{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,9]],"date-time":"2026-02-09T21:43:20Z","timestamp":1770673400566,"version":"3.49.0"},"reference-count":23,"publisher":"SAGE Publications","issue":"12","license":[{"start":{"date-parts":[[2025,12,1]],"date-time":"2025-12-01T00:00:00Z","timestamp":1764547200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100003995","name":"Natural Science Foundation of Anhui Province","doi-asserted-by":"crossref","award":["No. 2208085MA02"],"award-info":[{"award-number":["No. 2208085MA02"]}],"id":[{"id":"10.13039\/501100003995","id-type":"DOI","asserted-by":"crossref"}]},{"name":"National Science and Technology Council, Taiwan","award":["NSTC-113-2115-M-004-004-MY3"],"award-info":[{"award-number":["NSTC-113-2115-M-004-004-MY3"]}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational Biology"],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:p>\n                    An enumerative study of RNA secondary structures according to various characteristics is a topic of key importance in computational biology. RNA secondary structure pairs have also been studied in various contexts. Recently, the homology groups of the simplicial complices induced by pairs of secondary structures have been studied by Bura, He, and Reidys, providing a new way for characterizing these structure pairs. In particular, the homology group\n                    <jats:inline-formula>\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\" overflow=\"scroll\">\n                        <mml:mrow>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mrow>\n                                <mml:mi>H<\/mml:mi>\n                              <\/mml:mrow>\n                              <mml:mn>2<\/mml:mn>\n                            <\/mml:msub>\n                          <\/mml:mrow>\n                        <\/mml:mrow>\n                      <\/mml:math>\n                    <\/jats:inline-formula>\n                    corresponding to any pair has been shown to be a open-access group. In this article, we provide enumerative results, both exactly and asymptotically, for those pairs giving a open-access group of rank zero. The asymptotic number of these structure pairs of length\n                    <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    is shown to be (0.2774624151\u2026)(4.8105752536\u2026)\n                    <jats:sup>\n                      <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    <\/jats:sup>\n                    <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    <jats:sup>\u22123\/2<\/jats:sup>\n                    . We also prove that the distribution of the number of base pairs in those pairs of secondary structures is asymptotically normal.\n                  <\/jats:p>","DOI":"10.1177\/15578666251370765","type":"journal-article","created":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T15:52:50Z","timestamp":1764172370000},"page":"1147-1159","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Counting RNA Loop Interaction Networks of Homology Group Rank Zero"],"prefix":"10.1177","volume":"32","author":[{"given":"Zi-Wei","family":"Bai","sequence":"first","affiliation":[{"name":"School of Mathematics, Hefei University of Technology, Hefei, PR China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1061-3049","authenticated-orcid":false,"given":"Ricky X.F.","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics, Hefei University of Technology, Hefei, PR China."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8891-6897","authenticated-orcid":false,"given":"Michael","family":"Fuchs","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, National Chengchi University, Taipei, Taiwan."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2026,1,20]]},"reference":[{"key":"e_1_3_4_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2021.112371"},{"key":"e_1_3_4_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10801-022-01132-3"},{"key":"e_1_3_4_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-023-01128-5"},{"key":"e_1_3_4_5_1","doi-asserted-by":"publisher","DOI":"10.37236\/8540"},{"key":"e_1_3_4_6_1","doi-asserted-by":"publisher","DOI":"10.1089\/cmb.2006.13.1640"},{"key":"e_1_3_4_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2004.04.001"},{"key":"e_1_3_4_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-211-75357-6"},{"key":"e_1_3_4_9_1","doi-asserted-by":"publisher","DOI":"10.1002\/(sici)1098-2418(199701\/03)10:1\/2<103::aid-rsa5>3.0.co;2-z"},{"key":"e_1_3_4_10_1","doi-asserted-by":"publisher","DOI":"10.1017\/S1355838201000863"},{"key":"e_1_3_4_11_1","doi-asserted-by":"publisher","DOI":"10.1089\/cmb.2013.0128"},{"key":"e_1_3_4_12_1","doi-asserted-by":"publisher","DOI":"10.1006\/bulm.1998.0085"},{"key":"e_1_3_4_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-40193-0_7"},{"key":"e_1_3_4_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(98)00073-0"},{"key":"e_1_3_4_15_1","doi-asserted-by":"publisher","DOI":"10.1006\/eujc.1997.0179"},{"key":"e_1_3_4_16_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11538-018-0411-9"},{"key":"e_1_3_4_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2012.09.006"},{"key":"e_1_3_4_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2004.05.004"},{"key":"e_1_3_4_19_1","doi-asserted-by":"publisher","DOI":"10.1089\/cmb.2006.0153"},{"key":"e_1_3_4_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.mbs.2004.05.004"},{"key":"e_1_3_4_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(92)00038-N"},{"key":"e_1_3_4_22_1","first-page":"31","article-title":"RNA secondary structure","volume":"42","author":"Smith TF","year":"1978","unstructured":"Smith TF, , Waterman MS. RNA secondary structure. Math. Biol, 1978; 42:31\u201349.","journal-title":"Math. Biol"},{"key":"e_1_3_4_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(79)90033-5"},{"key":"e_1_3_4_24_1","first-page":"167","volume-title":"Studies on Foundations and Combinatorics, Advances in Mathematics Supplementary Studies","author":"Waterman MS","year":"1978","unstructured":"Waterman MS. Secondary structure of single-stranded nucleic acids. In: Studies on Foundations and Combinatorics, Advances in Mathematics Supplementary Studies (Rota G.-C. eds.). 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