# Red Dots, Blue Dots

In this blog entry I’d like to showcase just one of a number of remarkable findings that comprise the basis for the generative fixation hypothesis—a new explanation for the adaptive capacity of recombinative genetic algorithms.

Consider the following stochastic function which takes a bitstring of length $\ell$ as input and returns a real value as output.

fitness(bitstring)
accum = 0
for i = 1 to 4
accum = accum + bitstring[pivotalLoci[i]]
end
if accum is odd
return a random value from normal distribution N(+0.25,1)
else
return a random value from normal distribution N(-0.25,1)
end


The variable pivotalLoci is an array of four distinct integers between 1and $\ell$ which specifies the location of  four loci—let’s call them A, B, C, D—of an input bitstring that matter in the determination the bitstring’s fitness. These four loci are said to be pivotal. Continue reading “Red Dots, Blue Dots”

# Thanks!

Thanks everyone for your good wishes. My defense went smoothly, and I got some excellent suggestions from my committee.

# Dissertation Defense

My dissertation defense is scheduled for Friday June 19, 2009. I’m currently working on my presentation. Wish me luck :-)