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Articles 1 - 6 of 6
Full-Text Articles in Applied Mathematics
Basins Of Attraction And Metaoptimization For Particle Swarm Optimization Methods, David Ma
Basins Of Attraction And Metaoptimization For Particle Swarm Optimization Methods, David Ma
Honors Projects
Particle swarm optimization (PSO) is a metaheuristic optimization method that finds near- optima by spawning particles which explore within a given search space while exploiting the best candidate solutions of the swarm. PSO algorithms emulate the behavior of, say, a flock of birds or a school of fish, and encapsulate the randomness that is present in natural processes. In this paper, we discuss different initialization schemes and meta-optimizations for PSO, its performances on various multi-minima functions, and the unique intricacies and obstacles that the method faces when attempting to produce images for basins of attraction, which are the sets of …
Sensitivity Analysis Of Basins Of Attraction For Nelder-Mead, Sonia K. Shah
Sensitivity Analysis Of Basins Of Attraction For Nelder-Mead, Sonia K. Shah
Honors Projects
The Nelder-Mead optimization method is a numerical method used to find the minimum of an objective function in a multidimensional space. In this paper, we use this method to study functions - specifically functions with three-dimensional graphs - and create images of the basin of attraction of the function. Three different methods are used to create these images named the systematic point method, randomized centroid method, and systemized centroid method. This paper applies these methods to different functions. The first function has two minima with an equivalent function value. The second function has one global minimum and one local minimum. …
Sensitivity Analysis Of Basins Of Attraction For Gradient-Based Optimization Methods, Gillian King
Sensitivity Analysis Of Basins Of Attraction For Gradient-Based Optimization Methods, Gillian King
Honors Projects
This project is an analysis of the effectiveness of five distinct optimization methods in their ability in producing clear images of the basins of attraction, which is the set of initial points that approach the same minimum for a given function. Basin images are similar to contour plots, except that they depict the distinct regions of points--in unique colors--that approach the same minimum. Though distinct in goal, contour plots are useful to basin research in that idealized basin images can be inferred from the steepness levels and location of extrema they depict. Effectiveness of the method changes slightly depending on …
The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas
The Pope's Rhinoceros And Quantum Mechanics, Michael Gulas
Honors Projects
In this project, I unravel various mathematical milestones and relate them to the human experience. I show and explain the solution to the Tautochrone, a popular variation on the Brachistochrone, which details a major battle between Leibniz and Newton for the title of inventor of Calculus. One way to solve the Tautochrone is using Laplace Transforms; in this project I expound on common functions that get transformed and how those can be used to solve the Tautochrone. I then connect the solution of the Tautochrone to clock making. From this understanding of clocks, I examine mankind’s understanding of time and …
A Statistical Study Of Student Success In The Bgsu Honors College, Sarah Hercules
A Statistical Study Of Student Success In The Bgsu Honors College, Sarah Hercules
Honors Projects
Higher education has long tried to find the best measures to predict student success. Different colleges often have different guidelines, requiring different criteria to be evaluated. The BGSU Honors College has struggled with retention and recruitment of underrepresented students with their current admission criteria. This analysis studies different measures of student success such as BGSU GPA and number of completed Honors credits for high-achieving BGSU students who enrolled from Fall 2013 through Fall 2016 to find the best predictors of student success through regression analysis. Throughout this paper, the impact of ethnicity, gender, the college of a student’s program, high …
Mathematical Modeling Of The American Lobster Cardiac Muscle Cell: An Investigation Of Calcium Ion Permeability And Force Of Contractions, Lauren A. Skerritt
Mathematical Modeling Of The American Lobster Cardiac Muscle Cell: An Investigation Of Calcium Ion Permeability And Force Of Contractions, Lauren A. Skerritt
Honors Projects
In the American lobster (Homarus americanus), neurogenic stimulation of the heart drives fluxes of calcium (Ca2+) into the cytoplasm of a muscle cell resulting in heart muscle contraction. The heartbeat is completed by the active transport of calcium out of the cytoplasm into extracellular and intracellular spaces. An increase in the frequency of calcium release is expected to increase amplitude and duration of muscle contraction. This makes sense because an increase in cytoplasmic calcium should increase the activation of the muscle contractile elements (actin and myosin). Since calcium cycling is a reaction-diffusion process, the extent to …