where j is a general reinforcement rule. The Hebbian rule is a special case where rj,k = xj,k Yk. 7.3-3

Hecht-Nielsen (1990) defines an ANN as follows:

A neural network is a parallel, distributed information processing structure consisting of processing elements (which can possess a local memory and can carry out localized information processing operations) interconnected via unidirectional signal channels called connections. Each processing element has a single output connection that branches ("fans out") into as many collateral connections as desired: each carries the same signal — the processing element output signal. The processing element output signal can be of any mathematical type desired. The information processing that goes on within each processing element can be defined arbitrarily with the restriction that it must be completely local; that is, it must depend only on the current values of the input signals arriving at the processing element via impinging connections and on values stored in the processing element's local memory.

Modern, powerful ANNs have many technical uses in areas such as:

Pattern recognition, with applications including, but not limited to, recognition of visual objects including faces, fingerprints, retinas, iris patterns, recognition of printed and written words, recognition of speech, classification of two-dimensional curves such as spectrophotometer and chromato-gram outputs, ECG and EEG records, detection of cancers and aneurysms in X rays, CT scans, and MRI images, detection of targets in radar and sonar scans, and oil, gas, and water exploration, etc. Control applications, including, but not limited to, autopilots, weapons guidance, control of robot manipulators, adaptive control of systems with timevariable plant parameters, guidance of autonomous vehicles and robots, etc. Financial applications, including, but not limited to, credit application evaluations, market analysis, bond rating, stock trading advisory systems, real estate appraisal, mortgage application screening, manufacturing expense reduction, machine maintenance analysis, etc.

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