{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T14:35:41Z","timestamp":1787236541114,"version":"build-2736575974"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Dyn. Syst."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>We consider the following question on the relationship between the asymptotic behaviors of asynchronous dynamics of Boolean networks and their regulatory structures: Does the presence of a cyclic attractor imply the existence of a local negative circuit in the regulatory graph? When the number of model components $n$ verifies $n \\geq 6$, the answer is known to be negative. We show that the question can be translated into a Boolean satisfiability problem on $n \\cdot 2^n$ variables. A Boolean formula expressing the absence of local negative circuits and a necessary condition for the existence of cyclic attractors is found to be unsatisfiable for $n \\leq 5$. In other words, for Boolean networks with up to $5$ components, the presence of a cyclic attractor requires the existence of a local negative circuit.<\/jats:p>","DOI":"10.1137\/18m1173988","type":"journal-article","created":{"date-parts":[[2019,1,15]],"date-time":"2019-01-15T11:33:25Z","timestamp":1547552005000},"page":"68-79","source":"Crossref","is-referenced-by-count":2,"title":["Local Negative Circuits and Cyclic Attractors in Boolean Networks with at most Five Components"],"prefix":"10.1137","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5182-4216","authenticated-orcid":true,"given":"Elisa","family":"Tonello","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Etienne","family":"Farcot","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2350-0756","authenticated-orcid":true,"given":"Claudine","family":"Chaouiya","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,1,15]]},"reference":[{"key":"atypb1","first-page":"44","author":"Biere A.","year":"2016","journal-title":"Proceedings of SAT Competition"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/TCBB.2010.20"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jtbi.2017.12.013"},{"key":"atypb4","first-page":"457","author":"Lammich P.","year":"2017","journal-title":"Cham"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2007.11.003"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2007.05.006"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2009.11.011"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2011.01.010"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2007.04.019"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2012.10.022"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1017\/S096012951400036X"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2017.01.001"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.aam.2004.06.002"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1953-020-x"},{"key":"atypb15","doi-asserted-by":"crossref","unstructured":"T. Tamura and T. Akutsu,\n                      Detecting a singleton attractor in a Boolean network utilizing SAT algorithms\n                      , IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences, E92-A (2009), pp. 493-501.","DOI":"10.1587\/transfun.E92.A.493"},{"key":"atypb16","first-page":"180","author":"Thomas R.","year":"1981","journal-title":"New York"},{"key":"atypb17","unstructured":"E. Tonello,\n                      On the Conversion of Multivalued to Boolean Dynamics\n                      , preprint,https:\/\/arxiv.org\/abs\/1703.06746, 2017."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2018.03.011"},{"key":"atypb19","first-page":"422","author":"Wetzler N.","year":"2014","journal-title":"Cham"}],"container-title":["SIAM Journal on Applied Dynamical Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1173988","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:45:20Z","timestamp":1787233520000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1173988"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M1173988"],"URL":"https:\/\/doi.org\/10.1137\/18m1173988","relation":{},"ISSN":["1536-0040"],"issn-type":[{"value":"1536-0040","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}