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Full-Text Articles in Physical Sciences and Mathematics

Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu May 2019

Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, Chi Jin, Keqin Gu, Islam Boussaada, Silviu-Iulian Niculescu

SIUE Faculty Research, Scholarship, and Creative Activity

This paper presents a systematic method to analyse the stability of systems with single delay in which the coefficient polynomials of the characteristic equation depend on the delay. Such systems often arise in, for example, life science and engineering systems. A method to analyze such systems was presented by Beretta and Kuang in a 2002 paper, but with some very restrictive assumptions. This work extends their results to the general case with the exception of some degenerate cases. It is found that a much richer behavior is possible when the restrictive assumptions are removed. The interval of interest for the ...


Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski Dec 2018

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.


Discontinuity Propagation In Delay Differential-Algebraic Equations, Benjamin Unger Dec 2018

Discontinuity Propagation In Delay Differential-Algebraic Equations, Benjamin Unger

Electronic Journal of Linear Algebra

The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Based on the (quasi-) Weierstra{\ss} form for regular matrix pencils, a complete characterization of the different propagation types is given and algebraic criteria in terms of the matrices are developed. The analysis, which is based on the method of steps, takes into account all possible inhomogeneities and history functions and thus serves as a worst-case scenario. Moreover, it reveals possible hidden delays in the DDAE and allows to study exponential stability of the DDAE based on the spectral abscissa. The new classification ...


Asymptotic Results On The Condition Number Of Fd Matrices Approximating Semi-Elliptic Pdes, Paris Vassalos Dec 2018

Asymptotic Results On The Condition Number Of Fd Matrices Approximating Semi-Elliptic Pdes, Paris Vassalos

Electronic Journal of Linear Algebra

This work studies the asymptotic behavior of the spectral condition number of the matrices $A_{nn}$ arising from the discretization of semi-elliptic partial differential equations of the form \bdm -\left( a(x,y)u_{xx}+b(x,y)u_{yy}\right)=f(x,y), \edm on the square $\Omega=(0,1)^2,$ with Dirichlet boundary conditions, where the smooth enough variable coefficients $a(x,y), b(x,y)$ are nonnegative functions on $\overline{\Omega}$ with zeros. In the case of coefficient functions with a single and common zero, it is discovered that apart from the minimum order of the zero ...


A Normal Form For Words In The Temperley-Lieb Algebra And The Artin Braid Group On Three Strands, Jack Hartsell Dec 2018

A Normal Form For Words In The Temperley-Lieb Algebra And The Artin Braid Group On Three Strands, Jack Hartsell

Electronic Theses and Dissertations

The motivation for this thesis is the computer-assisted calculation of the Jones poly- nomial from braid words in the Artin braid group on three strands, denoted B3. The method used for calculation of the Jones polynomial is the original method that was created when the Jones polynomial was first discovered by Vaughan Jones in 1984. This method utilizes the Temperley-Lieb algebra, and in our case the Temperley-Lieb Algebra on three strands, denoted A3, thus generalizations about A3 that assist with the process of calculation are pursued.


Performance Assessment Of The Extended Gower Coefficient On Mixed Data With Varying Types Of Functional Data., Obed Koomson Dec 2018

Performance Assessment Of The Extended Gower Coefficient On Mixed Data With Varying Types Of Functional Data., Obed Koomson

Electronic Theses and Dissertations

Clustering is a widely used technique in data mining applications to source, manage, analyze and extract vital information from large amounts of data. Most clustering procedures are limited in their performance when it comes to data with mixed attributes. In recent times, mixed data have evolved to include directional and functional data. In this study, we will give an introduction to clustering with an eye towards the application of the extended Gower coefficient by Hendrickson (2014). We will conduct a simulation study to assess the performance of this coefficient on mixed data whose functional component has strictly-decreasing signal curves and ...


Examining Teacher Perceptions When Utilizing Volunteers In School-Based Agricultural Education Programs, Ashley B. Cromer Dec 2018

Examining Teacher Perceptions When Utilizing Volunteers In School-Based Agricultural Education Programs, Ashley B. Cromer

All Graduate Theses and Dissertations

There has been little research conducted related to how school-based agricultural (SBAE) teachers perceive the utilization of volunteers in the classroom. The United States is facing a shortage of SBAE teachers, and with turnover rates that are not sustainable, solutions for support and reduction of the SBAE teachers’ workload must be sought with diligence. There is potential for volunteers to reduce some of the responsibilities that the SBAE teacher is faced with. The purposes of this study are to determine the demographic characteristics of the volunteers being utilized and of the SBAE teachers, determine the perceived benefits, barriers and beliefs ...


Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg Dec 2018

Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, Jacob Kullberg

All Graduate Plan B and other Reports

Lie algebra cohomology is an important tool in many branches of mathematics. It is used in the Topology of homogeneous spaces, Deformation theory, and Extension theory. There exists extensive theory for calculating the cohomology of semi simple Lie algebras, but more tools are needed for calculating the cohomology of general Lie algebras. To calculate the cohomology of general Lie algebras, I used the symbolic software program called Maple. I wrote software to calculate the cohomology in several different ways. I wrote several programs to calculate the cohomology directly. This proved to be computationally expensive as the number of differential forms ...


Stochastic Lanczos Likelihood Estimation Of Genomic Variance Components, Richard Border Nov 2018

Stochastic Lanczos Likelihood Estimation Of Genomic Variance Components, Richard Border

Applied Mathematics Graduate Theses & Dissertations

Genomic variance components analysis seeks to estimate the extent to which interindividual variation in a given trait can be attributed to genetic similarity. Likelihood estimation of such models involves computationally expensive operations on large, dense, and unstructured matrices of high rank. As a result, standard estimation procedures relying on direct matrix methods become prohibitively expensive as sample sizes increase. We propose a novel estimation procedure that uses the Lanczos process and stochastic Lanczos quadrature to approximate the likelihood for an initial choice of parameter values. Then, by identifying the variance components parameter space with a family of shifted linear systems ...


Structured Eigenvalue/Eigenvector Backward Errors Of Matrix Pencils Arising In Optimal Control, Christian Mehl, Volker Mehrmann, Punit Sharma Nov 2018

Structured Eigenvalue/Eigenvector Backward Errors Of Matrix Pencils Arising In Optimal Control, Christian Mehl, Volker Mehrmann, Punit Sharma

Electronic Journal of Linear Algebra

Eigenvalue and eigenpair backward errors are computed for matrix pencils arising in optimal control. In particular, formulas for backward errors are developed that are obtained under block-structure-preserving and symmetry-structure-preserving perturbations. It is shown that these eigenvalue and eigenpair backward errors are sometimes significantly larger than the corresponding backward errors that are obtained under perturbations that ignore the special structure of the pencil.


Perturbation Results And The Forward Order Law For The Moore-Penrose Inverse Of A Product, Nieves Castro-Gonzalez, Robert E. Hartwig Nov 2018

Perturbation Results And The Forward Order Law For The Moore-Penrose Inverse Of A Product, Nieves Castro-Gonzalez, Robert E. Hartwig

Electronic Journal of Linear Algebra

New expressions are given for the Moore-Penrose inverse of a product $AB$ of two complex matrices. Furthermore, an expression for $(AB)\dg - B\dg A\dg$ for the case where $A$ or $B$ is of full rank is provided. Necessary and sufficient conditions for the forward order law for the Moore-Penrose inverse of a product to hold are established. The perturbation results presented in this paper are applied to characterize some mixed-typed reverse order laws for the Moore-Penrose inverse, as well as the reverse order law.


Convergence Of A Modified Newton Method For A Matrix Polynomial Equation Arising In Stochastic Problem, Sang-Hyup Seo Mr., Jong-Hyeon Seo Dr., Hyun-Min Kim Prof. Nov 2018

Convergence Of A Modified Newton Method For A Matrix Polynomial Equation Arising In Stochastic Problem, Sang-Hyup Seo Mr., Jong-Hyeon Seo Dr., Hyun-Min Kim Prof.

Electronic Journal of Linear Algebra

The Newton iteration is considered for a matrix polynomial equation which arises in stochastic problem. In this paper, it is shown that the elementwise minimal nonnegative solution of the matrix polynomial equation can be obtained using Newton's method if the equation satisfies the sufficient condition, and the convergence rate of the iteration is quadratic if the solution is simple. Moreover, it is shown that the convergence rate is at least linear if the solution is non-simple, but a modified Newton method whose iteration number is less than the pure Newton iteration number can be applied. Finally, numerical experiments are ...


Two Applications Of High Order Methods: Wave Propagation And Accelerator Physics, Oleksii Beznosov Nov 2018

Two Applications Of High Order Methods: Wave Propagation And Accelerator Physics, Oleksii Beznosov

Shared Knowledge Conference

Numerical simulations of partial differential equations (PDE) are used to predict the behavior of complex physics phenomena when the real life experiments are expensive. Discretization of a PDE is the representation of the continuous problem as a discrete problem that can be solved on a computer. The discretization always introduces a certain inaccuracy caused by the numerical approximation. By increasing the computational cost of the numerical algorithm the solution can be computed more accurately. In the theory of numerical analysis this fact is called the convergence of the numerical algorithm. The idea behind high order methods is to improve the ...


Reaction Simulations: A Rapid Development Framework, Brendan Drake Donohoe Nov 2018

Reaction Simulations: A Rapid Development Framework, Brendan Drake Donohoe

Shared Knowledge Conference

Chemical Reaction Networks (CRNs) are a popular tool in the chemical sciences for providing a means of analyzing and modeling complex reaction systems. In recent years, CRNs have attracted attention in the field of molecular computing for their ability to simulate the components of a digital computer. The reactions within such networks may occur at several different scales relative to one another – at rates often too difficult to directly measure and analyze in a laboratory setting. To facilitate the construction and analysis of such networks, we propose a reduced order model for simulating such networks as a system of Differential ...


Estimators Comparison Of Separable Covariance Structure With One Component As Compound Symmetry Matrix, Katarzyna Filipiak, Daniel Klein, Monika Mokrzycka Nov 2018

Estimators Comparison Of Separable Covariance Structure With One Component As Compound Symmetry Matrix, Katarzyna Filipiak, Daniel Klein, Monika Mokrzycka

Electronic Journal of Linear Algebra

The maximum likelihood estimation (MLE) of separable covariance structure with one component as compound symmetry matrix has been widely studied in the literature. Nevertheless, the proposed estimates are not given in explicit form and can be determined only numerically. In this paper we give an alternative form of MLE and we show that this new algorithm is much quicker than the algorithms given in the literature.\\ Another estimator of covariance structure can be found by minimizing the entropy loss function. In this paper we give three methods of finding the best approximation of separable covariance structure with one component as ...


17 - Stability Analysis Of Stochastically Switching Kuramoto Networks, Ratislav Krylov, Igor Belykh Prof. Nov 2018

17 - Stability Analysis Of Stochastically Switching Kuramoto Networks, Ratislav Krylov, Igor Belykh Prof.

Georgia Undergraduate Research Conference (GURC)

Motivated by real-world networks with evolving connections, we analyze how stochastic switching affects patterns of synchrony and their stability in networks of identical Kuramoto oscillators with inertia. Stochastic dynamical networks are a useful model for many physical, biological, and engineering systems that have evolving topology, but they have proven to be difficult to work with, and the analytical results are rare. These networks have two characteristic time scales, one is associated with intrinsic dynamics of individual oscillators comprising the network, and the other corresponds to switching period of on-off connections. In the limit of fast switching, the relation between the ...


Bifurcation Analysis Of Two Biological Systems: A Tritrophic Food Chain Model And An Oscillating Networks Model, Xiangyu Wang Oct 2018

Bifurcation Analysis Of Two Biological Systems: A Tritrophic Food Chain Model And An Oscillating Networks Model, Xiangyu Wang

Electronic Thesis and Dissertation Repository

In this thesis, we apply bifurcation theory to study two biological systems. Main attention is focused on complex dynamical behaviors such as stability and bifurcation of limit cycles. Hopf bifurcation is particularly considered to show bistable or even tristable phenomenon which may occur in biological systems. Recurrence is also investigated to show that such complex behavior is common in biological systems.

First we consider a tritrophic food chain model with Holling functional response types III and IV for the predator and superpredator, respectively. Main attention is focused on the sta- bility and bifurcation of equilibria when the prey has a ...


Ecology And Evolution Of Dispersal In Metapopulations, Jingjing Xu Oct 2018

Ecology And Evolution Of Dispersal In Metapopulations, Jingjing Xu

Electronic Thesis and Dissertation Repository

Dispersal plays a key role in the persistence of metapopulations, as the balance between local extinction and colonization is affected by dispersal. Herein, I present three pieces of work related to dispersal. The first two are devoted to the ecological aspect of delayed dispersal in metapopulations. The first one focuses on how dispersal may disrupt the social structure on patches from which dispersers depart. Examinations of bifurcation diagrams of the dynamical system show a metapopulation will, in general, be either in the state of global extinction or persistence, and dispersal only has a limited effect on metapopulation persistence. The second ...


On Projection Of A Positive Definite Matrix On A Cone Of Nonnegative Definite Toeplitz Matrices, Katarzyna Filipiak, Augustyn Markiewicz, Adam Mieldzioc, Aneta Sawikowska Oct 2018

On Projection Of A Positive Definite Matrix On A Cone Of Nonnegative Definite Toeplitz Matrices, Katarzyna Filipiak, Augustyn Markiewicz, Adam Mieldzioc, Aneta Sawikowska

Electronic Journal of Linear Algebra

We consider approximation of a given positive definite matrix by nonnegative definite banded Toeplitz matrices. We show that the projection on linear space of Toeplitz matrices does not always preserve nonnegative definiteness. Therefore we characterize a convex cone of nonnegative definite banded Toeplitz matrices which depends on the matrix dimensions, and we show that the condition of positive definiteness given by Parter [{\em Numer. Math. 4}, 293--295, 1962] characterizes the asymptotic cone. In this paper we give methodology and numerical algorithm of the projection basing on the properties of a cone of nonnegative definite Toeplitz matrices. This problem can be ...


Positive And Z-Operators On Closed Convex Cones, Michael J. Orlitzky Oct 2018

Positive And Z-Operators On Closed Convex Cones, Michael J. Orlitzky

Electronic Journal of Linear Algebra

Let $K$ be a closed convex cone with dual $\dual{K}$ in a finite-dimensional real Hilbert space. A \emph{positive operator} on $K$ is a linear operator $L$ such that $L\of{K} \subseteq K$. Positive operators generalize the nonnegative matrices and are essential to the Perron-Frobenius theory. It is said that $L$ is a \emph{\textbf{Z}-operator} on $K$ if % \begin{equation*} \ip{L\of{x}}{s} \le 0 \;\text{ for all } \pair{x}{s} \in \cartprod{K}{\dual{K}} \text{ such that } \ip{x}{s} = 0. \end{equation*} % The \textbf{Z}-operators are generalizations of \textbf{Z ...


Of Mice And Math: Four Models, Four Collaborations., Ami Radunskaya Oct 2018

Of Mice And Math: Four Models, Four Collaborations., Ami Radunskaya

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Novel Cell-Based Model Of The Generation And Maintenance Of The Shape And Structure Of The Multi-Layered Shoot Apical Meristem Of Arabidopsis Thaliana, Mikahl Banwarth-Kuhn, Ali Nematbakhsh, Stephen Snipes, Kevin Rodriguez, Carolyn Rasmussen, G. Venugopala Reddy, Mark Alber Oct 2018

Novel Cell-Based Model Of The Generation And Maintenance Of The Shape And Structure Of The Multi-Layered Shoot Apical Meristem Of Arabidopsis Thaliana, Mikahl Banwarth-Kuhn, Ali Nematbakhsh, Stephen Snipes, Kevin Rodriguez, Carolyn Rasmussen, G. Venugopala Reddy, Mark Alber

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


A Mathematical Model Of The Inflammatory Response To Pathogen Challenge, Lester Caudill, Fiona Lynch Oct 2018

A Mathematical Model Of The Inflammatory Response To Pathogen Challenge, Lester Caudill, Fiona Lynch

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Analyzing Bigger Networks With Polynomial Algebra, Ian H. Dinwoodie Oct 2018

Analyzing Bigger Networks With Polynomial Algebra, Ian H. Dinwoodie

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Application Of Data Assimilation In Forecasting Of Influenza In The United States, Hannah Biegel Oct 2018

Application Of Data Assimilation In Forecasting Of Influenza In The United States, Hannah Biegel

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley Oct 2018

Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Modeling The Transmission Of Wolbachia In Mosquitoes For Controlling Mosquito-Borne Diseases, Zhuolin Qu Oct 2018

Modeling The Transmission Of Wolbachia In Mosquitoes For Controlling Mosquito-Borne Diseases, Zhuolin Qu

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka Oct 2018

The Influence Of Canalization On The Robustness Of Finite Dynamical Systems, Claus Kadelka

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Using Canalization For The Control Of Discrete Networks, David Murrugarra Oct 2018

Using Canalization For The Control Of Discrete Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Modeling Influenza Outbreaks On A College Campus, Eli Goldwyn, Subekshya Bidari Oct 2018

Modeling Influenza Outbreaks On A College Campus, Eli Goldwyn, Subekshya Bidari

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.