Undergraduate Research Projects

These are undergraduate in the sense of not requiring research-level mathematical probability knowledge (see Open Problems for ones which do). On the other hand they are serious in that successful results will often become a small part of some future published scholarly paper. For undergraduate ``course projects" which are less serious, click here.

As of March 2008 three students are working on projects, indicated by [Name].

Contact me before starting work!

Data collection

Route-lengths in transportation networks. I want the following type of data. Take the 10 [or 20 or 40] largest cities in some State or Country, and find the distances between each pair by road [or rail] and in straight line. See Figure 1 of this paper for an example; but I would like to expand the 2 data-sets there to 10 data-sets.
Amazon.com book reviews. Sample books with (say) 30-100 reviews. For each review, note date posted and number of favorable votes. There is a strong association between these variables, which one might model by any of numerous theoretical models. But first I want to see some exploratory data analysis of some data. [Robert Huang]
Coincidences in Wikipedia. My co-author of this draft paper has disappeared without a trace, and I want someone to finish the data collection. Basically this requires 40 hours trawling Wikipedia to estimate numbers of pages on different topics.

Simulation - drawing static pictures

Empires and percolation I would like to see pictures of this model for different choices of rate function.
A model for city growth. Here is a slightly complicated model for city growth in which cites have positions, populations and spheres of influence. It's not hard to simulate the process, but I want some pretty pictures of the spheres of influence, in the style of the "stable allocations" picture at the bottom of this page.

Simulation - drawing moving pictures

The processes below are very easy to simulate, but I want "moving pictures", in Java or whatever, to illustrate their dynamics.

A parking process. This is the process studied in this paper. The point is that there are 3 different limiting regimes corresponding to different spatial regions and time scalings.
Another one bites the dust. This birth-and-assassination process would look good accompanied by the Queen song.

Inventing good heuristic algorithms and writing code

Optimal spatial networks. Given positions of n cities, we want to connect them with a road network which is optimal according to certain criteria. Finding the optimal network is not easy --see section 1.2 of this paper for details on the project. [Julian Shun]

Math theory

I don't encourage undergrads to attempt to do new math research. [Tamar Lando] is doing a Master's thesis involving some theory for the "Optimal spatial networks" project.

Previous projects and students

In Summer 2006 Fayd Shelley worked on the "Coincidences in Wikipedia" project.
In Fall 2006 Dennis Moy did an undergraduate honors thesis in A regression model using common baseball statistics to project offensive and defensive efficiency.
In Spring 2007 I mentored a URAP and VIGRE group of students (Yanjiao Cheng. Jesse Friedman, Yu-Jay Huoh, Wayne Lee, Harrison Liu) who produced Figure 1 of this paper.