{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,26]],"date-time":"2025-10-26T14:05:52Z","timestamp":1761487552231},"reference-count":10,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2006,3]]},"abstract":"<jats:p> The main result of the paper is the use of orthogonal Hermite polynomials as the basis functions of feedforward neural networks. The proposed neural networks have some interesting properties: (i) the basis functions are invariant under the Fourier transform, subject only to a change of scale, (ii) the basis functions are the eigenstates of the quantum harmonic oscillator, and stem from the solution of Schr\u00f6dinger's diffusion equation. The proposed feed-forward neural networks demonstrate the particle-wave nature of information and can be used in nonparametric estimation. Possible applications of the proposed neural networks include function approximation, image processing and system modelling. <\/jats:p>","DOI":"10.1007\/s11080-006-7265-6","type":"journal-article","created":{"date-parts":[[2006,3,4]],"date-time":"2006-03-04T06:37:46Z","timestamp":1141454266000},"page":"27-41","source":"Crossref","is-referenced-by-count":12,"title":["Neural Structures Using the Eigenstates of a Quantum Harmonic Oscillator"],"prefix":"10.1142","volume":"13","author":[{"given":"Gerasimos","family":"Rigatos","sequence":"first","affiliation":[{"name":"Unit of Industrial Automation, Industrial Systems Institute, 26504 Rion Patras, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Spyros","family":"Tzafestas","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, National Technical University of Athens, 15773 Zografou Athens, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,17]]},"reference":[{"key":"rf1","volume-title":"M\u00e9canique Quantique I","author":"Cohen-Tannoudji C.","year":"1998"},{"key":"rf2","volume-title":"Partial Differential Equations: An Introduction","author":"Strauss W. A.","year":"1992"},{"key":"rf3","volume-title":"Neural networks and fuzzy systems: A dynamical systems approach to machine intelligence","author":"Kosko B.","year":"1992"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0255(99)00101-2"},{"key":"rf5","first-page":"249","author":"Resconi G.","journal-title":"Information Sciences, Elsevier"},{"key":"rf6","first-page":"157","volume":"4","author":"Perus M.","journal-title":"Nonlinear Phenomena in Complex Systems"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1109\/TFUZZ.2002.800690"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1046\/j.1365-8711.2003.05901.x"},{"key":"rf10","volume-title":"Neural Networks: A Comprehensive Foundation","author":"Haykin S.","year":"1994"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1109\/TNN.2005.851786"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1007\/s11080-006-7265-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:03:29Z","timestamp":1565121809000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1007\/s11080-006-7265-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,3]]},"references-count":10,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2012,4,17]]},"published-print":{"date-parts":[[2006,3]]}},"alternative-id":["10.1007\/s11080-006-7265-6"],"URL":"https:\/\/doi.org\/10.1007\/s11080-006-7265-6","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,3]]}}}