Current Research Activity
I currently have two active research plans, one well underway and the other brewing.
Presently, I'm being funded through a UDMPU mini-grant to investigate connected graphs,
endeavoring to categorize which graphs possess a property called "group-magicness."
It's a lot to explain in this format, but you may click here
to read the proposal.
The second idea I have brewing involves tracking down sources of misinformation
within an intelligence or general communication network. If we consider directed graphs
with no terminal vertices, is it possible to time-stamp the edges in advance so that, if
the communications are then run in repetition, any misinforming vertex can be identified?
If so, the graph is "teleorectory," and the time-stamp solution is its "teleology."
Ideas for Senior Research Projects
If you're looking for an idea for a Mathematics & Software Engineering Seminar project, read on.
I've enjoyed working on projects with math students before, dealing with such topics as
redundancy in circuit design and the mechanics of motion of backing up a car trailer.
I'd love to hear your ideas, or perhaps one of the following might interest you:
- Comparitive ratings systems in sports/games leagues
e.g. Sagarin ratings, BCS ratings
- Analysis of Baseball Strategy using Markov chains
- Artificial Intelligence to Predict Opponent's Decisions
Previous Math and Science Research
You read earlier about what first inspired me to begin mathematics research;
for the paper that resulted, which was published in Congressus Numerantium.
We later submitted two more papers to Congressus.
This paper discusses the use of
algebraic factorization to create a path-generation algorithm for Cayley groups in
general -- this could be an important breakthrough in parallel processing. Meanwhile,
I continued to research the "k-disjoint path problem," and have invented the "Nova Graph,"
which provides a guaranteed three disjoint paths in an symmetry group-styled interconnection
network, using the minimum number of edges and vertices to do so.
Click here for the Nova Graph paper.
Click here for the paper of which, to date, I am most proud.
In this paper, I prove not only that my invention can be generalized,
but that its generalization outperforms all other graphs of this type.
On occasion, I also have the pleasure of applying mathematics to other fields.
Mark Benvenuto, my incredibly prolific colleague from chemistry, asked me to help
out with some statistical analysis regarding the chemical compositions of ancient
coins. Click here for the first and here for
the second of the papers we've co-authored
with undergrduate chemistry students in the field of archaeological chemistry.