This book could be subtitled “a control engineer looks at neural nets.” Both the questions addressed and the techniques employed will probably be new to most workers in the neural net area.

It opens with a discussion of basic electrophysiology and develops the Hodgkin-Huxley and FitzHugh-Nagumo models. It then goes on to standard methods for the analysis of nonlinear systems. After this introduction, a series of chapters introduce new methods and apply them to a variety of problems. These chapters are fairly dense and probably could serve as standalone research papers.

Several chapters deal with standard questions like control, synchronization, and estimation. Rigatos uses a clever linearization technique, and then applies variants of linear control techniques to solve these problems for nonlinear models.

The remaining chapters deal with stochastic models. After setting up his stochastic models of neural nets, Rigatos shows that his models are at least analogous to quantum systems, and hence mathematical techniques from quantum mechanics can be used for neural models. As applications, he shows how his models can be used to design improved associative memories and more efficient image compression algorithms.

I recommend this book to those interested in neural nets who won’t be put off by the density of the mathematics.