Digital Commons Network^™

Mathematically Modeling Pcr: An Asymptotic Approximation With Potential For Optimization, Martha J. Garlick

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

A mathematical model for PCR (Polymerase Chain Reaction) is developed using the law of mass action. Differential equations are written from the chemical equations, preserving the detail of the complementary DNA single strand being extended one bas e pair at a time. The equations for the annealing stage are solved analytically. The method of multiple scales is used to approximate solutions for the extension stage. A map is then developed from the solutions to simulate PCR. The advantage of this model is the ability to use the map to optimize the process. Our results suggest that dynamically optimizing the extension …

Sas Macro For Hierarchical Dependence In Meta Analysis, Matthew Wayne Maw

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This project implemented a simple and useful SAS (Statistical Analysis Software) macro for meta-analysis. The macro was specifically designed for hierarchically dependent meta-analysis but may also be used for independent meta-analysis. Two data files are necessary for this macro. One data file contains the study names, control and treatment group sizes with corresponding means and standard errors, covariates to be tested, an indicator variable noting hierarchically dependent study groups, and a variable providing the degrees of freedom for interdependent studies. The second file contains a variance/covariance matrix for the studies. The macro returns useful information such as study estimates and …

Black-Scholes And Extended Black-Scholes Models: A Comparative Statistical Analysis, Bradley Thomas Bush

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Much research has been done on options pricing. Black and Scholes [12] set the benchmark in 1973 with their model for arbitrage-free, risk-neutral options valuation. Arbitrage-free refers to a market environment where prices are such that trading opportunities with no risk do not exist and risk-neutral commodities earn a risk free interest rate. Since then the literature has seen a multitude of models improving the fit of the traditional Black -Scholes (BS) model. A brief overview of options and these models is given. A derivation and discussion of BS is followed by a derivation and discussion of the Extended Black-Scholes …

Decomposing Vector Space Representations Of The Lie Algebras S[2c And S[2r, Brian W. Gleason

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

It is known that any finite-dimensional representation of a semi-simple Lie algebra is decomposable into a direct sum of irreducible representations. Here we prove some theoretical results that allow us to construct an efficient algorithm for computing such a decomposition for representations of s[2C and s[2R. We then implement this algorithm in a procedure for the computer algebra system Maple that will quickly and easily perform the decomposition. We also give several examples of this decomposition performed by the procedure in order to illustrate its advantages over calculations done ‘by hand'.

Carlisle And Intermountain Indian Schools: A Comparison Of Native American Boarding School Models, Danene Dustin

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

American Indian educational policy has had a troubled existence from its inception, as exemplified by the Pratt model of the Carlisle Indian School that was established in 1879. Pratt's model entailed the elimination of culture from the Native American students, often administering inhumane punishments for inappropriate behavior and never allowing parental visits. However, not all of the models that emerged from Pratt's have been negative. One positive example of American Indian education is the Intermountain Indian School founded at Brigham City, Utah, in 1950. Intermountain Indian School (IIS) functioned for 34 years, educating thousands of students with the goal of …

Design Guidelines For The Historic Downtown Of The City Of St. George, Utah, Bronson R. Tatton

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

This document proposes historic preservation guidelines for the downtown area of the City of St. George, Utah. It grew from a summer internship with the city where I took inventory of the streetscape in the Historic Downtown and prepared recommendations in the form of a PowerPoint Presentation that was given to the city council. This paper summarizes the summer internship and introduces a more appropriate approach based on reflection of the intern ship. The new approach involves a thorough inventory of the historic character, in depth research of the historic elements that contribute to the historic character, development of design …

A Catalog And The Perceived Effectiveness Of Stormwater Best Management Practices Bmps Used On Municipal Sites In Northern Utah, Saadia E. Ahmed

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Stormwater, as a result of hydrological events and urbanization, has contributed to problem s of water quality and flooding. Stormwater picks up pollutants and flows into sewer systems ultimately impacting water sheds and wildlife habitat. The primary method to control storm water discharge is by the use of best management practices. This research seeks to evaluate the perceived effectiveness of stormwater structural Best Management Practice s (BMPs) installed on municipal sites in northern Utah. A representative sample of sites is chosen using a snowballing sampling method. Selected sites are visited and surveys addressing effectiveness and maintenance issue s are answered …

Combating Childhood Obesity: Changing Our Environment, Anna Mitchell

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

A review of literature was conducted to identify risk factors and prevention strategies for childhood obesity. Factors contributing to childhood obesity include poor food choices, physical inactivity, and genetics. Complications of obesity include respiratory, musculoskeletal, cardiovascular, and endocrine diseases, cancer, gallbladder disease, poor health status, depression, low self-esteem, and social withdrawal. Since childhood obesity, largely due to the environment that children live in today, is increasing in the United States, strategies must be implemented that will contribute to the prevention of childhood obesity. Changes that promote a healthy environment must involve all aspects of society to ensure that the prevention …

A Method For Finding Standard Error Estimates For Rma Expression Levels Using Bootstrap, Gabriel Nicholas

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Oligonucleotide arrays are used in many applications. Affymetrix GeneChip arrays are widely used. Before researchers can use the information from these arrays, the raw data must be transformed and summarized into a more meaningful and usable form. One of the more popular methods for doing so is RMA (Robust Multi-array Analysis).

A problem with RMA is that the end result (estimated gene expression levels) is based on a fairly complicated process that is unusual. Specifically, there is no closed-form estimate of standard errors for the estimated gene expression levels. The current recommendation is to use a naive estimate for the …

Rapid Identification: River Guides, Storytelling, And Sharing Identity, Alisha Paxton

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

I moved to Moab from another Utah town in the spring of 2005 to train and guide on the Colorado River. Over the course of two summers I rowed or paddled on three Colorado River sections-Fisher Towers, Westwater and Cataract Canyon-as well as Desolation/Gray Canyons on the Green River and the Main Fork of the Salmon River. The next fall, during my first semester of graduate study in folklore, I became interested in studying river guides as a folk group. I wanted to study the formation of "community" based upon both guide and passenger interactions on river trips. However, because …

Capstone Mathematics And Technology: A Collection Of Mathematical Technology Enhanced Activities For Students And Teachers, Heidi Eastman

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The purpose of this project is to provide an introduction to how technology can be used in the mathematical classroom to enhance students' learning of mathematics, while at the same time leading students to a richer and deeper understanding of those mathematical concepts. The topics were selected based on their relevance to the Utah State Core Curriculum for middle and secondary mathematics courses. It was intended that each lesson plan would challenge a preservice mathematics educator to build relationships between different areas of mathematics and/or to create deeper understandings of specific mathematical concepts. At the same time many of the …