title: On the respresentation of multi-input systems: computational properties of polynomial algorithms.
abstract: This paper introduces a theoretical frame-work 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.
mesh_terms: D008433:Mathematics; D009424:Nervous System Physiological Phenomena; D010786:Photoreceptor Cells / Q000502:physiology*