Undergraduate Seminar In Mathematics

Purpose: This seminar is for undergraduate students to present their progress reports / results from their summer research /REU / senior / honors projects.

Place: OHM 139

Time: Thursday 4:30

Organizer: Wai Lau

Abstract

8/28/08

Iterated Line Graphs

In this presentation, I describe line graphs and iterated line graphs.  Also explored is the connection between iterated line graphs and the growth of maximum and minimum degrees, as established by Hartke and Higgins.  Finally, an algorithmic approach to solving problems involving maximum degree growth of iterated line graphs is discussed.

8/21/08

A Linear Trend Test for Including Duplicate Genotype Data in a Genetic Test for Association

Student Researchers:  Bryce Borchers (Rose-Hulman Institute of Technology), Marshall Brown (Seattle Pacific University), Brian McLellan (Hope College)
Faculty Mentors: Nathan Tintle (Hope College), Airat Bekmetjev (Hope College)

In genome wide association studies researchers often duplicate genotype between 2 and 10% of the sample as a quality control measure.  Typically, duplicate data is discarded before testing for association between genotype and phenotype.  However, we demonstrate that statistical power is increased by including duplicate genotype data in the test.  To include duplicate genotype data we propose a modified linear trend test (LTT) of association and demonstrate its asymptotic properties.  Further, we demonstrate that in many practical cases, the most cost effective use of resources would be to collect duplicate genotype data on the entire sample, instead of only a small fraction.  We present software that assists researchers in deciding if the collection of duplicate genotype data is cost-effective, as well as to compute the modified LTT.

Work supported by NIH R15-HG004543 and the Tanis Fund for statistics research at Hope College.