Percolation and Frustration in Neural Networks

  • A. J. Noest
Conference paper
Part of the NATO ASI Series book series (volume 20)


There are reasons to believe that the theoretical and computational techniques of solid state physics can be used to get an understanding of the dynamics of the brain. Here I shall approach along similar lines a related, but less ambitious set of problems stemming from tissue-culture experiments with foetal rat cortex neurons [1]. Starting from a planar array of disconnected cells, dendrites and axons grow out slowly, leading via the formation of clusters of connected cells to a percolating network. After a week, synapses develop at the contacts, allowing the cells to transmit spike-signals by a discrete stochastic process. Growth of the network is much slower than spike-propagation. Two main cell types exist: excitatory cells that increase the spike rate of their target cells, and inhibitory cells that decrease it.


Critical Exponent Universality Class Inhibitory Cell Spike Rate Spacetime Structure 
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  1. 1-.
    F.van Huizen,H.J.Romijn and A.M.M.C. Habets, Dev.Brain Res, 19(1985)67CrossRefGoogle Scholar
  2. 2-.
    W.Kinzel, In:”Percolation Structures and Processes”, G.Deutsch,R.Zallen and J.Adler ,Eds.,Adam Hilger,Bristol,1983Google Scholar
  3. 3-.
    L.S.Schulman and P.E.Seiden,In:”Percolation Structures and Processes”, G.Deutsch,R.Zallen and J. Adler,Eds.,Adam Hilger,Bristol,1983Google Scholar
  4. 4-.
    “Biological Growth and Spread”,Lect.Notes in Biomathematics #38, W.Jaeger, H.Rost and P.Tautu,Eds.,Springer,Berlin,1979Google Scholar
  5. 5-.
    A.B.Harris,J.Phys.C 7(1974)1671CrossRefGoogle Scholar
  6. 6-.
    D.Andelman and A.N.Berker,Phys.Rev.B 29(1984)2630CrossRefGoogle Scholar
  7. 7-.
    J.Vannimenus,J.P.Nadal and H.Martin,J. Phys.A 17(1984)L351-L356MathSciNetCrossRefGoogle Scholar
  8. 8-.
    W.Kinzel,Z.Phys.B(Condensed Matter) 58(1985)229–244zbMATHMathSciNetCrossRefGoogle Scholar
  9. 9-.
    E.Domany and W.Kinzel,Phys.Rev.Lett. 53(1984)311MathSciNetCrossRefGoogle Scholar
  10. 10-.
    W.F.Wolff and J.Zittarz,In:”Heidelberg Colloqium on Spinglasses”, Lect.Notes in Physics #192,J.L.van Hemmen and I.Morgenstein, Eds.,Springer,Berlin,1983Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • A. J. Noest
    • 1
  1. 1.Netherlands Institute for Brain ResearchAmsterdamThe Netherlands

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