Advertisement

Development of Neural Network Structure with Biological Mechanisms

  • Samuel Johnson
  • Joaquín Marro
  • Jorge F. Mejias
  • Joaquín J. Torres
Conference paper
  • 1.3k Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5517)

Abstract

We present an evolving neural network model in which synapses appear and disappear stochastically according to bio-inspired probabilities. These are in general nonlinear functions of the local fields felt by neurons—akin to electrical stimulation—and of the global average field—representing total energy consumption. We find that initial degree distributions then evolve towards stationary states which can either be fairly homogeneous or highly heterogeneous, depending on parameters. The critical cases—which can result in scale-free distributions—are shown to correspond, under a mean-field approximation, to nonlinear drift-diffusion equations. We show how appropriate choices of parameters yield good quantitative agreement with published experimental data concerning synaptic densities during brain development (synaptic pruning).

Keywords

Neural networks Brain development synaptic pruning 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 79, 2554–2558 (1982)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Amit, D.J.: Modeling Brain Function. Cambridge Univ. Press, Cambridge (1989)CrossRefzbMATHGoogle Scholar
  3. 3.
    Mejias, J.F., Torres, J.J.: The role of synaptic facilitation in coincidence spike detection. J. Comp. Neurosci. 24, 222–234 (2008)CrossRefGoogle Scholar
  4. 4.
    Johnson, S., Marro, J., Torres, J.J.: Functional optimization in complex excitable networks. EPL 83, 46006 (2008)CrossRefGoogle Scholar
  5. 5.
    Huttenlocher, P.R., Dabholkar, A.S.: Regional differences in synaptogenesis in human cerebral cortex. Joural of Comparative Neurology 387, 167–178 (1997)CrossRefGoogle Scholar
  6. 6.
    De Roo, M., Klauser, P., Mendez, P., Poglia, L., Muller, D.: Activity-dependent PSD formation and stabilization of newly formed spines in hippocampal slice cultures. Cerebral Cortex 18, 151–161 (2008)CrossRefGoogle Scholar
  7. 7.
    Klintsova, A.Y., Greenough, W.T.: Synaptic plasticity in cortical systems. Current Opinion in Neurobiology 9, 203–208 (1999)CrossRefGoogle Scholar
  8. 8.
    Chechik, G., Meilijson, I., Ruppin, E.: Synaptic pruning in development: A computational account. Neural Comput. 10(7), 1759–1777 (1998)CrossRefGoogle Scholar
  9. 9.
    Chechik, G., Meilijson, I., Ruppin, E.: Neuronal regulation: A mechanism for synaptic pruning during brain maturation. Neural Comp. 11(8), 2061–2080 (1999)CrossRefGoogle Scholar
  10. 10.
    Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: Structure and dynamics. Phys. Rep. 424, 175 (2006)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Hebb, D.O.: The organization of behavior. Wiley, New YorkGoogle Scholar
  12. 12.
    Mejias, J.F., Torres, J.J.: Maximum memory capacity on neural networks with short-term synaptic depression and facilitation. Neural Comp. 21(3), 851–871 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 509–512 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Johnson, S., Marro, J., Torres, J.J.: Nonlinear preferential rewiring in fixed-size networks as a diffusion process (submitted)Google Scholar
  15. 15.
    Johnson, S., Marro, J., Torres, J.J.: A nonlinear evolving network model, and its application to brain development (submitted)Google Scholar
  16. 16.
    Eguíluz, V.M., Chialvo, D.R., Cecchi, G.A., Baliki, M., Apkarian, A.V.: Scale-free brain functional networks. Phys. Rev. Lett. 94, 018102 (2005)CrossRefGoogle Scholar
  17. 17.
    Zhou, C., Zemanova, L., Zamora, G., Hilgetag, C.C., Kurths, J.: Hierarchical organization unveiled by functional connectivity in complex brain networks. Phys. Rev. Lett. 97, 238103 (2006)CrossRefGoogle Scholar
  18. 18.
    Kaiser, M., Martin, R., Andras, P., Young, M.P.: Simulation of robustness against lesions of cortical networks. Eur. J. Neurosci. 25 (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Samuel Johnson
    • 1
  • Joaquín Marro
    • 1
  • Jorge F. Mejias
    • 1
  • Joaquín J. Torres
    • 1
  1. 1.Instituto Carlos I de Física Teórica y Computacional, and Departmento de Electromagnetismo y Física de la MateriaUniversity of GranadaSpain

Personalised recommendations