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## Mathematical Analyses of Artificial Neural Networks

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Artificial neural networks are abstract mathematical models of brain
structures and functions. An ANN (artificial neural network) is sometimes
referred to as either a
"connectionist system", "neurocomputer", or
"PDP (parallel distributed processing)" model.
An ANN system usually
consists of a large collection of units where each unit has
a scalar real-valued state which is called the unit's activation level.
The activation levels of all units in the ANN system may also be arranged
as elements of a vector. This vector is referred to as an
activation pattern.
A parameter of the ANN system which can be interpreted as describing
the degree to which the activation level of one unit in the system influences
the activation level of another unit is often referred to as a
connection weight.
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Most ANN systems are very complex high-dimensional nonlinear information
processing systems. Unlike linear
systems, closed form solutions to nonlinear information processing systems
do not typically exist. On the other hand, a great deal of the qualitative
characteristics of an ANN system's behavior can be analyzed and described
using well-known engineering tools and techniques.
Currently, Dr. Golden has published
a book for describing methods for the analysis of stochastic and
deterministic high-dimensional nonlinear artificial neural network systems.
The title of this book is
Golden, R. M. (1996).
Mathematical Methods for Neural Network Analysis and Design.

Dr. Golden has additionally published a number of papers in the area of
artificial neural network analysis and design including a mathematical
analysis of Dr. James A. Anderson's nonlinear Brain-State-in-a-Box neural model.

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