Convergence Of A Modified Newton Method For A Matrix Polynomial Equation Arising In Stochastic Problem, 2018 Pusan National University

#### 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 ...

Divisibility In The Stone-Cech Compactiﬁcation Of N, 2018 University of Missouri, St. Louis

#### Divisibility In The Stone-Cech Compactiﬁcation Of N, Salahddeen Khalifa

*Dissertations*

Let S a discrete semigroup. The associative operation on S extends naturally to an associative operation on βS,the Stone Cech compactiﬁcation of S. This involves both topology and algebra and leads us to think how to extend properties and operations that are deﬁned on S to βS. A good application of this is the extension of relations and divisibility operations that are deﬁned on the discrete semigroup of natural numbers (N,.) with multiplication as operation to relations and divisibility operations that are deﬁned on (βN,?) where (?) is the extension of the operation (.). In this research I studied extending the ...

Two Applications Of High Order Methods: Wave Propagation And Accelerator Physics, 2018 University of New Mexico

#### 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, 2018 University of New Mexico - Main Campus

#### 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, 2018 Poznan University of Technology

#### 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, 2018 Georgia State University

#### 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, 2018 The University of Western Ontario

#### 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, 2018 The University of Western Ontario

#### 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, 2018 Poznań University Of Technology

#### 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, 2018 University of Maryland Baltimore County

#### 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., 2018 Pomona College

#### 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, 2018 University of California, Riverside

#### 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, 2018 University of Richmond

#### 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, 2018 Portland State University

#### 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, 2018 University of Arizona

#### 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, 2018 Illinois State University

#### 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, 2018 Illinois State University

#### 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, 2018 Illinois State University

#### 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, 2018 University of Kentucky

#### 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, 2018 University of Colorado Boulder

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

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

No abstract provided.