Neural structures using the eigenstates of a quantum harmonic oscillator

Rigatos, G; Tzafestas, S

dc.contributor.author	Rigatos, G	en
dc.contributor.author	Tzafestas, S	en
dc.date.accessioned	2014-03-01T01:24:42Z
dc.date.available	2014-03-01T01:24:42Z
dc.date.issued	2006	en
dc.identifier.issn	1230-1612	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/17405
dc.subject	Diffusion Equation	en
dc.subject	Feed Forward Neural Network	en
dc.subject	Function Approximation	en
dc.subject	Harmonic Oscillator	en
dc.subject	Hermite Polynomial	en
dc.subject	Nonparametric Estimation	en
dc.subject	System Modelling	en
dc.subject	Feedforward Neural Network	en
dc.subject	Fourier Transform	en
dc.subject	Neural Network	en
dc.subject.classification	Thermodynamics	en
dc.subject.classification	Computer Science, Information Systems	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.classification	Mechanics	en
dc.subject.classification	Physics, Mathematical	en
dc.subject.classification	Statistics & Probability	en
dc.title	Neural structures using the eigenstates of a quantum harmonic oscillator	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s11080-006-7265-6	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s11080-006-7265-6	en
heal.language	English	en
heal.publicationDate	2006	en
heal.abstract	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 Schrödinger'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. © Springer 2006.	en
heal.publisher	SPRINGER	en
heal.journalName	Open Systems and Information Dynamics	en
dc.identifier.doi	10.1007/s11080-006-7265-6	en
dc.identifier.isi	ISI:000235808600003	en
dc.identifier.volume	13	en
dc.identifier.issue	1	en
dc.identifier.spage	27	en
dc.identifier.epage	41	en