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Published December 2019 | public
Journal Article

The Entropy Rate of Some Pólya String Models

Abstract

We study random string-duplication systems, which we call Pólya string models. These are motivated by a class of mutations that are common in most organisms and lead to an abundance of repeated sequences in their genomes. Unlike previous works that study the combinatorial capacity of string-duplication systems, or in a probabilistic setting, various string statistics, this work provides the exact entropy rate or bounds on it, for several probabilistic models. The entropy rate determines the compressibility of the resulting sequences, as well as quantifying the amount of sequence diversity that these mutations can create. In particular, we study the entropy rate of noisy string-duplication systems, including the tandem-duplication, end-duplication, and interspersed-duplication systems, where in all cases we study duplication of length 1 only. Interesting connections are drawn between some systems and the signature of random permutations, as well as to the beta distribution common in population genetics.

Additional Information

© 2019 IEEE. Manuscript received August 20, 2018; revised May 15, 2019; accepted August 9, 2019. Date of publication August 22, 2019; date of current version November 20, 2019. This work was supported in part by the National Foundation under Grant CCF-1317694, Grant CCF-1755773, Grant CCF-1816409, Grant CCF-1816965, and Grant CCF-1717884 and in part by the United States–Israel Binational Science Foundation (BSF) under Grant 2017652. This article was presented in part at the 2016 IEEE International Symposium on Information Theory. The authors would like to thank the associate editor and the anonymous reviewers, whose comments improved the presentation of the paper.

Additional details

Created:
August 19, 2023
Modified:
October 18, 2023