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Combinatorial topology. --- Differential topology. --- Low-dimensional topology. --- Topological manifolds.

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The subject of Kleinian groups and hyperbolic 3-manifolds is currently undergoing explosively fast development, the last few years having seen the resolution of many longstanding conjectures. This volume contains important expositions and original work by some of the main contributors on topics such as topology and geometry of 3-manifolds, curve complexes, classical Ahlfors-Bers theory, computer explorations and projective structures. Researchers in these and related areas will find much of interest here.

Kleinian groups. --- Three-manifolds (Topology) --- Geometry, Hyperbolic. --- Hyperbolic geometry --- Lobachevski geometry --- Lobatschevski geometry --- Geometry, Non-Euclidean --- 3-manifolds (Topology) --- Manifolds, Three dimensional (Topology) --- Three-dimensional manifolds (Topology) --- Low-dimensional topology --- Topological manifolds --- Groups, Kleinian --- Discontinuous groups --- Hyperbolic 3-manifolds

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Presents reissued articles from two classic sources on hyperbolic manifolds. Part I is an exposition of Chapters 8 and 9 of Thurston's pioneering Princeton Notes; there is a new introduction describing recent advances, with an up-to-date bibliography, giving a contemporary context in which the work can be set. Part II expounds the theory of convex hull boundaries and their bending laminations. A new appendix describes recent work. Part III is Thurston's famous paper that presents the notion of earthquakes in hyperbolic geometry and proves the earthquake theorem. The final part introduces the theory of measures on the limit set, drawing attention to related ergodic theory and the exponent of convergence. The book will be welcomed by graduate students and professional mathematicians who want a rigorous introduction to some basic tools essential for the modern theory of hyperbolic manifolds.

Geometry, Hyperbolic --- Hyperbolic spaces --- Three-manifolds (Topology) --- Kleinian groups --- Groups, Kleinian --- Discontinuous groups --- 3-manifolds (Topology) --- Manifolds, Three dimensional (Topology) --- Three-dimensional manifolds (Topology) --- Low-dimensional topology --- Topological manifolds --- Hyperbolic complex manifolds --- Manifolds, Hyperbolic complex --- Spaces, Hyperbolic --- Geometry, Non-Euclidean --- Hyperbolic geometry --- Lobachevski geometry --- Lobatschevski geometry

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The subject of pattern analysis and recognition pervades many aspects of our daily lives, including user authentication in banking, object retrieval from databases in the consumer sector, and the omnipresent surveillance and security measures around sensitive areas. Shape analysis, a fundamental building block in many approaches to these applications, is also used in statistics, biomedical applications (Magnetic Resonance Imaging), and many other related disciplines. With contributions from some of the leading experts and pioneers in the field, this self-contained, unified volume is the first comprehensive treatment of theory, methods, and algorithms, available in a single resource, without the typical quagmire of vast information scattered over a wide body of literature. Developments are discussed from a rapidly increasing number of research papers in diverse fields, including the mathematical and physical sciences, engineering, and medicine. The initial chapters explore the statistical modeling of landmarks while subsequent chapters address the probabilistic modeling of entire shapes. The latter part of the book, with the exception of the last two chapters, concentrates on case studies as well as implementational and practical challenges in real systems. Extensive illustrations throughout help readers overcome the sometimes terse technical details of the geometric and probabilistic formalism. Knowledge of advanced calculus and basic statistics and probability theory are the only prerequisites for the reader. Statistics and Analysis of Shapes will be an essential learning kit for statistical researchers, engineers, scientists, medical researchers, and students seeking a rapid introduction to the field. It may be used as a textbook for a graduate-level special topics course in statistics and signal/image analysis, or for an intensive short course on shape analysis and modeling. The state-of-the-art techniques presented will also be useful for experienced researchers and practitioners in academia and industry.

Shape theory (Topology) --- Pattern perception --- Théorie de la forme (Topologie) --- Perception des structures --- Statistical methods. --- Méthodes statistiques --- Applied Mathematics --- Engineering & Applied Sciences --- Statistical methods --- Théorie de la forme (Topologie) --- Méthodes statistiques --- EPUB-LIV-FT LIVMATHE SPRINGER-B --- Design perception --- Pattern recognition --- Mathematics. --- Pattern recognition. --- Visualization. --- Mathematical models. --- Probabilities. --- Statistics. --- Mathematical Modeling and Industrial Mathematics. --- Probability Theory and Stochastic Processes. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Pattern Recognition. --- Signal, Image and Speech Processing. --- Form perception --- Perception --- Figure-ground perception --- Homotopy theory --- Mappings (Mathematics) --- Topological manifolds --- Topological spaces --- Distribution (Probability theory. --- Optical pattern recognition. --- Optical data processing --- Perceptrons --- Visual discrimination --- Visualisation --- Imagination --- Visual perception --- Imagery (Psychology) --- Statistical analysis --- Statistical data --- Statistical science --- Mathematics --- Econometrics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Statistics . --- Signal processing. --- Image processing. --- Speech processing systems. --- Models, Mathematical --- Simulation methods --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Math --- Science --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk