What is the term project?

We'll devote a class meeting in December to reports of your proposals, allotting 8 minutes per student. This is not much time, so you will have to put some effort in preparing a succinct and clear description of what you plan to do. Think of it in terms of one overhead.

We'll also schedule longer oral presentations of about 20 minutes each at the end of reading period for your final report. And of course you must submit a written version that is coherently written and completely documented. Here's a tip: start taking notes immediately on your sources, if you haven't already. Write down a complete and accurate reference for every source you read, with notes on the content. This will save you immeasurable trouble when you come to the writeup, and ensure that you reference your sources properly.

I don't want to tie you down to a particular form of report, but typically I would expect it to include at least

• description of topic
• background and previous work
• statement of an open problem or question that you investigate
• method of attack, algorithms used, programs written
• computational results
• analysis of results and conclusions
• reference and document all sources

Choosing a topic

Below are some suggestions for term projects. These are just suggestions, some very general. You are certainly not limited to these. On the contrary, the wider ranging the projects, the more interesting. I've provided some references, but a trip to the online catalog, a search on the web, and a perusal of current periodials should provide you with lots of leads on most of these topics. Also, check the COS 323 links and references page. This points to the master reference list and some other sources that may stimulate your imagination or provide more information on given topics.

• Cellular Automata:
  
  
  • Lattice gasses

    These are discrete, binary, particle models for gasses, an alternative to differential equations for modeling fluid flow. Some good elementary material is in Gould and Tobochnik [GT96].

  • Embedded computation:

    To get started, see [SKW88, SS94, JSS97] and papers by Melanie Mitchell about evolving cellular automata.

  • Anthropology
  • Epidemics
  
  
• Modeling prehistoric settlement behavior:

  If you're interested in learning more about this, see Dr. Peter Bogucki (Assistant Dean for Undergraduate Affairs, bogucki@princeton.edu), who studies the establishment of agricultural communities in north-central Europe.

• n-Body simulation
  
  
• Nonlinear pendulums
  
  
• Weather simulations
  
  
• Model the collapse of sand piles (check literature, this has been worked on). Model other "catastrophes" (see "catastrophe theory").
  
  
• Physical modeling of musical instruments
  
  
• Sonify the Fermi-Pasta-Ulam-Tsingou experiment

  Can you make the recurrence clear by converting to sound? (MatLab does sound.) This project migt ise some interesting digital signal processing to filter, select frequency bands, down- or up-convert, etc.

• Solitons in optical fibers, water, plasmas
  
  
• Option Pricing:

  In 1973, F. Black and M. Scholes derived a formula to price European call options on nondividend paying stocks. The formula has been generalized since then and is now used by professionals to price stock options, stock index options, currency options, and numerous other forms of options [Gib91].

• Use the EOS framework being developed here for a simulation of some economic world.
  
  
• Chaos in economic systems
  
  
• Protein Folding:

  See, for example, Peter Coles' term project summary (1997).

• Computation of equilibria in economic systems, game theory
  
  
• Physical modeling of human motion
  
  
• Cleaning up scans of text:

  It might be interesting to look at the best way to scan in text so that it can ultimately be converted to readable pdf. If you look my scan of the Fermi, Pasta, Ulam paper, for example, you'll see some print-through, and, furthermore, the readability is not all that great. I did find that scanning at high resolution using the black-and-white option gave me better results than grey-scale. I then blurred using a 3x3 mask, and saved as grey-scale postscript. I think what is needed here is a nonlinear filtering algorithm that removes small "islands" in the black-and-white image (in this case gif). The general problem of combining nonlinear and linear filtering is very interesting, and optimizing for scanned text is a good application.

• Physical modeling of paper marbling [Cha86]:

  Paper marbling is a technique for making decorative paper, and has been widely used for book endpapers and edge decoration for centuries. Simply put, colors are floated on a water-based solution, disturbed to make patterns, and paper is laid on the surface to register the pattern [Cha86]. For some beautiful examples of real marbling, see Paola Kathuria's page of marbling.

  
  

  Prof. Patrick M. Hanrahan writes:   "In terms of simulation, there have been a few related things. In 1986 Ken Perlin put together a nice procedure for generating noise, and he used it to simulate marble (the rock). Basically, he creates a 3D solid texture by putting a periodic function through a color table, and then perturbs the phase with the noise function. He has a nice marble vase in his paper. The reference is "The Image Synthesizer" by Perlin, in SIGGRAPH 1986."

  
  

  See also Brian Caputo's term project summary (1997).

  
  
• ODE's and PDE's for modeling epidemics

  How did predictions this year for H1N1 do? There's data, for example, at the CDC. Model the effects of a immuminization programs. (Check the literature, there must be lots of stuff out there.)

  
  
• Safe Burning of plutonium, using Monte Carlo simulations of neutron transport