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 ...

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.

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.

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.

Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, 2018 Illinois State University

#### Introducing The Fractional Differentiation For Clinical Data-Justified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak

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

No abstract provided.

Using Pair Approximation Methods To Analyze Behavior Of A Probabilistic Cellular Automaton Model For Intracellular Cardiac Calcium Dynamics, 2018 Loyola Marymount University

#### Using Pair Approximation Methods To Analyze Behavior Of A Probabilistic Cellular Automaton Model For Intracellular Cardiac Calcium Dynamics, Robert J. Rovetti

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

No abstract provided.

Assesing The Effects Of Modeling The Spectrum Of Clinical Symptoms On The Dynamics And Control Of Ebola, 2018 Illinois State University

#### Assesing The Effects Of Modeling The Spectrum Of Clinical Symptoms On The Dynamics And Control Of Ebola, Joan Ponce

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

No abstract provided.

Hopfield Networks: Modeling Memory, 2018 Illinois State University

#### Hopfield Networks: Modeling Memory, Maria Gabriela Navas Zuloaga

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

No abstract provided.

The Philosophical Foundations Of Plen: A Protocol-Theoretic Logic Of Epistemic Norms, 2018 The Graduate Center, City University of New York

#### The Philosophical Foundations Of Plen: A Protocol-Theoretic Logic Of Epistemic Norms, Ralph E. Jenkins

*All Dissertations, Theses, and Capstone Projects*

In this dissertation, I defend the protocol-theoretic account of epistemic norms. The protocol-theoretic account amounts to three theses: (i) There are norms of epistemic rationality that are procedural; epistemic rationality is at least partially defined by rules that restrict the possible ways in which epistemic actions and processes can be sequenced, combined, or chosen among under varying conditions. (ii) Epistemic rationality is ineliminably defined by procedural norms; procedural restrictions provide an irreducible unifying structure for even apparently non-procedural prescriptions and normative expressions, and they are practically indispensable in our cognitive lives. (iii) These procedural epistemic norms are best analyzed in ...

Investigation Of Chaos In Biological Systems, 2018 The University of Western Ontario

#### Investigation Of Chaos In Biological Systems, Navaneeth Mohan

*Electronic Thesis and Dissertation Repository*

Chaos is the seemingly irregular behavior arising from a deterministic system. Chaos is observed in many real-world systems. Edward Lorenz’s seminal discovery of chaotic behavior in a weather model has prompted researchers to develop tools that distinguish chaos from non-chaotic behavior. In the first chapter of this thesis, I survey the tools for detecting chaos namely, Poincaré maps, Lyapunov exponents, surrogate data analysis, recurrence plots and correlation integral plots. In chapter two, I investigate blood pressure fluctuations for chaotic signatures. Though my analysis reveals interesting evidence in support of chaos, the utility such an analysis lies in a different ...

Dynamics Of Quadratic Networks, 2018 SUNY New Paltz

#### Dynamics Of Quadratic Networks, Simone Evans

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Predicting Critical Transitions In Spatially Distributed Populations With Cubical Homology, 2018 College of William and Mary

#### Predicting Critical Transitions In Spatially Distributed Populations With Cubical Homology, Laura Storch, Sarah Day

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Axonal Transport With Attachment And Detachment To Parallel Microtubule Network, 2018 Rensselaer Polytechnic Institute

#### Axonal Transport With Attachment And Detachment To Parallel Microtubule Network, Abhishek Choudhary Mr.

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

The Computational Study Of Fly Swarms & Complexity, 2018 Linfield College

#### The Computational Study Of Fly Swarms & Complexity, Austin Bebee

*Senior Theses*

A system is considered complex if it is composed of individual parts that abide by their own set of rules, while the system, as a whole, will produce non-deterministic properties. This prevents the behavior of such systems from being accurately predicted. The motivation for studying complexity spurs from the fact that it is a fundamental aspect of innumerable systems. Among complex systems, fly swarms are relatively simple, but even so they are still not well understood. In this research, several computational models were developed to assist with the understanding of fly swarms. These models were primarily analyzed by using the ...

Power-Law Scaling Of Extreme Dynamics Near Higher-Order Exceptional Points, 2018 Michigan Technological University

#### Power-Law Scaling Of Extreme Dynamics Near Higher-Order Exceptional Points, Q. Zhong, Demetrios N. Christodoulides, M. Khajavikhan, K. G. Makris, Ramy El-Ganainy

*Ramy El-Ganainy*

We investigate the extreme dynamics of non-Hermitian systems near higher-order exceptional points in photonic networks constructed using the bosonic algebra method. We show that strong power oscillations for certain initial conditions can occur as a result of the peculiar eigenspace geometry and its dimensionality collapse near these singularities. By using complementary numerical and analytical approaches, we show that, in the parity-time (PT) phase near exceptional points, the logarithm of the maximum optical power amplification scales linearly with the order of the exceptional point. We focus in our discussion on photonic systems, but we note that our results apply to other ...

Analyzing Lagrangian Statistics Of Eddy-Permitting Models, 2018 University of Colorado, Boulder

#### Analyzing Lagrangian Statistics Of Eddy-Permitting Models, Amy Chen

*Applied Mathematics Graduate Theses & Dissertations*

Mesoscale eddies are the strongest currents in the world oceans and transport properties such as heat, dissolved nutrients, and carbon. The current inability to effectively diagnose and parameterize mesoscale eddy processes in oceanic turbulence is a critical limitation upon the ability to accurately model large-scale oceanic circulations. This investigation analyzes the Lagrangian statistics for four faster and less computationally expensive eddy-permitting models --- Biharmonic, Leith, Jansen & Held Deterministic, and Jansen & Held Stochastic --- and compares them against each other and an eddy-resolving quasigeostrophic Reference model. Results from single-particle climatology show that all models exhibit similar behaviour in large-scale movement over long times ...

Rotordynamic Analysis Of Theoretical Models And Experimental Systems, 2018 California Polytechnic State University - San Luis Obispo

#### Rotordynamic Analysis Of Theoretical Models And Experimental Systems, Cameron R. Naugle, Cameron Rex Naugle

*Master's Theses and Project Reports*

This thesis is intended to provide fundamental information for the construction and

analysis of rotordynamic theoretical models, and their comparison the experimental

systems. Finite Element Method (FEM) is used to construct models using Timoshenko

beam elements with viscous and hysteretic internal damping. Eigenvalues

and eigenvectors of state space equations are used to perform stability analysis, produce

critical speed maps, and visualize mode shapes. Frequency domain analysis

of theoretical models is used to provide Bode diagrams and in experimental data

full spectrum cascade plots. Experimental and theoretical model analyses are used

to optimize the control algorithm for an Active Magnetic Bearing ...

Asymptotic Estimate Of Variance With Applications To Stochastic Differential Equations Arises In Mathematical Neuroscience, 2018 University of North Florida

#### Asymptotic Estimate Of Variance With Applications To Stochastic Differential Equations Arises In Mathematical Neuroscience, Mahbubur Rahman 6203748

*Showcase of Faculty Scholarly & Creative Activity*

Approximation of stochastic differential equations (SDEs) with parametric noise plays an important role in a range of application areas, including engineering, mechanics, epidemiology, and neuroscience. A complete understanding of SDE theory with perturbed noise requires familiarity with advanced probability and stochastic processes. In this paper, we derive an asymptotic estimate of variance, and it is shown that numerical method gives a useful step toward solving SDEs with perturbed noise. Our goal is to diffuse the results to an audience not entirely familiar with functional notations or semi-group theory, but who might nonetheless be interested in the practical simulation of dynamical ...