• On Enumeration of Conjugacy Classes of Coxeter Elements. (With H.S. Mortveit). Proceedings of the AMS. In press.
• Order Independence in Asynchronous Cellular Automata. (With J. McCammond, H.S. Mortveit). Journal of Cellular Automata. 3 (1), 2008:37-56.
• Locational Market Power in Network Constrained Markets. (With K. Atkins, J. Chen, A. Kumar, A. Marathe). To appear in Journal of Economic Behavior and Organization, 2008.
• Role of Network and Production Capacity in Allocating Market Power. (With J. Chen, A. Marathe). Proceedings of the Trans-Atlantic INFRADAY Conference on Applied Infrastructure Modeling and Policy Analysis. College Park, MD. November, 2007.
• Protesters Lack Key Facts on Nukes, UC. Daily Nexus, Issue 121 / Volume 87. Thursday, May 10, 2007.
• Locational Market Power in Network Constrained Markets. (With K. Atkins, J. Chen, A. Kumar, A. Marathe). Proceedings of the 29th IAEE Interational Conference. Potsdam, Germany. June 2006.
• Juggling By The Numbers. (Book review). Math Horizons, Feb. 2004.
• Thinking Outside the Box and Over the Elephant. (With M. Banister, M. Smukler). The Journal of Undergraduate Mathematics and Its Applications. 24 (3), 2003.
I've also got a bunch of papers in the Journal of Unpublished Results. As you can see from their website, this is a very difficult place to publish, but I have managed to crack though their system on multiple occasions.
Submitted
• Dynamics Groups of Asynchronous Cellular Automata. (With J. McCammond, H.S. Mortveit)
• A Novel Proof of the Heine-Borel Theorem. (With B. Rabern, L. Rabern)
• Equivalences on Acyclic Orientations. (With H.S. Mortveit.)
• Cycle Equivalence of Graph Dynamical Systems. (With H.S. Mortveit.)
• Role of Network and Production Capacity in Allocating Market Power. (With J. Chen, A. Marathe).
• Truthful Auctions in Resource Constrained Markets. (With J. Chen, A. Marathe, M.V. Marathe, V.S.A. Kumar).
Completed
• Coxeter Theory and Discrete Dynamical Systems. Ph.D. Thesis. University of California, Santa Barbara, 2008.
• Braids and Juggling Patterns. Senior Thesis. Harvey Mudd College, 2003.
On hold (but almost done)
• Computing Special Jordan Pencils. (With E. Blew, Y. Grabovsky, M. Jacobs, J. Quah, E. Ruppin.) pdf
• Braids and Juggling Patterns. (With M. Orrison). pdf
In Progress
• Role of Transmissibility and Network Topology on Disease
Dynamics. (With A. Apolloni)
• Analysis of Disease Spread by Age-groups. (With
R. Beckman, M. Khan, E. Nsoesie).
• Morphisms of Graph Dynamical Systems. (With H.S. Mortveit.)
• Automorphism Groups of Stochastic Sequential Dynamical Systems.
• Instability of Stochastic Sequential Dynamical Systems. (With H.S. Mortveit, A. Kumar.)
• Mathematical and Computational Aspects of Market Power over Networks. (With J. Chen, V.S.A. Kumar, A. Marathe).
• Applications of Rank Functions of Graphs
me <--> Jiangzhuo Chen <--> László Lovász <--> Paul
Erdős
me <--> Achla Marathe <--> Vance Faber <--> Paul
Erdős
The database probably isn't aware, though, because the path goes through an economics paper.
Speaking of small-world network measures, I appeared as a unicyclist in the movie "Slackers". Technically, I was a "special ability extra", which despite not paying much more than a regular extra, does have the perk that the actors actually thought we were cool. It took over 12 hours to film what ended up being roughly a 5-second scene. But Margaret Easley had a small role in the film (and it wasn't even on a unicycle), and she has a Kevin Bacon number of 1 (From "We Married Margo"). So, if this counts, my Erdős-Bacon number is 5. In contrast, Stephen Hawking has an Erdős-Bacon number of 7, and Carl Sagan and Richard Feynman have Erdős-Bacon numbers of 6.
I am also the undisputed world-record holder in having the lowest Erdős-Bacon-Bigfoot number. As everybody knows, Bigfoot was a regular in the Monster Truck Show for years, and in the late 1990s, I performed (juggled) in the opening of several shows in the now-demolished Kingdome. This gives me a Bigfoot number of 1, and an Erdős-Bacon-Bigfoot number of 2+3+1=6.