

Modelling the Brains Labyrinth
23.27. September 2006
Fodele Beach Hotel
Crete island, Greece
Wave Interference Networks  State of Research
Gerd Heinz, GFaI Berlin, info@gheinz.de
The possibility to excite any neuron is higher if different excitements reach it in the same time. But every excitement is delayed by different circumstances on different paths.
The abstraction ‘Interference Network’ (IN)
http://www.gheinz.de/publications/intro/interferenznetzwerk.htm
allows the analysis and simulation of complex, delaying networks without too much knowledge about details. A graph of the threedimensional structure with delays, with neuronal timefunctions and with integration behaviour offers a lot about the general behaviour of a nerve net.
For example we will find that the delay structure of a large net defines different excitatory and inhibiting possibilities, resulting in signaltheoretical descriptions of neural functions, compare to
http://www.gheinz.de/historic/biomodel/models.htm
Implementing the term “Interference Integral” (I²), relations between emitting source points and receiving source points can be found. Interference projections for far communications over long fibres can be understood in opticallike relations: the interference integrals appear mirrored, comparable to lens projections, if we suppose single impulses or long intervals between pulses. Analysing meeting points of periodical waves, we find a kind of frequency maps, see
http://www.gheinz.de/historic/pressinf/pattern.gif
In the sight of IN, the difference between to see and to hear results only in different network parameters. A specific investigation of such parameters offers, that both possibilities match in a holomorphic way. Projections and frequency maps, seeing and hearing are organized in hologramlike structures, compare with a 3channel interference projection of Glike arranged emissions
http://www.gheinz.de/historic/pressinf/g_pr10c.gif
Analysing the influence of velocities on long fibres, we detect a possibility to move the projections on a neural ‘screen’. Analysing changing field velocities, we find zooming projections,
http://www.gheinz.de/historic/pressinf/bilder_d.htm
Combining fibres from different sources, the interference integrals merge, see
http://www.gheinz.de/historic/pressinf/gh_konj4.gif
Reasoned by phaseinvariants, a field theoretical investigation shows, that interference networks disrupt the range of complex number theory in real applications. That means that Fourier, Wavelet or Gabor Transformations can not be applied for the analysis of nerve networks. But not only interferences in nerve nets, also quantum field analysis are concerned.
For further reading see papers on
http://www.gheinz.de/publications/index.htm
Proceedings T26, p. 53
