Luigi A. Radicati Di Brozolo - Böcker

This book, based on lectures given at the Accademia dei Lincei, is an accessible and leisurely account of systems that display a chaotic time evolution. This behaviour, though deterministic, has features more characteristic of stochastic systems. The analysis here is based on a statistical technique known as time series analysis and so avoids complex mathematics, yet provides a good understanding of the fundamentals. Professor Ruelle is one of the world's authorities on chaos and dynamical systems and his account here will be welcomed by scientists in physics, engineering, biology, chemistry and economics who encounter nonlinear systems in their research.

These notes arise from lectures presented in Florence under the auspices of the Accadamia dei Lincee and deal with an area that lies at the crossroads of mathematics and physics. The material presented here rests primarily on the pioneering work of Vaughan Jones and Edward Witten relating polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions. Professor Atiyah here presents an introduction to Witten's ideas from the mathematical point of view. The book will be essential reading for all geometers and gauge theorists as an exposition of new and interesting ideas in a rapidly developing area.

Understanding the role of neural activity in the development of the brain has been a major concern of many modern neurobiologists. The reason is plain enough: since the world influences the brain by means of action potentials and synaptic potentials, activity must be the chief cause of the neural changes wrought by experience. This 1994 volume explores the hypothesis that neural activity generated by experience modulates the ongoing growth of the brain during maturation, thus sculpting in each of us a unique nervous system according to the events of our early life. Brain growth is considered at a macroscopic level by examining brain maps and their modular substructure, and at a cellular level by investigating the neuronal interactions that influence the formation and maintenance of these structures. The ways that experience influences the maturation of the brain at both macroscopic and microscopic levels are described, and the conventional wisdom is re-examined.