Immanuel's DIMACS REU Webpage

Contact Information:
Office: CoRE 451
Email: wim1 at email dot arizona dot edu

Project Information:
PowerPoint Presentation 1 (12 Jun 2009: preliminary report on some background and goals)
PowerPoint Presentation 2 (17 Jul 2009: report of results to date)
My project has to do with port security, cost of detection, and game theory. So far, the particular avenues of research we are investigating are the multiple-port problem and retesting using many (approaching infinite) stochastically independent sensors.
My mentor is Dr. Paul Kantor.

Program Information:
For specific information: DIMACS REU Webpage
For more general information: NSF REU Webpage

Weekly Log (beginning dates noted):
Week 1 (1 June): Arrival and orientation. Began background reading on game theory; Dr. Kantor arrived on Thursday, and we had our first meeting.
Week 2 (8 June): Continued background reading and familiarized myself with Dr. Menkov's project-related software. Gave a preliminary presentation (above).
Week 3 (15 June): Made progress solving some example game theory problems by hand and with MATLAB software. Dr. Kantor left Wednesday; we are corresponding via email.
Week 4 (22 June): Began reading and sample problems relating to infinite games. Began analyzing Dr. Kantor's multiple-port problem model.
Week 5 (29 June): Dr. Kantor returned Monday, and we had a meeting. I began looking into using linear programming for solutions to continuous games and solutions to 2-player continuous games where each player controls multiple variables. I also went on a group field trip to Telcordia.
Week 6 (6 July): I met with Dr. Kantor again, and we discussed both problems. I made some progress into the retesting problem through determining the validity of some conjectures about the use of multiple sensors. Went on the group field trip to Bell Labs.
Week 7 (13 July): Dr. Kantor sent me a linear programming model of the multi-port problem, which I worked on through MATLAB to find solutions to the game for given values of the applicable constants. Prepared and gave a summary presentation (above) of my results from the program.
Week 8 (20 July): Experimented with the LP model and a possible solution. Departure on Friday.

References and Resources Used:
Davis, Morton D., Game Theory: A Nontechnical Introduction. Basic Books, Inc. 1970.
McKinsey, J.C.C., Introduction to the Theory of Games. McGraw-Hill Book Company, Inc. 1952.
Luce and Raiffa, Games and Decisions: Introduction and Critical Survey. John Wiley and Sons, Inc. 1957.
Karlin, Samuel, Mathematical Methods and Theory in Games, Programming, and Economics. Addison-Wesley 1959.
Wolfram|Alpha Computational Knowledge Engine.

About Me:
I am a student at the University of Arizona going into my final year as a math major. I have particular interests in combinatorics, graph theory, and game theory, and plan to start graduate study in mathematics toward a PhD.
My personal UA webpage is here.

Last modification 20 July 2009