This article presents preliminary research on the general problem of reducing the number of neurons needed in a neural network so that the network can perform a specific recognition task. We consider a singlehidden-layer feedforward network in which only McCulloch-Pitts units are employed in the hidden layer. We show that if only interconnections between adjacent layers are allowed, the minimum size of the hidden layer required to solve the n-bit parity problem is n when n ≤ 4.

The authors investigate the pricing of discretely monitored dynamic fund protections when the fund price follows a lognormal process or a constant elasticity of variance (CEV) process. A backward recursive pricing formula is derived. By employing a numerical technique that combines function approximation and numerical quadrature, the authors demonstrate how to complete each recursion level efficiently. Numerical experiments show that the results compare favorably with those obtained by other pricing methods.

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