Elementary Holograms, Artificial Neural Networks, and Theta — Null Values
Walter Schempp · Birkhäuser Basel eBooks · 1989
Based on a unified nilpotent harmonic analysis approach to artificial neural net work models implemented with coherent optical or analog electronic neurocomputer architectures, the paper establishes a new identity for the matching polynomials of complete bichromatic graphs. The key idea is to identify the hologram plane with the three-dimensional Heisenberg nilpotent Lie group quotiented by its one-dimensional center and then to restrict the holographic transform to the holographic lattices located inside the hologram plane. The quantum mechanical treatment of optical holography is also useful in microoptics or amacronics since atoms coherently excited by short laser pulses may be as large as some transistors in microelectronic circuits and the pathways between them inside the VLSI chips. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.