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Articles 1 - 13 of 13
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 …
Modeling Oyster Growth Dynamics In Flupsy Systems To Develop A Decision Support Tool For Seed Management, Gretchen Clauss
Modeling Oyster Growth Dynamics In Flupsy Systems To Develop A Decision Support Tool For Seed Management, Gretchen Clauss
Honors Projects
As the Gulf of Maine warms and lobsters move north to colder waters, Maine’s working water front has begun to diversify. There is a thriving new ecosystem of aquaculturists looking to keep Maine’s waterfront traditions alive in a lasting, sustainable way. One of the most popular aquaculture industries is oyster farming. With an increasing number of oyster farms developing in Midcoast Maine each year, we seek to develop a decision support tool to aid farmers in seed management. Oyster farmers can choose weather or not to use an upweller on their farm, and our goal is to provide guidance on …
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 …
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. …
Staying One Step Ahead Of The Growing Electric Vehicle Market, Russell Molter
Staying One Step Ahead Of The Growing Electric Vehicle Market, Russell Molter
Honors Projects
Electric vehicles are becoming more popular among drivers as they become more affordable and as people become more aware of the benefits of electric vehicles. Because of this, the demand for electric car chargers is quickly increasing across the country. This includes BGSU’s campus. Right now, there are seven chargers available on campus, but with the trends in how the electric vehicle market is growing, BGSU should create a plan to install many more chargers to meet the increasing demand for charging stations. This strategy will allow BGSU to keep up with the growing electric vehicle market, which will additionally …
Modeling Coupled Disease-Behavior Dynamics Of Sars-Cov-2 Using Influence Networks, Juliana C. Taube
Modeling Coupled Disease-Behavior Dynamics Of Sars-Cov-2 Using Influence Networks, Juliana C. Taube
Honors Projects
SARS-CoV-2, the virus that causes COVID-19, has caused significant human morbidity and mortality since its emergence in late 2019. Not only have over three million people died, but humans have been forced to change their behavior in a variety of ways, including limiting their contacts, social distancing, and wearing masks. Early infectious disease models, like the classical SIR model by Kermack and McKendrick, do not account for differing contact structures and behavior. More recent work has demonstrated that contact structures and behavior can considerably impact disease dynamics. We construct a coupled disease-behavior dynamical model for SARS-CoV-2 by incorporating heterogeneous contact …
Classifying Flow-Kick Equilibria: Reactivity And Transient Behavior In The Variational Equation, Alanna Haslam
Classifying Flow-Kick Equilibria: Reactivity And Transient Behavior In The Variational Equation, Alanna Haslam
Honors Projects
In light of concerns about climate change, there is interest in how sustainable management can maintain the resilience of ecosystems. We use flow-kick dynamical systems to model ecosystems subject to a constant kick occurring every τ time units. We classify the stability of flow-kick equilibria to determine which management strategies result in desirable long-term characteristics. To classify the stability of a flow-kick equilibrium, we classify the linearization of the time-τ map given by the time-τ map of the variational equation about the equilibrium trajectory. Since the variational equation is a non-autonomous linear differential equation, we conjecture that the asymptotic stability …
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 …
Statistical Analysis Of Momentum In Basketball, Mackenzi Stump
Statistical Analysis Of Momentum In Basketball, Mackenzi Stump
Honors Projects
The “hot hand” in sports has been debated for as long as sports have been around. The debate involves whether streaks and slumps in sports are true phenomena or just simply perceptions in the mind of the human viewer. This statistical analysis of momentum in basketball analyzes the distribution of time between scoring events for the BGSU Women’s Basketball team from 2011-2017. We discuss how the distribution of time between scoring events changes with normal game factors such as location of the game, game outcome, and several other factors. If scoring events during a game were always randomly distributed, or …
Stretch Feedback In The Lobster Heart: Experimental And Computational Analysis, Katelyn J. Suchyta
Stretch Feedback In The Lobster Heart: Experimental And Computational Analysis, Katelyn J. Suchyta
Honors Projects
No abstract provided.
Mathematical Notions Of Resilience: The Effects Of Disturbancei In One-Dimensional Nonlinear Systems, Stephen Ligtenberg
Mathematical Notions Of Resilience: The Effects Of Disturbancei In One-Dimensional Nonlinear Systems, Stephen Ligtenberg
Honors Projects
No abstract provided.
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 …