Heterogeneous Boolean Networks With Two Totalistic Rules, 2019 University of Nebraska at Omaha

#### Heterogeneous Boolean Networks With Two Totalistic Rules, Katherine Toh

*Student Research and Creative Activity Fair*

Boolean Networks are being used to analyze models in biology, economics, social sciences, and many other areas. These models simplify the reality by assuming that each element in the network can take on only two possible values, such as ON and OFF. The node evolution is governed by its interaction with other nodes in its neighborhood, which is described mathematically by a Boolean function or rule. For simplicity reasons, many models assume that all nodes follow the same Boolean rule. However, real networks often use more than one Boolean rule and therefore are heterogeneous networks. Heterogeneous networks have not yet ...

An Information Theory-Based Approach To Assessing Spatial Patterns In Complex Systems, 2019 U.S. Environmental Protection Agency

#### An Information Theory-Based Approach To Assessing Spatial Patterns In Complex Systems, Tarsha Eason, Wen Ching-Chuang, Shana Sundstrom, Heriberto Cabezas

*Papers in Natural Resources*

Given the intensity and frequency of environmental change, the linked and cross-scale nature of social-ecological systems, and the proliferation of big data, methods that can help synthesize complex system behavior over a geographical area are of great value. Fisher information evaluates order in data and has been established as a robust and effective tool for capturing changes in system dynamics, including the detection of regimes and regime shifts. The methods developed to compute Fisher information can accommodate multivariate data of various types and requires no a priori decisions about system drivers, making it a unique and powerful tool. However, the ...

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, 2018 Wojciech Budzianowski Consulting Services

#### 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, 2018 Technische Universität Berlin

#### 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 ...

Structured Eigenvalue/Eigenvector Backward Errors Of Matrix Pencils Arising In Optimal Control, 2018 Technische Universitaet Berlin

#### 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.

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 ...

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.

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.

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.

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.