{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T17:26:38Z","timestamp":1754155598778,"version":"3.41.2"},"reference-count":47,"publisher":"Emerald","issue":"2","license":[{"start":{"date-parts":[[2017,2,6]],"date-time":"2017-02-06T00:00:00Z","timestamp":1486339200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.emerald.com\/insight\/site-policies"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["K"],"published-print":{"date-parts":[[2017,2,6]]},"abstract":"<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Purpose<\/jats:title>\n<jats:p>This paper aims to explain, first of all, signal modeling steps using Poincar\u00e9, and then considering the occurred events, concept of information applying Poincar\u00e9 section and information approach, the brain pattern variations in autism spectrum disorder (ASD) cases will be diagnosed. A kind of representation of electroencephalogram (EEG) signal, namely, complementary plot, in which the main characteristic is special attention to asymmetry and symmetry coexist in natural and human processes, is introduced. In this paper, a new model is provided whose variations of patterns are similar to EEG\u2019s when the transformation parameter is changed. A significant difference between ASD and healthy cases was also observed, which could be used to distinguish between various types of systems.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Design\/methodology\/approach<\/jats:title>\n<jats:p>Complementary plot method is one of the most proper representations for Poincar\u00e9 section of complex dynamics, because, as it was said about its characteristics, it has a qualitative approach toward signal (Sabelli, 2000, 2001, 2003, 2008, 2005, Sabelli <jats:italic>et al.<\/jats:italic>, 2011). Considering the special conditions of this representation, here, intersection with a circle <jats:italic>y<jats:sup>2<\/jats:sup> + x<jats:sup>2<\/jats:sup> = r<jats:sup>2<\/jats:sup><\/jats:italic> will be used; the important fact is, on the contrary to previous representations in which circular section had energy concept, here circular section considers phases. For finding trajectory intersection points, after calculating the sin and cosine of each term of EEG, plotting them in XY plane and drawing a chord between successive points of presentation transitions, then its intersections with the assumed circle are determined. But considering the sampling frequency, chords and Poincar\u00e9 section, in this space, a minimum error \u2013 as the threshold \u2013 should be assumed in the program.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Findings<\/jats:title>\n<jats:p>Natural and human processes are biotic (life-like) and creative (Sabelli and Galilei), and studying coexisting opposites by calculating the sine and cosine of each term in heartbeat intervals, weather variables and integer biotic series or random walk reveals an astonishingly regular mandala pattern; these patterns are not generated by random, periodic or chaotic series (Sabelli, 2005). This paper shows that in EEG of ASD children, mandala-like patterns of concentric rings are emergent in all situations (baseline \u2013 watching animation with voice and without voice) and electrode site (C3 and C4), but not in healthy individuals. The authors take the relation between sine and cosine functions as a mathematical model for complementary opposition, because it involves reciprocity and orthogonality sine and cosine are natural models for information. In fact, trigonometric analyses of empirical data to be described in this paper suggest expanding the concept of co-creative opposition to include uncorrelated opposites and partial opposites, i.e. partial agonists and partial antagonists that are neither linear nor orthogonal. Using Poincar\u00e9 sections, it is shown that the difference in information and creativity of the data is the distinctive characteristic in ASD and healthy cases. Creation is the generation of novelty, diversity and complexity in complex systems.<\/jats:p>\n<\/jats:sec>\n<jats:sec>\n<jats:title content-type=\"abstract-subheading\">Originality\/value<\/jats:title>\n<jats:p>This paper is an original paper based on cybernetic approaches for studying the variations of ASD children.<\/jats:p>\n<\/jats:sec>","DOI":"10.1108\/k-12-2015-0306","type":"journal-article","created":{"date-parts":[[2017,2,10]],"date-time":"2017-02-10T06:36:11Z","timestamp":1486708571000},"page":"364-382","source":"Crossref","is-referenced-by-count":7,"title":["Poincar\u00e9 section analysis of the electroencephalogram in autism spectrum disorder using complement plots"],"prefix":"10.1108","volume":"46","author":[{"given":"Ghasem","family":"Sadeghi Bajestani","sequence":"first","affiliation":[]},{"given":"Mohammad Reza","family":"Hashemi Golpayegani","sequence":"additional","affiliation":[]},{"given":"Ali","family":"Sheikhani","sequence":"additional","affiliation":[]},{"given":"Farah","family":"Ashrafzadeh","sequence":"additional","affiliation":[]}],"member":"140","reference":[{"issue":"12","key":"key2020120902212538400_ref001","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1007\/s11517-006-0119-0","article-title":"Heart rate variability: a review","volume":"44","year":"2006","journal-title":"Medical and Biological Engineering and Computing"},{"key":"key2020120902212538400_ref002","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1097\/WNP.0b013e3181f40dc8","article-title":"Fractality and a Wavelet-Chaos-Neural Network Methodology for EEG-Based diagnosis of autistic spectrum disorder","volume":"27","year":"2010","journal-title":"Journal of Clinical Neurophysiology"},{"issue":"3","key":"key2020120902212538400_ref003","article-title":"A hierarchical model for autism spectrum disorder (HMASD)","volume":"4","year":"2016","journal-title":"Razavi International Journal of Medicine"},{"issue":"1","key":"key2020120902212538400_ref004","article-title":"Cybernetic approach in identification of brain pattern variations in autism spectrum disorder","volume":"28,","year":"2016","journal-title":"Biomedical Engineering: Applications, Basis and Communications"},{"volume-title":"L\u2019ordre dans le chaos: Vers une approche deterministe de la turbulence (Collection Enseignement des sciences) (French Edition)","year":"1988","key":"key2020120902212538400_ref005"},{"key":"key2020120902212538400_ref006","first-page":"1","article-title":"On the application of quantitative EEG for characterizing autistic brain: a systematic review","volume":"7","year":"2013","journal-title":"Frontiers in Human Neuroscience"},{"key":"key2020120902212538400_ref007","article-title":"EEG complexity as a biomarker for autism spectrum disorder risk","volume":"9","year":"2011","journal-title":"BMC Medicine"},{"issue":"5","key":"key2020120902212538400_ref008","doi-asserted-by":"crossref","first-page":"1873","DOI":"10.1152\/ajpheart.00405.2000","article-title":"Poincar\u00e9 plot interpretation using a physiological","volume":"283","year":"2002","journal-title":"American Journal of Physiology - 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