{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T09:16:48Z","timestamp":1762507008755,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,2,16]],"date-time":"2017-02-16T00:00:00Z","timestamp":1487203200000},"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>The identification of critical states is a major task in complex systems, and the availability of measures to detect such conditions is of utmost importance. In general, criticality refers to the existence of two qualitatively different behaviors that the same system can exhibit, depending on the values of some parameters. In this paper, we show that the relevance index may be effectively used to identify critical states in complex systems. The relevance index was originally developed to identify relevant sets of variables in dynamical systems, but in this paper, we show that it is also able to capture features of criticality. The index is applied to two prominent examples showing slightly different meanings of criticality, namely the Ising model and random Boolean networks. Results show that this index is maximized at critical states and is robust with respect to system size and sampling effort. It can therefore be used to detect criticality.<\/jats:p>","DOI":"10.3390\/e19020073","type":"journal-article","created":{"date-parts":[[2017,2,16]],"date-time":"2017-02-16T12:55:34Z","timestamp":1487249734000},"page":"73","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Identifying Critical States through the Relevance Index"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9891-5441","authenticated-orcid":false,"given":"Andrea","family":"Roli","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, <i>Alma Mater Studiorum<\/i> Universit\u00e0 di Bologna, Campus of Cesena, Cesena I-47521, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5991-5470","authenticated-orcid":false,"given":"Marco","family":"Villani","sequence":"additional","affiliation":[{"name":"Department of Physics, Informatics and Mathematics, Universit\u00e0 di Modena e Reggio Emilia, Modena I-41125, Italy"},{"name":"European Centre for Living Technology, Venezia I-30124, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Riccardo","family":"Caprari","sequence":"additional","affiliation":[{"name":"Department of Physics, Informatics and Mathematics, Universit\u00e0 di Modena e Reggio Emilia, Modena I-41125, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1417-5106","authenticated-orcid":false,"given":"Roberto","family":"Serra","sequence":"additional","affiliation":[{"name":"Department of Physics, Informatics and Mathematics, Universit\u00e0 di Modena e Reggio Emilia, Modena I-41125, Italy"},{"name":"European Centre for Living Technology, Venezia I-30124, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,2,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"041116","DOI":"10.1103\/PhysRevE.84.041116","article-title":"Relating Fisher information to order parameters","volume":"84","author":"Prokopenko","year":"2011","journal-title":"Phys. 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