My 2005 SURF students

Tomorrow is SURF seminar day for Caltech SURFers. I have two students speaking in the Session V (a math session in Keck 111). Sophomore Rudd Sean Li will be speaking at 2:30 on toy models of plankton food webs and Senior Lloydie Eric Kelsic will be speaking at 2:50 on community structure in social networks. (Eric's paper will still be tweaked slightly, but the posted version is nearly final.)

Sean looked at some simple food webs. He sometimes also considered the effects of resource (light) fluctuations on various timescales (say, in 24 hours versus over a season). The choice of plankton in such models is because one can actually do experiments in the lab. Sean built on some prior work by students of mine (both of whom are applying for grad school this year---one in financial math and the other in urban plannning) that is ready to be written up and then submitted once we lazy advisors finally have a chance to do it. Eric did some numerical investigations and also did some work on how to use normal form theory to approximate the cyclic dynamics of plankton when phytoplankton and zooplankton coexist. (The normal form stuff needs further elaboration because it's only at it's beginning stages, but it looks like some nice stuff can come out of it.)

I'll give some more details on Eric's studies because the application is very accessible: He used Facebook data to study social networks in universities in an attempt to devise methodologies to study overlap between different communities (which basically nobody knows how to do yet except for one 2005 paper in Nature that has a method that can work for sparse networks). In doing research like this, it's extremely useful to use data one knows well, so the data of choice to illustrate things was the Caltech social network (as defined by Facebook data, so obviously we're not talking about exact data here). While this is a very nice example (for Techers, especially), of broader scientific interest is to do comparisons across multiple universities, which will be done by some combination of Eric, future students, my collaborators, their students, and me. The foundation is there, but lots of sweat is still necessary.