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 interval embeddings are ...

The Number Of Zeros Of A Polynomial In A Disk As A Consequence Of Coefficient Inequalities With Multiple Reversals, 2015 East Tennessee State University

#### The Number Of Zeros Of A Polynomial In A Disk As A Consequence Of Coefficient Inequalities With Multiple Reversals, Derek T. Bryant

*Electronic Theses and Dissertations*

In this thesis, we explore the effect of restricting the coefficients of polynomials on the bounds for the number of zeros in a given region. The results presented herein build on a body of work, culminating in the generalization of bounds among three classes of polynomials. The hypotheses of monotonicity on each class of polynomials were further subdivided into sections concerning r reversals among the moduli, real parts, and both real and imaginary parts of the coefficients.

Predicting Intraday Financial Market Dynamics Using Takens' Vectors; Incorporating Causality Testing And Machine Learning Techniques, 2015 East Tennessee State University

#### Predicting Intraday Financial Market Dynamics Using Takens' Vectors; Incorporating Causality Testing And Machine Learning Techniques, Abubakar-Sadiq Bouda Abdulai

*Electronic Theses and Dissertations*

Traditional approaches to predicting financial market dynamics tend to be linear and stationary, whereas financial time series data is increasingly nonlinear and non-stationary. Lately, advances in dynamical systems theory have enabled the extraction of complex dynamics from time series data. These developments include theory of time delay embedding and phase space reconstruction of dynamical systems from a scalar time series. In this thesis, a time delay embedding approach for predicting intraday stock or stock index movement is developed. The approach combines methods of nonlinear time series analysis with those of causality testing, theory of dynamical systems and machine learning (artificial ...

On Properties Of RW-Regular Graphs, 2015 East Tennessee State University

#### On Properties Of RW-Regular Graphs, Franklina Samani

*Electronic Theses and Dissertations*

If every vertex in a graph G has the same degree, then the graph is called a regular graph. That is, if deg(v) = r for all vertices in the graph, then it is denoted as an r-regular graph. A graph G is said to be vertex-weighted if all of the vertices are assigned weights. A generalized definition for degree regularity for vertex-weighted graphs can be stated as follows: A vertex-weighted graph is said to be r_{w}-regular if the sum of the weights in the neighborhood of every vertex is r_{w}. If all vertices are assigned the ...

Constructions And Isomorphism Types Of Images, 2015 California State University - San Bernardino

#### Constructions And Isomorphism Types Of Images, Jessica Luna Ramirez

*Electronic Theses, Projects, and Dissertations*

In this thesis, we have presented our discovery of true finite homomorphic images of various permutation and monomial progenitors, such as 2^{*}^{7}: D_{14}, 2^{*7 }: (7 : 2), 2^{*6 }: S_{3 }x 2, 2^{*8}: S_{4}, 2*^{72}: (3^{2}:(2S_{4})), and 11^{*2} :_{m }D_{10}. We have given delightful symmetric presentations and very nice permutation representations of these images which include, the Mathieu groups M_{11}, M_{12}, the 4-fold cover of the Mathieu group M_{22}, 2 x L_{2}(8), and L_{2}(13). Moreover, we have given constructions, by using the ...

Local Existence Of Dynamically Allowed Brackets And A Local Existence Of A Hamiltonian Associated With These Brackets, For A Given, Possibly Time Dependent, N-Dimensional Equations Of Motion That May Include Constraints, 2015 University of North Georgia

#### Local Existence Of Dynamically Allowed Brackets And A Local Existence Of A Hamiltonian Associated With These Brackets, For A Given, Possibly Time Dependent, N-Dimensional Equations Of Motion That May Include Constraints, Piotr W. Hebda, Beata A. Hebda

*Faculty Publications*

Dynamically Allowed Brackets are defined for given equations of motion for an N-dimensional mechanical system. The equations of motion may be explicitly time dependent, and may include explicitly time dependent constraints. Local existence of the Dynamically Allowed Brackets is shown. The local existence of a Hamiltonian reproducing the given equations of motion with the use of these Dynamically Allowed Brackets is proven.

Bayes Multiple Binary Classifier - How To Make Decisions Like A Bayesian, 2015 Florida International University

#### Bayes Multiple Binary Classifier - How To Make Decisions Like A Bayesian, Wensong Wu

*Mathematics Colloquium Series*

This presentation will start by a general introduction of Bayesian statistics, which has become popular in the era of big data. Then we consider a two-class classification problem, where the goal is to predict the class membership of M units based on the values of high-dimensional categorical predictor variables as well as both the values of predictor variables and the class membership of other N independent units. We focus on applying generalized linear regression models with Boolean expressions of categorical predictors. We consider a Bayesian and decision-theoretic framework, and develop a general form of Bayes multiple binary classification functions with ...

Line Segments On The Boundary Of The Numerical Ranges Of Some Tridiagonal Matrices, 2015 NYUAD and College of William and Mary

#### Line Segments On The Boundary Of The Numerical Ranges Of Some Tridiagonal Matrices, Ilya M. Spitkovsky, Claire Marie Thomas

*Electronic Journal of Linear Algebra*

Tridiagonal matrices are considered for which the main diagonal consists of zeroes, the sup-diagonal of all ones, and the entries on the sub-diagonal form a geometric progression. The criterion for the numerical range of such matrices to have line segments on its boundary is established, and the number and orientation of these segments is described.

Spectral Properties Of Finite-Dimensional Waveguide Systems, 2015 Istanbul Technical University

#### Spectral Properties Of Finite-Dimensional Waveguide Systems, Nurhan Colakoglu, Peter Lancaster

*Electronic Journal of Linear Algebra*

This is a largely expository paper in which we study a finite dimensional model for gyroscopic/waveguiding systems. We study properties of the spectrum that play an important role when computing with such models. The notion of "waveguide type" is defined and explored in this context and Theorem 3.1 provides a form of the central result (due to Abramov) concerning the existence of real spectrum for such systems. The roles of semisimple/defective eigenvalues are discussed, as well as the roles played by eigenvalue "types" (or "Krein signatures"). The theory is illustrated with examples.

Filters And Matrix Factorization, 2015 Southern Illinois University Edwardsville

#### Filters And Matrix Factorization, Myung-Sin Song, Palle E. T. Jorgensen

*SIUE Faculty Research, Scholarship, and Creative Activity*

We give a number of explicit matrix-algorithms for analysis/synthesis

in multi-phase filtering; i.e., the operation on discrete-time signals which

allow a separation into frequency-band components, one for each of the

ranges of bands, say N , starting with low-pass, and then corresponding

filtering in the other band-ranges. If there are N bands, the individual

filters will be combined into a single matrix action; so a representation of

the combined operation on all N bands by an N x N matrix, where the

corresponding matrix-entries are periodic functions; or their extensions to

functions of a complex variable. Hence our setting ...

P-38 On The Riemannian Submersion Invariant, 2015 Andrews University

#### P-38 On The Riemannian Submersion Invariant, Yun Myung Oh

*Celebration of Research and Creative Scholarship Programs*

For a Riemannian submersion pi:*M ^{n}*->

*B*with totally geodesic fibers, the submersion invariant (see attached abstract for equation) was introduced using the integrability tensor of the submersion. B. Y. Chen has provided the inequality on this invariant if the manifold

^{b}*M*admits an isometric immersion into a Riemannian manifold

*M*. Some of the recent results on this invariant are included with examples. This is a continuation of the work published in 2013.

^{m}*See attached abstract for full equations.*

Flexible Gating Of Contextual Influences In Natural Vision, 2015 University of Miami

#### Flexible Gating Of Contextual Influences In Natural Vision, Odelia Schwartz

*Mathematics Colloquium Series*

An appealing hypothesis suggests that neurons represent inputs in a coordinate system that is matched to the statistical structure of images in the natural environment. I discuss theoretical work on unsupervised learning of statistical regularities in natural images. In the model, Bayesian inference amounts to a generalized form of divisive normalization, a canonical computation that has been implicated in many neural areas. In our framework, divisive normalization is flexible: it is recruited only when the image is inferred to contain dependencies, and muted otherwise. I particularly focus on recent work in which we have applied this approach to understanding spatial ...

Path-Tables Of Trees: A Survey And Some New Results, 2015 University of Malta

#### Path-Tables Of Trees: A Survey And Some New Results, Kevin Asciak

*Theory and Applications of Graphs*

The (vertex) path-table of a tree $T$ contains quantitative information about the paths in $T$. The entry $(i,j)$ of this table gives the number of paths of length $j$ passing through vertex $v_i$. The path-table is a slight variation of the notion of path layer matrix. In this survey we review some work done on the vertex path-table of a tree and also introduce the edge path-table. We show that in general, any type of path-table of a tree $T$ does not determine $T$ uniquely. We shall show that in trees, the number of paths passing through edge $xy ...

Flipped Calculus: A Study Of Student Performance And Perceptions, 2015 Macalester College

#### Flipped Calculus: A Study Of Student Performance And Perceptions, Lori Beth Ziegelmeier, Chad M. Topaz

*Lori Beth Ziegelmeier*

No abstract provided.

Directed Paths: From Ramsey To Ruzsa And Szemeredi, 2015 Carnegie Mellon University

#### Directed Paths: From Ramsey To Ruzsa And Szemeredi, Po-Shen Loh

*Department of Mathematical Sciences*

Starting from an innocent Ramsey-theoretic question regarding directed paths in tournaments, we discover a series of rich and surprising connections that lead into the theory around a fundamental problem in Combinatorics: the Ruzsa-Szemeredi induced matching problem. Using these relationships, we prove that every coloring of the edges of the transitive n-vertex tournament using three colors contains a directed path of length at least n−−√⋅e^{log∗n} which entirely avoids some color. We also expose connections to a family of constructions for Ramsey tournaments, and introduce and resolve some natural generalizations of the Ruzsa-Szemeredi problem which we encounter through our ...

Scheduling N Burgers For A K-Burger Grill: Chromatic Numbers With Restrictions, 2015 Auburn University Main Campus

#### Scheduling N Burgers For A K-Burger Grill: Chromatic Numbers With Restrictions, Peter Johnson, Xiaoya Zha

*Theory and Applications of Graphs*

The chromatic number has a well-known interpretation in the area of scheduling. If the vertices of a finite, simple graph are committees, and adjacency of two committees indicates that they must never be in session simultaneously, then the chromatic number of the graph is the smallest number of hours during which the committees/vertices of the graph may all have properly scheduled meetings of one continuous hour each. Slivnik [3] showed that the fractional chromatic number can be similarly characterized. In that characterization, the meetings are allowed to be broken into a finite number of disjoint intervals. Here we consider ...

Coagulation-Fragmentation Model For Animal Group-Size Statistics (15-Cna-017), 2015 Imperial College London

#### Coagulation-Fragmentation Model For Animal Group-Size Statistics (15-Cna-017), Pierre Degond, Jian-Guo Liu, Robert Pego

*Department of Mathematical Sciences*

We study coagulation-fragmentation equations inspired by a simple model proposed in fisheries science to explain data for the size distribution of schools of pelagic fish. Although the equations lack detailed balance and admit no H-theorem, we are able to develop a rather complete description of equilibrium profiles and large-time behavior, based on recent developments in complex function theory for Bernstein and Pick functions. In the large-population continuum limit, a scaling-invariant regime is reached in which all equilibria are determined by a single scaling profile. This universal profile exhibits power-law behavior crossing over from exponent −2/3 for small size to ...

Manzanar Murakami As Radical Mathematician, 2015 Clark University

#### Manzanar Murakami As Radical Mathematician, Logan Bishop-Van Horn

*Scholarly Undergraduate Research Journal at Clark*

In Karen Tei Yamashita’s Tropic of Orange, characters attempt to make meaning of the many complex structures in which they are situated. In his unique meaning-making process, Manzanar Murakami, a homeless Sansei, “conducts” the Los Angeles traffic with a silver baton from atop a highway overpass. In conducting his music, Murakami per- forms complex mathematics, finding meaning in connection by mapping the rhythmic flow of humans, machines, and goods. Through his baton, to the sounds of a beautiful orchestra, he translates precisely the relationships he sees before him. Murakami’s music and Yamashita’s fantastic images constitute a “mathematical ...

Using Nitrate, Chloride, Sodium, And Sulfate To Calculate Groundwater Age, 2015 Crawford Environmental Services

#### Using Nitrate, Chloride, Sodium, And Sulfate To Calculate Groundwater Age, Kimm Crawford, Terry Lee

*Sinkhole Conference 2015*

Regression analysis is used to identify monotonic trends to assign water age using ion data from two large well water databases from southeast Minnesota (SE MN). Nitrate (NO3-N), chloride (Cl), sodium (Na), and sulfate (SO4) ions in the commonly used aquifers in SE MN can be used as groundwater tracers since they are either entirely or partly anthropogenic in their sources, their loading occurs on a regional scale, and they are almost entirely conserved. Ion concentrations over time are used to establish six trend patterns. Two patterns are unchanging (background and stable above background), and four are changing (linear up ...

Learning From Lionfish: Modeling Marine Invaded Systems, 2015 Nova Southeastern University

#### Learning From Lionfish: Modeling Marine Invaded Systems, Matthew Johnston

*Mathematics Colloquium Series*

Simulating marine invaded systems requires broad consideration of physical oceanographic processes, such as ocean circulation patterns and temperature, and biological traits of the invader, such as their reproductive strategy and tolerances to their environment. Through this understanding of baseline biological and oceanographic function, models can be developed in order to forecast the incursion patterns of marine invasive species - helpful both to predict their spread as well as forewarn of impacts. To facilitate this understanding, computer simulation is useful in order to quickly and efficiently assimilate large biological and oceanographic datasets into digestible products. Data derived from such simulations are useful ...