What is #P (Sharp P)

#P is the set of counting problems whose corresponding decision problem is in NP.  Or more formally (from here):

A function [math]f:left{0,1right}^*rightarrow mathbb{N}[/math] is in #[math]bf{P}[/math] if there exists a polynomial [math]p: mathbb{N}rightarrow mathbb{N}[/math] and a polynomial-time TM (turing machine) such that for every [math]xin left{0,1right}^*[/math]

[math]f(x)=left|{left{yin left{0,1right}^{p^{(|x|)}}:M(x,y)=1right}}right|[/math].

I later intend to find a proof or develop a proof myself that shows that the number of subset sums problem is in #P.

No Free Lunch (NFL)

My friend Indranil introduced me to the theory of “No Free Lunch”.  From Wikipedia article:

A conventional, but not entirely accurate, interpretation of the NFL results is that “a general-purpose universal optimization strategy is theoretically impossible, and the only way one strategy can outperform another is if it is specialized to the specific problem under consideration”

 

It is definitely something that I must keep in mind whenever doing research.

Java 3D and Mason

Well I got MASON installed and working.  The 3D simulations are pretty neat.  But you need to get Java 3D and install it.

Some things to remember to speed the process of setting up netbeans for MASON would be that in order to add dll files you need to add something like:

-Djava.library.path=”C:Program FilesJavaJava3D1.5.1bin”

to the VM options in the run section of the properties of the project.  Also, you must remember to add the 3D Java jar files to the libraries section.  Otherwise you can just follow the tutorial here to get started.

We intend on using MASON as our test bed for the identification of swarms using the Shapley value idea.

Chicago Pizza

So far in my life Chicago deep dish (stuffed crust) pizza is the most unique pizza I have eaten.  While there I ate at Giordanos and Gino’s East.  The pizza at both taste really good.  I liked the atmosphere at Gino’s East better than Giordanos.  Man, I am getting hungry…