blog status & probability

I wish I had something to write about. I just wanted to have something new on this site to let people know that I'm not dead. I've done a lot of really fun things... if you could ever consider school work fun. First off, as of 20 minutes ago, my main page has a slightly new and cleaner look and my resume is updated. If by some off chance someone is looking to hire me, my pdf resume is available to oggle.

As for school, I think what I've been doing is extremely interesting. I've been modeling neurons in the brain as electrical circuits. The most baffling part, and Professor Lazar could give you the mathematical details, is that we discover that the neurons and dendritic trees in your brain are non-linear circuits BUT they can be very accurately modeled by linear circuits. Go figure, the man is a genius. It really makes you think though, how good the model we are using is. We modeled the neurons as time encoding machines, they hit a threshold and spike and we take the spike times and recover a signal. You really must wonder how closely organic structures like neurons behave just like... common electrical circuits, like a sample and hold circuit, how the dendritic trees and axons are like antennas.

The more you delve into this, the more you wonder how much is "intelligent design" and how much is trial and error that nature slowly progressed towards. I didn't do so well in my Probability class, but the more you look at the world as probabilistic events, the less you, well, at least I, believe in God. Observe the initial example and I'll get to something else later:

0th order Markov (each character generated independently and identically distributed with frequencies matching English text):

OCRO HLI RGWR NMIELWIS EU LL NBNESEBYA TH EEI ALHENHTTPA OOBTTVA NAH BRL

1st order Markov: (each character generated with frequencies depending on previous character)

ON IE ANTSOUTINYS ARE T INCTORE ST BE S DEAMY ACHIN D ILONASIVE TUCOOWE AT TEASONARE FUSO TIZIN ANDY TOBE SEACE CTISBE

2nd order Markov: (each character generated with frequencies depending on two previous characters)

IN NO IST LAT WHEY CRATICT FROURE BERS GROCID PONDENOME OF DEMONSTRURES OF THE REPTAGIN IS REGOACTIONA OF CRE

3rd order Markov: (each character generated with frequencies depending on three previous characters)

THE GENERATED JOB PROVIDUAL BETTER TRAND THE DISPLAYED CODE ABOVERY UPONDULTS WELL THE CODERST IN THESTICAL IT DO HOCK BOTHE MERG INSTATES CONS ERATION NEVER ANY OF PUBLE AND TO THEORY EVENTIAL CALLEGAND TO ELAST BENERATED IN WITH PIES AS IS WITH THE

This is the power of Markov Chains. Markov Chains is the key behind genetics and proteins. DNA sequences are largely iterations of markov chains, after you reach a high enough order, the coherency and meaningfulness of things is almost ridiculous. There was a point in studying for my genomics midterm that it dawned on me that Markov Chains are glaring evidence against the existence of God. Too bad it's 6:30 am and I don't remember the details so I can walk everyone through the thought process. Maybe some other time. In the meantime...

I was trying to generate a short Matlab function yesterday that would allow me to plot a set of cosines to approximate output intensity degradation with angular misalignment for a LED. What I got was a loop screw up. Cosines produce some crazy shit.
This is how simple the code was:
clear all;
theta=0:0.01:pi;
m=0:.5:10;
for n=1:length(m)
for l=1:length(theta)
a(n,l)=(cos(theta(l)))^m(n);
end
end
plot(a)

This is the end result: eek! how about that for "intelligent design"?