Problem Set 1 Clarifications
mr...@cec.wustl.edu
> Sorry to bother you again; I realize you're probably rather busy. I went
> to Whitaker computer lab today and stayed there from 2:30 till 5:30 and
> Michael never seemed to show up. I must have been in the wrong part of
> Whitaker, but I am not sure. I still have some questions regarding the
> homework. If you feel like looking at them I'll list them below.
OK; I'll look into this. Thanks for letting me know.
> -I am still having a really hard time trying to figure out how to do
> number 2. The hints given both in and out of class helped to some degree
> in the set up, and on Friday after solving for the normalization factor in
> terms of the det(A), I thought I had a pretty good idea of where to go
> from there. But every time I sit down I just seem incapable of making the
> intuitive connections necessary to further the problem. I realize you can
> only help us so much, but I really have spent a lot (hours) of time trying
> to figure out how to find A in terms of C (covariance matrix), and each
> time I come up with nothing.
An alternative way to approach this problem is to forego the
additional vector $\vec{b}$ altogether and simply differentiate the
partition function with respect to $A_{ij}$. We solved for the
partition function in class, so this shouldn't be too hard to derive.
You will need to look up some information about derivatives of
determinants but otherwise this route to solve the problem is pretty
straightforward.
> -For number 3, I approached it as one would a differential equation,
> except at the end with B being a matrix that maps v onto u. Considering
> the second part of the problem, is this a too simplified view of solving
> the differential equation? When you are asking about B, v(0), and alpha,
> are you looking for a formulaic definition, or a simple identification of
> what they represent within the problem?
I'm looking for a matrix definition of B (and the other variables) in
terms of A or some related set of vectors derived from A.
> -For number 5, given the assumption that the charge distribution is zero,
> and the fact that the dielectric constant does have a derivative, does
> this mean we should take the electrostatic potential to be linear with a
> second derivative equal to zero?
Umm... no. The electrostatic potential is definitely not linear
because the dielectric coefficient is nonlinear. However, everything
is integrable... at least with Matlab.
> Thank you for taking the time to address my concerns and thank you for the
> help that you have already given both me and the class.
Sure. Can you do me a favor? I didn't know if you'd feel comfortable
if I Cc'ed your original questions to the class. However, to keep
everyone on equal footing, can you please post a version of your
questions and these answers to the class mailing list
(bio-...@googlegroups.com)?
Thanks,
Nathan
--
Associate Professor, Dept. of Biochemistry and Molecular Biophysics
Center for Computational Biology, Washington University in St. Louis
Web: http://cholla.wustl.edu/