The capacity of some Pólya string models

Ohad Elishco; Farzad Farnoud; Moshe Schwartz; Jehoshua Bruck

doi:https://doi.org/10.1109/ISIT.2016.7541303

The capacity of some Pólya string models

Ohad Elishco, Farzad Farnoud, Moshe Schwartz, Jehoshua Bruck

Ben-Gurion University of the Negev

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We study random string-duplication systems, called Pólya string models, motivated by certain random mutation processes in the genome of living organisms. Unlike previous works that study the combinatorial capacity of string-duplication systems, or peripheral properties such as symbol frequency, this work provides exact capacity or bounds on it, for several probabilistic models. In particular, we give the exact capacity of the random tandem-duplication system, and the end-duplication system, and bound the capacity of the complement tandem-duplication system. Interesting connections are drawn between the former and the beta distribution common to population genetics, as well as between the latter system and signatures of random permutations.

Original language	American English
Title of host publication	Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
Pages	270-274
Number of pages	5
ISBN (Electronic)	9781509018062
DOIs	https://doi.org/10.1109/ISIT.2016.7541303
State	Published - 10 Aug 2016
Event	2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain Duration: 10 Jul 2016 → 15 Jul 2016

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2016-August

Conference

Conference	2016 IEEE International Symposium on Information Theory, ISIT 2016
Country/Territory	Spain
City	Barcelona
Period	10/07/16 → 15/07/16

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modelling and Simulation
Applied Mathematics

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Cite this

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title = "The capacity of some P{\'o}lya string models",

abstract = "We study random string-duplication systems, called P{\'o}lya string models, motivated by certain random mutation processes in the genome of living organisms. Unlike previous works that study the combinatorial capacity of string-duplication systems, or peripheral properties such as symbol frequency, this work provides exact capacity or bounds on it, for several probabilistic models. In particular, we give the exact capacity of the random tandem-duplication system, and the end-duplication system, and bound the capacity of the complement tandem-duplication system. Interesting connections are drawn between the former and the beta distribution common to population genetics, as well as between the latter system and signatures of random permutations.",

author = "Ohad Elishco and Farzad Farnoud and Moshe Schwartz and Jehoshua Bruck",

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Elishco, O, Farnoud, F, Schwartz, M & Bruck, J 2016, The capacity of some Pólya string models. in Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory., 7541303, IEEE International Symposium on Information Theory - Proceedings, vol. 2016-August, pp. 270-274, 2016 IEEE International Symposium on Information Theory, ISIT 2016, Barcelona, Spain, 10/07/16. https://doi.org/10.1109/ISIT.2016.7541303

The capacity of some Pólya string models. / Elishco, Ohad; Farnoud, Farzad; Schwartz, Moshe et al.
Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory. 2016. p. 270-274 7541303 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2016-August).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - We study random string-duplication systems, called Pólya string models, motivated by certain random mutation processes in the genome of living organisms. Unlike previous works that study the combinatorial capacity of string-duplication systems, or peripheral properties such as symbol frequency, this work provides exact capacity or bounds on it, for several probabilistic models. In particular, we give the exact capacity of the random tandem-duplication system, and the end-duplication system, and bound the capacity of the complement tandem-duplication system. Interesting connections are drawn between the former and the beta distribution common to population genetics, as well as between the latter system and signatures of random permutations.

AB - We study random string-duplication systems, called Pólya string models, motivated by certain random mutation processes in the genome of living organisms. Unlike previous works that study the combinatorial capacity of string-duplication systems, or peripheral properties such as symbol frequency, this work provides exact capacity or bounds on it, for several probabilistic models. In particular, we give the exact capacity of the random tandem-duplication system, and the end-duplication system, and bound the capacity of the complement tandem-duplication system. Interesting connections are drawn between the former and the beta distribution common to population genetics, as well as between the latter system and signatures of random permutations.

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The capacity of some Pólya string models

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