Replica procedure for probabilistic algorithms as a model of gene duplication

TL;DR

This paper models gene duplication in biological evolution using probabilistic algorithms, specifically introducing a replica procedure for hidden Markov models with p-adic state spaces, offering a novel computational perspective.

Contribution

It proposes a new replica procedure for probabilistic algorithms to model gene duplication, including specific constructions for hidden Markov models with p-adic state spaces.

Findings

Developed a replica procedure for hidden Markov models.

Constructed models with states as finite additive groups with p-adic metrics.

Applied the replica procedure to biological gene network modeling.

Abstract

In the present paper we propose to describe gene networks in biological systems using probabilistic algorithms. We describe gene duplication in the process of biological evolution using introduction of the replica procedure for probabilistic algorithms. We construct the examples of such a replica procedure for hidden Markov models. We introduce the family of hidden Markov models where the set of hidden states is a finite additive group with a p-adic metric and build the replica procedure for this family of markovian models.