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This book explains why complex systems research is important in understanding the structure, function and dynamics of complex natural and social phenomena. It illuminates how complex collective behavior emerges from the parts of a system, due to the interaction between the system and its environment. You will learn the basic concepts and methods of complex system research. It is shown that very different complex phenomena of nature and society can be analyzed and understood by nonlinear dynamics since many systems of very different fields, such as physics, chemistry, biology, economics, psychology and sociology etc. have similar architecture. "Complexity Explained" is not highly technical and mathematical, but teaches and uses the basic mathematical notions of dynamical system theory making the book useful for students of science majors and graduate courses, but it should be readable for a more general audience; actually for those, who ask: What complex systems really are?

Computational Complexity --- Computational complexity. --- Computational complexity --- Complexité de calcul (Informatique) --- EPUB-LIV-FT LIVINGEN SPRINGER-B

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Tensors: The Mathematics of Relativity Theory and Continuum Mechanics, by Anadijiban Das, emerged from courses taught over the years at the University College of Dublin, Carnegie-Mellon University and Simon Fraser University. This book will serve readers well as a modern introduction to the theories of tensor algebra and tensor analysis. Throughout Tensors, examples and worked-out problems are furnished from the theory of relativity and continuum mechanics. Topics covered in this book include, but are not limited to: -tensor algebra -differential manifold -tensor analysis -differential forms -connection forms -curvature tensors -Riemannian and pseudo-Riemannian manifolds The extensive presentation of the mathematical tools, examples and problems make the book a unique text for the pursuit of both the mathematical relativity theory and continuum mechanics.

Mathematical physics --- fysica --- wiskunde --- Tensor algebra. --- Calculus of tensors. --- Riemannian manifolds. --- Algèbre tensorielle --- Calcul tensoriel --- Riemann, Variétés de --- EPUB-LIV-FT LIVPHYSI SPRINGER-B

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Emergence and complexity refer to the appearance of higher-level properties and behaviours of a system that obviously comes from the collective dynamics of that system's components. These properties are not directly deductable from the lower-level motion of that system. Emergent properties are properties of the "whole'' that are not possessed by any of the individual parts making up that whole. Such phenomena exist in various domains and can be described, using complexity concepts and thematic knowledges. This book highlights complexity modelling through dynamical or behavioral systems. The pluridisciplinary purposes, developped along the chapters, are enable to design links between a wide-range of fundamental and applicative Sciences. Developing such links - instead of focusing on specific and narrow researches - is characteristic of the Science of Complexity that we try to promote by this contribution.

analyse (wiskunde) --- dynamica --- informatica --- informatietheorie --- Ergodic theory. Information theory --- Engineering sciences. Technology --- ingenieurswetenschappen --- Computer science --- Classical mechanics. Field theory --- Computational complexity. --- System analysis. --- Complexité de calcul (Informatique) --- Analyse de systèmes --- EPUB-LIV-FT LIVPHYSI SPRINGER-B

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Graph algorithms are easy to visualize and indeed there already exists a variety of packages and programs to animate the dynamics when solving problems from graph theory. Still, and somewhat surprisingly, it can be difficult to understand the ideas behind the algorithm from the dynamic display alone. CATBox consists of a software system for animating graph algorithms and a course book which we developed simultaneously. The software system presents both the algorithm and the graph and puts the user always in control of the actual code that is executed. He or she can set breakpoints, proceed in single steps and trace into subroutines. The graph, and additional auxiliary graphs like residual networks, are displayed and provide visual feedback. The course book, intended for readers at advanced undergraduate or graduate level, introduces the ideas and discusses the mathematical background necessary for understanding and verifying the correctness of the algorithms and their complexity. Computer exercises and examples replace the usual static pictures of algorithm dynamics. For this volume we have chosen solely algorithms for classical problems from combinatorial optimization, such as minimum spanning trees, shortest paths, maximum flows, minimum cost flows as well as weighted and unweighted matchings both for bipartite and non-bipartite graphs. We consider non-bipartite weighted matching, in particular in the geometrical case, a highlight of combinatorial optimization. In order to enable the reader to fully enjoy the beauty of the primal-dual solution algorithm for weighted matching, we present all mathematical material not only from the point of view of graph theory, but also with an emphasis on linear programming and its duality. This yields insightful and aesthetically pleasing pictures for matchings, but also for minimum spanning trees. You can find more information at http://schliep.org/CATBox/.

Mathematics. --- Combinatorics. --- Optimization. --- Operations Research, Mathematical Programming. --- Discrete Mathematics in Computer Science. --- Game Theory/Mathematical Methods. --- Computational complexity. --- Mathematical optimization. --- Operations research. --- Economics, Mathematical. --- Mathématiques --- Complexité de calcul (Informatique) --- Optimisation mathématique --- Recherche opérationnelle --- Mathématiques économiques --- Combinatorial optimization --- Graph algorithms. --- Data processing.

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The computer interpretation of line drawings is a classic problem in artificial intelligence and has inspired the development of some fundamental AI tools, including constraint propagation, probabilistic relaxation, tractable constraints, and (most recently) local simplification of optimisation problems. Based on the author’s considerable research experience, this book looks at line drawing interpretation and constraint satisfaction, covering several landmark results in the field. It contains state-of-the-art reviews of work in both drawing interpretation and discrete optimisation, and is not just restricted to drawings of polyhedral objects, but also covers complex curved objects. Its novel approach to drawing interpretation combines new constraints with recent advances in soft constraint programming. The book will become a standard reference in the field with its coverage of many theoretical results with formal proofs, particularly concerning necessary-and-sufficient conditions for realizability, simplification operations for combinatorial problems and tractability of drawing interpretation. Martin Cooper makes this fascinating topic accessible not only to computer scientists, but also to mathematicians, psychologists and cognitive scientists – indeed to anyone intrigued by optical illusions and impossible or ambiguous figures.

Computer Science. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Computer-Aided Engineering (CAD, CAE) and Design. --- Mathematical Logic and Formal Languages. --- Image Processing and Computer Vision. --- Cognitive Psychology. --- Discrete Mathematics in Computer Science. --- Computer science. --- Computational complexity. --- Computer vision. --- Computer aided design. --- Consciousness. --- Informatique --- Complexité de calcul (Informatique) --- Vision par ordinateur --- Conception assistée par ordinateur --- Conscience --- Optical pattern recognition --- Computer graphics --- Engineering & Applied Sciences --- Applied Physics --- Optical pattern recognition. --- Computer graphics. --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Mathematical logic. --- Computer science --- Image processing. --- Computer-aided engineering. --- Cognitive psychology. --- Mathematics. --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Digital techniques --- Optical data processing --- Pattern perception --- Perceptrons --- Visual discrimination