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In this paper, a fuzzy-logic FAM (fuzzy associative memory) matrix classifier is used for the classification (diagnosis) of breast cancer. It is implemented in Mathematica 3.0 and tested on two features (radius and perimeter) from the Wisconsin breast cancer database. The sensitivity of the FAM-matrix classifier is 94.29%, and its specificity is 73.33%.

Like standard discrete artificial neural networks (ANNs), continual neurodynamical systems can be used for the classification and diagnosis of breast cancer. In this paper, a two-feature generalized bidirectional associative memory (GBAM) classifier is formulated in tensorial invariant form. It is implemented in Mathematica 3.0 and tested on two sample features (the radius and perimeter of cell nuclei in fine-needle aspiration slides) from the Wisconsin breast-cancer database. The classification accuracy obtained (86%), together with the invariance of the classification result upon the variation of the dimensions and output form of the neural activation fields, shows the potential classification ability of theoretical classifiers that are directly implemented in computer algebra systems.

This paper contains results on the design of optimum equalizers to eliminate intersymbol interference in linear non-minimum phase channels conveying binary signals. The optimization is with respect to an open eye condition with a given delay. For causal stable channels with non-minimum phase zeros, we argue that this problem requires only the consideration of the FIR modified channel that has all the non-minimum phase zeros of the original channel. We show that if this modified channel can be equalized to yield an equalized system that is open eye with a specified delay, then the optimizing equalizer is, in fact FIR with all zeros outside the unit circle, and the impulse response of the equalised channel does not extend beyond the delay. We also give a simple necessary and sufficient condition to determine if for a particular delay, a given channel can be equalized to achieve an equalized response that is open eye.