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Discrete mathematics --- System analysis --- Dynamics --- Chaotic behavior in systems --- Differentiable dynamical systems --- Analyse de systèmes --- Dynamique --- Chaos --- Dynamique différentiable --- Periodicals --- Périodiques --- Chaotic behavior in systems. --- Differentiable dynamical systems. --- Dynamics. --- System analysis. --- Information Technology --- Mathematical Sciences --- Modelling & Simulation --- Applied Mathematics --- Complex Analysis --- General and Others --- Mathematical Analysis & Logic --- Numerical Analysis --- mathematical models --- complex systems --- discrete modelling --- non-linear phenomena --- chaotic systems --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Nonlinear theories --- System theory --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Network theory --- Systems analysis --- Mathematical optimization --- Network analysis --- Network science
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This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, and on pure mathematics and its practical applications. The interaction of these facets is demonstrated by concrete examples, including discrete conformal mappings, discrete complex analysis, discrete curvatures and special surfaces, discrete integrable systems, conformal texture mappings in computer graphics, and free-form architecture. This richly illustrated book will convince readers that this new branch of mathematics is both beautiful and useful. It will appeal to graduate students and researchers in differential geometry, complex analysis, mathematical physics, numerical methods, discrete geometry, as well as computer graphics and geometry processing.
Mathematics. --- Computer graphics. --- Dynamics. --- Ergodic theory. --- Functions of complex variables. --- Differential geometry. --- Physics. --- Differential Geometry. --- Functions of a Complex Variable. --- Dynamical Systems and Ergodic Theory. --- Computer Graphics. --- Numerical and Computational Physics. --- Natural philosophy --- Philosophy, Natural --- Differential geometry --- Complex variables --- Dynamical systems --- Kinetics --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Math --- Ergodic transformations --- Physical sciences --- Dynamics --- Elliptic functions --- Functions of real variables --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Science --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Digital techniques --- Global differential geometry. --- Differentiable dynamical systems. --- Numerical and Computational Physics, Simulation. --- Geometry, Differential --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Differential Geometry --- Geometry, Differential.
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This open access book focuses on both the theory and practice associated with the tools and approaches for decisionmaking in the face of deep uncertainty. It explores approaches and tools supporting the design of strategic plans under deep uncertainty, and their testing in the real world, including barriers and enablers for their use in practice. The book broadens traditional approaches and tools to include the analysis of actors and networks related to the problem at hand. It also shows how lessons learned in the application process can be used to improve the approaches and tools used in the design process. The book offers guidance in identifying and applying appropriate approaches and tools to design plans, as well as advice on implementing these plans in the real world. For decisionmakers and practitioners, the book includes realistic examples and practical guidelines that should help them understand what decisionmaking under deep uncertainty is and how it may be of assistance to them. Decision Making under Deep Uncertainty: From Theory to Practice is divided into four parts. Part I presents five approaches for designing strategic plans under deep uncertainty: Robust Decision Making, Dynamic Adaptive Planning, Dynamic Adaptive Policy Pathways, Info-Gap Decision Theory, and Engineering Options Analysis. Each approach is worked out in terms of its theoretical foundations, methodological steps to follow when using the approach, latest methodological insights, and challenges for improvement. In Part II, applications of each of these approaches are presented. Based on recent case studies, the practical implications of applying each approach are discussed in depth. Part III focuses on using the approaches and tools in real-world contexts, based on insights from real-world cases. Part IV contains conclusions and a synthesis of the lessons that can be drawn for designing, applying, and implementing strategic plans under deep uncertainty, as well as recommendations for future work. The publication of this book has been funded by the Radboud University, the RAND Corporation, Delft University of Technology, and Deltares.
Operations research. --- Differentiable dynamical systems. --- Distribution (Probability theory. --- Operations Research/Decision Theory. --- Dynamical Systems and Ergodic Theory. --- Probability Theory and Stochastic Processes. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Decision making. --- Dynamics. --- Ergodic theory. --- Probabilities. --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Decision making --- Business --- Operations research --- Dynamics --- Ergodic theory
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