Review
"The author undoubtedly has a strong and thorough knowledge of both mathematics and neurosciences which allows him to put the reader on what he calls 'the launching point'...an excellent door that opens the researcher to further exploration of the mysteries of the brain. I conclude this review by repeating what is at the end of this very well written book: 'Mathematics is needed to understand how the brain works.'" Catherine Garcia-Reimbert
"...a brief and nice introduction to the mathematical methods and models used in the theory of neural networks and their applications." Monatshefte fur Mathematik
Book Description
This book describes signal processing aspects of neural networks, how we receive and assess information. Beginning with a presentation of the necessary background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences, it proceeds to applications. These applications include small networks of neurons, such as those used in control of warm-up and flight in moths and control of respiration during exercise in humans. Next, Hoppensteadt develops a theory of mnemonic surfaces and presents material on pattern formation and cellular automata. Finally, the text addresses the large networks, such as the thalamus-reticular complex circuit, that may be involved in focusing attention, and the development of connections in the visual cortex. This book will serve as an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine and life sciences.
Card catalog description
Signal processing aspects of neural networks are presented and studied in this book. Background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences is presented first, followed by three chapters of applications. Throughout, the focus is on the network's behavior near places where phase changes can occur. In mathematical terminology, this is reduction to analysis of canonical models near bifurcation points. The canonical problem derived here near a saddle-node bifurcations is the VCON model that is equivalent to an electronic circuit, similar to a phase-locked loop and it is described in the frequency domain rather than the time domain. This is an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine, and life sciences.
An Introduction to the Mathematics of Neurons: Modeling in the Frequency Domain FROM THE PUBLISHER
Signal processing aspects of neural networks are presented and studied in this book. Background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences is presented first, followed by three chapters of applications. Throughout, the focus is on the network's behavior near places where phase changes can occur. In mathematical terminology, this is reduction to analysis of canonical models near bifurcation points. The canonical problem derived here near a saddle-node bifurcations is the VCON model that is equivalent to an electronic circuit, similar to a phase-locked loop and it is described in the frequency domain rather than the time domain. This is an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine, and life sciences.
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