ACMS Conference Proceedings 2013

There are numerous overseas opportunities in which to apply your knowledge and interest in mathematics. These international experiences allow you to expand your scholarship, to extend your teaching skills, to offer professional services to K-12 teachers or other university instructors, and to provide much personal enrichment as well. Examples from recent professional experiences in Liberia, Haiti, Guatemala, and Ecuador will be shared to illustrate the connections to teaching, scholarship, and service. Information regarding MAA Study Tours, Fulbright Specialist grants, and other relevant organizations will be provided.

Euler And The Ongoing Search For Odd Perfect Numbers, Brian D. Beasley

ACMS Conference Proceedings 2013

Leonhard Euler, after proving that every even perfect number has the form given by Euclid, turned his attention to finding odd perfect numbers. Euler established a basic factorization pattern that every odd perfect number must have, and mathematicians have expanded upon this Eulerian form ever since. This paper will present a brief summary of Euler’s result and some recent generalizations. It will also note connections between odd perfect numbers and the abundancy index (the abundancy index of a positive integer is the ratio of the sum of its positive divisors to itself). In particular, finding a positive integer with an …

Computing Foundations For The Scientist, Catherine Bareiss, Larry Vail

ACMS Conference Proceedings 2013

There is a need for a new style of supporting a computer course. Although it is widely recognized that computer technology provides essential tools for all current scientific work, few university curricula adequately ground science majors in the fundamentals that underlie this technology. Introducing science students to computational thinking in the areas of algorithms and data structures, data representation and accuracy, abstraction, performance issues, and database concepts can enable future scientists to become intelligent, creative and effective users of this technology. The intent of this course is not to turn scientists into computer scientists, but rather to enhance their ability …

A Different Approach, Catherine Crockett

ACMS Conference Proceedings 2013

This paper discusses an approach used to encourage science majors to rethink their attitudes and study habits in a first semester calculus course. Two activities were used to enhance study habits. They are outlining concepts and in-class quizzes designed for self-evaluation of skills. After using both methods in two sections of the calculus course, the students were surveyed to determine if these activities were successful. A majority of the students felt the activities were helpful and wanted to continue them.

Reading Assignments And Assessments: Are Your Students Reading Math Texts Before Class, After Class, Both, Or Neither?, David Klanderman, Mandi Maxwell, Sharon Robbert, Bill Boerman-Cornell

ACMS Conference Proceedings 2013

In his recent book What the Best College Students Do [Bain, 2012], Ken Bain defines a number of different types of students including “surface learners,” “strategic learners,” “routine experts,” and finally, “deep learners.” In our mathematics courses at Trinity, we have found examples of all of these student types. A major determinant of their preferred approach to learning appears to be the ways and degrees to which mathematical texts and other written materials are read prior to class sessions. Each full-time member of the department both assigns and assesses the reading of mathematical materials prior to class sessions. Assessment methods, …

Philosophy Of “Spinning Wheels”, Loredana Ciurariu

ACMS Conference Proceedings 2013

In this material I will speak about some well-known mechanisms studied by students and engineers emphasizing the impact which “spinning wheels” had and have in development of the society, on Christians and the church. Also the discovery of the machineries determines major changes in the people’s outlook and leads to new trends in philosophy and Christianity. Then, I will give some examples from the Bible where “spinning wheels” it seems to appear: Judges 16:21, Ezekiel 1 and Revelation. It is also interesting to see 2 Kings 2:9-12, 2 Kings 6:13-18 and maybe Daniel 7:9.

In addition, an avi file where …

An Investigation Of Hi Ho! Cherry-O Using Markov Chains, Nicholas C. Zoller

ACMS Conference Proceedings 2013

In the children’s board game Hi Ho! Cherry-O, players attempt to move 10 cherries from their trees to a bucket in the center of the game board. A spinner determines whether a turn includes moving cherries from tree to bucket or bucket to tree. The winner of the game is the first player to move all of her cherries from her tree to the bucket. We model the gameplay using a Markov chain and calculate the expected number of turns needed to complete one game. Then we investigate what happens when the rules are changed. We discover that rules …

The Structures Of The Actual World, Walter J. Schultz, Lisanne D’ Andrea Winslow

ACMS Conference Proceedings 2013

Scripture teaches that God has a plan for the universe. In this paper we argue that in order for it to function as a plan, it must have a temporal structure, a representational structure, and a proto-causal structure. This paper presents a formal model of the these three structures. As it turns out, the structures of God’s plan are best understood as the structures of a musical composition. We, then very briefly describe its implications. The first is that this model (based ultimately in the doctrine of God) grounds a metaphysics of science. Second, it grounds a structuralist philosophy of …

Perspectives On Chaos: Reflections Of A Mathematical Physicist, Kyle Spyksma

ACMS Conference Proceedings 2013

Chaos Theory, the mathematical media darling of the ’90s, has become less of a societal fad and research interest over the past couple of decades. However, from a mathematical physicists’ perspective, issues surrounding Chaos Theory can be valuable aides in forming views on how mathematics, science and reality relate. In this talk, I will briefly explore how Chaos Theory can shape views of these relationships, with a focus on the language we use and (perhaps unintentionally) abuse when doing science and mathematics.

Stability Of Multiwavelet Frames With Different Matrix Dilations And Matrix Translations, F. A. Shah, Sunita Goyal

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we study the stability of multiwavelet frames with different matrix dilations and matrix translations by means of operator theory and show that these frames remain stable over some kinds of perturbations of the basic generators.

A Subdivision-Regularization Framework For Preventing Over Fitting Of Data By A Model, Ghulam Mustafa, Abdul Ghaffar, Muhammad Aslam

Applications and Applied Mathematics: An International Journal (AAM)

First, we explore the properties of families of odd-point odd-ary parametric approximating subdivision schemes. Then we fine-tune the parameters involved in the family of schemes to maximize the smoothness of the limit curve and error bounds for the distance between the limit curve and the kth level control polygon. After that, we present the subdivision-regularization framework for preventing over fitting of data by model. Demonstration shows that the proposed unified frame work can work well for both noise removal and overfitting prevention in subdivision as well as regularization.

Hydro-Thermal Convective Solutions For An Aquifer System Heated From Below, Dambaru Bhatta

School of Mathematical & Statistical Sciences Faculty Publications

We investigate the effect of hydro-thermal convection in an aquifer system. It is assumed that the aquifer is bounded below and above by impermeable boundaries and it is heated from below. The solution of the governing system is expressed in terms of the basic steady state solution and perturbed solution. We obtain the critical Rayleigh number and critical wavenumber using Runge-Kutta method in combination of shooting method and present the marginal stability curve. The amplitude equation is derived by introducing the adjoint system. After amplitude is obtained, we compute the linear solutions for super-critical and sub-critical cases. Numerical results for …

Galileo's Muse: Renaissance Mathematics And The Arts (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Galileo's Muse: Renaissance Mathematics and the Arts by Mark A. Peterson. Cambridge, MA: Harvard University Press, 2011, 336 pages. ISBN 9780674059726.

The Application Of Bayesian Adaptive Design And Markov Model In Clinical Trials, Xiaoyu Lu

Dissertations

In this research, two new designs in clinical trials are proposed. The first problem is a new Bayesian adaptive dose-finding design and its application in an oncology clinical trial. This design is used for phase IB studies with the biomarker as the endpoint and with the fewer patients. The second problem is another new Bayesian adaptive dose-finding design with longitudinal analysis and its application in phase II depression clinical trial. This design is best fit for phase II dosing-finding clinical trials with clinical endpoints. MTD information has been obtained before the trials.

In adaptive dose-finding clinical trials, the strategy is …

Mathematical Models For Bistable Nematic Liquid Crystal Displays, Chenjing Cai

Dissertations

Bistable Liquid Crystal Displays (LCDs) offer the potential for considerable power savings, compared with conventional (monostable) LCDs. The existence of two (or more) stable field-free states that are optically-distinct means that contrast can be maintained in a display without an externally-applied electric field. An applied field is required only to switch the device from one state to the other, as needed. This dissertation focuses on theoretical models of a possible bistable nematic device, whose operating principle relies on controlling surface anchoring conditions. Switching between the two stable steady states is achieved by application of a transient electric field. A 1D …

Introduction (2013), Eric Gossett

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

American Spread Option Models And Valuation, Yu Hu

Theses and Dissertations

Spread options are derivative securities, which are written on the difference between the values of two underlying market variables. They are very important tools to hedge the correlation risk. American style spread options allow the holder to exercise the option at any time up to and including maturity. Although they are widely used to hedge and speculate in financial market, the valuation of the American spread option is very challenging. Because even under the classic assumptions that the underlying assets follow the log-normal distribution, the resulting spread doesn't have a distribution with a simple closed formula. In this dissertation, we …

Paper Abstracts (2013), Association Of Christians In The Mathematical Sciences

ACMS Conference Proceedings 2013

Nineteenth Conference of the Association of Christians in the Mathematical Sciences

A Numerical Method For Electro-Kinetic Flow With Deformable Interfaces, Manman Ma

Dissertations

We consider two-phase flow of ionic fluids whose motion is driven by an imposed electric field. At a fluid-fluid interface, a screening cloud of ions develops and forms an electro-chemical double layer or ‘Debye layer’. The applied electric field acts on the ionic cloud it induces, resulting in a strong slip flow near the interface. This is known as ‘induced-charge electro-kinetic flow’, and is an important phenomenon in microfluidic applications and in the manipulation of biological cells. The models with two different cases including the fast or slow charging time scales are studied both analytically and numerically. We address a …