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.