A couple of posts ago, I talked about a simple monte carlo simulation for diffusion limited aggregation. In this post, I’m going to talk about another algorithm that, at its heart, is based on random numbers. Unlike DLA though, this algorithm isn’t about simulating a physical system. Instead, it is about a method for solving optimization problems that are generally poorly suited to traditional numerical optimization techniques. This post describes an application of a library implementing the GEP method posed by Cândida Ferreira nearly 10 years ago. I started messing with GEP shortly after the paper “Gene Expression Programming: A New Adaptive Algorithm for Solving Problems” was published in the journal Complex Systems. The paper sat in a pile for a while, and about two years ago I picked it up again and started to implement it as a Haskell library.
- Ref: cds.cern.ch/record/2700109
- This book contains 57 selected articles by Professor Radha Charan Gupta—a doyen of history of mathematics—written on a variety of important topics in Indian astronomy and mathematics, and deals with the bibliographical sketches of a few veteran historians of Indian mathematics
L. Wittgenstein. University Of Chicago Press, Chicago, (October 1989)characterizes mathematical propositions: - Do not have a temporal sense (pp. 34). - Are rules of expression. "the connection between a mathematical proposition and its application is roughly that between a rule of expression and the expression itself in use" (pp. 47). A rule of expression defines what is meaningful and what not, how a particular form should be used, etc. - Is invented to suit experience and then made independent of experience (pp. 43). "In mathematics we have propositions which contain the same symbols as, for example, "write down the integral of..", etc., with the difference that when we have a mathemaitical proposition time doesn't enter into it and in the other it does. Now this is not a metaphisical statement." (pp 34).