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Neural Structures Using the Eigenstates of a Quantum Harmonic Oscillator

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Open Systems & Information Dynamics

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.

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Authors and Affiliations

  1. Unit of Industrial Automation, Industrial Systems Institute, 26504, Rion Patras, Greece

    Gerasimos Rigatos

  2. Department of Electrical and Computer Engineering, National Technical University of Athens, 15773, Zografou Athens, Greece

    Spyros Tzafestas

Authors
  1. Gerasimos Rigatos
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  2. Spyros Tzafestas
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Correspondence to Gerasimos Rigatos.

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Rigatos, G., Tzafestas, S. Neural Structures Using the Eigenstates of a Quantum Harmonic Oscillator. Open Syst Inf Dyn 13, 27–41 (2006). https://doi.org/10.1007/s11080-006-7265-6

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  • DOI: https://doi.org/10.1007/s11080-006-7265-6

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