M. Sobottka | Searcharxiv

arXiv2019

A Markovian genomic concatenation model guided by persymmetric matrices

The aim of this work is to provide a rigorous mathematical analysis of a stochastic concatenation model presented by Sobottka and Hart (2011) which allows approximation of the first-order stochastic structure in bacterial DNA by means of a stationary Markov chain. Two probabilistic constructions that rigorously formalize the model are presented. Necessary and sufficient conditions for a Markov chain to be generated by the model are given, as well as the theoretical background needed for designing new algorithms for statistical analyses of real bacterial genomes. It is shown that the model encompasses the Markov chains satisfying intra-strand parity, a property observed in most DNA sequences.

q-bio.GN↗

arXiv2017

Dualities for Multi-State Probabilistic Cellular Automata

In this paper a new form of duality for probabilistic cellular automata (PCA) is introduced. Using this duality, an ergodicity result for processes having a dual is proved. Also, conditions on the probabilities defining the evolution of the processes for the existence of a dual are provided. The results are applied to wide classes of PCA which include multi-opinion voter models, competition models and the Domany-Kinzel model.

math.PR↗