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Homeomorphisms Of The Sierpinski Carpet, Karuna S. Sangam 2018 Bard College

Homeomorphisms Of The Sierpinski Carpet, Karuna S. Sangam

Senior Projects Spring 2018

The Sierpinski carpet is a fractal formed by dividing the unit square into nine congruent squares, removing the center one, and repeating the process for each of the eight remaining squares, continuing infinitely many times. It is a well-known fractal with many fascinating topological properties that appears in a variety of different contexts, including as rational Julia sets. In this project, we study self-homeomorphisms of the Sierpinski carpet. We investigate the structure of the homeomorphism group, identify its finite subgroups, and attempt to define a transducer homeomorphism of the carpet. In particular, we find that the symmetry groups of platonic ...


Extensions Of The Morse-Hedlund Theorem, Eben Blaisdell 2018 Bucknell University

Extensions Of The Morse-Hedlund Theorem, Eben Blaisdell

Honors Theses

Bi-infinite words are sequences of characters that are infinite forwards and backwards; for example "...ababababab...". The Morse-Hedlund theorem says that a bi-infinite word f repeats itself, in at most n letters, if and only if the number of distinct subwords of length n is at most n. Using the example, "...ababababab...", there are 2 subwords of length 3, namely "aba" and "bab". Since 2 is less than 3, we must have that "...ababababab..." repeats itself after at most 3 letters. In fact it does repeat itself every two letters. Interestingly, there are many extensions of this theorem to multiple dimensions ...


Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo 2017 Cylance, Inc.

Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


An Improved Pairwise- Approximation Technique For Studying The Dynamics Of A Probabilistic, Two- State Lattice Model Of Intracellular Cardiac Calcium, Robert J. Rovetti 2017 Loyola Marymount University

An Improved Pairwise- Approximation Technique For Studying The Dynamics Of A Probabilistic, Two- State Lattice Model Of Intracellular Cardiac Calcium, Robert J. Rovetti

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Mathematical Modeling Of Inhibitory Effects On Chemically Coupled Neurons, Nathhaniel Harraman, Epaminondas Rosa 2017 Illinois State University

Mathematical Modeling Of Inhibitory Effects On Chemically Coupled Neurons, Nathhaniel Harraman, Epaminondas Rosa

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Temperature Effects On Neuronal Tonic-To-Bursting Transitions, Manuela Burek, Epaminondas Rosa 2017 Illinois State University

Temperature Effects On Neuronal Tonic-To-Bursting Transitions, Manuela Burek, Epaminondas Rosa

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


A Brief History Of Neuroscience, Zachary Mobille, Epaminondas Rosa 2017 Illinois State University

A Brief History Of Neuroscience, Zachary Mobille, Epaminondas Rosa

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Asymptotic Counting Formulas For Markoff-Hurwitz Tuples, Ryan Ronan 2017 The Graduate Center, City University of New York

Asymptotic Counting Formulas For Markoff-Hurwitz Tuples, Ryan Ronan

All Dissertations, Theses, and Capstone Projects

The Markoff equation is a Diophantine equation in 3 variables first studied in Markoff's celebrated work on indefinite binary quadratic forms. We study the growth of solutions to an n variable generalization of the Markoff equation, which we refer to as the Markoff-Hurwitz equation. We prove explicit asymptotic formulas counting solutions to this generalized equation with and without a congruence restriction. After normalizing and linearizing the equation, we show that all but finitely many solutions appear in the orbit of a certain semigroup of maps acting on finitely many root solutions. We then pass to an accelerated subsemigroup of ...


Time Varying Parameter Estimation Scheme For A Linear Stochastic Differential Equation, Olusegun Michael Otunuga 2017 Marshall University

Time Varying Parameter Estimation Scheme For A Linear Stochastic Differential Equation, Olusegun Michael Otunuga

Mathematics Faculty Research

In this work, an attempt is made to estimate time varying parameters in a linear stochastic differential equation. By defining mk as the local admissible sample/data observation size at time tk, parameters and state at time tk are estimated using past data on interval [tkmk+1, tk]. We show that the parameter estimates at each time tk converge in probability to the true value of the parameters being estimated. A numerical simulation is presented by applying the local lagged adapted generalized method of moments (LLGMM) method to the stochastic differential models governing prices of energy commodities and stock ...


Morphogenesis And Growth Driven By Selection Of Dynamical Properties, Yuri Cantor 2017 The Graduate Center, City University of New York

Morphogenesis And Growth Driven By Selection Of Dynamical Properties, Yuri Cantor

All Dissertations, Theses, and Capstone Projects

Organisms are understood to be complex adaptive systems that evolved to thrive in hostile environments. Though widely studied, the phenomena of organism development and growth, and their relationship to organism dynamics is not well understood. Indeed, the large number of components, their interconnectivity, and complex system interactions all obscure our ability to see, describe, and understand the functioning of biological organisms.

Here we take a synthetic and computational approach to the problem, abstracting the organism as a cellular automaton. Such systems are discrete digital models of real-world environments, making them more accessible and easier to study then their physical world ...


Modeling Economic Systems As Locally-Constructive Sequential Games, Leigh Tesfatsion 2017 Iowa State University

Modeling Economic Systems As Locally-Constructive Sequential Games, Leigh Tesfatsion

Economics Working Papers

Real-world economies are open-ended dynamic systems consisting of heterogeneous interacting participants. Human participants are decision-makers who strategically take into account the past actions and potential future actions of other participants. All participants are forced to be locally constructive, meaning their actions at any given time must be based on their local states; and participant actions at any given time affect future local states. Taken together, these properties imply real-world economies are locally-constructive sequential games. This study discusses a modeling approach, agent-based computational economics (ACE), that permits researchers to study economic systems from this point of view. ACE modeling principles and ...


On The Analysis Of The Sir Epidemic Model For Small Networks: An Application In Hospital Settings, Martin Lopez-Garcia 2017 University of Leeds

On The Analysis Of The Sir Epidemic Model For Small Networks: An Application In Hospital Settings, Martin Lopez-Garcia

Biology and Medicine Through Mathematics Conference

No abstract provided.


Balanced Excitation And Inhibition Shapes The Dynamics Of A Neuronal Network For Movement And Reward, Anca R. Radulescu 2017 State University of New York at New Paltz

Balanced Excitation And Inhibition Shapes The Dynamics Of A Neuronal Network For Movement And Reward, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.


Models Of Nation-Building Via Systems Of Differential Equations, Carissa F. Slone, Darryl K. Ahner, Mark E. Oxley, William P. Baker 2017 Cedarville University

Models Of Nation-Building Via Systems Of Differential Equations, Carissa F. Slone, Darryl K. Ahner, Mark E. Oxley, William P. Baker

The Research and Scholarship Symposium

Nation-building modeling is an important field of research given the increasing number of candidate nations and the limited resources available. A modeling methodology and a system of differential equations model are presented to investigate the dynamics of nation-building. The methodology is based upon parameter identification techniques applied to a system of differential equations, to evaluate nation-building operations. Data from Operation Iraqi Freedom (OIF) and Afghanistan are used to demonstrate the validity of different models as well as the comparison of models.


Generalized Thomas-Fermi Equations As The Lampariello Class Of Emden-Fowler Equations, Haret C. Rosu, Stefan C. Mancas 2017 IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica

Generalized Thomas-Fermi Equations As The Lampariello Class Of Emden-Fowler Equations, Haret C. Rosu, Stefan C. Mancas

Publications

A one-parameter family of Emden-Fowler equations defined by Lampariello’s parameter p which, upon using Thomas-Fermi boundary conditions, turns into a set of generalized Thomas-Fermi equations comprising the standard Thomas-Fermi equation for p = 1 is studied in this paper. The entire family is shown to be non integrable by reduction to the corresponding Abel equations whose invariants do not satisfy a known integrability condition. We also discuss the equivalent dynamical system of equations for the standard Thomas-Fermi equation and perform its phase-plane analysis. The results of the latter analysis are similar for the whole class.


Zero Forcing, Linear And Quantum Controllability For Systems Evolving On Networks, Daniel Burgarth, Domenico D'Alessandro, Leslie Hogben, Simone Severini, Michael Young 2017 Aberystwyth University

Zero Forcing, Linear And Quantum Controllability For Systems Evolving On Networks, Daniel Burgarth, Domenico D'Alessandro, Leslie Hogben, Simone Severini, Michael Young

Leslie Hogben

We study the dynamics of systems on networks from a linear algebraic perspective. The control theoretic concept of controllability describes the set of states that can be reached for these systems. Our main result says that controllability in the quantum sense, expressed by the Lie algebra rank condition, and controllability in the sense of linear systems, expressed by the controllability matrix rank condition, are equivalent conditions. We also investigate how the graph theoretic concept of a zero forcing set impacts the controllability property; if a set of vertices is a zero forcing set, the associated dynamical system is controllable. These ...


The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz 2017 Schoolcraft College

The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz

Journal of Humanistic Mathematics

Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to ...


Data Predictive Control For Building Energy Management, Achin Jain, Madhur Behl, Rahul Mangharam 2017 University of Pennsylvania

Data Predictive Control For Building Energy Management, Achin Jain, Madhur Behl, Rahul Mangharam

Real-Time and Embedded Systems Lab (mLAB)

Decisions on how to best optimize energy systems operations are becoming ever so complex and conflicting, that model-based predictive control (MPC) algorithms must play an important role. However, a key factor prohibiting the widespread adoption of MPC in buildings, is the cost, time, and effort associated with learning first-principles based dynamical models of the underlying physical system. This paper introduces an alternative approach for implementing finite-time receding horizon control using control-oriented data-driven models. We call this approach Data Predictive Control (DPC). Specifically, by utilizing separation of variables, two novel algorithms for implementing DPC using a single regression tree and with ...


Global Stability Of Nonlinear Stochastic Sei Epidemic Model With Fluctuations In Transmission Rate Of Disease, Olusegun Michael Otunuga 2017 Marshall University

Global Stability Of Nonlinear Stochastic Sei Epidemic Model With Fluctuations In Transmission Rate Of Disease, Olusegun Michael Otunuga

Mathematics Faculty Research

We derive and analyze the dynamic of a stochastic SEI epidemic model for disease spread. Fluctuations in the transmission rate of the disease bring about stochasticity in model. We discuss the asymptotic stability of the infection-free equilibrium by first deriving the closed form deterministic (R0) and stochastic (R0) basic reproductive number. Contrary to some author’s remark that different diffusion rates have no effect on the stability of the disease-free equilibrium, we showed that even if no epidemic invasion occurs with respect to the deterministic version of the SEI model (i.e., R0 < 1), epidemic can still grow initially (if R0 > 1) because ...


C.V. - Wojciech Budzianowski, Wojciech M. Budzianowski 2017 Wojciech Budzianowski Consulting Services

C.V. - Wojciech Budzianowski, Wojciech M. Budzianowski

Wojciech Budzianowski

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