The Capacity of Some P\'olya String Models
Information Theory
2018-08-21 v1 Combinatorics
math.IT
Abstract
We study random string-duplication systems, which we call P\'olya string models. These are motivated by DNA storage in living organisms, and certain random mutation processes that affect their genome. Unlike previous works that study the combinatorial capacity of string-duplication systems, or various string statistics, this work provides exact capacity or bounds on it, for several probabilistic models. In particular, we study the capacity of noisy string-duplication systems, including the tandem-duplication, end-duplication, and interspersed-duplication systems. Interesting connections are drawn between some systems and the signature of random permutations, as well as to the beta distribution common in population genetics.
Keywords
Cite
@article{arxiv.1808.06062,
title = {The Capacity of Some P\'olya String Models},
author = {Ohad Elishco and Farzad Farnoud and Moshe Schwartz and Jehoshua Bruck},
journal= {arXiv preprint arXiv:1808.06062},
year = {2018}
}