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Optinalysis: A New Method of Data Analysis and Comparison
Version 1
: Received: 3 August 2020 / Approved: 5 August 2020 / Online: 5 August 2020 (03:43:11 CEST)
Version 2 : Received: 12 September 2021 / Approved: 13 September 2021 / Online: 13 September 2021 (13:27:39 CEST)
Version 3 : Received: 26 October 2022 / Approved: 26 October 2022 / Online: 26 October 2022 (09:39:11 CEST)
Version 2 : Received: 12 September 2021 / Approved: 13 September 2021 / Online: 13 September 2021 (13:27:39 CEST)
Version 3 : Received: 26 October 2022 / Approved: 26 October 2022 / Online: 26 October 2022 (09:39:11 CEST)
How to cite: Abdullahi, K.B. Optinalysis: A New Method of Data Analysis and Comparison . Preprints 2020, 2020080072. https://doi.org/10.20944/preprints202008.0072.v2 Abdullahi, K.B. Optinalysis: A New Method of Data Analysis and Comparison . Preprints 2020, 2020080072. https://doi.org/10.20944/preprints202008.0072.v2
Abstract
The key concepts in symmetry detection and similarity, identity measures are automorphism and isomorphism respectively. Therefore, methods for symmetry detection and similarity, identity measures should be functionally bijective, inverse, and invariance under a set of mathematical operations. Nevertheless, few or no existing method is functional for these properties. In this paper, a new methodological paradigm, called optinalysis, is presented for symmetry detections, similarity, and identity measures between isoreflective or autoreflective pair of mathematical structures. The paradigm of optinalysis is the re-mapping of isoreflective or autoreflective pairs with an optical scale. Optinalysis is characterized as invariant under a set of transformations and its isoreflective polymorphism behaves on polynomial and non-polynomial models.
Keywords
Autoreflectivity; Identity; Isoreflectivity; Kabirian coefficient; Similarity; Symmetry
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Commenter: Kabir Bindawa Abdullahi
Commenter's Conflict of Interests: Author
1. Grammer checked.
2. Further details and clarifications on the concept of optinalysis.
2. Sections were re-structured and edited.