We study a light-cone model of the nucleon and the $S_{11}\mathrm{}\left(1535\right)\mathrm{}$ resonance which provides a relativistic generalization of the constituent-quark model in the nonperturbative low-$Q^2$ regime. The two parameters of the model, namely, the size parameter $\alpha$ and the constituent-quark mass $m_q\approx 300$ MeV, are fixed by the axial form factor. We find good agreement for the electromagnetic form factors of the nucleon up to $Q^2\approx 1-2$ Ge${\mathrm{V}}^2$. All static properties of the nucleon, except for the neutron charge radius, are reproduced within 10%. In addition, we show that the electromagnetic current of the nucleon is conserved. The $S_{11}\mathrm{}\left(1535\right)\mathrm{}$ transition amplitudes, where gauge invariance is achieved by including a three-body current, are calculated from a constraint-free form-factor set. They are in reasonable agreement with the available photo- and electroproduction data.

A large attraction of neural systems lies in their promise of replacing programming by learning. A problem with many current neural models is that with realistically large input patterns learning time explodes. This is a problem inherent in a notion of learning that is based almost entirely on statistical estimation. We propose here a different learning style where significant relations in the input pattern are recognized and expressed by the unsupervised self-organization of dynamic links. The power of this mechanism is due to the very general a priori principle of conservation of topological structure. We demonstrate that style with a system that learns to classify mirror symmetric pixel patterns from single examples.