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. 2017 Aug 23;7:9172. doi: 10.1038/s41598-017-08028-4

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© The Author(s) 2017

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Borrowing vs. similarity. This figure reports the Average Common Substring (ACS) vs. the values of the cross-entropies for all the artificial sequences generated with the Maximum Entropy (ME) model (a), the variable-order (VO) Markov model (b) and the fixed-order (FO) Markov model (c). Everything is computed with respect to the sequence of J.S. Bach’s first violin Partita (see Section S3 of the SI). Filled circles correspond to the artificial sequences. Colors code for the values of K _max in each different model. In addition in each panel the empty circles reports the same quantities for other original sequences of Bach (represented with blue circles) and other classical authors - Beethoven, Schumann, Chopin, Liszt and Albeniz - (AllClass represented with grey circles). Note that the main panel for FO is truncated at values of ACS equal to 8, while the complete plot is shown in the inset.