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On the Topological Representation of Signals in Self-Organizing Nerve Fields

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Part of the book series: Lecture Notes in Biomathematics ((LNBM,volume 71))

Abstract

The brain can self-organize its structure based on environmental information. More specifically, when a set of signals is applied repeatedly to a nerve system, for each signal in the set, the system forms by self-organization sets of representative cells that are excited in response to particular signals but are not excited by any other signals. Such a representation may be regarded as a model of the outer world formed in the nervous system. This is one simple aspect of self-organization taking place in the brain. Physiologists have so far found hypercolumnar and microcolumnar structures in the primary visual cortex in which orientation-detecting cells, i.e., cells representative of lines of various orientations, are formed and fixed by self-organization. Moreover, hypercolumns are arranged retinotopically, and orientation-detecting cells are arranged in each hypercolumn in the order of preferable orientations. Physiologists have also found in various parts of the cerebrum cells which are responsive to specific shapes of objects, specific types of motions, and, in particular, faces of men or monkeys.

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References

  • Amari, S. [1977]: Dynamics of Pattern Formation in Lateral-Inhibition Type Neural Fields. Biological Cybernetics, Vol.27, pp.77–87

    Article  MATH  MathSciNet  Google Scholar 

  • Amari, S. [1980]: Topolographic Organization of Nerve Fields. Bull. of Math. Biology, Vol.42, pp.339–364

    MATH  MathSciNet  Google Scholar 

  • Amari, S. [1983]: Field theory of self-organizing neural nets, IEEE Trans. Systems, Man and Cybernetics, Vol.SMC-13, No.9 & 10, pp.741–748

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  • Kohohen, T. [1984]: Self-Organization and Associative Memory, Springer

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  • Takeuchi, A. and Amari, S. [1979]: Formation of topographic maps and columnar microstructures, Biological Cybernetics, Vol.35, pp.63–72

    Article  MATH  MathSciNet  Google Scholar 

  • Willshaw, D.J. and Malsburg, C. von der [1976]: How patterned neural connections can be set up by self-organization, Proc. Roy. Soc. Lond., B-194, pp.431–445

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© 1987 Springer-Verlag Berlin Heidelberg

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Amari, Si., Maruyama, M. (1987). On the Topological Representation of Signals in Self-Organizing Nerve Fields. In: Teramoto, E., Yumaguti, M. (eds) Mathematical Topics in Population Biology, Morphogenesis and Neurosciences. Lecture Notes in Biomathematics, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93360-8_27

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  • DOI: https://doi.org/10.1007/978-3-642-93360-8_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17875-0

  • Online ISBN: 978-3-642-93360-8

  • eBook Packages: Springer Book Archive

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