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Articles 1  30 of 261
FullText Articles in Dynamical Systems
Characterizing The Permanence And Stationary Distribution For A Family Of Malaria Stochastic Models, Divine Wanduku
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
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
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
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
New Experimental Investigations For The 3x+1 Problem: The Binary Projection Of The Collatz Map, Benjamin Bairrington, Aaron Okano
RoseHulman 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
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 largescale 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 nonlinear, 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
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
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 89, Wrocław, Poland, Wojciech M. Budzianowski
Call For Abstracts  Resrb 2019, July 89, Wrocław, Poland, Wojciech M. Budzianowski
Wojciech Budzianowski
No abstract provided.
A Companion To The Introduction To Modern Dynamics, David D. Nolte
A Companion To The Introduction To Modern Dynamics, David D. Nolte
David D Nolte
SemiTensor Product Representations Of Boolean Networks, Matthew Macauley
SemiTensor 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 DataJustified Prostate Cancer Modelling Under Iad Therapy, Ozlem Ozturk Mizrak
Introducing The Fractional Differentiation For Clinical DataJustified 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
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 AngleResolved 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 realtime observation of subfemtosecond (1 fs = 10^{15} s) electron dynamics in gases and solids. Combining attosecond light pulses with angleresolved photoelectron spectroscopy (attoARPES) 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 farabovebandgap excited electronic states, as well as fundamental electron interactions such as scattering and screening. In addition, the same attoARPES technique can also be used to measure the ...
Multi SelfAdapting Particle Swarm Optimization Algorithm (Msapso)., Gerhard Koch
Multi SelfAdapting 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 selfoptimization approach for the respective parameters (inertia weight, social and cognition). The effects of selfadaption 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.
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 GinzburgLandau equation (RGLE), the linear Schroedinger equation, along with various forms of the nonlinear Schroedinger equation (NLSE) including an application towards an ultrashort pulse modelocked 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
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 ...
P46 A Periodic Matrix Model Of Seabird Behavior And Population Dynamics, Mykhaylo M. Malakhov, Benjamin Macdonald, Shandelle M. Henson, J. M. Cushing
P46 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 surfacefeeding seabirds, and have been correlated with several marked behavioral changes. Namely, higher SSTs are associated with increased egg cannibalism and egglaying synchrony in the colony. We study the longterm effects of climate change on population dynamics and survival by considering a simplified, crossseason model that incorporates both of these behaviors in addition to densitydependent 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
Learning And Control Using Gaussian Processes, Achin Jain, Truong X Nghiem, Manfred Morari, Rahul Mangharam
RealTime and Embedded Systems Lab (mLAB)
Building physicsbased models of complex physical systems like buildings and chemical plants is extremely cost and time prohibitive for applications such as realtime optimal control, production planning and supply chain logistics. Machine learning algorithms can reduce this cost and time complexity, and are, consequently, more scalable for largescale physical systems. However, there are many practical challenges that must be addressed before employing machine learning for closedloop control. This paper proposes the use of Gaussian Processes (GP) for learning controloriented 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
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 feedforward 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
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 wellknown fractal with many fascinating topological properties that appears in a variety of different contexts, including as rational Julia sets. In this project, we study selfhomeomorphisms 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 MorseHedlund Theorem, Eben Blaisdell
Extensions Of The MorseHedlund Theorem, Eben Blaisdell
Honors Theses
Biinfinite words are sequences of characters that are infinite forwards and backwards; for example "...ababababab...". The MorseHedlund theorem says that a biinfinite 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
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
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
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 TonicToBursting Transitions, Manuela Burek, Epaminondas Rosa
Temperature Effects On Neuronal TonicToBursting 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
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 MarkoffHurwitz Tuples, Ryan Ronan
Asymptotic Counting Formulas For MarkoffHurwitz 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 MarkoffHurwitz 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
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 [tk−mk+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
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 realworld environments, making them more accessible and easier to study then their physical world ...