Cyclic Polynomials In Two Variables,
2016
Washington University in St. Louis
Cyclic Polynomials In Two Variables, Catherine Bénéteau, Greg Knese, Łukasz Kosiński, Constanze Liaw, Daniel Seco, Alan Sola
Mathematics Faculty Research
We give a complete characterization of polynomials in two complex variables that are cyclic with respect to the coordinate shifts acting on Dirichlet-type spaces in the bidisk, which include the Hardy space and the Dirichlet space of the bidisk. The cyclicity of a polynomial depends on both the size and nature of the zero set of the polynomial on the distinguished boundary. The techniques in the proof come from real analytic function theory, determinantal representations for polynomials, and harmonic analysis on curves.
Systems Perturbation Analysis Of A Large-Scale Signal Transduction Model Reveals Potentially Influential Candidates For Cancer Therapeutics,
2016
University of Nebraska - Lincoln
Systems Perturbation Analysis Of A Large-Scale Signal Transduction Model Reveals Potentially Influential Candidates For Cancer Therapeutics, Bhanwar L. Puniya, Laura Allen, Colleen Hochfelder, Mahbubul Majumder, Tomáš Helikar
Mathematics Faculty Publications
Dysregulation in signal transduction pathways can lead to a variety of complex disorders, including cancer. Computational approaches such as network analysis are important tools to understand system dynamics as well as to identify critical components that could be further explored as therapeutic targets. Here, we performed perturbation analysis of a large-scale signal transduction model in extracellular environments that stimulate cell death, growth, motility, and quiescence. Each of the model’s components was perturbed under both loss-of-function and gain-of-function mutations. Using 1,300 simulations under both types of perturbations across various extracellular conditions, we identified the most and least influential components based on …
Commutators In The Two-Weight Setting,
2016
Washington University in St. Louis
Commutators In The Two-Weight Setting, Irina Holmes, Michael T. Lacey, Brett D. Wick
Mathematics Faculty Research
Let R be the vector of Riesz transforms on Rn and let μ,λ∈Ap be two weights on Rn, 1p(μ)→Lp(λ)|| is shown to be equivalent to the function b being in a BMO space adapted to μ and λ. This is a common extension of a result of Coifman–Rochberg–Weiss in the case of both λ and μ being Lebesgue measure, and Bloom in the case of dimension one.
Modeling Lotic Organism Populations With Partial Differential Equations,
2016
University of Denver
Modeling Lotic Organism Populations With Partial Differential Equations, Chase Viss, Tom Clark, Eric Eager
Faculty Work Comprehensive List
We present in this paper a mathematical model for a population of caddisfly larvae in the Upper Mississippi River, which can either live in the current of the water or fix themselves to large wood debris submerged throughout the river. The model consists of a system of partial differential equations which captures these coupled dynamics. After introducing the model, we give a qualitative analysis of the dynamics, which includes a steady state solution followed by a numerical solution to the system using a finite difference scheme implemented in R. Finally, we extend the model to a competitive system with the …
Second Order Approximation For Heat Conduction: Dissipation Principle And Free Energies,
2016
University of Pisa, Italy
Second Order Approximation For Heat Conduction: Dissipation Principle And Free Energies, Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden, Barbara Lazzari
Articles
In the context of new models of heat conduction, the second-order approximation of Tzou’s theory, derived by Quintanilla and Racke, has been studied recently by two of the present authors, where it was proved equivalent to a fading memory material. The importance of determining free energy functionals for such materials, and indeed for any material with memory, is emphasized. Because the kernel does not satisfy certain convexity restrictions that allow us to obtain various traditional free energies for materials with fading memory, it is necessary to restrict the study to the minimum and related free energies, which do not require …
A Note On The Γ-Coefficients Of The Tree Eulerian Polynomial,
2016
University of Kentucky
A Note On The Γ-Coefficients Of The Tree Eulerian Polynomial, Rafael S. González D'León
Mathematics Faculty Publications
We consider the generating polynomial of the number of rooted trees on the set {1,2,...,n} counted by the number of descending edges (a parent with a greater label than a child). This polynomial is an extension of the descent generating polynomial of the set of permutations of a totally ordered n-set, known as the Eulerian polynomial. We show how this extension shares some of the properties of the classical one. A classical product formula shows that this polynomial factors completely over the integers. From this product formula it can be concluded that this polynomial has positive coefficients …
Off The Lip Conference - Transdisciplinary Approaches To Cognitive Innovation. Conference Proceedings,
2016
University of Plymouth
Off The Lip Conference - Transdisciplinary Approaches To Cognitive Innovation. Conference Proceedings, Sue Denham, Michael Punt, Edith Doove, Martha Blassnigg, Raluca Briazu, Kathryn Francis, Agi Haynes, Guy Edmonds, Adam Benjamin, Matthew Emmett, Iris Garrelfs, Christopher B. Germann, Joanna Griffin, Diane Humphrey, Bryanna Lucyk, Christie Purchase, Rachel Sansone, Emily Baxter, Amy Ione, Frank Loesche, Abigail Jackson, Alexis Kirke, Eduardo Miranda, Luke Rendell, Simon Ingram, Yutaka Nakamura, Gi Taek Ryoo, Eugenia Stamboliev, Michael Straeubig, Chun-Wei Hsu, Pinar Oztop, Mihaela Taranu, Sundar Sarukkai, James Sweeting, Minami Hirayama
Off the Lip Conference - Transdisciplinary Approaches to Cognitive Innovation
The promise of cognitive innovation as a collaborative project in the sciences, arts and humanities is that we can approach creativity as a bootstrapping cognitive process in which the energies that shape the poem are necessarily indistinguishable from those that shape the poet. For the purposes of this conference the exploration of the idea of cognitive innovation concerns an understanding of creativity that is not exclusively concerned with conscious human thought and action but also as intrinsic to our cognitive development. As a consequence, we see the possibility for cognitive innovation to provide a theoretical and practical platform from which …
Impartial Avoidance Games For Generating Finite Groups,
2016
College of Saint Benedict/Saint John's University
Impartial Avoidance Games For Generating Finite Groups, Bret J. Benesh, Dana C. Ernst, Nándor Sieben
Mathematics Faculty Publications
We study an impartial avoidance game introduced by Anderson and Harary. The game is played by two players who alternately select previously unselected elements of a finite group. The first player who cannot select an element without making the set of jointly-selected elements into a generating set for the group loses the game. We develop criteria on the maximal subgroups that determine the nim-numbers of these games and use our criteria to study our game for several families of groups, including nilpotent, sporadic, and symmetric groups.
Knowledge And Tasks Connecting Elementary, Secondary, And Disciplinary Mathematics,
2016
University of Nebraska-Lincoln
Knowledge And Tasks Connecting Elementary, Secondary, And Disciplinary Mathematics, Yvonne Lai
Discipline-Based Education Research Group Speaker Series
A well-prepared teacher should be able to help her students see mathematics as ideas that develop over time. Mathematics courses designed specifically for prospective secondary teachers aim for prospective teachers to see and find connections across elementary, secondary, and disciplinary mathematics, and beyond that to be able to use those connections in their future teaching. While there is broad agreement with these aims, there is also little consensus around how to carry them out. Two challenges in meeting these aims are identifying content that lends itself to such connections and designing tasks that can be used to engage with that …
Spectral Graph Theory For Weighted Digraphs,
2016
Brigham Young University
Spectral Graph Theory For Weighted Digraphs, Alexander Zaitzeff, Jeffrey Humpherys
Journal of Undergraduate Research
For digraphs weighted and unweighted, one important application is ranking: Given a directed graph, whether it be the Internet or a social network, which node (representing a web page or a person) is the most important? There are many different methods to find answer this question. A few are highest indegree, closeness centrality1, betweeness centrality2, eigenvector centrality, Katz Centrality3, and PageRank4. Our idea is to use sparsity, or the idea that in a network only has a few important nodes, to determine the ranking on a graph.
Generating Functions And Wilf Equivalence For Generalized Interval Embeddings,
2016
Trinity University
Generating Functions And Wilf Equivalence For Generalized Interval Embeddings, Russell Chamberlain, Garner Cochran, Sam Ginsburg, Brian K. Miceli, Manda Riehl, Chi Zhang
Mathematics Faculty Research
In 1999 in [J. Difference Equ. Appl. 5, 355–377], Noonan and Zeilberger extended the Goulden-Jackson Cluster Method to find generating functions of word factors. Then in 2009 in [Electron. J. Combin. 16(2), RZZ], Kitaev, Liese, Remmel and Sagan found generating functions for word embeddings and proved several results on Wilf-equivalence in that setting. In this article, the authors focus on generalized interval embeddings, which encapsulate both factors and embeddings, as well as the “space between” these two ideas. The authors present some results in the most general case of interval embeddings. Two special cases of …
Why Min-Based Conditioning,
2016
Université d'Artois
Why Min-Based Conditioning, Salem Benferhat, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we do not have full information about which alternatives are possible and which are not. In such situations, an expert can estimate, for each alternative, the degree to which this alternative is possible. Sometimes, experts can produce numerical estimates of their degrees, but often, they can only provide us with qualitative estimates: they inform us which degrees are higher, but do not provide us with numerical values for these degrees. After we get these degrees from the experts, we often gain additional information, because of which some alternatives which were previously considered possible are now excluded. …
Assessing Mathematical Knowledge For Teaching: The Role Of Teaching Context,
2016
University of Montana
Assessing Mathematical Knowledge For Teaching: The Role Of Teaching Context, Geoffrey Phelps, Heather Howell
The Mathematics Enthusiast
Assessments of mathematical knowledge for teaching (MKT), which are often designed to measure specialized types of mathematical knowledge, typically include a representation of teaching practice in the assessment task. This analysis makes use of an existing, validated set of 10 assessment tasks to both describe and explore the function of the teaching contexts represented. We found that teaching context serves a variety of functions, some more critical than others. These context features play an important role in both the design of assessments of MKT and the types of mathematical knowledge assessed.
Cyclic Critical Groups Of Graphs,
2016
Gettysburg College
Cyclic Critical Groups Of Graphs, Ryan P. Becker, Darren B. Glass
Math Faculty Publications
In this note, we describe a construction that leads to families of graphs whose critical groups are cyclic. For some of these families we are able to give a formula for the number of spanning trees of the graph, which then determines the group exactly.
Guest Editorial: Mathematical Knowledge For Teaching: Developing Measures And Measuring Development,
2016
University of Montana
Guest Editorial: Mathematical Knowledge For Teaching: Developing Measures And Measuring Development, Reidar Mosvold, Mark Hoover
The Mathematics Enthusiast
No abstract provided.
Interview Prompts To Uncover Mathematical Knowledge For Teaching: Focus On Providing Written Feedback,
2016
University of Montana
Interview Prompts To Uncover Mathematical Knowledge For Teaching: Focus On Providing Written Feedback, Yeon Kim
The Mathematics Enthusiast
One area of study that has been gathering enthusiastic attention and interest is mathematical knowledge for teaching (MKT). How to research MKT, however, is still unsettled despite the plethora of unexamined areas of practice. As one of ways to unearth and measure MKT, this study uses interview prompts designed to providing written feedback, as a target area of practice. This study specifies in what ways the interview prompts are used in order to provide a comprehensive method to researching MKT. From interviews across professional communities with different kinds of mathematical expertise, the author develops a conceptual model based on the …
Spanning Eulerian Subgraphs And Catlin’S Reduced Graphs,
2016
Butler University
Spanning Eulerian Subgraphs And Catlin’S Reduced Graphs, Wei-Guo Chen, Zhi-Hong Chen
Scholarship and Professional Work - LAS
A graph G is collapsible if for every even subset R ⊆ V (G), there is a spanning connected subgraph HR of G whose set of odd degree vertices is R. A graph is reduced if it has no nontrivial collapsible subgraphs. Catlin [4] showed that the existence of spanning Eulerian subgraphs in a graph G can be determined by the reduced graph obtained from G by contracting all the collapsible subgraphs of G. In this paper, we present a result on 3-edge-connected reduced graphs of small orders. Then, we prove that a 3-edge-connected graph G of order n …
Evaluation Of Nasa's Merra Precipitation Product In Reproducing The Observed Trend And Distribution Of Extreme Precipitation Events In The United States,
2016
University of California, Irvine
Evaluation Of Nasa's Merra Precipitation Product In Reproducing The Observed Trend And Distribution Of Extreme Precipitation Events In The United States, Hamed Ashouri, Soroosh Sorooshian, Kuo-Lin Hsu, Michael G. Bosilovich, Jaechoul Lee, Michael F. Wehner, Allison Collow
Mathematics Faculty Publications and Presentations
This study evaluates the performance of NASA’s Modern-Era Retrospective Analysis for Research and Applications (MERRA) precipitation product in reproducing the trend and distribution of extreme precipitation events. Utilizing the extreme value theory, time-invariant and time-variant extreme value distributions are developed to model the trends and changes in the patterns of extreme precipitation events over the contiguous United States during 1979–2010. The Climate Prediction Center (CPC) U.S. Unified gridded observation data are used as the observational dataset. The CPC analysis shows that the eastern and western parts of the United States are experiencing positive and negative trends in annual maxima, respectively. …
Why Defining The Construct Matters: An Examination Of Teacher Knowledge Using Different Lenses On One Assessment,
2016
University of Montana
Why Defining The Construct Matters: An Examination Of Teacher Knowledge Using Different Lenses On One Assessment, Chandra H. Orrill, Allan S. Cohen
The Mathematics Enthusiast
What does it mean to align an assessment to the domain of interest? In this paper, we analyze teachers’ performance on the Learning Mathematics for Teaching assessment of Proportional Reasoning. Using a mixture Rasch model, we analyze their performance on the entire assessment, then on two different subsets of items from the original assessment. We consider the affordances of different conceptualizations of the domain and consider the implications of the domain definition on the claims we can make about teacher performance. We use a single assessment to illustrate the differences in results that can arise based on the ways in …
Single Valued Neutrosophic Graphs,
2016
University of New Mexico
Single Valued Neutrosophic Graphs, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea
Branch Mathematics and Statistics Faculty and Staff Publications
The notion of single valued neutrosophic sets is a generalization of fuzzy sets, intuitionistic fuzzy sets. We apply the concept of single valued neutrosophic sets, an instance of neutrosophic sets, to graphs. We introduce certain types of single valued neutrosophic graphs (SVNG) and investigate some of their properties with proofs and examples.
