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Molecules, galaxies, art galleries, sculptures, viruses, crystals, architecture, and more: Shaping Space—Exploring Polyhedra in Nature, Art, and the Geometrical Imagination is an exuberant survey of polyhedra and at the same time a hands-on, mind-boggling introduction to one of the oldest and most fascinating branches of mathematics. Some of the world’s leading geometers present a treasury of ideas, history, and culture to make the beauty of polyhedra accessible to students, teachers, polyhedra hobbyists, and professionals such as architects and designers, painters and sculptors, biologists and chemists, crystallographers, physicists and earth scientists, engineers and model builders, mathematicians and computer scientists. The creative chapters by more than 25 authors explore almost every imaginable side of polyhedra.  From the beauty of natural forms to the monumental constructions made by man, there is something to fascinate every reader. The book is dedicated to the memory of the legendary geometer H. S. M. Coxeter and the multifaceted design scientist Arthur L. Loeb. Contributing Authors: P. Ash, T. F. Banchoff, J. Baracs, E. Bolker, C. Chieh, R. Connelly, H.S.M. Coxeter, H. Crapo, E. Demaine, M. Demaine, G. Fleck, B. Grünbaum, I. Hargittai, M. Hargittai, G. Hart, V. Hart, A. Loeb, J. Malkevitch, B. Monson, J. O'Rourke, J. Pedersen, D. Schattschneider, M. Schmitt, E. Schulte, M. Senechal, G.C. Shephard, I. Streinu, M. Walter, M. Wenninger, W. Whiteley, J. M. Wills, and G. M. Ziegler.

Polyhedra. --- Shapes. --- Forms (Shapes) --- Shape --- Polyhedral figures --- Polyhedrons --- Mathematics. --- Design. --- Geometry. --- Crystallography. --- Design, general. --- Geometry --- Surfaces --- Geometry, Solid --- Shapes --- Design and construction. --- Crystallography and Scattering Methods. --- Leptology --- Physical sciences --- Mineralogy --- Mathematics --- Euclid's Elements --- Creation (Literary, artistic, etc.)

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The concept of 'shape' is at the heart of image processing and computer vision, yet researchers still have some way to go to replicate the human brain's ability to extrapolate meaning from the most basic of outlines. This volume reflects the advances of the last decade, which have also opened up tough new challenges in image processing. Today's applications require flexible models as well as efficient, mathematically justified algorithms that allow data processing within an acceptable timeframe. Examining important topics in continuous-scale and discrete modeling, as well as in modern algorithms, the book is the product of a key seminar focused on innovations in the field. It is a thorough introduction to the latest technology, especially given the tutorial style of a number of chapters. It also succeeds in identifying promising avenues for future research. The topics covered include mathematical morphology, skeletonization, statistical shape modeling, continuous-scale shape models such as partial differential equations and the theory of discrete shape descriptors. Some authors highlight new areas of enquiry such as partite skeletons, multi-component shapes, deformable shape models, and the use of distance fields. Combining the latest theoretical analysis with cutting-edge applications, this book will attract both academics and engineers.

Image analysis -- Data processing. --- Image processing -- Digital techniques. --- Technology and engineering -- Imaging systems. --- Engineering & Applied Sciences --- Computer Science --- Shapes. --- Shapes --- Mathematical models. --- Forms (Shapes) --- Shape --- Mathematics. --- Computer graphics. --- Computer mathematics. --- Visualization. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Computational Mathematics and Numerical Analysis. --- Geometry --- Surfaces --- Computer vision. --- Computer science --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Visualisation --- Imagination --- Visual perception --- Imagery (Psychology) --- Mathematics --- Optical data processing. --- Optical computing --- Visual data processing --- Bionics --- Integrated optics --- Photonics --- Computers --- Math --- Science --- Optical equipment

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In recent years, research in K3 surfaces and Calabi–Yau varieties has seen spectacular progress from both the arithmetic and geometric points of view, which in turn continues to have a huge influence and impact in theoretical physics—in particular, in string theory. The workshop on  Arithmetic and Geometry of  K3 surfaces and Calabi–Yau threefolds, held at the Fields Institute (August 16–25, 2011), aimed to give a state-of-the-art survey of these new developments. This proceedings volume includes a representative sampling of the broad range of topics covered by the workshop. While the subjects range from arithmetic geometry through algebraic geometry and differential geometry to mathematical physics, the papers are naturally related by the common theme of Calabi–Yau varieties. With the large variety of branches of mathematics and mathematical physics touched upon, this area reveals many deep connections between subjects previously considered unrelated. Unlike most other conferences, the 2011 Calabi–Yau workshop started with three days of introductory lectures. A selection of four of these lectures is included in this volume. These lectures can be used as a starting point for graduate students and other junior researchers, or as a guide to the subject.

Manifolds (Mathematics). --- Surfaces. --- Threefolds (Algebraic geometry) --- Surfaces, Algebraic --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Manifolds (Mathematics) --- Curved surfaces --- Mathematics. --- Algebraic geometry. --- Differential geometry. --- Number theory. --- Mathematical physics. --- Algebraic Geometry. --- Number Theory. --- Differential Geometry. --- Mathematical Physics. --- Geometry, Differential --- Topology --- Shapes --- Geometry, algebraic. --- Global differential geometry. --- Algebraic geometry --- Number study --- Numbers, Theory of --- Algebra --- Physical mathematics --- Physics --- Differential geometry

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Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization. The authors look at a family of derivative-free numerical algorithms applying space-filling curves to reduce the dimensionality of the global optimization problem; along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search. Convergence conditions of the described algorithms are studied in depth and theoretical considerations are illustrated through numerical examples. This work also contains a code for implementing space-filling curves that can be used for constructing new global optimization algorithms. Basic ideas from this text can be applied to a number of problems including problems with multiextremal and partially defined constraints and non-redundant parallel computations can be organized. Professors, students, researchers, engineers, and other professionals in the fields of pure mathematics, nonlinear sciences studying fractals, operations research, management science, industrial and applied mathematics, computer science, engineering, economics, and the environmental sciences will find this title useful . .

Mathematical optimization --- Nonconvex programming --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Curves --- Curves on surfaces --- Mathematical models. --- Surfaces, Curves on --- Mathematics. --- Algebraic geometry. --- Computer software. --- Numerical analysis. --- Operations research. --- Management science. --- Manifolds (Mathematics). --- Complex manifolds. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Operations Research, Management Science. --- Mathematical Software. --- Numerical Analysis. --- Algebraic Geometry. --- Calculus --- Conic sections --- Geometry, Analytic --- Geometry, Differential --- Geometry, Enumerative --- Shapes --- Cell aggregation --- Geometry, algebraic. --- Algebraic geometry --- Mathematical analysis --- Software, Computer --- Computer systems --- Aggregation, Cell --- Cell patterning --- Cell interaction --- Microbial aggregation --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Analytic spaces --- Manifolds (Mathematics) --- Topology --- Mathematical optimization. --- Nonconvex programming.