Abstract
This paper presents a family of differential equations which describe in a concise way various phenomena of ontogenetic organisation in the Central Nervous System. We consider four different types of “pattern formation”: (i) development of stimulus selectivity in individual neurons, (ii) spatial organisation of selectivity in the nervous tissue, (iii) development of topographic mappings, (iv) development of spatially periodic mappings. In the last two decades, many mathematical models have been proposed with the common goal of explaining how such global, or “macroscopic”, regularities can arise from local, or “microscopic”, interactions. This work is essentially an effort towards unification: in providing a simple evolution scheme, the asymptotic behaviour of which is sufficiently rich to account for the main patterns of organisation, our aim is to make explicit what the minimal ingredients are. These ingredients, or principles, present in virtually all the models proposed so far, are cooperation and competition. It is our belief that analogous principles are responsible for many self-organisation phenomena in various domains. Thus, the model that is presented here, in providing some suggestions as to how the elementary bricks should be put together, could help to design a framework for a simple theory of self-organisation.
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References
Bienenstock, E.L., Cooper, L.N., and Munro, P. (1982), Theory for the development of neuron selectivity: orientation specificity and binocular interaction in visual cortex. The Journal of Neuroscience 2, N°1, 32–48.
von der Malsburg, Ch. (1973), Self-organisation of orientation sensitive cells in the striate cortex. Kybernetik 14, 85–100.
Cooper, L.N., Lieberman, F., and Oja, E. (1979), A theory for the acquisition and loss of neuron specificity in visual cortex. Biol. Cybern. 33, 9–28.
Eigen, M. (1971), Selforganization of Matter and the Evolution of Biological Macromolecules. Naturwissenschaften 58, 465–523.
Grossberg, S. (1980), Biological competition: Decision rules, pattern formation, and oscillations. Proc. Natl. Acad. Sci. USA 77, N° 4, 2338–2342.
Swindale, N.V. (1982), A model for the formation of orientation columns. Proc. R. Soc. Lond. B215, 211–230.
von der Malsburg, Ch., and Cowan, J.D. (1982), Outline of a Theory for the Ontogenesis of Iso-Orientation Domains in Visual Cortex. Biol. Cybern. 45, 49–56.
Willshaw, D.J., and von der Malsburg, Ch. (1976), How patterned neural connections can be set up by self organization. Proc. R. Soc. Lond. B194, 431–445.
von der Malsburg, Ch., and Willshaw, D.J. (1977), How to label nerve cells so that they can interconnect in an ordered fashion. Proc. Natl. Acad. Sci. USA 74, N°11, 5176–5178.
Willshaw, D.J., and von der Malsburg, Ch. (1979), A marker induction mechanism for the establishment of ordered neural mappings: its applications to the retinotectal problem. Philosoph. Trans. R. Soc. Lond. B287, 203–243
von der Malsburg, Ch., and Willshaw, D.J. (1981), Differential equations for the development of topological nerve fibre projections. SIAM-AMS Proceedings 13, 39–47.
Häussier, A.F., and von der Malsburg, Ch. (1983), Development of retinotopic projections — An analytic treatment. J. Theor. Neurobiol. (in press).
von der Malsburg, Ch. (1983), How are nervous structures organized? This volume.
Haken, H. (1978), Synergetics, an Introduction. Springer Verlag, Berlin, Heidelberg, New-York.
von der Malsburg, Ch. (1979), Development of ocularity domains and growth behavior of axon terminals. Biol. Cybernetics 32, 49–62.
Swindale, N.V. (1980), A model for the formation of ocular dominance stripes. Proc. R. Soc. Lond. B208, 243–264.
von der Malsburg, Ch. (1981), The Correlation Theory of Brain Function. Internal report 81–82, Dept. of Neurobiology, Max-Planck-Institute for Biophysical Chemistry, D-3400 Göttingen, W.-Germany.
Geman, S. (1981), Notes on a self-organizing machine. In: Parallel Models of Associative Memory. Ed. by J. Anderson and G. Hinton, Lawrence Erlbaum Associates, Hillsdale, N.J.
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© 1983 Springer-Verlag Berlin Heidelberg
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Bienenstock, E. (1983). Cooperation and Competition in Central Nervous System Development: A Unifying Approach. In: Başar, E., Flohr, H., Haken, H., Mandell, A.J. (eds) Synergetics of the Brain. Springer Series in Synergetics, vol 23. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-69421-9_20
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DOI: https://doi.org/10.1007/978-3-642-69421-9_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-69423-3
Online ISBN: 978-3-642-69421-9
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