{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:20:52Z","timestamp":1760149252700,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,20]],"date-time":"2023-07-20T00:00:00Z","timestamp":1689811200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, first, it is confirmed that a recently introduced symbolic time-series-analysis method based on the prime-numbers-based algorithm (PNA), referred to as the \u201cPNA-based symbolic time-series analysis method\u201d (PNA-STSM), can accurately determine the exponent of the distribution of waiting times in the symbolic dynamics of two symbols produced by the 3D Ising model in its critical state. After this numerical verification of the reliability of PNA-STSM, three examples of how PNA-STSM can be applied to the category of systems that obey the dynamics of the on\u2013off intermittency are presented. Usually, such time series, with on\u2013off intermittency, present bimodal amplitude distributions (i.e., with two lobes). As has recently been found, the phenomenon of on\u2013off intermittency is associated with the spontaneous symmetry breaking (SSB) of the second-order phase transition. Thus, the revelation that a system is close to SSB supports a deeper understanding of its dynamics in terms of criticality, which is quite useful in applications such as the analysis of pre-earthquake fracture-induced electromagnetic emission (also known as fracture-induced electromagnetic radiation) (FEME\/FEMR) signals. Beyond the case of on\u2013off intermittency, PNA-STSM can provide credible results for the dynamics of any two-symbol symbolic dynamics, even in cases in which there is an imbalance in the probability of the appearance of the two respective symbols since the two symbols are not considered separately but, instead, simultaneously, considering the information from both branches of the symbolic dynamics.<\/jats:p>","DOI":"10.3390\/sym15071448","type":"journal-article","created":{"date-parts":[[2023,7,20]],"date-time":"2023-07-20T04:27:13Z","timestamp":1689827233000},"page":"1448","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Spontaneous Symmetry Breaking in Systems Obeying the Dynamics of On\u2013Off Intermittency and Presenting Bimodal Amplitude Distributions"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5928-4587","authenticated-orcid":false,"given":"Stelios M.","family":"Potirakis","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronics Engineering, University of West Attica, 12244 Athens, Greece"},{"name":"Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, Metaxa and Vasileos Pavlou, 15236 Athens, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8268-253X","authenticated-orcid":false,"given":"Pericles","family":"Papadopoulos","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, University of West Attica, 12244 Athens, Greece"}]},{"given":"Niki-Lina","family":"Matiadou","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, University of West Attica, 12244 Athens, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0918-9343","authenticated-orcid":false,"given":"Michael P.","family":"Hanias","sequence":"additional","affiliation":[{"name":"Department of Physics, International Hellenic University, 65404 Kavala, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8484-1402","authenticated-orcid":false,"given":"Stavros G.","family":"Stavrinides","sequence":"additional","affiliation":[{"name":"Department of Physics, International Hellenic University, 65404 Kavala, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7342-0557","authenticated-orcid":false,"given":"Georgios","family":"Balasis","sequence":"additional","affiliation":[{"name":"Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens, Metaxa and Vasileos Pavlou, 15236 Athens, Greece"}]},{"given":"Yiannis","family":"Contoyiannis","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronics Engineering, University of West Attica, 12244 Athens, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1140\/epjb\/e2013-40852-1","article-title":"Magnetic field fluctuations in an array of randomly directed circular currents","volume":"86","author":"Anagiannis","year":"2013","journal-title":"Eur. 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