Ganesh Swami

Real life has been kicking my ass lately. My brain has been working over-time, so I’m taking some time off to relax. I’m fortunate to have a lot of friends with birthdays this week, so that helps. Anyways, here’s an update on what I’ve been upto…

Parabolic excitation

Working on a homework problem for my non-linear physics class has been a huge timesink. This week, we were asked to solve the general low viscosity Mathieu equation

for a parabolic excitation signal. My professor, Dr. Bechhoefer had published a paper to describe parametrically excited surface waves with delta and triangle excitation signals. We were asked to extend this. At the end, you get a complicated implicit equation for the threshold condition. I had to learn how to solve implicit equations numerically in Matlab (numerically because Maple couldn’t do it analytically.)

Geometry of Diffusion Tensors

As I’m working a lot with Diffusion Tensors, I wanted to get a better feel for the computations on them. I found this paper(pdf) by Dr. Joshi titled “Principal Geodesic Analysis on Symmetric Spaces: Statistics of Diffusion Tensors” really helpful. Ofcourse, I couldn’t understand some of the mathematical terms, so it’s more reading for me. I also realized that not all graduate students are on top of their game — they sometimes can mislead you. It’s better to mislead yourself than to be misled.

Geodesic Shooting

As part of my weekly reading, a friend and I are trying to understand this paper titled “Geodesic Shooting for Computational Anatomy.” Amidst all the complicated math, the basic idea they are trying to show is that flows on the deformation diffeomorphism conserve momentum. And because of this conservation law, you only need the velocity at t=0 to completely determine the flow. In the grand scheme of things, you do not and cannot average images just by averaging pixel/voxel intensities. This is because these images do not form a vector space and simple linear averaging does not respect the curved aspect of the space. The space of the velocity vectors form a vector space, and we can average those instead.

MRI scan

I also had my first MRI scan last week. I had to go all the way to the UBC hospital for that. A graduate friend of mine is doing some research on parameter optimization on the MR machine, but with about 400 controls you can tune, this is a very difficult problem. It was an interesting experience for me, though I slept through most of it. To take your mind off the heavy beating (and for claustrophobic people I guess,) they give you headphones. I wondered for a long time how electronic headphones worked in presence of a strong magnetic field (MR machines have a magnetic field strength of 1.5 to 3.0 tesla, in contrast to the earth’s field of 30 to 60 microteslas.) I’ll leave that question unanswered because it makes me feel too dumb.

That’s all for now. I’ll save the rest for later.

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This entry was posted on Wednesday, March 7th, 2007 at 12:58 am and is filed under Computing, Physics. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.