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Computation Of Invariants In Continuous And Discrete Manifolds

Report Number: AMRL TDR 63-40
Author: Inselberg, Alfred
Author: Foerster, Heinz
Author: von Yeh, Raymond
Author: Cheng, Shih-mei
Corporate Author: Illinois Univ Urbana Electrical Engineering Research Lab
Laboratory: Biophysics Laboratory
Date of Publication: 1963-05
Pages: 114
Contract: AF 33(616)-6428
Project: 7232
Task: 723205
AD Number: AD0411300

Systems capable of identifying objects must be able to detect the properties (invariants) these objects possess. It is shown that property de tecting systems consisting of networks of linear or non-linear elements in parallel may be con structed without accurate point to point connec tions as long as certain constraints on the dis tribution of connectivity among elements in the network are satisfied. The report discusses in three parts a general approach toward ''property detection'' and considers in particular networks capable of detecting acoustical invariants. While the first part ''Computation of Invariants in Linearly Interacting Continua'' considers networks whose elements constitute a continum, the second part ''Kinds of Interaction in Sets of Discrete Linear Elements'' treats discrete networks. In both papers the distinction is made between interaction phenomena within a network and action phenomena from one network to another network. It is shown that under fairly general conditions action and interaction systems are equivalent. The third part ''Simulation of Interaction Func tions on PACE Analog Computer'' is concerned with the simulation of some action and interaction nomena on an analog computer.

Lockheed Martin Missiles & Fire Control
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