
Artificial neural networks are a method of computation and information processing that takes advantage of today's technology. Mimicking the processes found in biological neurons, artificial neural networks are used to predict and learn from a given set a data. Neural networks are more robust at data analysis than statistical methods because of their ability to handle small variations of parameters and noise. 
The basic element of a neural network is the perceptron.
First proposed by Frank Rosenblatt in 1958 at 
A more technical investigation of a Single Neuron Perceptron
shows that it can have an input vector X of N dimensions. These inputs go
through a vector W of Weights of N dimension. Processed by the Summation
Node, "a" is generated where "a" is the "dot
product" of vectors X and W plus a Bias. "A" is then processed
through an activation function which compares the value of "a" to a
predefined Threshold. If "a" is below the Threshold, the perceptron
will not fire. If it is above the Threshold, the perceptron will fire one
pulse whose amplitude is predefined. 

Perceptrons can be added in series or parallel. In either case, a perceptron learns by adjusting the weights in such a way as to minimize the error between the output generated and the correct answer. This is called training a neural network and is best summarized by the Perceptron Learning Theorem which states that if a solution is possible, it will be found eventually. 
Today neural networks are used in areas like pattern recognition, optical character recognition, predicting outcomes, and problem classification. Neural networks can be created by either software or hardware. Hephaistus uses advanced neural network development techniques to solve problems in the area of medical decision making, contentbased image retrieval, and decision tree pruning. To learn more about neural networks, books listed below are a good starting point to learn about this advanced computing technique. 

An
Introduction to Neural Networks.James A. Anderson.
MIT Press.
ISBN 0262011441
Neural Network Design.Martin T Hagen, Howard B. Demuth, Mark Beale.
PWS
Publishing Co.
ISBN 0534943322
Neural
Networks in Computer Intelligence. LiMin Fu.
McGrawHill, Inc.
ISBN 0079118178
Neural
Network Fundatmentals with Graphics, Algorithms and
Applications.
N.K. Bose, P. Liang.
McGrawHill, Inc.
ISBN 0070066183
Neural Networks: A
Comprehensive Foundation. Simon Haykin.
Macmillan College Publishing
Company Inc. 1994
ISBN 0023527617