## Introduction

**What is an artificial neural network? **

An Artificial Neural Network is an algorithm designed specifically for the processing of information that permits the reconstruction, in a particularly effective way, the approximate rules that relate a certain set of “explicative” data for a specific problem (input) with a set of data (output) for which a correct prediction or a replication of the conditions of informative incompleteness is required.

The use of the ANNs is indicated only when the relationship between input and output, that is, the content of the black box in the figure, is very complicated; otherwise it is by far simpler and less computationally expensive to use other more traditional mathematical methods of analysis.

Why can the relationship between variables of input and output be so complicated?

This can be explained with a simple example. Suppose we wish to consider the relationship that links the monetary asset of an individual to its degree of satisfaction. We could naively imagine a relationship of simple direct proportionality between wealth and satisfaction might exist. If this were true, an ANN would not be necessary in order to rebuild the reconstruction that links the two variables. If instead we suppose that such a relationship is not characterized by a direct proportionality at all, but rather by changes that are significant with the consistency of the assets, (that is to say, from a beginning point of have only a little money, then having more money implies more satisfaction, but the more the assets increases, concerns for the use of money prevail, generating a decline in satisfaction, that, on the other hand, regain the height when another threshold is passed etc.) generate a behaviour similar to the one shown in the figure. The use of an ANNs might be a proper and more effective means in better understanding the real nature of the relationship.

**Historical outline **

The first learning system was developed by Marvin Minsky in 1951 (Minsky 1954).

Afterwards, in 1962, Frank Rosenblatt built an ANNs able to compute every linear function (Rosenblatt 1962).

In 1969, M. Minsky and S. Papert, in a famous book, highlighted the limits of the ANN built by Rosenblatt (Minsky 1969). From then up to 1980 Minsky’s and Papert’s criticisms induced most of the researchers of Artificial Intelligence to ignore the ANNs.

Only a small group of isolated researchers (Grossberg, Kohonen, Werbos, and a few others) continued analysing the inner mathematics of the ANNs (Grossberg 1973-1980; Kohonen 1972; Werbos 1974).

From 1980 to 1986, at last, other researchers emerged, among whom is the famous physicist Jon Hopfield (1982-1986) and afterwards, a group of researchers of San Diego University published two volumes that became the ANNs’ milestones (Rumelhart 1986).

With this contribution the researcher now had the equations that permitted ANNs to solve any continuous, non linear function.

From 1988 to 1994 the ANNs were used to analyse real problems (Buscema 1993, 1994) and from 1995 until today the ANNs continue to show themselves able to be applied in any scientific sector (Arbib 1995; Buscema 1998, 1999). New ANNs and Artificial Organisms have been mathematically designed and implemented (Buscema 1998, 1999) and have been published in appropriate journals and books.

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