This book describes the signal processing aspects of neural networks. It begins with a presentation of the necessary background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences, and then 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, a theory of mnemonic surfaces is developed and studied and material on pattern formation and cellular automata is presented. Finally, large networks are studied, such as the thalamus-reticular complex circuit, believed to be involved in focusing attention, and the development of connections in the visual cortex. Additional material is also provided about nonlinear wave propagation in networks. This book will serve as an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine and life scie
This book describes the signal processing aspects of neural networks. It begins with a presentation of the necessary background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences, and then 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, a theory of mnemonic surfaces is developed and studied and material on pattern formation and cellular automata is presented. Finally, large networks are studied, such as the thalamus-reticular complex circuit, believed to be involved in focusing attention, and the development of connections in the visual cortex. Additional material is also provided about nonlinear wave propagation in networks. This book will serve as an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine and life scie
This introduction to mathematical methods that are useful for studying population phenomena is intended for advanced undergraduate and graduate students, and will be accessible to scientists who do not have a strong mathematics background. The material is graded in mathematical difficulty. The earlier parts of the book involve elementary diference equations while later chapters present topics that require more mathematical preparation. Models of total population and population age structure are first derived and studied, and then models of random population events are presented in terms of Markov chains. The last two chapters deal with mathematical methods used to uncover qualitative behaviour of more complicated difference equations. Each chapter begins with a simple model, usually of some historical interest, that defines the primary goals of the chapter. Exercises, for which solutions are provided, illustrate material in the text and also deal with models more advanced than those de
This second edition provides an introduction to mathematical modeling in the areas of medicine and the life sciences. The wide diversity of applications presented range from population phenomena of g
Devoted to local and global analysis of weakly connected systems with applications to neurosciences, this book uses bifurcation theory and canonical models as the major tools of analysis. It presents
