The synchronization of impulse generation in non-oscillating networks of excitatorily coupled formal neurons is investigated. The influence of network parameters and of the external stimulation on the attainable level of synchrony is quantified. It turns out that synchrony accurate to a of few tenths of the impulse duration can be achieved and that it is barely influenced by moderate deviations from the optimum parameter values.

This tutorial starts from the most basic form of pattern classification – that permits unequivocal signal reconstruction and can be applied, if all signals of interest are known – and then introduces to the principles of geometrically invariant classification. The main part deals with two prominent kinds of classifiers – namely polynomial (Perceptron-like) and multi-linear (SigmaPi-like) approaches – that permit ideal or near to ideal class definitions and are suited for geometrically invariant classification. For unrestricted translation invariant classification, the methods are compared with respect to performance and computational costs. The theoretical considerations are exemplified by easy to understand examples.

A theorem is proven that serves as the mathematical basis for the proposed global shift-vector extraction. This theorem states the identity of the difference vector between the centres of gravity (centroids) of two arbitrary n-dimensional density functions, with the centroid vector of their cross-correlation function. Consequently, the centroid of the cross-correlation function of consecutive manifestations of an arbitrarily transforming density function indicates its incremental shift vector. Advantages of this approach for implementations in massively parallel computing structures as well as applications, such as visual velocity estimation of non-rigid objects, are discussed.