"Profitability in Market of Competing Complementary Goods in Terms of Quality"
Research was previously done on examining a market between a good produced by one producer and a perfect complementary good produced by more than one producer. The results led to this paper in which research was done in an attempt to expand on ideas of that paper. The idea is that we have complementary goods are being produced on two sides of a market, monopoly and oligopoly. The good being produced on the oligopoly side will have a differentiating quality product depending on the decision of the leader in a Stackelberg style model. The questions being asked deals with profitability of a firm who decided to differentiate themselves in terms of quality. This was found but depends on the preference parameters of the consumers in the market.
Advisor: Caroline Padgett, Ph.D.
"Economic Effects of Regulations On Barbering and Cosmetology"
For over a century individual states have been regulating the barber and cosmetology industry. The work done in this paper outlines both occupations by going over a brief history of licensing, regulations in the industry, state level economic factors that may influence the industry, and more. A potential new way to measure the barriers to entry, and the effects of regulations within this industry are proposed in this paper.
Advisor: David Franck, Ph.D.
"A Rank-Sum Test for Significance of Difference in Copy Variation"
Copy number variation (CNV) results from duplications and deletions of genomic DNA, and is known to correlate with a number of genetic diseases. Typically, a subject being screened for a particular disease will have measurements from k sections of DNA, and these measurements are compared to those from a collection of N-controls. Here we describe a rank sum statistic useful for determining whether the subject is at risk for disease.
We derive the exact distribution of this statistic and compare the exact distribution to an approximate distribution proposed in the literature. We demonstrate that use of the approximate distribution of the rank sum statistic results in higher than nominal Type 1 error rate and an exaggeration of power.
Advisor: Scott Linder, Ph.D. [Submitted for Publication]
"Closing the Gap on Multifold Triple Systems"
In part of a dissertation completed by N. Newman, he fully solved the problem of lambda-fold 4-cycle systems, but only partially solved the problem of enclosing a triple system of TS(v, lambda) in a triple system of TS(v + s, lambda + m). Enclosings were found for all admissible values outside of a quadratic gap. This problem of enclosing a triple system in another one has not been fully solved yet, but research I am doing under his direction attempts to close the gap and fully solve this problem.
Advisor: Nicholas Newman, Ph.D.
"New Method to Find Overall Best Lifter at a Powerlifting Meet"
I have found that in the sport of powerlifting to determine the best overall lifter they use one of six methods. In my research I am going to focus on the one widely used in the United States, namely the Wilks formula. This formula shows bias towards absolute strength versus relative strength. I have derived a much simpler formula that uses the age, bodyweight, and total weight lifted to give an unbiased decision when determining the best overall lifter.
"Brief History on Mathematical Optimization and the Applications to Profit Maximization"
Mathematical optimization is present in many different disciplines. It is used to find optimal solutions to problems dealing with maximums and minimums. We can see it is an applied field of mathematics, but where did it come from and how were problems solved historically? In this research, we are going to consider the different types of optimization used throughout history. Specifically, we are going to examine how ancient civilizations solved their optimization problems, and how their methods compare to the modern way of doing optimization with a profit maximization problem.
Advisor: Sharon O'Kelley, Ph.D.