Theories of how the brain computes can be differentiated in three general conceptions: the algorithmic approach, the neural information processing (neurocomputational) approach and the dynamical systems approach. The discussion of key features of brain organization (i.e. structure with function) demonstrates the self-organizing character of brain processes at the various spatio-temporal scales. It is argued that the features associated with the brain are in support of its description in terms of dynamical systems theory, and of a concept of computation to be developed further within this framework.


Stellate Cell Brain Organization Dynamical System Theory Computational Unit Functional Architecture 
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.
    Heylighen, F., Gershenson, C.: The meaning of self-organization in computing. IEEE Intelligent Systems, 72–86 (2003)Google Scholar
  2. 2.
    Schierwagen, A.: Real neurons and their circuitry: Implications for brain theory. iir-reporte, AdW der DDR, Eberswalde, 17–20 (1989)Google Scholar
  3. 3.
    Schierwagen, A.: Modelle der Neuroinformatik als Mittler zwischen neurobiologischen Fakten und Kognitionstheorien. In: Maaz, J. (ed.) Das sichtbare Denken, pp. 131–152. Rodopi-Verlag, Amsterdam (1993)Google Scholar
  4. 4.
    Senjowski, T.J., Koch, C., Churchland, P.S.: Computational Neuroscience. Science 241, 1299–1306 (1988)CrossRefGoogle Scholar
  5. 5.
    Schierwagen, A.: Growth, structure and dynamics of real neurons: Model studies and experimental results. Biomed. Biochim. Acta 49, 709–722 (1990)Google Scholar
  6. 6.
    Schierwagen, A., Claus, C.: Dendritic morphology and signal delay in superior colliculus neurons. Neurocomputing 38-40, 343–350 (2001)CrossRefGoogle Scholar
  7. 7.
    Schierwagen, A., Van Pelt, J.: Synaptic input processing in complex neurons: A model study. In: Moreno-Diaz jr., R., Quesada-Arencibia, A., Rodriguez, J.-C. (eds.) CAST and Tools for Complexity in Biological, Physical and Engineering Systems - EUROCAST 2003, pp. 221–225. IUCTC, Las Palmas (2003)Google Scholar
  8. 8.
    Van Pelt, J., Schierwagen, A.: Morphological analysis and modeling of neuronal dendrites. Math. Biosciences 188, 147–155 (2004)CrossRefzbMATHGoogle Scholar
  9. 9.
    Schierwagen, A., Alpár, A., Gärtner, U.: Scaling properties of pyramidal neurons in mice neocortex. Mathematical Biosciences (2006), doi:10.1016/j.mbs.2006.08.019Google Scholar
  10. 10.
    Van Ooyen, A. (ed.): Modeling Neural Development. MIT Press, Cambridge (2003)Google Scholar
  11. 11.
    Segev, I.: Cable and Compartmental Models of Dendritic Trees. In: Bower, J.M., Beeman, D. (eds.) The Book of GENESIS: Exploring Realistic Neural Models with the GEneral NEural SImulation System, pp. 53–81. Telos, Santa Clara (1998)Google Scholar
  12. 12.
    Schierwagen, A., Grantyn, R.: Quantitative morphological analysis of deep superior colliculus neurons stained intracellularly with HRP in the cat. J. Hirnforsch. 27, 611–623 (1986)Google Scholar
  13. 13.
    Braitenberg, V., Schüz, A.: Anatomy of the Cortex: Statistics and Geometry. Springer, Berlin (1991)Google Scholar
  14. 14.
    Creutzfeld, O.: Cortex cerebri. Leistung, strukturelle und funktionelle Organisation der Hirnrinde. Springer, Berlin (1983)Google Scholar
  15. 15.
    Hubel, D.H., Wiesel, T.N.: Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. J. Physiol. 160, 106–154 (1962)Google Scholar
  16. 16.
    Hubel, D.H., Wiesel, T.N.: Receptive fields and functional architecture of monkey striate cortex. J. Physiol. 195, 215–243 (1968)Google Scholar
  17. 17.
    Sporns, O., Tononi, G., Edelman, G.M.: Theoretical neuroanatomy and the connectivity of the cerebral cortex. Behav. Brain Res. 135, 69–74 (2002)CrossRefGoogle Scholar
  18. 18.
    Watts, D.J., Strogatz, S.H.: Collective dynamics of “small-world” networks. Nature 393, 440–442 (1998)CrossRefGoogle Scholar
  19. 19.
    Churchland, P., Grush, R.: Computation and the brain. In: Keil, F., Wilson, R.A. (eds.) The MIT Encyclopedia of Cognitive Sciences, pp. 155–158. MIT Press, Cambridge (1999)Google Scholar
  20. 20.
    Turing, A.M.: On computable numbers, with an application to the Entscheidungsproblem. Proc. Lond. Math. Soc. 42, 230–265 (1936)CrossRefzbMATHGoogle Scholar
  21. 21.
    Mira, J., Delgado, A.E.: On how the computational paradigm can help us to model and interpret the neural function. Natural Computing (2006), doi:10.1007/s11047-006-9008-6Google Scholar
  22. 22.
    de Charms, R.C., Zador, A.M.: Neural representation and the cortical code. Ann. l Rev. Neurosci. 23, 613–647 (2000)CrossRefGoogle Scholar
  23. 23.
    Searle, J.R.: Is the brain a digital computer? Proc. Amer. Philos. Assoc. 64, 21–37 (1990)CrossRefGoogle Scholar
  24. 24.
    Grush, R.: The semantic challenge to computational neuroscience. In: Machamer, P.K., Grush, R., McLaughlin, P. (eds.) Theory and method in the neurosciences, pp. 155–172. University of Pittsburgh Press, Pittsburg (2001)Google Scholar
  25. 25.
    McCulloch, W.S., Pitts, W.: A logical calculus of the ideas immanent in nervous activity. Bull. Math. Biol. 52, 99–115 (1943)Google Scholar
  26. 26.
    Euler, T., Denk, W.: Dendritic processing. Curr. Opin. Neurobiol. 11, 415–422 (2001)CrossRefGoogle Scholar
  27. 27.
    Polsky, A., Mel, B.W., Schiller, J.: Computational subunits in thin dendrites of pyramidal cells. Nature Neurosci. 7, 621–627 (2004)CrossRefGoogle Scholar
  28. 28.
    London, M., Hausser, M.: Dendritic computation. Annu. Rev. Neurosci. 28, 503–532 (2005)CrossRefGoogle Scholar
  29. 29.
    Maass, W., Zador, A.M.: Synapses as Computational Units. Neural Computation 11, 903–917 (1999)CrossRefGoogle Scholar
  30. 30.
    Zador, A.M.: The basic unit of computation. Nature Neurosci. 3(Suppl.), 1167 (2000)Google Scholar
  31. 31.
    Hubel, D.H., Wiesel, T.N.: Functional architecture of macaque monkey cortex. Proc. R. Soc. London Ser. B 198, 1–59 (1977)CrossRefGoogle Scholar
  32. 32.
    Mountcastle, V.B.: The columnar organization of the neocortex. Brain 120, 701–722 (1997)CrossRefGoogle Scholar
  33. 33.
    Szentágothai, J.: The modular architectonic principle of neural centers. Rev. Physiol. Bioche. Pharmacol. 98, 11–61 (1983)CrossRefGoogle Scholar
  34. 34.
    Markram, H.: The Blue Brain Project. Nature Rev. Neurosci. 7, 153–160 (2006)CrossRefGoogle Scholar
  35. 35.
    Maass, W., Markram, H.: Theory of the computational function of microcircuit dynamics. In: Grillner, S., Graybiel, A.M. (eds.) The Interface between Neurons and Global Brain Function, Dahlem Workshop Report 93, pp. 371–390. MIT Press, Cambridge (2006)Google Scholar
  36. 36.
    DeFelipe, J., Alonso-Nanclares, L., Arellano, J.I.: Microstructure of the neocortex: Comparative aspects. J. Neurocytol. 31, 299–316 (2002)CrossRefGoogle Scholar
  37. 37.
    Horton, J.C., Adams, D.L.: The cortical column: a structure without a function. Phil. Trans. R. Soc. B 360, 837–862 (2005)CrossRefGoogle Scholar
  38. 38.
    Siegelmann, H.T., Fishman, S.: Analog computation with dynamical systems. Physica D 120, 214–235 (1998)CrossRefzbMATHGoogle Scholar
  39. 39.
    Siegelmann, H.T.: Neural Networks and Analog Computation: Beyond the Turing Limit. Birkhauser, Boston (1999)zbMATHGoogle Scholar
  40. 40.
    Schierwagen, A., Werner, H.: Analog computations with mapped neural fields. In: Trappl, R. (ed.) Cybernetics and Systems ’96, pp. 1084–1089. Austrian Society for Cybernetic Studies, Vienna (1996)Google Scholar
  41. 41.
    Schierwagen, A., Werner, H.: Fast orienting movements to visual targets: Neural field model of dynamic gaze control. In: 6th European Symposium on Artificial Neural Networks - ESANN ’98, pp. 91–98. D-facto publications, Brussels (1998)Google Scholar
  42. 42.
    Wellner, J., Schierwagen, A.: Cellular-Automata-like Simulations of Dynamic Neural Fields. In: Holcombe, M., Paton, R.C. (eds.) Information Processing in Cells and Tissues, pp. 295–304. Plenum, New York (1998)Google Scholar
  43. 43.
    Adamatzky, A.: Computing in Nonlinear Media: Make Waves, Study Collisions. In: Kelemen, J., Sosík, P. (eds.) ECAL 2001. LNCS (LNAI), vol. 2159, pp. 1–10. Springer, Heidelberg (2001)Google Scholar
  44. 44.
    Sienko, T., Adamatzky, A., Rambidi, N.G., Conrad, M. (eds.): Molecular Computing. MIT Press, Cambridge (2003)zbMATHGoogle Scholar
  45. 45.
    Sporns, O., Chialvo, D.R., Kaiser, M., Hilgetag, C.C.: Organization, development and function of complex brain networks. Trends Cogn. Sci. 8, 418–425 (2004)CrossRefGoogle Scholar
  46. 46.
    Buzsaki, G., Geisler, C., Henze, D.A., Wang, X.J.: Interneuron diversity series: circuit complexity and axon wiring economy of cortical interneurons. Trends Neurosci. 27, 186–193 (2004)CrossRefGoogle Scholar
  47. 47.
    Bassett, D.S., Bullmore, E.: Small-world brain networks. Neuroscientist 12, 512–523 (2006)CrossRefGoogle Scholar
  48. 48.
    Shimizu, H.: Biological autonomy: the self-creation of constraints. Applied Mathematics and Computation 56, 177–201 (1993)CrossRefzbMATHGoogle Scholar
  49. 49.
    Pasemann, F.: Neuromodules: A dynamical systems approach to brain modelling. In: Herrmann, H.J., Wolf, D.E., Poppel, E. (eds.) Supercomputing in Brain Research: From Tomography to Neural Networks, pp. 331–348. World Scientific, Singapore (1995)Google Scholar
  50. 50.
    Hülse, M., Wischmann, S., Pasemann, F.: The role of non-linearity for evolved multifunctional robot behavior. In: Moreno, J.M., Madrenas, J., Cosp, J. (eds.) ICES 2005. LNCS, vol. 3637, pp. 108–118. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Andreas Schierwagen
    • 1
  1. 1.Institute for Computer Science, Intelligent Systems Department, University of Leipzig, LeipzigGermany

Personalised recommendations