A view of the Scripture revelations concerning a future by Richard Whately

By Richard Whately

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Derivative as stated by Werbos ( 1 988), will be used stimuli were calculated with an algorithm that here. The conventional partial derivative 8J/8xi(k) resembles the BIT algorithm. After a certain refers to the direct causal impact of xi(k) on J, constant begin state has been chosen steps b, c and while the ordered derivative a +J/8xi(k) (notice the d of the BIT algorithm were performed, followed plus sign) refers to the total causal impact, by an adaptation of ui(k) in the negative direction including both direct and indirect effects.

That is, if f is the nonlinear function Figure 1 : A feed forward network with one hidden which we want to approximate then Y1c = J(X1c ) layer. for k = 1 . . N . Collect all weights and thresholds into a parameter vector 0. The network will then chosen so that the loss function, be expressed by a function, g( . , ·), which is param­ N eterized by 0 and has current value of X1c as input. 6) VN ( O, Z ) = The resulting error obtained by the network, t:, can 2N k=l be written t:(O, z,. ) Y,. - g(O, x,.

Recent theoretical results (Cybenko, 1989; Funahashi, 1989) have in fact rigorously proven that most realisable vector functions can be approximated arbitrarily by a feedforward network with only a single hidden layer of nonlinear elements. Utilising the nonlinear vector function approximation capabilities of the feedforward neural network has offered many interesting possibilities for the modelling and the control of nonlinear and ill-defined plants common in industrial applications (eg. Willis, Di Massimo, Montague, Tham and Morris, 199 1 ; Wu, Hogg and Irwin, 1 992).

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