Bethe Ansatz in the Bernoulli Matching Model of Random Sequence Alignment

TL;DR

This paper applies the Bethe ansatz method to the Bernoulli Matching model of sequence alignment, providing exact results for the average LCS length and nucleation centers, advancing analytical understanding of sequence alignment models.

Contribution

It introduces an exact Bethe ansatz solution for the Bernoulli Matching model, linking it to the 5-vertex model and calculating key statistical properties.

Findings

Reproduces the average length of the Longest Common Subsequence.

Calculates the average number of nucleation centers.

Establishes a mapping to the 5-vertex model.

Abstract

For the Bernoulli Matching model of sequence alignment problem we apply the Bethe ansatz technique via an exact mapping to the 5--vertex model on a square lattice. Considering the terrace--like representation of the sequence alignment problem, we reproduce by the Bethe ansatz the results for the averaged length of the Longest Common Subsequence in Bernoulli approximation. In addition, we compute the average number of nucleation centers of the terraces.