Non-recursive Interference Calculi - A Mathematical Calculus Immanent in Nervous Activity

  • Gerd Karl HeinzEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 391)


Interference networks (IN) and interference systems have a comparable mathematical-physical background, reaching from photonic wave interference in optics over signal interference in digital filters (FIR, IIR), wave interference in Radar- or Sonar- devices to ionic pulse interference in nerve nets. Special properties of IN are short wavelength, relative timing and non-locality of function. Behind concepts of cybernetics and informatics, we find in interference integrals a hidden functional principle for nerve nets, the non-locality of function. The paper highlights integration methods in non-recursive IN. It reflects on simulation movies on the web [9].


Time Function Wave Space Interference System Interference Network Photo Plate 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bullock, T.H.: Signals and signs in the nervous system: The dynamic anatomy of electrical activity. Proc. Natl. Acad. Sci. 94(1), 1–6 (1997), MathSciNetCrossRefGoogle Scholar
  2. 2.
    Gerstner, W., Kistler, W.M.: Spiking Neuron Models. Single Neurons, Populations, Plasticity.Cambridge University Press (2002), ISBN 0 521 89079 9,
  3. 3.
    Hamilton, W.R.: Theory of Systems of Rays. In: Wilkins, D.R. (ed.) Transactions of the Royal Irish Academy, vol. 15(1828), pp. 69–174 (1828),
  4. 4.
    Heinz, G.: Zur Physik bildgebender Rekonstruktion akustischer Bilder und Filme im Zeitbereich. 33. Deutsche Jahrestagung für Akustik, Uni Stuttgart (2007),
  5. 5.
    Heinz, G.: Relativität elektrischer Impulsausbreitung.- Schlüssel zur Informatik biologischer Systeme. 39. IWK TU Ilmenau 27.-30.9, S. 238-245 (1994),
  6. 6.
    Heinz, G.: Introduction to Wave Interference Networks. In: Proceedings of Workshop 2010 Autonomous Systems, Camp de Mar, Mallorca, Spain, October 24-29, Shaker-Verlag (2010), ISBN 978-3-8322-9514-1, ISSN 1866-7791
  7. 7.
    Heinz, G.: Interference Networks as a Generalizing Signal Theory. Plenary invited lecture. In: 7th Int. Conference on Computing and Information Technology IC2IT, May 11-12, King Mongkut’s University of Technology, Bangkok (2011),
  8. 8.
    Heinz, G.: Neuronale Interferenzen, p. 300 (1993) (manuskript),
  9. 9.
    Heinz, G.: Interference integral animations (1995-2009),
  10. 10.
    Heinz, G.: Interferential Projections in Inhomogeneous Space, web-page (1997) on,
  11. 11.
    Lapicque, L.: Recherches quantitatives sur l’excitation électrique des nerfs traitée comme une polarisation. J. Physiol. Pathol. Gen. 9, 620–635 (1907)Google Scholar
  12. 12.
    McCulloch, W., Pitts, W.: A Logical Calculus of the Ideas Immanent in Nervous Activity. Bulletin of Mathematical Biophysics 5, 115–133 Google Scholar
  13. 13.
    Packard, A.: Organization of cephalopod chromatophore systems: a neuromuscular image-generator. In: Abbott, N.J., Williamson, R., Maddock, L., Cephalopod Neurobiology, pp. 331-367. Oxford Press (1995),
  14. 14.

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Gesellschaft zur Förderung angewandter Informatik e.V. (GFaI)BerlinGermany

Personalised recommendations