Constructive approximations for neural networks by sigmoidal functions

Article Abstract:

Mappings of a real continuous function f(x) can be efficiently approximated using finite linear combinations of bounded sigmoidal functions. A function sigma(x) is sigmoidal if the limit of the function as x approaches +(infinity) = 1 and the limit of the function as x approaches -(infinity) = 0. A continuous function can be approximated by a finite sum of continuous ridge functions. By determining the sigmoidal approximation on the interval from 0 to 1, the general approximation can be determined by a ridge expansion.

Neural networks, Algorithms, Algorithm, Mathematics of Computing, Approximation, Function Analysis, technical, Neural Network

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Switching Functions and Solid Geometrical Modeler

Article Abstract:

A set-operations solid geometrical modeler is based on representation of objects by switching functions and can perform set operations very efficiently. An extended three-dimensional Karnaugh map provides graphical support and communication with the real world. Example objects and set operations are illustrated.

Geometry, Modeling, Data modeling software, Boolean Algebra, Solids Modeling, Solid models

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