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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
Border-Collision Bifurcations Of Cardiac Calcium Cycling, Jacob Michael Kahle
Border-Collision Bifurcations Of Cardiac Calcium Cycling, Jacob Michael Kahle
Masters Theses
In this thesis, we study the nonlinear dynamics of calcium cycling within a cardiac cell. We develop piecewise smooth mapping models to describe intracellular calcium cycling in cardiac myocyte. Then, border-collision bifurcations that arise in these piecewise maps are investigated. These studies are carried out using both one-dimensional and two-dimensional models. Studies in this work lead to interesting insights on the stability of cardiac dynamics, suggesting possible mechanisms for cardiac alternans. Alternans is the precursor of sudden cardiac arrests, a leading cause of death in the United States.
Mechanisms For Social Influence, Jeremy David Auerbach
Mechanisms For Social Influence, Jeremy David Auerbach
Masters Theses
Throughout the thesis, I study mathematical models that can help explain the dependency of social phenomena in animals and humans on individual traits. The first chapter investigates consensus building in human groups through communication of individual preferences for a course of action. Individuals share and modify these preferences through speaker listener interactions. Personality traits, reputations, and social networks structures effect these modifications and eventually the group will reach a consensus. If there is variation in personality traits, the time to reach consensus is delayed. Reputation models are introduced and explored, finding that those who can best estimate the average initial …
Symmetry Detection In Integer Linear Programs, Jonathan David Schrock
Symmetry Detection In Integer Linear Programs, Jonathan David Schrock
Masters Theses
Symmetry has long been recognized as a major obstacle in integer programming. Unless properly recognized and exploited, the branch-and-bound tree generated when solving highly symmetric integer programs (IPs) can contain many identical subproblems, resulting in a waste of computational effort. Effective methods have been developed to exploit known symmetry. This thesis focuses on improving methods that compute the symmetry group of an IP. In the literature, computing the symmetry group of an IP is performed by generating a graph with a similar structure as the IP, and then computing the automorphism group of the graph. Unfortunately, these graphs may be …
Numerical Methods For Solving Optimal Control Problems, Garrett Robert Rose
Numerical Methods For Solving Optimal Control Problems, Garrett Robert Rose
Masters Theses
There are many different numerical processes for approximating an optimal control problem. Three of those are explained here: The Forward Backward Sweep, the Shooter Method, and an Optimization Method using the MATLAB Optimization Tool Box. The methods will be explained, and then applied to three different test problems to see how they perform. The results show that the Forward Backward Sweep is the best of the three methods with the Shooter Method being a competitor.
A Model Of Activity And Intervention Across Social Networks, Allison Marie Heming
A Model Of Activity And Intervention Across Social Networks, Allison Marie Heming
Masters Theses
Social network analysis is a growing field used to measure connectivity and activity of people and communities. We develop a model that creates a network and measures the overall activity of that network. We then apply interventions to this model and measure the change in overall activity. Through an optimization process we are able to determine the best course of action that minimizes or maximizes the overall activity of the network.
Flexible Memory Allocation In Kinetic Monte Carlo Simulations, Aaron David Craig
Flexible Memory Allocation In Kinetic Monte Carlo Simulations, Aaron David Craig
Masters Theses
We introduce two new algorithms for Kinetic Monte Carlo simulations: the minimal and flexible allocation algorithms. The theory and computational challenges associated with K.M.C. simulations are briefly discussed. We outline the simple cubic, solid-on-solid model of epitaxial growth and analyze four methods for its simulation: the linear search, standard inverted list, minimal allocation, and flexible allocation algorithms. We then implement these algorithms, analyze their performances, and discuss implications of the results.
Application Of Loglinear Models To Claims Triangle Runoff Data, Netanya Lee Martin
Application Of Loglinear Models To Claims Triangle Runoff Data, Netanya Lee Martin
Masters Theses
"In this thesis, we presented in detail different aspects of Verrall's chain ladder method and their advantages and disadvantages. Insurance companies must ensure there are enough reserves to cover future claims. To that end, it is useful to estimate mean expected losses. The chain ladder technique under a general linear model is the most widely used method for such estimation in property and casualty insurance. Verrall's chain ladder technique develops estimators for loss development ratios, mean expected ultimate claims, Bayesian premiums, and Bühlmann credibility premiums. The chain ladder technique can be used to estimate loss development in cases where data …
Some Combinatorial Applications Of Sage, An Open Source Program, Jessica Ruth Chowning
Some Combinatorial Applications Of Sage, An Open Source Program, Jessica Ruth Chowning
Masters Theses
"In this thesis, we consider the usefulness of Sage, an online and open-source program, in analyzing permutation puzzles such as the Rubik's cube and a specific combinatorial structure called the projective plane. Many programs exist to expedite calculations in research and provide previously-unavailable solutions; some require purchase, while others, such as Sage, are available for free online. Sage is asked to handle a small permutation puzzle called Swap, and then we explore how it calculates solutions for a Rubik's cube. We then discuss projective planes, Sage's library of functions for dealing with projective planes, and how they relate to the …