Going through the

*Legends III* page proofs has been absolutely mind-numbing -- I'm now on page 57 out of 96. Note that this is not just random reading; I need to read things extremely carefully, and that's just a tiring job.

I also have two movies and season 1 of

*Buffy* to review, but I'll do those later. For now, I want to discuss the projects of my 2007 SURF students, as they have now been finalized (the two on the waiting list got awarded their SURFs today).

There are four students with me as the main advisor and Mike Cross as the secondary one, and two with Mike as the main advisor and me as the secondary one. (I have been working closely with one of thse two -- as I recruited her -- but I technically haven't yet met the other one.) One student got his SURF project rejected, but he still plans to work with me this summer, so I'll discuss that project as well.

**Students with me as the main advisor (alphabetical order)**:

1.

*Natasha ("Alex") Cayco Gajic*: Alex, a Sophomore in Ricketts, will be working on a project in

synchronization (see also

this page). In particular, she'll be studying basins of attraction of synchronized states and other states in coupled phase oscillators (along the lines of the Kuramoto model). In particular, Alex will be building on a 2006 paper by Dan Wiley, Steve Strogatz, and Michelle Girvan. Alex's mother is a math prof at San Jose State University, and Alex is already attending the Joint Mathematics Meeting that takes place in January. She has a mathematical tattoo that looks like a pentagram but has another name (it's either the 5-clique or the 5-clique minus the "outside" connections that would make it an Euler graph... my memory is failing me here; I don't remember if those links were present in the tattoo).

2.

*Olga Mandelshtam*: Olga, a Sophomore in Blacker, will be working on attachment mechanisms in online friendship networks. There is an idea that is sometimes called

preferential attachment which stipulates that the rich get richer when networks are growing. This has been used most frequently in modeling the growth of the web (one is more likely to link to google than this blog in starting a new web page), though the results one gets don't actually do a good job of modeling the structure of the web (despite claims by some people in the literature...). Before that (and before the name preferential attachment was coined), these sorts of mechanisms were used in the study of citation networks (dating all the way back to the work of Polya, despite claims by certain people that they invented it...). Anyway, I think that these sorts of mechanisms may do a nice job with online networks like Facebook, Orkut, LinkedIn, and so on. Different online networks have slightly different rules for adding friends and these are reflected by different attachment mechanisms. A key question is how to these ("microscopic") differences in attachment mechanisms manifest in terms of the networks "macroscopic" statistics. A (much) harder inverse problem (that we won't get to this summer) is if one wants a desired statistical property in a network (say, a particular degree distribution), how can one design a specific attachment mechanism (or family thereof) to achieve it. Unsurprisingly, the Caltech Alumni Association is seriously interested in this project.

3.

*Liuyi ("Ye") Pei*: Ye, a frosh in Page, is going to be looking at Congressional roll call votes using network theory. This is the third separate Congressional dataset my group will be studying, so she'll be comparing her results with the House committee networks and (especially!) the House and Senate legislation cosponsorship networks. She'll also be comparing what she finds with previous data-mining work that has been done on the roll call data. We have this data for the entire history of the US, so Ye will be looking at historical questions --- shifts of political parties, what's happening now with the 110th Congress, etc. Ironically, Ye lives in the same town as Yan Zhang, who worked with me on the legislation cosponsorship network (and who is finishing up some plots for a paper on the topic that is currently in progress). Their parents know each other, but I don't know if they have ever actually met (even though they're in the same House). I believe Ye said she saw Yan walking around once.

**Students with me as secondary advisor (alphabetical order)**:

1.

*Sherry Chen*: Sherry, a frosh who is rooming with Ye in Page (yeah, roommate SURFers!), is working on a project in synchronization. She is adapting a paper from a few years ago that dealt with a certain situation in a neuroscience application (involving getting more precise control in the presence of extrensic noise) to work for "antiferromagnetic" synchronization in nanomechanical oscillators. There are both positive and negative connections, and an antiferromagnetic situation would refer to an alternation of spin up and spin down, so in this context you basically have half the oscillators synchronized with each other and the other half 180 degrees apart from the first group but synchronized with each other. (The coupling between oscillators in separate groups is negative, and this can complicate the situation. One can also generalize the 180 degrees to more complicated situations.) Sherry will ultimately need to deal with not only phase oscillators but also ones with amplitude dynamics. There will be both numerics and analytics, and eventually we hope to compare to work being done in the Roukes experimental group (which is local). Sherry has begun working on the project already. Cat is the one who first referred Sherry to me, so he gets an assist on this one. (I need to see if one can pay for people to get floated at Page dinners because I am very amused by the idea of me, the advisor, floating a pair of roommates who are both research students of mine.)

2.

*Matt Glau*: I haven't actually met Matt, and I can't remember if he's a freshman or a sophomore. He's also working on synchronization in nanomechanics, though he'll be focusing on coupling between small numbers of oscillators so he can get some analytical stuff done with them.

**The other student working with Mike and me this summer**:

*Kausteya Roy*: Kausteya is working on solitary waves in Bose-Einstein condensates with spatially-dependent scattering lengths (i.e., spatially varying nonlinearity coefficients). In particular, he'll be considering various sorts of piecewise constant coefficients to hopefully be able to do some analytical work with them as well as numerics to set the stage. He'll start with one jump, but eventually work up to a situation in which the coefficients are periodic and piecewise constant. Solitary waves that one finds in such situations are known as "surface" solitary waves.

Now that I've written these descriptions, I've done part of the work in adding short descriptions to my research website. I also need to add these students to the advisees listen in my CV.