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Articles 1 - 30 of 261

Full-Text Articles in Dynamical Systems

Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku May 2019

Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku

Biology and Medicine Through Mathematics Conference

No abstract provided.


Bifurcation Analysis Of A Photoreceptor Interaction Model For Retinitis Pigmentosa, Anca R. Radulescu May 2019

Bifurcation Analysis Of A Photoreceptor Interaction Model For Retinitis Pigmentosa, Anca R. Radulescu

Biology and Medicine Through Mathematics Conference

No abstract provided.


Spiking Activity In Networks Of Neurons Impacted By Axonal Swelling, Brian Frost, Stan Mintchev May 2019

Spiking Activity In Networks Of Neurons Impacted By Axonal Swelling, Brian Frost, Stan Mintchev

Biology and Medicine Through Mathematics Conference

No abstract provided.


Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer Apr 2019

Mathematical Models: The Lanchester Equations And The Zombie Apocalypse, Hailey Bauer

Undergraduate Theses and Capstone Projects

This research study used mathematical models to analyze and depicted specific battle situations and the outcomes of the zombie apocalypse. The original models that predicted warfare were the Lanchester models, while the zombie apocalypse models were fictional expansions upon mathematical models used to examine infectious diseases. In this paper, I analyzed and compared different mathematical models by examining each model’s set of assumptions and the impact of the change in variables on the population classes. The purpose of this study was to understand the basics of the discrete dynamical systems and to determine the similarities between imaginary and realistic ...


New Experimental Investigations For The 3x+1 Problem: The Binary Projection Of The Collatz Map, Benjamin Bairrington, Aaron Okano Mar 2019

New Experimental Investigations For The 3x+1 Problem: The Binary Projection Of The Collatz Map, Benjamin Bairrington, Aaron Okano

Rose-Hulman Undergraduate Mathematics Journal

The 3x + 1 Problem, or the Collatz Conjecture, was originally developed in the early 1930's. It has remained unsolved for over eighty years. Throughout its history, traditional methods of mathematical problem solving have only succeeded in proving heuristic properties of the mapping. Because the problem has proven to be so difficult to solve, many think it might be undecidable. In this paper we brie y follow the history of the 3x + 1 problem from its creation in the 1930's to the modern day. Its history is tied into the development of the Cosper Algorithm, which maps binary sequences ...


Large Scale Dynamical Model Of Macrophage/Hiv Interactions, Sean T. Bresnahan, Matthew M. Froid Mar 2019

Large Scale Dynamical Model Of Macrophage/Hiv Interactions, Sean T. Bresnahan, Matthew M. Froid

Student Research and Creative Activity Fair

Properties emerge from the dynamics of large-scale molecular networks that are not discernible at the individual gene or protein level. Mathematical models - such as probabilistic Boolean networks - of molecular systems offer a deeper insight into how these emergent properties arise. Here, we introduce a non-linear, deterministic Boolean model of protein, gene, and chemical interactions in human macrophage cells during HIV infection. Our model is composed of 713 nodes with 1583 interactions between nodes and is responsive to 38 different inputs including signaling molecules, bacteria, viruses, and HIV viral particles. Additionally, the model accurately simulates the dynamics of over 50 different ...


Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene Feb 2019

Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene

CODEE Journal

The environmental phenomenon of climate change is of critical importance to today's science and global communities. Differential equations give a powerful lens onto this phenomenon, and so we should commit to discussing the mathematics of this environmental issue in differential equations courses. Doing so highlights the power of linking differential equations to environmental and social justice causes, and also brings important science to the forefront in the mathematics classroom. In this paper, we provide an extended problem, appropriate for a first course in differential equations, that uses bifurcation analysis to study climate change. Specifically, through studying hysteresis, this problem ...


Role Of Combinatorial Complexity In Genetic Networks, Sharon Yang Feb 2019

Role Of Combinatorial Complexity In Genetic Networks, Sharon Yang

SMU Journal of Undergraduate Research

A common motif found in genetic networks is the formation of large complexes. One difficulty in modeling this motif is the large number of possible intermediate complexes that can form. For instance, if a complex could contain up to 10 different proteins, 210 possible intermediate complexes can form. Keeping track of all complexes is difficult and often ignored in mathematical models. Here we present an algorithm to code ordinary differential equations (ODEs) to model genetic networks with combinatorial complexity. In these routines, the general binding rules, which counts for the majority of the reactions, are implemented automatically, thus the users ...


Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski Dec 2018

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.


A Companion To The Introduction To Modern Dynamics, David D. Nolte Dec 2018

A Companion To The Introduction To Modern Dynamics, David D. Nolte

David D Nolte

A Jr/Sr Mechanics/Dynamics textbook from Oxford University Press, updating how we teach undergraduate physics majors with increased relevance for physics careers in changing times.

Additional materials, class notes and examples to go with the textbook Introduction to Modern Dynamics: Chaos, Networks, Space and Time (Oxford University Press, 2019).

The best parts of physics are the last topics that our students ever see.  These are the exciting new frontiers of nonlinear and complex systems that are at the forefront of university research and are the basis of many of our high-tech businesses.  Topics such as traffic on the World ...


Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley Oct 2018

Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley

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, Ozlem Ozturk Mizrak Oct 2018

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.


Ideals, Big Varieties, And Dynamic Networks, Ian H. Dinwoodie Sep 2018

Ideals, Big Varieties, And Dynamic Networks, Ian H. Dinwoodie

Mathematics and Statistics Faculty Publications and Presentations

The advantage of using algebraic geometry over enumeration for describing sets related to attractors in large dynamic networks from biology is advocated. Examples illustrate the gains.


Attosecond Light Pulses And Attosecond Electron Dynamics Probed Using Angle-Resolved Photoelectron Spectroscopy, Cong Chen Aug 2018

Attosecond Light Pulses And Attosecond Electron Dynamics Probed Using Angle-Resolved Photoelectron Spectroscopy, Cong Chen

Physics Graduate Theses & Dissertations

Recent advances in the generation and control of attosecond light pulses have opened up new opportunities for the real-time observation of sub-femtosecond (1 fs = 10-15 s) electron dynamics in gases and solids. Combining attosecond light pulses with angle-resolved photoelectron spectroscopy (atto-ARPES) provides a powerful new technique to study the influence of material band structure on attosecond electron dynamics in materials. Electron dynamics that are only now accessible include the lifetime of far-above-bandgap excited electronic states, as well as fundamental electron interactions such as scattering and screening. In addition, the same atto-ARPES technique can also be used to measure the ...


Multi Self-Adapting Particle Swarm Optimization Algorithm (Msapso)., Gerhard Koch May 2018

Multi Self-Adapting Particle Swarm Optimization Algorithm (Msapso)., Gerhard Koch

Electronic Theses and Dissertations

The performance and stability of the Particle Swarm Optimization algorithm depends on parameters that are typically tuned manually or adapted based on knowledge from empirical parameter studies. Such parameter selection is ineffectual when faced with a broad range of problem types, which often hinders the adoption of PSO to real world problems. This dissertation develops a dynamic self-optimization approach for the respective parameters (inertia weight, social and cognition). The effects of self-adaption for the optimal balance between superior performance (convergence) and the robustness (divergence) of the algorithm with regard to both simple and complex benchmark functions is investigated. This work ...


Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr. May 2018

Physical Applications Of The Geometric Minimum Action Method, George L. Poppe Jr.

All Dissertations, Theses, and Capstone Projects

This thesis extends the landscape of rare events problems solved on stochastic systems by means of the \textit{geometric minimum action method} (gMAM). These include partial differential equations (PDEs) such as the real Ginzburg-Landau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultra-short pulse mode-locked laser system (MLL).

Additionally we develop analytical tools that can be used alongside numerics to validate those solutions. This includes the use of instanton methods in deriving state transitions for the linear Schroedinger equation and the cubic diffusive NLSE.

These analytical solutions ...


Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam Apr 2018

Iterative Methods To Solve Systems Of Nonlinear Algebraic Equations, Md Shafiful Alam

Masters Theses & Specialist Projects

Iterative methods have been a very important area of study in numerical analysis since the inception of computational science. Their use ranges from solving algebraic equations to systems of differential equations and many more. In this thesis, we discuss several iterative methods, however our main focus is Newton's method. We present a detailed study of Newton's method, its order of convergence and the asymptotic error constant when solving problems of various types as well as analyze several pitfalls, which can affect convergence. We also pose some necessary and sufficient conditions on the function f for higher order of ...


P-46 A Periodic Matrix Model Of Seabird Behavior And Population Dynamics, Mykhaylo M. Malakhov, Benjamin Macdonald, Shandelle M. Henson, J. M. Cushing Mar 2018

P-46 A Periodic Matrix Model Of Seabird Behavior And Population Dynamics, Mykhaylo M. Malakhov, Benjamin Macdonald, Shandelle M. Henson, J. M. Cushing

Honors Scholars & Undergraduate Research Poster Symposium Programs

Rising sea surface temperatures (SSTs) in the Pacific Northwest lead to food resource reductions for surface-feeding seabirds, and have been correlated with several marked behavioral changes. Namely, higher SSTs are associated with increased egg cannibalism and egg-laying synchrony in the colony. We study the long-term effects of climate change on population dynamics and survival by considering a simplified, cross-season model that incorporates both of these behaviors in addition to density-dependent and environmental effects. We show that cannibalism can lead to backward bifurcations and strong Allee effects, allowing the population to survive at lower resource levels than would be possible otherwise.


Learning And Control Using Gaussian Processes, Achin Jain, Truong X Nghiem, Manfred Morari, Rahul Mangharam Feb 2018

Learning And Control Using Gaussian Processes, Achin Jain, Truong X Nghiem, Manfred Morari, Rahul Mangharam

Real-Time and Embedded Systems Lab (mLAB)

Building physics-based models of complex physical systems like buildings and chemical plants is extremely cost and time prohibitive for applications such as real-time optimal control, production planning and supply chain logistics. Machine learning algorithms can reduce this cost and time complexity, and are, consequently, more scalable for large-scale physical systems. However, there are many practical challenges that must be addressed before employing machine learning for closed-loop control. This paper proposes the use of Gaussian Processes (GP) for learning control-oriented models: (1) We develop methods for the optimal experiment design (OED) of functional tests to learn models of a physical system ...


Gradient Estimation For Attractor Networks, Thomas Flynn Feb 2018

Gradient Estimation For Attractor Networks, Thomas Flynn

All Dissertations, Theses, and Capstone Projects

It has been hypothesized that neural network models with cyclic connectivity may be more powerful than their feed-forward counterparts. This thesis investigates this hypothesis in several ways. We study the gradient estimation and optimization procedures for several variants of these networks. We show how the convergence of the gradient estimation procedures are related to the properties of the networks. Then we consider how to tune the relative rates of gradient estimation and parameter adaptation to ensure successful optimization in these models. We also derive new gradient estimators for stochastic models. First, we port the forward sensitivity analysis method to the ...


Homeomorphisms Of The Sierpinski Carpet, Karuna S. Sangam Jan 2018

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 Jan 2018

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 Oct 2017

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 Oct 2017

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 Oct 2017

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 Oct 2017

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 Oct 2017

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 Sep 2017

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 Sep 2017

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 Sep 2017

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 ...