Extraction of Quantifiable Information from Complex Systems

ISBN: 978-3-319-08158-8 (Print) 978-3-319-08159-5 (Online)

Table of contents (21 chapters)

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  1. Front Matter

    Pages i-xix

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    Chapter

    Pages 1-23

    Solving Stochastic Dynamic Programs by Convex Optimization and Simulation

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    Chapter

    Pages 25-51

    Efficient Resolution of Anisotropic Structures

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    Chapter

    Pages 53-67

    Regularity of the Parameter-to-State Map of a Parabolic Partial Differential Equation

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    Chapter

    Pages 69-81

    Piecewise Tensor Product Wavelet Bases by Extensions and Approximation Rates

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    Chapter

    Pages 83-107

    Adaptive Wavelet Methods for SPDEs

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    Chapter

    Pages 109-132

    Constructive Quantization and Multilevel Algorithms for Quadrature of Stochastic Differential Equations

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    Chapter

    Pages 133-159

    Bayesian Inverse Problems and Kalman Filters

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    Chapter

    Pages 161-178

    Robustness in Stochastic Filtering and Maximum Likelihood Estimation for SDEs

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    Chapter

    Pages 179-194

    Adaptive Sparse Grids in Reinforcement Learning

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    Chapter

    Pages 195-210

    A Review on Adaptive Low-Rank Approximation Techniques in the Hierarchical Tensor Format

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    Chapter

    Pages 211-235

    A Bond Order Dissection ANOVA Approach for Efficient Electronic Structure Calculations

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    Chapter

    Pages 237-261

    Tensor Spaces and Hierarchical Tensor Representations

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    Chapter

    Pages 263-279

    Nonlinear Eigenproblems in Data Analysis: Balanced Graph Cuts and the RatioDCA-Prox

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    Chapter

    Pages 281-302

    Adaptive Approximation Algorithms for Sparse Data Representation

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    Chapter

    Pages 303-319

    Error Bound for Hybrid Models of Two-Scaled Stochastic Reaction Systems

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    Chapter

    Pages 321-345

    Valuation of Structured Financial Products by Adaptive Multiwavelet Methods in High Dimensions

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    Chapter

    Pages 347-363

    Computational Methods for the Fourier Analysis of Sparse High-Dimensional Functions

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    Chapter

    Pages 365-379

    Sparsity and Compressed Sensing in Inverse Problems

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    Chapter

    Pages 381-396

    Low-Rank Dynamics

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    Chapter

    Pages 397-411

    Computation of Expectations by Markov Chain Monte Carlo Methods

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