Research Projects and Internships
Undergraduate Research Projects
Sergei Temkin, a 2007 graduate, majored in computer science. As a semester project for a linear algebra course, Sergei created a graphics software package that used matrix manipulation to visualize linear transformations. Through discussions with faculty in biology and mathematics, it became evident that Sergei's interests, and the flexibility of his graphics project were a great match for a emerging research effort involving c. elegans, a roundworm that has become an important model organism for the study of genetics, cell biology and neuroscience. Sergei is presently working on a system that captures video of the c. elegans, saves the video as individual images and analyzes their motion using image detection algorithms. As his project develops, it will be used as a tool for gathering information for numerous projects conducted by students and faculty working with c. elegans.
Emmy Scott, a 2006 Honors graduate, majored in mathematics. During her Sophomore, Junior and Senior years she explored problems in graph theory, dealing with the crossing numbers of the Cartesian product of complete bipartite graphs with cycles. Through her research, she joined the effort to solve open problems that have perplexed and engaged mathematicians since 1945. Emmy made great contributions to this area of research, having determined a general solution for the upper bound of the crossing number for Kr,s x Cn.
Lucy Watson, Parisa Fatheddin, Kacie Kleja, and Renee Torres , worked during the Spring of 2006 to generate examples of Plummer-Whitney systems. This project is an outgrowth of an earlier undergraduate research project by Jennifer Rowe (since graduated) on the properties of matroids and faculty research on well-covered graphs. The concept of a Plummer-Whitney system is a generalization of matroids, which were introduced by Whitney in 1935, and well-covered graphs, which were introduced by Plummer in 1970. All three of these concepts are examples of independence or hereditary systems and have the appeal that the greedy algorithm can be used to efficiently find a largest independent set in the system. The work of these students will be used to help discover patterns and establish conjectures about the properties of Plummer-Whitney systems.
David Ells, a 2006 graduate, has pursued research in Genetic Algorithms (GA), an area of computer science that uses strings of bits (1's and 0's) to encode problem solutions, much as DNA uses strings of nucleotides (A's, T's, G's, and C's) to encode instructions for life. Ells' research began with the observation of Belmont Alumnus Marshall Graves that much of the cell's DNA is organized into rings known as plasmids, and that GA's would benefit from a similar organization. Ells proved an interesting result about plasmids, and continues to explore the pros and cons of this form of GA.
Jeremy Stephens, a 2005 graduate, completed a generator for locally-2-connected (L2C) graphs as part of a project in graph theory under the direction of Dr. Glenn Acree. L2C graphs are conjectured, but not proven, to be Hamiltonian, and the exploration and visualization of their properties has been a long-term project for Dr. Acree and his students. Jeremy's L2C generator gave him and his classmates a new tool for testing conjectures, and was compatible with the GraphViewer program developed by 2004 graduate Justin Jordan. GraphViewer compatibility means that Jeremy's graphs--some with hundreds of nodes and thousands of links--can be visualized and manipulated with the GraphViewer interface, allowing insights hard to derive from the abstract graph descriptions. Together with Graphviewer, Jeremy's L2C generator provides a unique platform for further exploration of Hamiltonian graphs.
