Multidisciplinary Education And Research In Biomathematics For Solving Global Challenges, 2019 George Mason University

#### Multidisciplinary Education And Research In Biomathematics For Solving Global Challenges, Padmanabhan Seshaiyer

*Annual Symposium on Biomathematics and Ecology: Education and Research*

No abstract provided.

Graphicacy For Numeracy: Review Of Fundamentals Of Data Visualization: A Primer On Making Informative And Compelling Figures By Claus O. Wilke (2019), 2019 University of South Florida

#### Graphicacy For Numeracy: Review Of Fundamentals Of Data Visualization: A Primer On Making Informative And Compelling Figures By Claus O. Wilke (2019), Christy M. Bebeau

*Numeracy*

Wilke, Claus O. 2019. *Fundamentals of Data Visualization: A Primer on Making Informative and Compelling Figures*. (Sebastopol, CA: O’Reilly Media, Inc.). 390 pp. ISBN 978-1-492-03108-6. First edition. First release: 03-15-2019.

Claus O. Wilke has authored an excellent reference about producing and understanding static figures, figures used online, in print, and for presentations. His book is neither a statistics nor programming text, but familiarity with basic statistical concepts is helpful. Written in three parts, the book presents both the math and artistic design aspects of telling a story through figures. Wilke makes extensive use of examples, labels them good, bad ...

Matrix Shanks Transformations, 2019 University of Lille, France

#### Matrix Shanks Transformations, Claude Brezinski, Michela Redivo-Zaglia

*Electronic Journal of Linear Algebra*

Shanks' transformation is a well know sequence transformation for accelerating the convergence of scalar sequences. It has been extended to the case of sequences of vectors and sequences of square matrices satisfying a linear difference equation with scalar coefficients. In this paper, a more general extension to the matrix case where the matrices can be rectangular and satisfy a difference equation with matrix coefficients is proposed and studied. In the particular case of square matrices, the new transformation can be recursively implemented by the matrix $\varepsilon$-algorithm of Wynn. Then, the transformation is related to matrix Pad\'{e}-type and ...

Runge–Kutta–Gegenbauer Explicit Methods For Advection-Diffusion Problems, 2019 Technological University Dublin

#### Runge–Kutta–Gegenbauer Explicit Methods For Advection-Diffusion Problems, Stephen O'Sullivan

*Articles*

In this paper, Runge-Kutta-Gegenbauer (RKG) stability polynomials of arbitrarily high order of accuracy are introduced in closed form. The stability domain of RKG polynomials extends in the the real direction with the square of polynomial degree, and in the imaginary direction as an increasing function of Gegenbauer parameter. Consequently, the polynomials are naturally suited to the construction of high order stabilized Runge-Kutta (SRK) explicit methods for systems of PDEs of mixed hyperbolic-parabolic type.

We present SRK methods composed of L ordered forward Euler stages, with complex-valued stepsizes derived from the roots of RKG stability polynomials of degree $L$. Internal stability ...

Block Glt Sequences: Matrix Functions And Engineering Application, 2019 University of Insubria

#### Block Glt Sequences: Matrix Functions And Engineering Application, Carlo Garoni, Stefano Serra-Capizzano

*Electronic Journal of Linear Algebra*

The theory of block generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the spectral distribution of block-structured matrices arising from the discretization of differential problems, with a special reference to systems of differential equations (DEs) and to the higher-order finite element or discontinuous Galerkin approximation of both scalar and vectorial DEs. In the present paper, the theory of block GLT sequences is extended by proving that $\{f(A_n)\}_n$ is a block GLT sequence as long as $f$ is continuous and $\{A_n\}_n$ is a block GLT sequence formed by Hermitian matrices. It is also provided a ...

The Determinant Of A Complex Matrix And Gershgorin Circles, 2019 Hamburg University of Technology

#### The Determinant Of A Complex Matrix And Gershgorin Circles, Florian Bünger, Siegfried M. Rump

*Electronic Journal of Linear Algebra*

Each connected component of the Gershgorin circles of a matrix contains exactly as many eigenvalues as circles are involved. Thus, the Minkowski (set) product of all circles contains the determinant if all circles are disjoint. In [S.M. Rump. Bounds for the determinant by Gershgorin circles. Linear Algebra and its Applications, 563:215--219, 2019.], it was proved that statement to be true for real matrices whose circles need not to be disjoint. Moreover, it was asked whether the statement remains true for complex matrices. This note answers that in the affirmative. As a by-product, a parameterization of the outer loop ...

School Policy Evaluated With Time-Reversible Markov Chain, 2019 University of Connecticut - Storrs

#### School Policy Evaluated With Time-Reversible Markov Chain, Trajan Murphy, Iddo Ben-Ari

*Honors Scholar Theses*

In this work we propose a reversible Markov chain scheme to model for the mobility of students affected by a grade school leveling policy. This model provides unified and mathematically tractable framework in which transition functions are sampled uniformly from the set of {\bf reversible} transition functions. The results from the study appear to confirm the disadvantageous effects of this school policy, on par with the of a previous model on the same policy.

Parameter Identification For A Stochastic Seirs Epidemic Model: Case Study Influenza, 2019 Marshall University

#### Parameter Identification For A Stochastic Seirs Epidemic Model: Case Study Influenza, Olusegun M. Otunuga, Anna Mummert

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Spiking Activity In Networks Of Neurons Impacted By Axonal Swelling, 2019 Cooper Union for the Advancement of Science and Art

#### Spiking Activity In Networks Of Neurons Impacted By Axonal Swelling, Brian Frost, Stan Mintchev

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Immunofluorescence Image Feature Analysis And Clustering Pipeline For Distinguishing Epithelial-Mesenchymal Transition, 2019 Virginia Commonwealth University

#### Immunofluorescence Image Feature Analysis And Clustering Pipeline For Distinguishing Epithelial-Mesenchymal Transition, Shreyas Hirway, Nadiah Hassan, Dr. Christopher Lemmon, Dr. Seth Weinberg

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Predicting Dynamics From Hardwiring In Canonical Low-Dimensional Coupled Networks, 2019 State University of New York at New Paltz

#### Predicting Dynamics From Hardwiring In Canonical Low-Dimensional Coupled Networks, Anca R. Radulescu

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Stokes, Gauss, And Bayes Walk Into A Bar..., 2019 University of Colorado, Boulder

#### Stokes, Gauss, And Bayes Walk Into A Bar..., Eric P. Kightley

*Applied Mathematics Graduate Theses & Dissertations*

This thesis consists of three distinct projects. The first is a study of microbial aggregate fragmentation, in which we develop a dynamical model of aggregate deformation and breakage and use it to obtain a post-fragmentation density function. The second and third projects deal with dimensionality reduction in machine learning problems. In the second project, we derive a one-pass sparsified Gaussian mixture model to perform clustering analysis on high-dimensional streaming data. The model estimates parameters in dense space while storing and performing computations in a compressed space. In the final project, we build an expert system classifier with a Bayesian network ...

The Effects Of Finite Precision On The Simulation Of The Double Pendulum, 2019 James Madison University

#### The Effects Of Finite Precision On The Simulation Of The Double Pendulum, Rebecca Wild

*Senior Honors Projects, 2010-current*

We use mathematics to study physical problems because abstracting the information allows us to better analyze what could happen given any range and combination of parameters. The problem is that for complicated systems mathematical analysis becomes extremely cumbersome. The only effective and reasonable way to study the behavior of such systems is to simulate the event on a computer. However, the fact that the set of floating-point numbers is finite and the fact that they are unevenly distributed over the real number line raises a number of concerns when trying to simulate systems with chaotic behavior. In this research we ...

Determining The Influence Of Lateral Margin Mechanical Properties On Glacial Flow, 2019 University of Maine

#### Determining The Influence Of Lateral Margin Mechanical Properties On Glacial Flow, Kate Hruby

*Electronic Theses and Dissertations*

The lateral margins of glaciers and ice streams play a significant role in glacial flow. Depending on their properties, like temperature and ice crystal orientation, they can cause a resistance to flow or enhance it. In combination with our current changing climate, flow patterns can dictate the mass balance of an ice body. It is therefore more important than ever to understand the impact that variations at the margins can have on flow. However, the lateral margins of glaciers and ice streams are an often-neglected part of ice dynamics; they are harder to sample than the center of a glacier ...

Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, 2019 University of Lynchburg

#### Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer

*Undergraduate Theses and Capstone Projects*

This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic ...

Underground Storage Tank Impact Model, 2019 Carroll College

#### Underground Storage Tank Impact Model, Amy Telck

*Carroll College Student Undergraduate Research Festival*

Leaking underground storage tanks (UST) pose a threat to the surround- ing environment and population. The Montana Department of Environmental Quality has completed two phases of a risk analysis with the purpose of identifying the USTs at the greatest risk of leaking in order to reallocate department resources. This analysis builds upon prior analyses in three ways: (1) identify how UST upgrades can reduce the risk of UST leaking, (2) how UST characteristics and upgrades relate to the cost of remediation, and (3) estimating the environmental impact of a release.

Vector Spaces Of Generalized Linearizations For Rectangular Matrix Polynomials, 2019 Indian Institute of Technology Guwahati

#### Vector Spaces Of Generalized Linearizations For Rectangular Matrix Polynomials, Biswajit Das, Shreemayee Bora

*Electronic Journal of Linear Algebra*

The complete eigenvalue problem associated with a rectangular matrix polynomial is typically solved via the technique of linearization. This work introduces the concept of generalized linearizations of rectangular matrix polynomials. For a given rectangular matrix polynomial, it also proposes vector spaces of rectangular matrix pencils with the property that almost every pencil is a generalized linearization of the matrix polynomial which can then be used to solve the complete eigenvalue problem associated with the polynomial. The properties of these vector spaces are similar to those introduced in the literature for square matrix polynomials and in fact coincide with them when ...

A Survey Of Numerical Quadrature Methods For Highly Oscillatory Integrals, 2019 The University of Western Ontario

#### A Survey Of Numerical Quadrature Methods For Highly Oscillatory Integrals, Jeet Trivedi

*Electronic Thesis and Dissertation Repository*

In this thesis, we examine the main types of numerical quadrature methods for a special subclass of one-dimensional highly oscillatory integrals. Along with a presentation of the methods themselves and the error bounds, the thesis contains implementations of the methods in Maple and Python. The implementations take advantage of the symbolic computational abilities of Maple and allow for a larger class of problems to be solved with greater ease to the user. We also present a new variation on Levin integration which uses differentiation matrices in various interpolation bases.

Using Principle Component Analysis To Analyze Tertiary And Quaternary Spectral Mixtures, 2019 Olivet Nazarene University

#### Using Principle Component Analysis To Analyze Tertiary And Quaternary Spectral Mixtures, David Burnett

*Scholar Week 2016 - present*

CRISM images from Mars are expected to contain carbonates such as magnesite. Prior research has been successfully able to determine the approximate percent composition of phyllosilicates in binary lab mixtures using Principle Component Analysis (PCA). In order to expand this model to work on CRISM images, one of preliminary steps is allowing the algorithm to work on mixtures with more than two components, which was the primary purpose of this research.

Parameter Estimation And Optimal Design Techniques To Analyze A Mathematical Model In Wound Healing, 2019 Western Kentucky University

#### Parameter Estimation And Optimal Design Techniques To Analyze A Mathematical Model In Wound Healing, Nigar Karimli

*Masters Theses & Specialist Projects*

For this project, we use a modified version of a previously developed mathematical model, which describes the relationships among matrix metalloproteinases (MMPs), their tissue inhibitors (TIMPs), and extracellular matrix (ECM). Our ultimate goal is to quantify and understand differences in parameter estimates between patients in order to predict future responses and individualize treatment for each patient. By analyzing parameter confidence intervals and confidence and prediction intervals for the state variables, we develop a parameter space reduction algorithm that results in better future response predictions for each individual patient. Moreover, use of another subset selection method, namely Structured Covariance Analysis, that ...