{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:53:09Z","timestamp":1760151189380,"version":"build-2065373602"},"reference-count":48,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,1]],"date-time":"2022-03-01T00:00:00Z","timestamp":1646092800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"RUDN","award":["This paper has been supported by the RUDN University Strategic Academic Leadership Program."],"award-info":[{"award-number":["This paper has been supported by the RUDN University Strategic Academic Leadership Program."]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We study the proposed statistical kinetic model for describing the pre- and consciousness structures based on the cognitive neural networks. The method of statistics of the growth graph systems and a possible transition to symmetric structures (a kind of phase transition) is applied. With the complication of a random Erd\u0151os-R\u00e9nyi (ER) graph during the percolation transition from the tree structure to the large cluster structures is obtained. In the evolutionary model two classes of algorithms have been developed. The differences between the cycle parameters in the obtained neural network models can reach thousands or more times. This is due to the tree-like architecture of the neural graph, which mimics the columnar structures of the neocortex. These cluster and cyclic structures can be interpreted as the primary elements of consciousness and as a necessary condition for the effect of consciousness itself. The comparison with other known theoretical mainly statistical models of consciousness is discussed. The presented results are promising in neurocomputer interfaces, man-machine systems and artificial intelligence systems.<\/jats:p>","DOI":"10.3390\/sym14030505","type":"journal-article","created":{"date-parts":[[2022,3,1]],"date-time":"2022-03-01T21:31:47Z","timestamp":1646170307000},"page":"505","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Hypothesis of Cyclic Structures of Pre- and Consciousness as a Transition in Neuron-like Graphs to a Special Type of Symmetry"],"prefix":"10.3390","volume":"14","author":[{"given":"Vladimir","family":"Aristov","sequence":"first","affiliation":[{"name":"Federal Research Center of Computer Science and Control of Russian Academy of Sciences, Vavilov St. 42, 119333 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3176-5279","authenticated-orcid":false,"given":"Ivan","family":"Stepanyan","sequence":"additional","affiliation":[{"name":"Peoples\u2019 Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, 117198 Moscow, Russia"},{"name":"Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN) M. Kharitonyevskiy Pereulok, 101990 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,1]]},"reference":[{"key":"ref_1","unstructured":"Chalmers, D. (1996). The Conscious Mind: In Search of a Fundamental Theory, Oxford University Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1038\/s41567-020-1029-z","article-title":"Isotopy and energy of physical networks","volume":"17","author":"Liu","year":"2020","journal-title":"Nat. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2020.08.003","article-title":"Sequential dynamics of complex networks in mind: Consciousness and creativity","volume":"883","author":"Rabinovich","year":"2020","journal-title":"Phys. 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