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- All Subjects: Mathematics
- Creators: School of Mathematical and Statistical Sciences
- Status: Published
Description
A semi-implicit, fourth-order time-filtered leapfrog numerical scheme is investigated for accuracy and stability, and applied to several test cases, including one-dimensional advection and diffusion, the anelastic equations to simulate the Kelvin-Helmholtz instability, and the global shallow water spectral model to simulate the nonlinear evolution of twin tropical cyclones. The leapfrog scheme leads to computational modes in the solutions to highly nonlinear systems, and time-filters are often used to damp these modes. The proposed filter damps the computational modes without appreciably degrading the physical mode. Its performance in these metrics is superior to the second-order time-filtered leapfrog scheme developed by Robert and Asselin.
ContributorsBurke, Lee Matthew Moore (Author) / Moustaoui, Mohamed (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
According to the CDC, diabetes is the 7th leading cause of death in the U.S. and rates are continuing to rise nationally and internationally. Chronically elevated blood glucose levels can lead to type 2 diabetes and other complications. Medications can be used to treat diabetes, but often have side effects. Lifestyle and diet modifications can be just as effective as medications in helping to improve glycemic control, and prevent diabetes or improve the condition in those who have it. Studies have demonstrated that consuming vinegar with carbohydrates can positively impact postprandial glycemia in diabetic and healthy individuals. Continuous vinegar intake with meals may even reduce fasting blood glucose levels. Since vinegar is a primary ingredient in mustard, the purpose of this study was to determine if mustard consumption with a carbohydrate-rich meal (bagel and fruit juice) had an effect on the postprandial blood glucose levels of subjects. The results showed that mustard improved glycemia by 17% when subjects consumed the meal with mustard as opposed to the control. A wide variety of vinegars exists. The defining ingredient in all vinegars is acetic acid, behind the improvement in glycemic response observed with vinegar ingestion. Vinegar-containing foods range from mustard, to vinaigrette dressings, to pickled foods. The benefits of vinegar ingestion with carbohydrates are dose-dependent, meaning that adding even small amounts to meals can help. Making a conscious effort to incorporate these foods into meals, in addition to an overall healthy lifestyle, could provide an additional tool for diabetics and nondiabetics alike to consume carbohydrates in a healthier manner.
ContributorsJimenez, Gabriela (Author) / Johnston, Carol (Thesis director) / Lespron, Christy (Committee member) / School of Nutrition and Health Promotion (Contributor) / School of International Letters and Cultures (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Honey bees (Apis mellifera) are responsible for pollinating nearly 80\% of all pollinated plants, meaning humans depend on honey bees to pollinate many staple crops. The success or failure of a colony is vital to global food production. There are various complex factors that can contribute to a colony's failure, including pesticides. Neonicotoids are a popular pesticide that have been used in recent times. In this study we concern ourselves with pesticides and its impact on honey bee colonies. Previous investigations that we draw significant inspiration from include Khoury et Al's \emph{A Quantitative Model of Honey Bee Colony Population Dynamics}, Henry et Al's \emph{A Common Pesticide Decreases Foraging Success and Survival in Honey Bees}, and Brown's \emph{ Mathematical Models of Honey Bee Populations: Rapid Population Decline}. In this project we extend a mathematical model to investigate the impact of pesticides on a honey bee colony, with birth rates and death rates being dependent on pesticides, and we see how these death rates influence the growth of a colony. Our studies have found an equilibrium point that depends on pesticides. Trace amounts of pesticide are detrimental as they not only affect death rates, but birth rates as well.
ContributorsSalinas, Armando (Author) / Vaz, Paul (Thesis director) / Jones, Donald (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
A Guide to Financial Mathematics is a comprehensive and easy-to-use study guide for students studying for the one of the first actuarial exams, Exam FM. While there are many resources available to students to study for these exams, this study is free to the students and offers an approach to the material similar to that of which is presented in class at ASU. The guide is available to students and professors in the new Actuarial Science degree program offered by ASU. There are twelve chapters, including financial calculator tips, detailed notes, examples, and practice exercises. Included at the end of the guide is a list of referenced material.
ContributorsDougher, Caroline Marie (Author) / Milovanovic, Jelena (Thesis director) / Boggess, May (Committee member) / Barrett, The Honors College (Contributor) / Department of Information Systems (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
Covering subsequences with sets of permutations arises in many applications, including event-sequence testing. Given a set of subsequences to cover, one is often interested in knowing the fewest number of permutations required to cover each subsequence, and in finding an explicit construction of such a set of permutations that has size close to or equal to the minimum possible. The construction of such permutation coverings has proven to be computationally difficult. While many examples for permutations of small length have been found, and strong asymptotic behavior is known, there are few explicit constructions for permutations of intermediate lengths. Most of these are generated from scratch using greedy algorithms. We explore a different approach here. Starting with a set of permutations with the desired coverage properties, we compute local changes to individual permutations that retain the total coverage of the set. By choosing these local changes so as to make one permutation less "essential" in maintaining the coverage of the set, our method attempts to make a permutation completely non-essential, so it can be removed without sacrificing total coverage. We develop a post-optimization method to do this and present results on sequence covering arrays and other types of permutation covering problems demonstrating that it is surprisingly effective.
ContributorsMurray, Patrick Charles (Author) / Colbourn, Charles (Thesis director) / Czygrinow, Andrzej (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor)
Created2014-12
Description
Deconvolution of noisy data is an ill-posed problem, and requires some form of regularization to stabilize its solution. Tikhonov regularization is the most common method used, but it depends on the choice of a regularization parameter λ which must generally be estimated using one of several common methods. These methods can be computationally intensive, so I consider their behavior when only a portion of the sampled data is used. I show that the results of these methods converge as the sampling resolution increases, and use this to suggest a method of downsampling to estimate λ. I then present numerical results showing that this method can be feasible, and propose future avenues of inquiry.
ContributorsHansen, Jakob Kristian (Author) / Renaut, Rosemary (Thesis director) / Cochran, Douglas (Committee member) / Barrett, The Honors College (Contributor) / School of Music (Contributor) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
The development of the Diabetic Physiological state is influenced by the Receptor for Advanced Glycation End Products (RAGE). This receptor was discovered in 1992, and the accumulation of research on this subject has been extensive. Structural characterization studies of the RAGE protein have shown that it is a transmembrane protein that binds a number of different motile ligands. The diversity of ligands that can attach to the binding domain is the primary factor that allows for RAGE to exhibit its wide-range effects on host cells. Two different studies were completed: one study dealt with the role of IAPP in beta cell death, and the second study was related to RAGE influence on cardiomyocytes and, more specifically, it was related to cardiac cell death. After the completion of the two studies, a comprehensive report was written for each topic. The two papers were merged into a single document. Molecular studies are important for understanding the underlying mechanisms that motivate pathophysiological presentation. In addition to a molecular understanding of the development of diabetes, a clinical research study was completed through the examination of appropriate literature sources. This clinical aspect allowed for the progression of different phases in the research process. A relationship between vinegar and lower plasma glucose was found. The exact mechanism behind this relationship will be studied in the future.
ContributorsGonzalez, Matthew Joseph (Author) / Johnston, Carol (Thesis director) / Collins, Michael (Committee member) / Barrett, The Honors College (Contributor) / School of Nutrition and Health Promotion (Contributor)
Created2015-05
Description
Background: The prevalence of childhood obesity has disproportionately affected Latino youth. This increase in obesity is seen with an increased incidence of Type 2 Diabetes. Objective/Hypothesis: The objective of this study was to determine the effects of a community based lifestyle intervention, which encompassed nutrition education and physical activity, on diabetes risk in pre-diabetic Latino adolescents. Diabetes risk was assessed using pancreatic beta cell function as measured by proinsulin: insulin ratio. It was hypothesized that reductions in added sugar intake and reductions in saturated fat intake will be associated with improved beta cell function as measured by proinsulin: insulin ratio. Study Design/Participants: In this quasi-experimental study design, n=17 pre-diabetic Latino adolescents between the ages of 14-16 participated in a lifestyle intervention. Methods: Anthropometric measurements (weight, height, waist circumference, BMI) and body composition (body %) were determined for all participants at baseline and post intervention. Fasting proinsulin (PI), fasting insulin (I) and 2hr-OGTT were also determined. Dietary intake was measured using the Block Kids Food Screener for kids ages 2-17y (2007). The intervention consisted of nutrition education classes and physical activity sessions for 12 weeks. Results: We found significant decreases in body fat % following the intervention. There were no significant decreases in fasting insulin. Proinsulin significantly decreased. However we did no see a significant change in PI/I (p= 0.003). Dietary behaviors of added sugar (p=0.03) and saturated fat (p=0.04) showed significant decreases. No significant associations were found between changes in added sugar to improvements in beta cell function, r=0.072, p-value= 0.7. We also did not observe significant associations between reductions in saturated fat intake and improvements in beta cell function, r=0.152, p-value =0.6. Conclusions: We concluded that a 12-week lifestyle intervention resulted in significant changes in dietary behaviors. These changes were not however associated with improvements in beta cell function.
ContributorsKaur, Manroop (Author) / Shaibi, Gabriel (Thesis director) / Bruening, Meredith (Committee member) / Barrett, The Honors College (Contributor) / School of Nutrition and Health Promotion (Contributor)
Created2015-05
Description
This paper focuses on the Szemerédi regularity lemma, a result in the field of extremal graph theory. The lemma says that every graph can be partitioned into bounded equal parts such that most edges of the graph span these partitions, and these edges are distributed in a fairly uniform way. Definitions and notation will be established, leading to explorations of three proofs of the regularity lemma. These are a version of the original proof, a Pythagoras proof utilizing elemental geometry, and a proof utilizing concepts of spectral graph theory. This paper is intended to supplement the proofs with background information about the concepts utilized. Furthermore, it is the hope that this paper will serve as another resource for students and others to begin study of the regularity lemma.
ContributorsByrne, Michael John (Author) / Czygrinow, Andrzej (Thesis director) / Kierstead, Hal (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2015-05
Description
Lights Out is a puzzle game where the goal is to turn off all the lights on a nxn board starting from a random configuration. In order to find the solution of a configuration, the game is constructed using a matrix basis in the span of the field Z mod 2.This the game can be modeled by the system Ap=s which will be the center of the investigation when determining the solvability for any n×n board since A is not always invertable leading to some interesting cases. The goal of this thesis was to construct a model that will allow the player to solve for the pushes to attain the zero-state for an nxn system. Constructing the model gave a procedure that will allow to solve the puzzle game. The procedure presented here first uses a simple clearing technique (valid for any board size) to turn off all the lights except in the last row, which we call the standard-clear. The heart of the technique, is to give a way to use the information about which lights remain lit in the last row to determine which switches in the first row need to be pushed before the standard-clear. This part of the solution algorithm we call the first row adjustment, and it depends heavily on the specific board size n of the problem. Finally, after these first row pushes are made, the standard clear will now turn off all the lights including (seemingly magically) the last row. Thus the solution to the Lights Out puzzle of a given size is reduced to finding a first row adjustment for that size. (Please refer to the actual thesis for the full abstract)
ContributorsBarraza, Jay Romeo (Author) / Vaz, Paul (Thesis director) / Paupert, Julien (Committee member) / Civil, Environmental and Sustainable Engineering Programs (Contributor) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05