Note: Intro -- Preface -- Contents -- 1 Artificial Neural Network -- 1.1 Network Architectures -- 1.1.1 Multilayer Feedforward Networks -- 1.1.2 Recurrent Networks -- 1.2 Perceptrons -- 1.2.1 Rosenblatt's Perceptron -- 1.2.2 Multilayer Perceptron -- 1.3 Linear Network and Bayes Classifier -- 1.4 Radial Basis Function Network -- 1.4.1 Radial Basis Function -- 1.4.2 Interpolation -- 1.4.3 Receptive Field -- 1.5 Generalized Regression Network -- 1.6 Self-organizing Network -- 1.6.1 Kohonen Self-organizing Map Network -- 1.6.2 Learning Vector Quantization Network -- 1.7 Hopfield Network -- 1.7.1 Continuous Hopfield Network -- 1.7.2 Discrete Hopfield Network -- Further Reading -- 2 Multivariate Harmonic Analysis -- 2.1 Fourier Transform -- 2.2 Discrete Fourier Transform -- 2.3 Discrete Cosine/Sine Transform -- 2.3.1 Four Forms of DCTs -- 2.3.2 Four Forms of DSTs -- 2.4 Filtering -- 2.5 Fractional Fourier Transform -- 2.5.1 Continuous FRFT -- 2.5.2 Discrete FRFT -- 2.5.3 Multivariate FRFT -- 2.6 Space--Frequency Distribution -- 2.6.1 Multivariate Windowed Fourier Transform -- 2.6.2 General Form -- 2.6.3 Popular Distributions -- 2.7 Multivariate Interpolation -- 2.7.1 Multivariate Polynomial Interpolation -- 2.7.2 Schoenberg Interpolation -- 2.7.3 Micchelli Interpolation -- 2.7.4 Interpolation on Spheres -- 2.8 Sparse Approximation -- 2.8.1 Approximation Kernels -- 2.8.2 Sparse Schemes -- 2.8.3 Greedy Algorithm -- 2.9 Spherical Harmonics -- 2.9.1 Spherical Harmonic Functions -- 2.9.2 Invariant Subspace under Fourier Transform -- 2.10 Harmonic Analysis on General Domains -- 2.10.1 Symmetric Kernels -- 2.10.2 Smooth Extensions and Approximation -- 2.11 Harmonic Analysis on Graphs -- 2.11.1 The Laplacian of a Graph -- 2.11.2 Eigenvalues and Eigenfunctions -- 2.11.3 Fourier Expansions -- Further Reading -- 3 Multivariate Wavelets -- 3.1 Multiresolution Analysis. , 3.1.1 Structure of MRA -- 3.1.2 Scaling Functions -- 3.2 Multivariate Orthogonal Wavelets -- 3.2.1 Separable Wavelets -- 3.2.2 Non-separable Wavelets -- 3.2.3 p-Band Wavelets -- 3.3 Biorthogonal Wavelets -- 3.3.1 Univariate Biorthogonal Wavelets -- 3.3.2 Multivariate Biorthogonal Wavelets -- 3.3.3 p-Band Biorthogonal Wavelets -- 3.3.4 Semi-orthogonal Wavelets -- 3.4 Wavelets on Domains -- 3.4.1 Continuous Extension -- 3.4.2 Wavelet Expansion -- 3.5 Discrete Wavelet Transforms -- 3.5.1 Discrete Orthogonal Wavelet Transforms -- 3.5.2 Discrete Biorthogonal Wavelet Transforms -- 3.5.3 Discrete Biorthogonal Periodic Wavelets Transforms -- 3.5.4 Discrete Harmonic Wavelet Transforms -- 3.6 Wavelet Packets -- 3.6.1 Continuous Wavelet Packets -- 3.6.2 Discrete Wavelet Packets -- 3.7 Wavelet Variance -- 3.7.1 Generalized Wavelet Decomposition -- 3.7.2 Maximal Overlap Discrete Wavelet Transform -- 3.7.3 Wavelet Variance -- 3.8 Significant Tests -- 3.8.1 Haar Wavelet Analysis -- 3.8.2 Morlet Wavelet Analysis -- 3.9 Wavelet Threshold and Shrinkage -- 3.9.1 Wavelet Threshold -- 3.9.2 Wavelet Shrinkage -- 3.9.3 Minimax Estimation -- 3.9.4 Adaptive Denoising Algorithm -- 3.10 Shearlets, Bandelets, and Curvelets -- 3.10.1 Shearlets -- 3.10.2 Bandelets -- 3.10.3 Curvelets -- Further Reading -- 4 Stochastic Representation and Modeling -- 4.1 Stochastic Processes -- 4.1.1 Vector Stochastic Processes -- 4.1.2 Gaussian, Markov, and Wiener Processes -- 4.2 Stationarity and Trend Tests -- 4.2.1 Stationarity Tests -- 4.2.2 Trend Tests -- 4.3 Patterns and Classification -- 4.3.1 Principal Component Analysis -- 4.3.2 Factor Analysis -- 4.3.3 Cluster Analysis -- 4.3.4 Discriminant Analysis -- 4.3.5 Canonical Correlation Analysis -- 4.4 Multidimensional Scaling -- 4.5 Vector ARMA Processes -- 4.5.1 Vector MA(q) Processes -- 4.5.2 Vector AR(p) Processes. , 4.5.3 Vector ARMA(p,q) Processes -- 4.6 Monte Carlo Methods -- 4.7 Black--Scholes Models -- 4.8 Stochastic Optimization -- Further Reading -- 5 Multivariate Spectral Analysis -- 5.1 Power Spectral Density -- 5.2 Periodogram and Correlogram -- 5.2.1 Algorithms -- 5.2.2 Bias Analysis -- 5.2.3 Variance Analysis -- 5.3 Blackman--Tukey Method -- 5.3.1 Blackman--Tukey Estimator -- 5.3.2 Several Common Windows -- 5.3.3 Positive Semidefinite Window -- 5.4 Welch Method -- 5.5 Multitaper Method -- 5.6 Maximum Entropy Method -- 5.7 Rational Spectral Estimation -- 5.8 Discrete Spectral Estimation -- 5.9 Vector ARMA Spectrum -- 5.10 Multichannel Singular Spectrum Analysis -- Further Reading -- 6 Climate Modeling -- 6.1 Greenhouse Gases -- 6.2 Impacts and Feedback of Climate Change -- 6.3 Framework of Climate Models -- 6.3.1 Basic Physical Laws Used in Climate Models -- 6.3.2 Discretization and Parameterization -- 6.3.3 The Hierarchy of Climate Models -- 6.4 Coupled Model Intercomparison Project -- Further Reading -- 7 Regional Climate Change -- 7.1 Middle East and Mediterranean Region -- 7.1.1 Precipitation -- 7.1.2 Air Temperature -- 7.1.3 Climate Modeling -- 7.1.4 Desert Dust -- 7.1.5 Water Resources -- 7.1.6 Soil Temperature -- 7.2 Asia-Pacific Region -- 7.2.1 Tibetan Plateau -- 7.2.2 El Nitildeno--Southern Oscillation -- 7.2.3 Indian Monsoon -- 7.2.4 Modeling Sea Surface Temperature -- 7.3 Arctic Region -- 7.3.1 Sea Ice -- 7.3.2 Permafrost Carbon -- Further Reading -- 8 Ecosystem and Carbon Cycle -- 8.1 Terrestrial Ecosystems -- 8.1.1 Terrestrial Hydrologic Cycle -- 8.1.2 Photosynthesis -- 8.1.3 Gross and Net Primary Production -- 8.1.4 Net Ecosystem Production -- 8.1.5 Terrestrial Nutrient Cycle -- 8.2 Ocean Ecosystems -- 8.2.1 Solubility and Air--Sea Gas Exchange -- 8.2.2 Oceanic Carbon Sink -- 8.2.3 Compounds in Seawater -- 8.2.4 Biogeochemical Cycles. , Further Reading -- 9 Paleoclimate Proxies -- 9.1 Tree-Rings -- 9.1.1 Field Works -- 9.1.2 Statistical Analysis -- 9.2 Ice Cores -- 9.2.1 Ice and Isotopes -- 9.2.2 Ice Core Samples -- 9.3 Speleothems -- 9.3.1 Oxygen Isotope Ratio -- 9.3.2 Carbon Isotope Ratio -- 9.3.3 Hydrogen Isotope Ratio -- Further Reading -- 10 Strategies for Climate Change Mitigation -- 10.1 Assessment Methods and Tools -- 10.1.1 Data Envelopment Analysis -- 10.1.2 Risk Assessment -- 10.1.3 Life Cycle Assessment -- 10.2 Carbon Emissions Reduction -- 10.2.1 Industrial Sector -- 10.2.2 Agriculture Sector -- 10.2.3 The Building Sector -- 10.2.4 The Transportation Sector -- 10.2.5 The Household Sector -- 10.2.6 Low-Carbon Energy -- 10.3 Carbon Capture, Transport, Utilization, and Storage -- 10.3.1 Carbon Capture -- 10.3.2 Transport of CO2 -- 10.3.3 Geological Storage of CO2 -- 10.3.4 Utilization of CO2 -- 10.4 Geoengineering -- 10.4.1 Space-Based Geoengineering -- 10.4.2 Atmosphere-Based Geoenginnering -- 10.4.3 Land-Based Geoengineering -- 10.4.4 Ocean-Based Geoengineering -- 10.4.5 Conclusions -- Further Reading.