The K-Dominating Graph,
2013
Smith College
The K-Dominating Graph, Ruth Haas, Karen Seyffarth
Mathematics Sciences: Faculty Publications
Abstract. Given a graph G, the k-dominating graph of G, Dk(G), is defined to be the graph whose vertices correspond to the dominating sets of G that have cardinality at most k. Two vertices in Dk(G) are adjacent if and only if the corresponding dominating sets of G differ by either adding or deleting a single vertex. The graph Dk(G) aids in studying the reconfiguration problem for dominating sets. In particular, one dominating set can be reconfigured to another by a sequence of single vertex additions and deletions, such that the intermediate set of …
Waring Decompositions Of Monomials,
2013
Institute of Mathematics of the Polish Academy of Sciences
Waring Decompositions Of Monomials, Weronika Buczyńska, Jarosław Buczyński, Zach Teitler
Mathematics Faculty Publications and Presentations
A Waring decomposition of a polynomial is an expression of the polynomial as a sum of powers of linear forms, where the number of summands is minimal possible. We prove that any Waring decomposition of a monomial is obtained from a complete intersection ideal, determine the dimension of the set of Waring decompositions, and give the conditions under which the Waring decomposition is unique up to scaling the variables.
Propeller,
2013
Claremont Colleges
Propeller, Joel Kahn
The Transdisciplinary STEAM+ Journal
This image is based on several different algorithms interconnected within a single program in the language BASIC-256. The fundamental structure involves a tightly wound spiral working outwards from the center of the image. As the spiral is drawn, different values of red, green and blue are modified through separate but related processes, producing the changing appearance. Algebra, trigonometry, geometry, and analytic geometry are all utilized in overlapping ways within the program. As with many works of algorithmic art, small changes in the program can produce dramatic alterations of the visual output, which makes lots of variations possible.
Stable Image Reconstruction Using Total Variation Minimization,
2013
Claremont McKenna College
Stable Image Reconstruction Using Total Variation Minimization, Deanna Needell, Rachel Ward
CMC Faculty Publications and Research
This article presents near-optimal guarantees for stable and robust image recovery from undersampled noisy measurements using total variation minimization. In particular, we show that from O(s log(N)) nonadaptive linear measurements, an image can be reconstructed to within the best s-term approximation of its gradient up to a logarithmic factor, and this factor can be removed by taking slightly more measurements. Along the way, we prove a strengthened Sobolev inequality for functions lying in the null space of suitably incoherent matrices.
Inverse Spectral Problems For Graphs,
2013
Brigham Young University
Inverse Spectral Problems For Graphs, Dr. Wayne Barrett
Journal of Undergraduate Research
This MEG grant made it possible to support several student research activ- ities from Spring 2009 through Winter 2010.
Fractional Calculus And Smallest Eigenvalues,
2013
Eastern Kentucky University
Fractional Calculus And Smallest Eigenvalues, Jeffrey T. Neugebauer
Mathematics Colloquium Series
This talk will introduce the subject of fractional calculus, which involves taking integrals and derivatives of arbitrary order. Neugebauer will show how the definitions of fractional derivatives and fractional integrals are natural extensions of the definitions of the derivative and the integral. In addition to showing some examples, Neugebauer will explore ongoing research on the comparison of smallest eigenvalues of a fractional-boundary-value problem with conjugate boundary conditions.
Character Tables Of Metacyclic Groups,
2013
Brigham Young University - Provo
Character Tables Of Metacyclic Groups, Dane Christian Skabelund
Theses and Dissertations
We show that any two split metacyclic groups with the same character tables are isomorphic. We then use this to show that among metacyclic groups that are either 2-groups or are of odd order divisible by at most two primes, that the dihedral and generalized quaternion groups of order 2^n, n = 3, are the only pairs that have the same character tables.
Euler’S Algebraic Creativity And Undergraduate Math,
2013
University of the Pacific
Euler’S Algebraic Creativity And Undergraduate Math, Christopher D. Goff
College of the Pacific Faculty Presentations
This talk will describe the author’s work translating a paper of Euler on number theory, and how researching the history of this paper led back to Lagrange, Fermat, and ultimately to a geometry problem of Diophantus. We will investigate Euler’s algebraic creativity and Lagrange’s explanation of his own method, inspired by Fermat. Moreover, we will demonstrate one way in which this paper of Euler’s has been used as part of a project in an undergraduate history of mathematics course. We will even investigate the continuation of Euler’s work.
Developing A Stem Teacher Recruitment Pipeline,
2013
Columbus State University
Developing A Stem Teacher Recruitment Pipeline, Kimberly Shaw, Cindy Ticknor, Tim Howard
Interdisciplinary STEM Teaching & Learning Conference (2012-2019) (Archived)
The Columbus Region Academy of Future Teachers of STEM (CRAFT-STEM), a Phase I Robert Noyce Teacher Scholarship Program, combines internships and scholarships, an exciting summer STEM Honors Camp, a new Teaching Connections Seminar, and an impressive array of existing resources to recruit, prepare, and graduate an increasing number of STEM teachers committed to serving high need high schools.
Integrating Manipulatives To Improve Fraction Concepts,
2013
Georgia Southern University
Integrating Manipulatives To Improve Fraction Concepts, Rachel Dunn
Interdisciplinary STEM Teaching & Learning Conference (2012-2019) (Archived)
The aim of this session is to demonstrate the tools used to help reinforce and recreate students’ conceptual knowledge of fractions, specifically targeting the unit of reference. These manipulatives will provide teachers with instructional support for Common Core Standards, which emphasize critical thinking skills and various representations of knowledge, specifically with fractions. Participants will become actively engaged in learning about these tools, including jumping on a number line floor mat, working with circular fraction pieces and placing fractions on a number line rope. By representing knowledge through circular and linear methods, students will use critical thinking skills and support will …
Integrating Manipulatives To Improve Fraction Concepts,
2013
Georgia Southern University
Integrating Manipulatives To Improve Fraction Concepts, Rachel Dunn
Interdisciplinary STEM Teaching & Learning Conference (2012-2019) (Archived)
Many students are overwhelmed by mathematics because the language is too difficult, the teaching strategies are insufficient or they have lost motivation. With a recent emphasis on meeting the Common Core expectations, using manipulatives to eliminate misconceptions in the mathematical classroom has become even more prevalent. I explored the misconceptions that many students struggle with and provided possible methods of eliminating them at all levels for learning. During this investigation, I studied the effect of manipulatives on students’ understanding of fraction concepts and the students’ conceptions of the unit of reference when working with fraction word problems. I learned that …
Trig-Star,
2013
Georgia State University
Trig-Star, James M. Anderson
Interdisciplinary STEM Teaching & Learning Conference (2012-2019) (Archived)
A TRIG-STAR is a mathematics student who has demonstrated in competition that he or she is the most skilled among classmates in the practical application of trigonometry. The competition for the honor is a timed exercise which is the solving of a trigonometry problem that incorporates the use of right triangle formulas, circle formulas, the law of sines, and the law of cosines. The contest helps to promote careers in surveying and mapping to students at the High Schools across the country. The award is sponsored by the National Society of Professional Surveyors and cosponsored locally. State winners also have …
A Classification Tool For Predictive Data Analysis In Healthcare,
2013
Brigham Young University - Provo
A Classification Tool For Predictive Data Analysis In Healthcare, Mason Lemoyne Victors
Theses and Dissertations
Hidden Markov Models (HMMs) have seen widespread use in a variety of applications ranging from speech recognition to gene prediction. While developed over forty years ago, they remain a standard tool for sequential data analysis. More recently, Latent Dirichlet Allocation (LDA) was developed and soon gained widespread popularity as a powerful topic analysis tool for text corpora. We thoroughly develop LDA and a generalization of HMMs and demonstrate the conjunctive use of both methods in predictive data analysis for health care problems. While these two tools (LDA and HMM) have been used in conjunction previously, we use LDA in a …
Why ℓ1 Is A Good Approximation To ℓ0: A Geometric Explanation,
2013
The University of Texas at El Paso
Why ℓ1 Is A Good Approximation To ℓ0: A Geometric Explanation, Carlos Ramirez, Vladik Kreinovich, Miguel Argaez
Departmental Technical Reports (CS)
In practice, we usually have partial information; as a result, we have several different possibilities consistent with the given measurements and the given knowledge. For example, in geosciences, several possible density distributions are consistent with the measurement results. It is reasonable to select the simplest among such distributions. A general solution can be described, e.g., as a linear combination of basic functions. A natural way to define the simplest solution is to select a one for which the number of the non-zero coefficients ci is the smallest. The corresponding "l0-optimization" problem is non-convex and therefore, difficult to …
Immersed Finite Element Methods For Parabolic Equations With Moving Interface,
2013
Missouri University of Science and Technology
Immersed Finite Element Methods For Parabolic Equations With Moving Interface, Xiaoming He, Tao Lin, Yanping Lin, Xu Zhang
Mathematics and Statistics Faculty Research & Creative Works
This article presents three Crank-Nicolson-type immersed finite element (IFE) methods for solving parabolic equations whose diffusion coefficient is discontinuous across a time dependent interface. These methods can use a fixed mesh because IFEs can handle interface jump conditions without requiring the mesh to be aligned with the interface. These methods will be compared analytically in the sense of accuracy and computational cost. Numerical examples are provided to demonstrate features of these three IFE methods. © 2012 Wiley Periodicals, Inc.
Properties Of Higher-Order Half-Linear Functional Differential Equations With Noncanonical Operators,
2013
Missouri University of Science and Technology
Properties Of Higher-Order Half-Linear Functional Differential Equations With Noncanonical Operators, Chenghui Zhang, Ravi P. Agarwal, Martin Bohner, Tongxing Li
Mathematics and Statistics Faculty Research & Creative Works
Some new results are presented for the oscillatory and asymptotic behavior of higher-order half-linear differential equations with a noncanonical operator. We study the delayed and advanced equations subject to various conditions. © 2013 Zhang et al.
How To Find A Levi Decomposition Of A Lie Algebra,
2013
Utah State University
How To Find A Levi Decomposition Of A Lie Algebra, Ian M. Anderson
How to... in 10 minutes or less
We show how to compute the Levi decomposition of a Lie algebra in Maple using the command LeviDecomposition. A worksheet and corresponding PDF can be found below.
How To Find Killing Vectors,
2013
Utah State University
How To Find Killing Vectors, Charles G. Torre
How to... in 10 minutes or less
We show how to compute the Lie algebra of Killing vector fields of a metric in Maple using the commands KillingVectors and LieAlgebraData. A Maple worksheet and a PDF version can be found below.
Estimating Third Central Moment C3 For Privacy Case Under Interval And Fuzzy Uncertainty,
2013
The University of Texas at El Paso
Estimating Third Central Moment C3 For Privacy Case Under Interval And Fuzzy Uncertainty, Ali Jalal-Kamali, Vladik Kreinovich
Departmental Technical Reports (CS)
Some probability distributions (e.g., Gaussian) are symmetric, some (e.g., lognormal) are non-symmetric ({\em skewed}). How can we gauge the skeweness? For symmetric distributions, the third central moment C3 = E[(x - E(x))3] is equal to 0; thus, this moment is used to characterize skewness. This moment is usually estimated, based on the observed (sample) values x1, ..., xn, as C3 = (1/n) * ((x1 - E)3 + ... + (xn - E)3), where E = (1/n) * (x1 + ... + xn). In many …
A Model Of Dendritic Cell Therapy For Melanoma,
2013
Harvey Mudd College
A Model Of Dendritic Cell Therapy For Melanoma, Lisette G. De Pillis, Angela Gallegos, Ami E. Radunskaya
All HMC Faculty Publications and Research
Dendritic cells are a promising immunotherapy tool for boosting an individual’s antigen-specific immune response to cancer. We develop a mathematical model using differential and delay-differential equations to describe the interactions between dendritic cells, effector-immune cells, and tumor cells. We account for the trafficking of immune cells between lymph, blood, and tumor compartments. Our model reflects experimental results both for dendritic cell trafficking and for immune suppression of tumor growth in mice. In addition, in silico experiments suggest more effective immunotherapy treatment protocols can be achieved by modifying dose location and schedule. A sensitivity analysis of the model reveals which patient-specific …
