# Metrics and Harmonic Analysis on DNA

## TL;DR

This paper introduces a mathematical algorithm based on the crystal basis model to analyze DNA and RNA sequences, enabling sequence comparison and Fourier analysis to explore genetic similarities and differences.

## Contribution

It presents a novel method to describe genetic sequences as integer strings, allowing for sequence comparison and harmonic analysis within the crystal basis framework.

## Key findings

- Defined a new sequence distance measure.
- Applied Fourier transform to genetic sequences.
- Compared sequences from different species.

## Abstract

A mathematical algorithm to describe DNA or RNA sequences of $N$ nucleotides by a string of $2N$ integers numbers is presented in the framework of the so called crystal basis model of the genetic code. The description allows to define a not trivial distance between two sequences and to perform the Discrete Fourier Transform on a sequence. Using the definition of distance the sequence of $\beta$-globin for Homo, Gallus and Opossum are compared. The Discrete Fourier Transform for some simple examples is computed.