The mathematical structure of the genetic code: a tool for inquiring on the origin of life

In this paper we present a review and some new thoughts on our work about the mathematical structure of the genetic code. The model proposed is a new theoretical tool that allows a fresh insight on many open problems related to the origin, the evolution and the present structure of the genetic machinery. In particular,we show that such model implies the existence of dichotomic classes, quantities that might play a preeminent role in the management of the genetic information including error control mechanisms. We introduce and use techniques for the analysis of dependent sequences in order to study the correlation structure of series of dichotomic classes derived from protein coding segments of DNA. The results show the existence of a complex context-dependent correlation structure; such dependence gives important information about coding and decoding strategies that nature has implemented along evolutionary times on DNA and RNA sequences.