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The question of reconstructing a geometric shape from spectra of operators (such as the Laplace operator) is decades old and an active area of research in mathematics and mathematical physics. This book focusses on the case of compact Riemannian manifolds, and, in particular, the question whether one can find finitely many natural operators that determine whether two such manifolds are isometric (coverings). The methods outlined in the book fit into the tradition of the famous work of Sunada on the construction of isospectral, non-isometric manifolds, and thus do not focus on analytic techniques, but rather on algebraic methods: in particular, the analogy with constructions in number theory, methods from representation theory, and from algebraic topology. The main goal of the book is to present the construction of finitely many “twisted” Laplace operators whose spectrum determines covering equivalence of two Riemannian manifolds. The book has a leisure pace and presents details and examples that are hard to find in the literature, concerning: fiber products of manifolds and orbifolds, the distinction between the spectrum and the spectral zeta function for general operators, strong isospectrality, twisted Laplacians, the action of isometry groups on homology groups, monomial structures on group representations, geometric and group-theoretical realisation of coverings with wreath products as covering groups, and “class field theory” for manifolds. The book contains a wealth of worked examples and open problems. After perusing the book, the reader will have a comfortable working knowledge of the algebraic approach to isospectrality. This is an open access book.

Isomorphisms (Mathematics) --- Categories (Mathematics) --- Group theory --- Morphisms (Mathematics) --- Set theory --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Number theory. --- Group theory. --- Algebraic topology. --- Geometry, Differential. --- Global Analysis and Analysis on Manifolds. --- Manifolds and Cell Complexes. --- Number Theory. --- Group Theory and Generalizations. --- Algebraic Topology. --- Differential Geometry. --- Differential geometry --- Topology --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Number study --- Numbers, Theory of --- Geometry, Differential --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Varietats de Riemann --- Isometria (Matemàtica) --- Global analysis (Mathematics) --- Manifolds (Mathematics)

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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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The book presents the state-of-the-art of forest resources assessments and monitoring and provides links to practical applications of forest and natural resource assessment programs. It gives an overview of current forest inventory systems and discusses forest mensuration, sampling techniques, remote sensing applications, geographic and forest information systems, and multi-resource forest inventory. In addition to the assessment of the productive functions of forests, particular attention is given to the quantification of non-wood goods and services and the relationship of forests to other landscape elements. All methodology is presented in the framework of sustainable management of the multiple functions that forests provide to the natural environment and to society. The book was developed as a reference text for (forest) biometricians, practitioners involved in forest and natural resources assessment and monitoring programs, and graduate students with a strong interest in becoming forest inventory specialists.

Forests and forestry --- Forest management. --- Measurement. --- Forest administration --- Forest plants --- Forest resource administration --- Forest resource management --- Forest stewardship --- Forest vegetation management --- Forestry management --- Stewardship, Forest --- Vegetation management, Forest --- Ecosystem management --- Natural resources --- Forest measurement --- Forest mensuration --- Log scaling --- Timber --- Measurement --- Management --- Administration --- Control --- Mensuration --- Forest inventories --- Sampling --- Geographical information systems --- Forests and forestry. --- Landscape ecology. --- Biodiversity. --- Statistics. --- Global analysis (Mathematics). --- Forestry. --- Forestry Management. --- Landscape Ecology. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Analysis. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Biological diversification --- Biological diversity --- Biotic diversity --- Diversification, Biological --- Diversity, Biological --- Biology --- Biocomplexity --- Ecological heterogeneity --- Numbers of species --- Ecology --- Forest land --- Forest lands --- Forest planting --- Forest production --- Forest sciences --- Forestation --- Forested lands --- Forestland --- Forestlands --- Forestry --- Forestry industry --- Forestry sciences --- Land, Forest --- Lands, Forest --- Silviculture --- Sylviculture --- Woodlands --- Woods (Forests) --- Agriculture --- Afforestation --- Arboriculture --- Logging --- Tree crops --- Trees --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Forestry management. --- Statistics . --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis

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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