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Hamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the Poincaré conjecture and Thurston's geometrization conjecture. This book gives a concise introduction to the subject with the hindsight of Perelman's breakthroughs from 2002/2003. After describing the basic properties of, and intuition behind the Ricci flow, core elements of the theory are discussed such as consequences of various forms of maximum principle, issues related to existence theory, and basic properties of singularities in the flow. A detailed exposition of Perelman's entropy functionals is combined with a description of Cheeger-Gromov-Hamilton compactness of manifolds and flows to show how a 'tangent' flow can be extracted from a singular Ricci flow. Finally, all these threads are pulled together to give a modern proof of Hamilton's theorem that a closed three-dimensional manifold whichcarries a metric of positive Ricci curvature is a spherical space form.

Ricci flow. --- Flow, Ricci --- Evolution equations --- Global differential geometry

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This book focuses like a laser beam on one of the hottest topics in evolutionary computation over the last decade or so: estimation of distribution algorithms (EDAs). EDAs are an important current technique that is leading to breakthroughs in genetic and evolutionary computation and in optimization more generally. I'm putting Scalable Optimization via Probabilistic Modeling in a prominent place in my library, and I urge you to do so as well. This volume summarizes the state of the art at the same time it points to where that art is going. Buy it, read it, and take its lessons to heart. David E Goldberg, University of Illinois at Urbana-Champaign This book is an excellent compilation of carefully selected topics in estimation of distribution algorithms---search algorithms that combine ideas from evolutionary algorithms and machine learning. The book covers a broad spectrum of important subjects ranging from design of robust and scalable optimization algorithms to efficiency enhancements and applications of these algorithms. The book should be of interest to theoreticians and practitioners alike, and is a must-have resource for those interested in stochastic optimization in general, and genetic and evolutionary algorithms in particular. John R. Koza, Stanford University This edited book portrays population-based optimization algorithms and applications, covering the entire gamut of optimization problems having single and multiple objectives, discrete and continuous variables, serial and parallel computations, and simple and complex function models. Anyone interested in population-based optimization methods, either knowingly or unknowingly, use some form of an estimation of distribution algorithm (EDA). This book is an eye-opener and a must-read text, covering easy-to-read yet erudite articles on established and emerging EDA methodologies from real experts in the field. Kalyanmoy Deb, Indian Institute of Technology Kanpur This book is an excellent comprehensive resource on estimation of distribution algorithms. It can serve as the primary EDA resource for practitioner or researcher. The book includes chapters from all major contributors to EDA state-of-the-art and covers the spectrum from EDA design to applications. These algorithms strategically combine the advantages of genetic and evolutionary computation with the advantages of statistical, model building machine learning techniques. EDAs are useful to solve classes of difficult real-world problems in a robust and scalable manner. Una-May O'Reilly, Massachusetts Institute of Technology Machine-learning methods continue to stir the public's imagination due to its futuristic implications. But, probability-based optimization methods can have great impact now on many scientific multiscale and engineering design problems, especially true with use of efficient and competent genetic algorithms (GA) which are the basis of the present volume. Even though efficient and competent GAs outperform standard techniques and prevent negative issues, such as solution stagnation, inherent in the older but more well-known GAs, they remain less known or embraced in the scientific and engineering communities. To that end, the editors have brought together a selection of experts that (1) introduce the current methodology and lexicography of the field with illustrative discussions and highly useful references, (2) exemplify these new techniques that dramatic improve performance in provable hard problems, and (3) provide real-world applications of these techniques, such as antenna design. As one who has strayed into the use of genetic algorithms and genetic programming for multiscale modeling in materials science, I can say it would have been personally more useful if this would have come out five years ago, but, for my students, it will be a boon. Duane D. Johnson, University of Illinois at Urbana-Champaign.

Distribution (Probablility theory) --- Genetic algorithms. --- Evolutionary computation. --- Machine learning. --- Combinatorial optimization. --- Distribution (Théorie des probabilités) --- Algorithmes génétiques --- Réseaux neuronaux à structure évolutive --- Apprentissage automatique --- Optimisation combinatoire --- Computer programs. --- Logiciels --- Combinatorial optimization --- Evolutionary computation --- Distribution (Probability theory) --- Genetic Algorithms --- Machine Learning --- Data processing --- Algorithms. --- Electronic books. -- local. --- Evolution equations -- Numerical solutions. --- Genetic algorithms --- Machine learning --- Civil Engineering --- Applied Mathematics --- Mathematical Statistics --- Operations Research --- Engineering & Applied Sciences --- Civil & Environmental Engineering --- Mathematics --- Physical Sciences & Mathematics --- Evolution equations --- Numerical solutions. --- Algorism --- Mathematics. --- Artificial intelligence. --- Probabilities. --- Applied mathematics. --- Engineering mathematics. --- Probability Theory and Stochastic Processes. --- Appl.Mathematics/Computational Methods of Engineering. --- Artificial Intelligence (incl. Robotics). --- Numerical analysis --- Algebra --- Arithmetic --- Foundations --- Distribution (Probability theory. --- Mathematical and Computational Engineering. --- Artificial Intelligence. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Engineering --- Engineering analysis --- Mathematical analysis --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Data processing. --- Optimization, Combinatorial --- Combinatorial analysis --- Mathematical optimization --- Computation, Evolutionary --- Neural networks (Computer science) --- GAs (Algorithms) --- Genetic searches (Algorithms) --- Algorithms --- Genetic programming (Computer science) --- Learning classifier systems --- Learning, Machine --- Artificial intelligence --- Distribution (Probability theory) - Data processing