Stability Analysis Of A More General Class Of Systems With Delay-Dependent Coefficients, 2019 Laboratoire des Signaux et Syst`emes (L2S) CentraleSup´elec-CNRS-Universit´e Paris Sud, 3 rue Joliot- Curie 91192 Gif-sur-Yvette cedex, France.

#### 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 ...

Calculating The Cohomology Of A Lie Algebra Using Maple And The Serre Hochschild Spectral Sequence, 2018 Utah State University

#### 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 ...

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.

Calcium Signaling In The Sperm Head, 2018 The California Maritime Academy

#### Calcium Signaling In The Sperm Head, Julie Simons, Lisa Fauci

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

No abstract provided.

Student Research In Algebraic And Combinatorial Mathematical Biology, 2018 Sweet Briar College

#### Student Research In Algebraic And Combinatorial Mathematical Biology, Raina Robeva

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

No abstract provided.

Dynamic Modeling Of Spread Of Waterborne Disease In Networks Impacting Public Health, 2018 Illinois State University

#### Dynamic Modeling Of Spread Of Waterborne Disease In Networks Impacting Public Health, Padmanabhan Seshaiyer

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

No abstract provided.

Combinatorial Geometry Of Threshold-Linear Networks, 2018 Illinois State University

#### Combinatorial Geometry Of Threshold-Linear Networks, Christopher Langdon

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

No abstract provided.

Heterogeneities In The Transmission Dynamics Of Leishmaniasis: Modeling Implications On Sustained Drive To Control It From Neglected Regions, 2018 Arizona State University at the Tempe Campus

#### Heterogeneities In The Transmission Dynamics Of Leishmaniasis: Modeling Implications On Sustained Drive To Control It From Neglected Regions, Anuj Mubayi

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

No abstract provided.

Dynamics Of Visceral Leishmaniasis For Different Distributions Of Non-Adherence To The Treatment In The Population Of Bihar, India And Its Effect On Elimination, 2018 Illinois State University

#### Dynamics Of Visceral Leishmaniasis For Different Distributions Of Non-Adherence To The Treatment In The Population Of Bihar, India And Its Effect On Elimination, Mugdha Thakur

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

No abstract provided.