Summer Undergraduate Research 2007

The John S. Rogers Science Research Program prepares outstanding students for careers in the sciences by supporting collaborative scientific research between students and faculty. The program aims to attract and retain outstanding students and faculty in the mathematical and natural sciences.

Detecting statistical signal in genetic linkage and association studies

Linkage disequilibrium refers to the fact that alleles at different loci co-occur on the same haplotype more often than expected by chance. Many studies have found haplotype block structure exhibited by alleles at nearby loci. Haplotype blocks can be useful in understanding the association between certain genomic markers and traits. This project will examine the genetic variations known as single nucleotide polymorphisms (SNPs). In particular, we will look at statistical measures that can be used to quantify pairs or multiple-locus linkage disequilibrium in SNPs. We will employ those measures to investigate possible approaches to detecting the block structure of the SNPs haplotype

Michael Sanders '08, Nick Tiller '09 and Yung-Pin Chen (Associate Professor)

Poster - Measuring Linkage Disequilibrium

Ubiquitous Computing, Sensor Networks and Security

An emerging class of small computers, outfitted with sensors and linked by radio transceivers, can form perceptive sensor networks that will more intimately connect the Internet to the real world of birds and trees, ships and bridges. MIT Technology Review lists sensor networks as one of "Ten Emerging Technologies That Will Change the World." We worked on three projects: First, we developed three additional TinyOS lab exercises where sensor nodes are remotely controlled. Second, we experimented with and developed lab exercises for the new Sun SPOT sensor nodes, with are programmed in Java Micro Edition. Third, we studied security and privacy issues. Currently available products such as the Nike + iPod Sport Kit are vulnerable to tracking because no secret codes are used. For the Sun SPOTs, we implemented traditional public key cryptography (RSA) and elliptic curve cryptography (ECC) in Java Micro Edition. Our measurements indicate that while a Sun SPOT is between 10 and 110 times slower than a 5-year old desktop computer, ECC is significantly faster than RSA. Thus, ECC has strong potential as a building block of security and privacy solutions for sensor networks and ubiquitous computing.

Elgin Dean '08, Kevin Imber '09 and Jens Mache, Department of Mathematical Sciences, Lewis & Clark College. (Joint work with Jeffrey Springer, University of Arizona, and William Sehorn, Whitworth; partially funded by a .Research Experiences for Undergraduates. grant from the National Science Foundation.)

Poster - Sensor Network Lab Exercises

Listening to Orbifolds and Orbigraphs

There is a beautiful pairing of theorems between the smooth world of geometric shapes and the discrete world of graph theory. For example, geometers proved that you can hear the volume of a smooth object. Using natural definitions of the volume and ‘sound’ of a graph, graph theorists obtained the analogous result. This summer we ask ‘What happens to this pairing if the geometric objects have sharp corners?’ These pointy shapes are called orbifolds. Our challenge is to define what an orbigraph should be, and then see if geometric facts about orbifolds correspond to graph theoretic facts about orbigraphs.

Parker Lewis '08 and Jessica Minnier '07 plus REU-RET students Shawna Dehler, Karsten Gimre and Indra Shottland, with Liz Stanhope (Asst. Professor)

Poster - Countable Families of Graphs