{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:41:33Z","timestamp":1760402493065,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,1,3]],"date-time":"2022-01-03T00:00:00Z","timestamp":1641168000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Today, the palindromic analysis of biological sequences, based exclusively on the study of \u201cmirror\u201d symmetry properties, is almost unavoidable. However, other types of symmetry, such as those present in friezes, could allow us to analyze binary sequences from another point of view. New tools, such as symmetropy and symmentropy, based on new types of palindromes allow us to discriminate binarized 1\/f noise sequences better than Lempel\u2013Ziv complexity. These new palindromes with new types of symmetry also allow for better discrimination of binarized DNA sequences. A relative error of 6% of symmetropy is obtained from the HUMHBB and YEAST1 DNA sequences. A factor of 4 between the slopes obtained from the linear fits of the local symmentropies for the two DNA sequences shows the discriminative capacity of the local symmentropy. Moreover, it is highlighted that a certain number of these new palindromes of sizes greater than 30 bits are more discriminating than those of smaller sizes assimilated to those from an independent and identically distributed random variable.<\/jats:p>","DOI":"10.3390\/e24010082","type":"journal-article","created":{"date-parts":[[2022,1,3]],"date-time":"2022-01-03T22:51:50Z","timestamp":1641250310000},"page":"82","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Palindromic Vectors, Symmetropy and Symmentropy as Symmetry Descriptors of Binary Data"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2356-885X","authenticated-orcid":false,"given":"Jean-Marc","family":"Girault","sequence":"first","affiliation":[{"name":"Groupe ESEO, 49000 Angers, France"},{"name":"Laboratoire d\u2019Acoustique de l\u2019Universit\u00e9 du Mans (LAUM), UMR 6613, Institut d\u2019Acoustique-Graduate School (IA-GS), CNRS, Le Mans Universit\u00e9, 72085 Le Mans, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7097-7533","authenticated-orcid":false,"given":"S\u00e9bastien","family":"M\u00e9nigot","sequence":"additional","affiliation":[{"name":"Groupe ESEO, 49000 Angers, France"},{"name":"Laboratoire d\u2019Acoustique de l\u2019Universit\u00e9 du Mans (LAUM), UMR 6613, Institut d\u2019Acoustique-Graduate School (IA-GS), CNRS, Le Mans Universit\u00e9, 72085 Le Mans, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1218","DOI":"10.1073\/pnas.86.4.1218","article-title":"Estrogen-responsive element of the human pS2 gene is an imperfectly palindromic sequence","volume":"86","author":"Berry","year":"1989","journal-title":"Proc. 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