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On the representation of multi-input systems: Computational properties of polynomial algorithms

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Poggio,  T
Former Department Information Processing in Insects, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Reichardt,  W
Former Department Information Processing in Insects, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Poggio, T., & Reichardt, W. (1980). On the representation of multi-input systems: Computational properties of polynomial algorithms. Biological Cybernetics, 37(3), 167-186. doi:10.1007/BF00355455.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-F100-9
Abstract
This paper introduces a theoretical framework for characterizing and classifying simple parallel algorithms and systems with many inputs, for example an array of photoreceptors. The polynomial representation (Taylor series development) of a large class of operators is introduced and its range of validity discussed. The problems involved in the polynomial approximation of systems are also briefly reviewed. Symmetry properties of the input-output map and their implications for the system structure (i.e. its kernels) are studied. Finally, the computational properties of polynomial mappings are characterized.