{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T03:02:44Z","timestamp":1760151764070,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,19]],"date-time":"2022-04-19T00:00:00Z","timestamp":1650326400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Friendship University of Russia (RUDN University)","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>This paper presents and visualizes examples of large amounts of genetic information using a new class of cognitive computer graphics algorithms. These algorithms are related to the semiotics of perception and allow the interpretation of those properties of nucleotide sequences that are difficult to perceive by simple reading or by standard means of statistical analysis. This article summarizes previously presented algorithms for visualizing long nucleic acids based on the primary Hadamard\u2013Walsh function system. The described methods allow us to produce one-dimensional mappings of nucleic acids by levels corresponding to their scale-integral physicochemical parameters and construct a spectral decomposition of the nucleotide composition. An example of the spectral decomposition of parametric representations of molecular genetic structures is given. In addition, a multiscale composition of genetic functional mappings visualizing the structural features of nucleic acids is discussed.<\/jats:p>","DOI":"10.3390\/sym14050844","type":"journal-article","created":{"date-parts":[[2022,4,20]],"date-time":"2022-04-20T00:22:43Z","timestamp":1650414163000},"page":"844","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Spectral Decomposition of Mappings of Molecular Genetic Information in the System Basis of Single Nucleotide Functions"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3176-5279","authenticated-orcid":false,"given":"Ivan","family":"Stepanyan","sequence":"first","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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5919-0190","authenticated-orcid":false,"given":"Michail","family":"Lednev","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN), M. 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(2020). Fourier spectral density of the coronavirus genome. bioRxiv.","DOI":"10.1101\/2020.06.30.180034"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s11120-020-00721-2","article-title":"Genetic architecture of photosynthesis energy partitioning as revealed by a genome-wide association approach","volume":"150","author":"Quero","year":"2020","journal-title":"Photosynth. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"e20190470","DOI":"10.1590\/0037-8682-0470-2019","article-title":"Evaluation of genome similarities using a wavelet-domain approach","volume":"53","author":"Ferreira","year":"2020","journal-title":"Rev. Soc. Bras. Med. Trop."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1121","DOI":"10.1111\/biom.13108","article-title":"Structural learning and integrative decomposition of multi-view data","volume":"75","author":"Gaynanova","year":"2019","journal-title":"Biometrics"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"e1435","DOI":"10.1002\/wsbm.1435","article-title":"Computational methods for analyzing and modeling genome structure and organization","volume":"11","author":"Lin","year":"2019","journal-title":"WIREs Syst. Biol. Med."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1038\/s41477-020-0695-2","article-title":"An inducible genome editing system for plants","volume":"6","author":"Wang","year":"2020","journal-title":"Nat. Plants"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"e12661","DOI":"10.7717\/peerj.12661","article-title":"Novel visual analytics approach for c hro-mosome territory analysis","volume":"9","author":"Tkacz","year":"2021","journal-title":"PeerJ"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Altinsoy, E., Yang, J., and Tu, E. (2021). An improved denoising of G-banding chromosome images using cascaded CNN and binary classification network. Vis. Comput., 1\u201314.","DOI":"10.1007\/s00371-021-02273-5"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"e2107092118","DOI":"10.1073\/pnas.2107092118","article-title":"Four-dimensional chromosome reconstruction elucidates the spatiotemporal reorganization of the mammalian X chromosome","volume":"118","author":"Lappala","year":"2021","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_13","unstructured":"Lappala, A., Lee, J., Tan, K., and Sanbonmatsu, K. (2022, January 14\u201318). 4D Chromosome Organization: Combining Polymer Physics, Knot Theory and High Performance Computing. Proceedings of the APS March Meeting 2022, Chicago, IL, USA."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Goel, M., and Schneeberger, K. (2022). Plotsr: Visualising structural similarities and rearrangements between multiple genomes. bioRxiv.","DOI":"10.1101\/2022.01.24.477489"},{"key":"ref_15","unstructured":"Petoukhov, S.V. (2022, April 01). Quantum biology, universal cooperative rules in genomes, and algebraic harmony in living bodies. In Hyojeong Academic Foundation, Korea. Available online: http:\/\/petoukhov.com\/PETOUKHOV%20ARTICLE%20FOR%20KOREA.pdf."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"104273","DOI":"10.1016\/j.biosystems.2020.104273","article-title":"Hyperbolic rules of the cooperative organization of eukaryotic and prokaryotic genomes","volume":"198","author":"Petoukhov","year":"2020","journal-title":"Biosystems"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Stepanyan, I.V., and Petoukhov, S.V. (2017). The Matrix Method of Representation, Analysis and Classification of Long Genetic Sequences. Information, 8.","DOI":"10.3390\/info8010012"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s10778-019-00958-y","article-title":"Bending vibrations of bimorph piezoceramic plates of non-canonical shape","volume":"55","author":"Mobarakeh","year":"2019","journal-title":"Int. Appl. Mech."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Schember, I., and Halfon, M.S. (2022). Common Themes and Future Challenges in Understanding Gene Regulatory Network Evolution. Cells, 11.","DOI":"10.3390\/cells11030510"},{"key":"ref_20","unstructured":"Stepanyan, I.V., and Lednev, M.Y. (2020). Algorithms for Visualization of Molecular Genetic Sequences in Spaces of Binary-Orthogonal Walsh Functions: Monograph, KDU. Available online: https:\/\/bookonlime.ru\/node\/5373."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/844\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:56:33Z","timestamp":1760136993000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/5\/844"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,19]]},"references-count":20,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,5]]}},"alternative-id":["sym14050844"],"URL":"https:\/\/doi.org\/10.3390\/sym14050844","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2022,4,19]]}}}