Controlling Theory

The aim of this book is to discuss the fundamental ideas which lie behind the statistical theory of learning and generalization. It considers learning as a general problem of function estimation based on empirical data. Omitting proofs and technical details, the author concentrates on discussing the main results of learning theory and their connections to fundamental problems in statistics. These include: * the setting of learning problems based on the model of minimizing the risk functional from empirical data * a comprehensive analysis of the empirical risk minimization principle including necessary and sufficient conditions for its consistency * non-asymptotic bounds for the risk achieved using the empirical risk minimization principle * principles for controlling the generalization ability of learning machines using small sample sizes based on these bounds * the Support Vector methods that control the generalization ability when estimating function using small sample size.

Controlling Chaos offers its reader an extensive selection of techniques to achieve three goals: the suppression, synchronization and generation of chaos, each of which is the focus of a separate part of the book. The text deals with the well-known Lorenz, Rössler and Hénon attractors and the Chua circuit, and with less celebrated novel systems. Modeling of chaos is accomplished using difference equations and ordinary and time-delayed differential equations.

Controlling Chaos offers its reader an extensive selection of techniques to achieve three goals: the suppression, synchronization and generation of chaos, each of which is the focus of a separate part of the book. The text deals with the well-known Lorenz, Rössler and Hénon attractors and the Chua circuit, and with less celebrated novel systems. Modeling of chaos is accomplished using difference equations and ordinary and time-delayed differential equations.