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"Integrates two classical approaches to computability. Offers detailed coverage of recent research at the interface of logic, computability theory, nd theoretical computer science. Presents new, never-before-published results and provides informtion not easily accessible in the literature."
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This book constitutes the refereed proceedings of the 13th International Symposium Fundamentals of Computation Theory, FCT 2001, as well as of the International Workshop on Efficient Algorithms, WEA 2001, held in Riga, Latvia, in August 2001. The 28 revised full FCT papers and 15 short papers presented together with six invited contributions and 8 revised full WEA papers as well as three invited WEA contributions have been carefully reviewed and selected. Among the topics addressed are a broad variety of topics from theoretical computer science, algorithmics and programming theory. The WEA papers deal with graph and network algorithms, flow and routing problems, scheduling and approximation algorithms, etc.
A Sobolev gradient of a real-valued functional is a gradient of that functional taken relative to the underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. Equal emphasis is placed on numerical and theoretical matters. Several concrete applications are made to illustrate the method. These applications include (1) Ginzburg-Landau functionals of superconductivity, (2) problems of transonic flow in which type depends locally on nonlinearities, and (3) minimal surface problems. Sobolev gradient constructions rely on a study of orthogonal projections onto graphs of closed densely defined linear transformations from one Hilbert space to another. These developments use work of Weyl, von Neumann and Beurling.
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This volume presents the proceedings of the Fourth International Workshop on Analogical and Inductive Inference (AII '94) and the Fifth International Workshop on Algorithmic Learning Theory (ALT '94), held jointly at Reinhardsbrunn Castle, Germany in October 1994. (In future the AII and ALT workshops will be amalgamated and held under the single title of Algorithmic Learning Theory.) The book contains revised versions of 45 papers on all current aspects of computational learning theory; in particular, algorithmic learning, machine learning, analogical inference, inductive logic, case-based reasoning, and formal language learning are addressed.
Computational Learning Theory presents the theoretical issues in machine learning and computational models of learning. This book covers a wide range of problems in concept learning, inductive inference, and pattern recognition. Organized into three parts encompassing 32 chapters, this book begins with an overview of the inductive principle based on weak convergence of probability measures. This text then examines the framework for constructing learning algorithms. Other chapters consider the formal theory of learning, which is learning in the sense of improving computational efficiency as opposed to concept learning. This book discusses as well the informed parsimonious (IP) inference that generalizes the compatibility and weighted parsimony techniques, which are most commonly applied in biology. The final chapter deals with the construction of prediction algorithms in a situation in which a learner faces a sequence of trials, with a prediction to be given in each and the goal of the learner is to make some mistakes. This book is a valuable resource for students and teachers.