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Mathematical Analyses of Artificial Neural Networks


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.
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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