Exploring Large Knots
This is an interdisciplinary project with faculty in Mathematics from WKU and from the University of North Carolina at Charlotte. A knot consists of one or more non-intersecting curves in 3-space. When projected to a plane, a knot can be viewed as a 4-regular planar graph. We are researching methods to generate large knots, to find algorithms to embed them in 3D, the determine bounds on the length of a rope needed to tie a knots, and address other interesting questions.
This research was partially supported by two NSF grants and so far 3 graduate students have written their thesis on a topic related to this research.
Cyber defense: Generating background traffic
I am a member in a large project which deals with many aspects of cyber defense. My current topic relates to developing software to run a network testbed. The software provides the necessary support for users to create and execute test runs to evaluate sofware modules which were developed to detect network attacks and/or anomalies.
This research is more of a playful nature. Take a number, reverse its digits and then add the original number and its reverse. Repeat the process with the number obtained until a palindrome is reached (a number which is the same backwards as forwards). There seem to be numbers (in base 10) which never lead to a palindrome. 'Seems' because nobody has a proof, but for at least one number (196) this process has been repeated until a number with several million digits was obtained - and still not palindrome. This research asks what happens if the numbers are subtracted and not added - and the absolute value of the result is taken. It turns out that there are palindromes as well as cycles. Both can be described using tools from mathematics and computer science.