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Articles 1  30 of 279
FullText Articles in Dynamical Systems
Network Structure And Dynamics Of Biological Systems, Deena R. Schmidt
Network Structure And Dynamics Of Biological Systems, Deena R. Schmidt
Annual Symposium on Biomathematics and Ecology: Education and Research
No abstract provided.
Efficient Control Methods For Stochastic Boolean Networks, David Murrugarra
Efficient Control Methods For Stochastic Boolean Networks, David Murrugarra
Annual Symposium on Biomathematics and Ecology: Education and Research
No abstract provided.
Topology And Dynamics Of Gene Regulatory Networks: A MetaAnalysis, Claus Kadelka
Topology And Dynamics Of Gene Regulatory Networks: A MetaAnalysis, Claus Kadelka
Annual Symposium on Biomathematics and Ecology: Education and Research
No abstract provided.
The LongRun Effects Of Tropical Cyclones On Infant Mortality, Isabel Miranda
The LongRun Effects Of Tropical Cyclones On Infant Mortality, Isabel Miranda
Master's Theses
In the United States alone, each tropical cyclone causes an average of $14.6 billion worth of damages. In addition to the destruction of physical infrastructure, natural disasters also negatively impact human capital formation. These losses are often more difficult to observe, and therefore, are over looked when quantifying the true costs of natural disasters. One particular effect is an increase in infant mortality rates, an important indicator of a country’s general socioeconomic level. This paper utilizes a model created by AnttilaHughes and Hsiang, that takes advantage of annual variation in tropical cyclones using annual spatial average maximum wind ...
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.
Periodicity And Invertibility Of Lattice Gas Cellular Automata, Jiawen Wang
Periodicity And Invertibility Of Lattice Gas Cellular Automata, Jiawen Wang
Mathematical Sciences Technical Reports (MSTR)
A cellular automaton is a type of mathematical system that models the behavior of a set of cells with discrete values in progressing time steps. The often complicated behaviors of cellular automata are studied in computer science, mathematics, biology, and other science related fields. Lattice gas cellular automata are used to simulate the movements of particles. This thesis aims to discuss the properties of lattice gas models, including periodicity and invertibility, and to examine their accuracy in reflecting the physics of particles in real life. Analysis of elementary cellular automata is presented to introduce the concept of cellular automata and ...
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 ...
The Waiting Time And Dynamic Partitions, Akhtam Dzhalilov, Mukhriddin Khomidov
The Waiting Time And Dynamic Partitions, Akhtam Dzhalilov, Mukhriddin Khomidov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
In the present paper we study the behaviour of normalized waiting times for linear irrational rotations. D.Kim and B.Seo investigated the waiting times for equidistance partitions. We consider waiting times with respect to dynamical partitions. The results show that limiting behaviour of waiting times essentially depend on type of partitions.
Analyzing A Method To Determine The Utility Of Adding A Classification System To A Sequence For Improved Accuracy, Kevin S. Pamilagas
Analyzing A Method To Determine The Utility Of Adding A Classification System To A Sequence For Improved Accuracy, Kevin S. Pamilagas
Theses and Dissertations
Frequently, ensembles of classification systems are combined into a sequence in order to better enhance the accuracy in classifying objects of interest. However, there is a point in which adding an additional system to a sequence no longer enhances the system as either the increase in operational costs exceeds the benefit of improvements in classification or the addition of the system does not increase accuracy at all. This research will examine a utility measure to determine the valid or invalid nature of adding a classification system to a sequence of such systems based on the ratio of the change in ...
Wall Model Large Eddy Simulation Of A Diffusing Serpentine Inlet Duct, Ryan J. Thompson
Wall Model Large Eddy Simulation Of A Diffusing Serpentine Inlet Duct, Ryan J. Thompson
Theses and Dissertations
The modeling focus on serpentine inlet ducts (Sduct), as with any inlet, is to quantify the total pressure recovery and ow distortion after the inlet, which directly impacts the performance of a turbine engine fed by the inlet. Accurate prediction of Sduct ow has yet to be achieved amongst the computational fluid dynamics (CFD) community to improve the reliance on modeling reducing costly testing. While direct numerical simulation of the turbulent ow in an Sduct is too cost prohibitive due to grid scaling with Reynolds number, wallmodeled large eddy simulation (WMLES) serves as a tractable alternative. US3D, a hypersonic research ...
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 ...
Local Lagged Adapted Generalized Method Of Moments And Applications, Olusegun Michael Otunuga, Gangaram S. Ladde, Nathan G. Ladde
Local Lagged Adapted Generalized Method Of Moments And Applications, Olusegun Michael Otunuga, Gangaram S. Ladde, Nathan G. Ladde
Olusegun Michael Otunuga
In this work, an attempt is made for developing the local lagged adapted generalized method of moments (LLGMM). This proposed method is composed of: (1) development of the stochastic model for continuoustime dynamic process, (2) development of the discretetime interconnected dynamic model for statistic process, (3) utilization of Eulertype discretized scheme for nonlinear and nonstationary system of stochastic differential equations, (4) development of generalized method of moment/observation equations by employing lagged adaptive expectation process, (5) introduction of the conceptual and computational parameter estimation problem, (6) formulation of the conceptual and computational state estimation scheme and (7) definition of the ...
Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, Olusegun Michael Otunuga, Gangaram S. Ladde
Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, Olusegun Michael Otunuga, Gangaram S. Ladde
Olusegun Michael Otunuga
Employing basic economic principles, we systematically develop both deterministic and stochastic dynamic models for the logspot price process of energy commodity. Furthermore, treating a diﬀusion coeﬃcient parameter in the nonseasonal logspot price dynamic system as a stochastic volatility functional of logspot price, an interconnected system of stochastic model for logspot price, expected logspot price and hereditary volatility process is developed. By outlining the riskneutral dynamics and pricing, suﬃcient conditions are given to guarantee that the riskneutral dynamic model is equivalent to the developed model. Furthermore, it is shown that the expectation of the square of volatility under the riskneutral measure ...
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
Olusegun Michael Otunuga
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 ...
Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga
Finding Positive Solutions Of Boundary Value Dynamic Equations On Time Scale, Olusegun Michael Otunuga
Olusegun Michael Otunuga
This thesis is on the study of dynamic equations on time scale. Most often, the derivatives and antiderivatives of functions are taken on the domain of real numbers, which cannot be used to solve some models like insect populations that are continuous while in season and then follow a difference scheme with variable stepsize. They die out in winter, while the eggs are incubating or dormant; and then they hatch in a new season, giving rise to a non overlapping population. The general idea of my thesis is to find the conditions for having a positive solution of any boundary ...
Global Stability Of Nonlinear Stochastic Sei Epidemic Model With Fluctuations In Transmission Rate Of Disease, Olusegun Michael Otunuga
Global Stability Of Nonlinear Stochastic Sei Epidemic Model With Fluctuations In Transmission Rate Of Disease, Olusegun Michael Otunuga
Olusegun Michael Otunuga
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 infectionfree equilibrium by first deriving the closed form deterministic (R_{0}) and stochastic (R_{0}) basic reproductive number. Contrary to some author’s remark that different diffusion rates have no effect on the stability of the diseasefree equilibrium, we showed that even if no epidemic invasion occurs with respect to the deterministic version of the SEI model (i.e., R_{0 }< 1), epidemic can still grow initially (if R_{0 }> 1) because ...
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 ...
From Optimization To Equilibration: Understanding An Emerging Paradigm In Artificial Intelligence And Machine Learning, Ian Gemp
Doctoral Dissertations
Many existing machine learning (ML) algorithms cannot be viewed as gradient descent on some single objective. The solution trajectories taken by these algorithms naturally exhibit rotation, sometimes forming cycles, a behavior that is not expected with (fullbatch) gradient descent. However, these algorithms can be viewed more generally as solving for the equilibrium of a game with possibly multiple competing objectives. Moreover, some recent ML models, specifically generative adversarial networks (GANs) and its variants, are now explicitly formulated as equilibrium problems. Equilibrium problems present challenges beyond those encountered in optimization such as limitcycles and chaotic attractors and are able to abstract ...
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
Control Theory: The Double Pendulum Inverted On A Cart, Ian J P CroweWright
Control Theory: The Double Pendulum Inverted On A Cart, Ian J P CroweWright
Mathematics & Statistics ETDs
In this thesis the Double Pendulum Inverted on a Cart (DPIC) system is modeled using the EulerLagrange equation for the chosen Lagrangian, giving a secondorder nonlinear system. This system can be approximated by a linear firstorder system in which linear control theory can be used. The important definitions and theorems of linear control theory are stated and proved to allow them to be utilized on a linear version of the DPIC system. Controllability and eigenvalue placement for the linear system are shown using MATLAB. Linear Optimal control theory is likewise explained in this section and its uses are applied to ...
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 ...