{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:41:55Z","timestamp":1760218915390,"version":"build-2065373602"},"reference-count":12,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2014,2,25]],"date-time":"2014-02-25T00:00:00Z","timestamp":1393286400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We show how transformation group ideas can be naturally used to generate efficient algorithms for scientific computations. The general approach is illustrated on the example of determining, from the experimental data, the dissociation constants related to multiple binding sites. We also explain how the general transformation group approach is related to the standard (backpropagation) neural networks; this relation justifies the potential universal applicability of the group-related approach.<\/jats:p>","DOI":"10.3390\/sym6010090","type":"journal-article","created":{"date-parts":[[2014,2,25]],"date-time":"2014-02-25T11:06:23Z","timestamp":1393326383000},"page":"90-102","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Using Symmetries (Beyond Geometric Symmetries) in Chemical Computations: Computing Parameters of Multiple Binding Sites"],"prefix":"10.3390","volume":"6","author":[{"given":"Andres","family":"Ortiz","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, University of Texas at El Paso, 500 W. University, El Paso, TX 79968, USA"},{"name":"Physics Department, University of Texas at El Paso, 500 W. University, El Paso, TX 79968, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vladik","family":"Kreinovich","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, TX 79968, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2014,2,25]]},"reference":[{"key":"ref_1","unstructured":"Jaff\u00e9, H.H., and MacKenzie, R.E. (2012). Symmetry in Chemistry, Dover."},{"key":"ref_2","unstructured":"Kettle, S.F.A. (2007). Symmetry and Structure: Readable Group Theory for Chemists, Wiley."},{"key":"ref_3","unstructured":"Wigner, E.P. (1959). Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra, Academic Press."},{"key":"ref_4","unstructured":"Garey, M.G., and Johnson, D.S. (1979). 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Applications of Continuous Mathematics to Computer Science, Kluwer.","DOI":"10.1007\/978-94-017-0743-5"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02787690","article-title":"Infinite groups of Lie and Cartan, Part 1","volume":"XV","author":"Singer","year":"1965","journal-title":"J. d'Anal. Math."},{"key":"ref_11","unstructured":"Bishop, C.M. (2006). Pattern Recognition and Machine Learning, Springer."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/0893-6080(91)90074-F","article-title":"Arbitrary nonlinearity is sufficient to represent all functions by neural networks: A theorem","volume":"4","author":"Kreinovich","year":"1991","journal-title":"Neural Netw."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/6\/1\/90\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:08:34Z","timestamp":1760216914000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/6\/1\/90"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,2,25]]},"references-count":12,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2014,3]]}},"alternative-id":["sym6010090"],"URL":"https:\/\/doi.org\/10.3390\/sym6010090","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2014,2,25]]}}}