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2016

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Articles 751 - 780 of 1329

Full-Text Articles in Mathematics

Essays In Dynamic Macroeconomics And Fiscal Policy., Pawan Gopalakrishnan Dr. Feb 2016

Essays In Dynamic Macroeconomics And Fiscal Policy., Pawan Gopalakrishnan Dr.

Doctoral Theses

In the last two decades, several events in the global economy, like the recession in Japan (1990-2010), the dot com crisis in the US, and the recent global economic and Önancial crisis (which started in 2007-08), to name a few, have brought issues related to Öscal policy back into the limelight. If we look back into the history of policy making, Öscal policy was Örst brought onto the centre-stage in the US during the Great Depression years of the 1930s (see Kopcke et al. (2005) and Feldstein (2009)). It was believed that expansionary Öscal policy would serve as an automatic …

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Efficient And Adaptively Secure Constructions Of Identity-Based Cyrptographic Primitives., Somindu Chaya Ramanna Dr. Feb 2016

Efficient And Adaptively Secure Constructions Of Identity-Based Cyrptographic Primitives., Somindu Chaya Ramanna Dr.

Doctoral Theses

Public-key encryption (PKE) is an elegant solution to the fundamental problem of cryptography – secure communication between two parties over a public (insecure) channel. The basic idea is that every user A holds two keys – a public key (PKA) and a secret key (SKA). A user who wants to send a message to A encrypts it with PKA and sends the resulting ciphertext along the public channel. A, at the other end of the channel, decrypts the ciphertext using SKA and obtains the message. SKA is known to user A alone. Any third party intercepting data on the public …

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Innumeracy: The Product Of Misrepresentation, Elizabeth Cundiff Feb 2016

Innumeracy: The Product Of Misrepresentation, Elizabeth Cundiff

Missouri S&T’s Peer to Peer

Innumeracy refers to one’s inability to understand mathematics. Or, more simply, innumeracy is mathematical illiteracy. The main problem with innumeracy is the fact that most of society does not see it as a problem. In fact, many people boast about their innumeracy. Consider a table of five people at a restaurant: they split the check and attempt to calculate the tip. More often than not, at least one individual at the table will joke about the fact that they don’t know how to do make that simple calculation. This flippancy toward the prevalence of mathematics has become an accepted norm, …

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A Counterexample For Lightning Flash Modules Over E(E1,E2), David Benson, Robert R. Bruner Feb 2016

A Counterexample For Lightning Flash Modules Over E(E1,E2), David Benson, Robert R. Bruner

Mathematics Faculty Research Publications

We give a counterexample to Theorem 5 in Section 18.2 of Margolis’ book, “Spectra and the Steenrod Algebra” and make remarks about the proofs of some later theorems in the book that depend on it. The counterexample is a module which does not split as a sum of lightning flash modules and free modules.

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Digital Circles And Balls: Characterization, Properties, And Applications To Image Analysis., Sahadev Bera Dr. Feb 2016

Digital Circles And Balls: Characterization, Properties, And Applications To Image Analysis., Sahadev Bera Dr.

Doctoral Theses

In this thesis, we have reported some new theoretical findings, empirical formulations, useful heuristics, and efficient algorithms related to digital circle, digital disc, and digital sphere, along with their practical applications to the analysis of geometric information embedded in a digital image. Detecting digital circles and circular arcs from a digital image is very important in shape recognition. Several image processing techniques were proposed over the years to extract circles and circular arc from a digital image and to interpret related issues. We have proposed a novel technique for the segmentation of a digital circle, which is based on a …

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Some Distribution-Free Two-Sample Tests Applicable To High Dimension, Low Sample Size Data., Munmun Biswas Dr. Feb 2016

Some Distribution-Free Two-Sample Tests Applicable To High Dimension, Low Sample Size Data., Munmun Biswas Dr.

Doctoral Theses

The advancement of data acquisition technologies and computing resources have greatly facilitated the analysis of massive data sets in various fields of sciences. Researchers from different disciplines rigorously investigate these data sets to extract useful information for new scientific discoveries. Many of these data sets contain large number of features but small number of observations. For instance, in the fields of chemometrics (see e.g., Schoonover et al. (2003)), medical image analysis (see e.g., Yushkevich et al. (2001)) and microarray gene expression data analysis (see e.g., Eisen and Brown (1999), Alter et al. (2000)), we often deal with data of dimensions …

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Existence Results For Functional Dynamic Equations With Delay, Gnana Bhaskar Tenali Feb 2016

Existence Results For Functional Dynamic Equations With Delay, Gnana Bhaskar Tenali

Mathematics Colloquium Series

Time scale, arbitrary nonempty closed subset of the real numbers (with the topology and ordering inherited from the real numbers) is an efficient and general framework to study different types of problems to discover the commonalities and highlight the essential differences. Sometimes, we may need to choose an appropriate time scale to establish parallels to known results. We present a few recent results from existence theory of funcational dynamic equations including a few (counter) examples. In particular, we discuss first order functional dynamic equations with delay xDelta(t)=f(t,xt) on a time scale. Here, xt is in Crd([-tau,0],Rn) and is given by …

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Review: A C*-Algebra Approach To Complex Symmetric Operators, Stephan Ramon Garcia Feb 2016

Review: A C*-Algebra Approach To Complex Symmetric Operators, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

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Simulating Surfactant Spreading: Impact Of A Physically Motivated Equation Of State, Dina Sinclair '17, Rachel Levy, Karen E. Daniels Feb 2016

Simulating Surfactant Spreading: Impact Of A Physically Motivated Equation Of State, Dina Sinclair '17, Rachel Levy, Karen E. Daniels

All HMC Faculty Publications and Research

For more than two decades, a single model for the spreading of a surfactant-driven thin liquid film has dominated the applied mathematics literature on the subject. Recently, through the use of fluorescently-tagged lipids, it has become possible to make direct, quantitative comparisons between experiments and models. These comparisons have revealed two important discrepancies between simulations and experiments: the spatial distribution of the surfactant layer, and the timescale over which spreading occurs. In this paper, we present numerical simulations that demonstrate the impact of the particular choice of the equation of state (EoS) relating the surfactant concentration to the surface tension. …

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A Feature Selection Algorithm To Compute Gene Centric Methylation From Probe Level Methylation Data, Brittany Baur, Serdar Bozdag Feb 2016

A Feature Selection Algorithm To Compute Gene Centric Methylation From Probe Level Methylation Data, Brittany Baur, Serdar Bozdag

Mathematics, Statistics and Computer Science Faculty Research and Publications

DNA methylation is an important epigenetic event that effects gene expression during development and various diseases such as cancer. Understanding the mechanism of action of DNA methylation is important for downstream analysis. In the Illumina Infinium HumanMethylation 450K array, there are tens of probes associated with each gene. Given methylation intensities of all these probes, it is necessary to compute which of these probes are most representative of the gene centric methylation level. In this study, we developed a feature selection algorithm based on sequential forward selection that utilized different classification methods to compute gene centric DNA methylation using probe …

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Cyclic Polynomials In Two Variables, Catherine Bénéteau, Greg Knese, Łukasz Kosiński, Constanze Liaw, Daniel Seco, Alan Sola Feb 2016

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.

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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 Feb 2016

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 …

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Commutators In The Two-Weight Setting, Irina Holmes, Michael T. Lacey, Brett D. Wick Feb 2016

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.

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Second Order Approximation For Heat Conduction: Dissipation Principle And Free Energies, Giovambattista Amendola, Mauro Fabrizio, John Murrough Golden, Barbara Lazzari Feb 2016

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 …

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Modeling Lotic Organism Populations With Partial Differential Equations, Chase Viss, Tom Clark, Eric Eager Feb 2016

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 …

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A Note On The Γ-Coefficients Of The Tree Eulerian Polynomial, Rafael S. González D'León Feb 2016

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 …

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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 Feb 2016

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 …

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Impartial Avoidance Games For Generating Finite Groups, Bret J. Benesh, Dana C. Ernst, Nándor Sieben Feb 2016

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.

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Knowledge And Tasks Connecting Elementary, Secondary, And Disciplinary Mathematics, Yvonne Lai Feb 2016

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 …

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Spectral Graph Theory For Weighted Digraphs, Alexander Zaitzeff, Jeffrey Humpherys Feb 2016

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.

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Generating Functions And Wilf Equivalence For Generalized Interval Embeddings, Russell Chamberlain, Garner Cochran, Sam Ginsburg, Brian K. Miceli, Manda Riehl, Chi Zhang Feb 2016

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 …

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Why Min-Based Conditioning, Salem Benferhat, Vladik Kreinovich Feb 2016

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. …

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Assessing Mathematical Knowledge For Teaching: The Role Of Teaching Context, Geoffrey Phelps, Heather Howell Feb 2016

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.

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Cyclic Critical Groups Of Graphs, Ryan P. Becker, Darren B. Glass Feb 2016

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.

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Guest Editorial: Mathematical Knowledge For Teaching: Developing Measures And Measuring Development, Reidar Mosvold, Mark Hoover Feb 2016

Guest Editorial: Mathematical Knowledge For Teaching: Developing Measures And Measuring Development, Reidar Mosvold, Mark Hoover

The Mathematics Enthusiast

No abstract provided.

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Interview Prompts To Uncover Mathematical Knowledge For Teaching: Focus On Providing Written Feedback, Yeon Kim Feb 2016

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 …

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Spanning Eulerian Subgraphs And Catlin’S Reduced Graphs, Wei-Guo Chen, Zhi-Hong Chen Feb 2016

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 …

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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 Feb 2016

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. …

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Supplemental Instruction For Developmental Mathematics: Two-Year Summary, Olen Dias, Alice W. Cunningham, Loreto Porte Feb 2016

Supplemental Instruction For Developmental Mathematics: Two-Year Summary, Olen Dias, Alice W. Cunningham, Loreto Porte

Publications and Research

Supplemental instruction—using trained peer tutors to conduct additional class sessions in a group-work format—has been in use for over forty years. However, its success in developmental mathematics has been inconclusive. In the two years since institution of the strategy for developmental mathematics students at Hostos Community College, overall results (n = 5403 students) show significantly improved course pass rates to at least a 99% confidence level. Although no significant course retention differences have yet appeared, academic success itself promotes future retention. The program has proved beneficial for the College’s developmental mathematics students and is being expanded. Future research including …

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Why Defining The Construct Matters: An Examination Of Teacher Knowledge Using Different Lenses On One Assessment, Chandra H. Orrill, Allan S. Cohen Feb 2016

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 …

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