Wilson-Cowan Coupled Dynamics In A Model Of The Cortico-Striato-Thalamo-Cortical Circuit, 2016 State University of New York at New Paltz

#### Wilson-Cowan Coupled Dynamics In A Model Of The Cortico-Striato-Thalamo-Cortical Circuit, Anca R. Radulescu

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Robust Traveling Waves In Chains Of Simple Neural Oscillators, 2016 The Cooper Union for the Advancement of Science and Art

#### Robust Traveling Waves In Chains Of Simple Neural Oscillators, Stanislav M. Mintchev

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Clustering-Based Robot Navigation And Control, 2016 University of Pennsylvania

#### Clustering-Based Robot Navigation And Control, Omur Arslan, Dan P. Guralnik, Daniel E. Koditschek

*Departmental Papers (ESE)*

In robotics, it is essential to model and understand the topologies of configuration spaces in order to design provably correct motion planners. The common practice in motion planning for modelling configuration spaces requires either a global, explicit representation of a configuration space in terms of standard geometric and topological models, or an asymptotically dense collection of sample configurations connected by simple paths. In this short note, we present an overview of our recent results that utilize clustering for closing the gap between these two complementary approaches. Traditionally an unsupervised learning method, clustering offers automated tools to discover hidden intrinsic structures ...

Applications Of The Sierpiński Triangle To Musical Composition, 2016 The University of Southern Mississippi

#### Applications Of The Sierpiński Triangle To Musical Composition, Samuel C. Dent

*Honors Theses*

The present paper builds on the idea of composing music via fractals, specifically the Sierpiński Triangle and the Sierpiński Pedal Triangle. The resulting methods are intended to produce not just a series of random notes, but a series that we think pleases the ear. One method utilizes the iterative process of generating the Sierpiński Triangle and Sierpiński Pedal Triangle via matrix operations by applying this process to a geometric configuration of note names. This technique designs the largest components of the musical work first, then creates subsequent layers where each layer adds more detail.

Using Predator Carrying Capacity For A Pathogenic Vector-Dynamic Differential Model, 2016 Georgia State University

#### Using Predator Carrying Capacity For A Pathogenic Vector-Dynamic Differential Model, Rosahn Bhattarai

*Georgia State Undergraduate Research Conference*

No abstract provided.

Memory Consolidation In Binary Inputs, 2016 Georgia State University

#### Memory Consolidation In Binary Inputs, Shateil C. French Mr., Ricardo J T Toscano

*Georgia State Undergraduate Research Conference*

No abstract provided.

Two Generalizations Of The Filippov Operation, 2016 Western Kentucky University

#### Two Generalizations Of The Filippov Operation, Menevse Eryuzlu

*Masters Theses & Specialist Projects*

The purpose of this thesis is to generalize Filippov's operation, and to get more useful results. It includes two main parts: The C-Filippov operation for the finite and countable cases and the Filippov operation with different measures. In the first chapter, we give brief information about the importance of Filippov's operation, our goal and the ideas behind our generalizations. In the second chapter, we give some sufficient background notes. In the third chapter, we introduce the Filippov operation, explain how to calculate the Filippov of a function and give some sufficient properties of it. In the fourth chapter ...

Growing Networks With Positive And Negative Links, 2016 College of William and Mary

#### Growing Networks With Positive And Negative Links, Corynne Smith Dech

*Undergraduate Honors Theses*

Scale-free networks grown via preferential attachment have been used to model real-world networks such as the Internet, citation networks, and social networks. Here we investigate signed scale-free networks where a link represents a positive or negative connection. We present analytic results and simulations for a growing signed network model and compare the signed network to an unsigned scale-free network. We discuss several options for preferential attachment in a signed network model. Lastly we measure preferential attachment in a real-world network and discuss the advantages and disadvantages of data fitting methods.

An Inverse Eigenproblem For Generalized Reflexive Matrices With Normal $K+1$-Potencies, 2016 East China Normal University

#### An Inverse Eigenproblem For Generalized Reflexive Matrices With Normal $K+1$-Potencies, Wei-Ru Xu, Guo-Liang Chen

*Electronic Journal of Linear Algebra*

Let $P,~Q\in\mathbb{C}^{n\times n}$ be two normal $\{k+1\}$-potent matrices, i.e., $PP^{*}=P^{*}P,~P^{k+1}=P$, $QQ^{*}=Q^{*}Q,~Q^{k+1}=Q$, $k\in\mathbb{N}$. A matrix $A\in\mathbb{C}^{n\times n}$ is referred to as generalized reflexive with two normal $\{k+1\}$-potent matrices $P$ and $Q$ if and only if $A=PAQ$. The set of all $n\times n$ generalized reflexive matrices which rely on the matrices $P$ and $Q$ is denoted by $\mathcal{GR}^{n\times n}(P,Q)$. The left and right inverse ...

Geometric Limits Of Julia Sets Of Maps Z^N + Exp(2Πiθ) As N → ∞, 2016 Butler University

#### Geometric Limits Of Julia Sets Of Maps Z^N + Exp(2Πiθ) As N → ∞, Scott Kaschner, Reaper Romero, David Simmons

*Scott Kaschner*

We show that the geometric limit as n → ∞ of the Julia sets J(Pn,c) for the maps Pn,c(z) = zn + c does not exist for almost every c on the unit circle. Furthermore, we show that there is always a subsequence along which the limit does exist and equals the unit circle.

Rational Map Of Cp^2 With No Invariant Foliation, 2016 Butler University

#### Rational Map Of Cp^2 With No Invariant Foliation, Scott Kaschner, Rodrigo Perez, Roland Roeder

*Scott Kaschner*

Conference Poster presented at: Midwest Dynamical Systems Conference, Champaign/Urbana, IL November 1-3, 2013.

Elements Of Dynamic Economic Modeling: Presentation And Analysis, 2016 Iowa State University

#### Elements Of Dynamic Economic Modeling: Presentation And Analysis, Leigh Tesfatsion

*Economics Working Papers (2002–2016)*

The primary goal of these introductory notes is to promote the clear presentation and rigorous analysis of dynamic economic models, whether expressed in equation or agent-based form. A secondary goal is to promote the use of state-space modeling with its respect for historical process, for cause leading to effect without top-down imposition of global constraints. If economic modelers truly wish to respect the rationality of decision-makers, they should have the courage of their convictions; they should not be doing for their modeled decision-makers what in reality these decision-makers must do for themselves.

Movement Path Tortuosity In Free Ambulation: Relationships To Age And Brain Disease, 2016 University of South Florida

#### Movement Path Tortuosity In Free Ambulation: Relationships To Age And Brain Disease, William Kearns, James Fozard, Vilis Nams

*William D. Kearns, PhD*

Procesy Cieplne I Aparaty (Lab), 2016 Wroclaw University of Technology

Inżynieria Chemiczna Lab., 2016 Wroclaw University of Technology

Tridiagonal Matrices And Boundary Conditions, 2016 Portland State University

#### Tridiagonal Matrices And Boundary Conditions, J. J. P. Veerman, David K. Hammond

*Mathematics and Statistics Faculty Publications and Presentations*

We describe the spectra of certain tridiagonal matrices arising from differential equations commonly used for modeling flocking behavior. In particular we consider systems resulting from allowing an arbitrary boundary condition for the end of a one-dimensional flock. We apply our results to demonstrate how asymptotic stability for consensus and flocking systems depends on the imposed boundary condition.

Full State Revivals In Linearly Coupled Chains With Commensurate Eigenspectra, 2016 Portland State University

#### Full State Revivals In Linearly Coupled Chains With Commensurate Eigenspectra, J. J. P. Veerman, Jovan Petrovic

*Mathematics and Statistics Faculty Publications and Presentations*

Coherent state transfer is an important requirement in the construction of quantum computer hardware. The state transfer can be realized by linear next-neighbour-coupled finite chains. Starting from the commensurability of chain eigenvalues as the general condition of periodic dynamics, we find chains that support full periodic state revivals. For short chains, exact solutions are found analytically by solving the inverse eigenvalue problem to obtain the coupling coefficients between chain elements. We apply the solutions to design optical waveguide arrays and perform numerical simulations of light propagation thorough realistic waveguide structures. Applications of the presented method to the realization of a ...

Signal Velocity In Oscillator Arrays, 2016 Portland State University

#### Signal Velocity In Oscillator Arrays, Carlos E. Cantos, David K. Hammond, J. J. P. Veerman

*Mathematics and Statistics Faculty Publications and Presentations*

We investigate a system of coupled oscillators on the circle, which arises from a simple model for behavior of large numbers of autonomous vehicles. The model considers asymmetric, linear, decentralized dynamics, where the acceleration of each vehicle depends on the relative positions and velocities between itself and a set of local neighbors. We first derive necessary and sufficient conditions for asymptotic stability, then derive expressions for the phase velocity of propagation of disturbances in velocity through this system. We show that the high frequencies exhibit damping, which implies existence of well-defined signal velocities c+>0 and c−f(x−c ...

Topological Data Analysis For Systems Of Coupled Oscillators, 2016 Harvey Mudd College

#### Topological Data Analysis For Systems Of Coupled Oscillators, Alec Dunton

*HMC Senior Theses*

Coupled oscillators, such as groups of fireflies or clusters of neurons, are found throughout nature and are frequently modeled in the applied mathematics literature. Earlier work by Kuramoto, Strogatz, and others has led to a deep understanding of the emergent behavior of systems of such oscillators using traditional dynamical systems methods. In this project we outline the application of techniques from topological data analysis to understanding the dynamics of systems of coupled oscillators. This includes the examination of partitions, partial synchronization, and attractors. By looking for clustering in a data space consisting of the phase change of oscillators over a ...

A Mechanical Investigation Of Second Order Homogeneous Dynamic Equations On A Time Scale, 2016 Marshall University

#### A Mechanical Investigation Of Second Order Homogeneous Dynamic Equations On A Time Scale, Jacob E. Fischer

*Theses, Dissertations and Capstones*

This thesis covers the basic aspects of time scale calculus, a branch of mathematics combining the theories of differential equations and difference equations. Using the properties of time scale calculus we analyze a second order homogeneous dynamic equation with constant coefficients, in particular, y ∆∆ − 1 6 y ∆ + 1 8 y = 0. Following the analysis, this problem will be graphically evaluated using Marshall University’s Differential Analyzer, affectionately named Art. A differential analyzer is a machine that mechanically integrates by way of related rates of rotating rods. The process for making the jump between intervals on a time scale will be ...