Tabla de Contenidos: “…-- 5.2.5 Generalized ARCH Models and Their Statistical Properties -- 5.2.6 A Few Additional, Popular ARCH Models -- 5.2.6.1 The Threshold GARCH (TARCH) Model -- 5.2.6.2 The Power ARCH and NAGARCH Models -- 5.2.6.3 The Component GARCH Model and the Differences Between Transitory and Permanent Variance Components -- 5.2.6.4 The GARCH-In-Mean Model -- 5.3 Advanced Univariate Volatility Modeling -- 5.3.1 Non-Gaussian Marginal Innovations -- 5.3.2 GARCH Models Augmented by Exogenous (Predetermined) Factors -- 5.4 Testing for ARCH -- 5.4.1 Lagrange Multiplier ARCH Tests -- 5.4.2 News Impact Curves and Testing for Asymmetric ARCH -- 5.5 Forecasting With GARCH Models -- 5.5.1 Long-Horizon, Point Forecasts -- 5.5.2 Forecasts of Variance for Sums of Returns or Shocks -- 5.6 Estimation of and Inference on GARCH Models -- 5.6.1 Maximum Likelihood Estimation -- 5.6.2 The Properties of MLE -- 5.6.3 Quasi MLE -- 5.6.4 Misspecification Tests -- 5.6.5 Sequential Estimation and QMLE -- 5.6.6 Data Frequency in Estimation and Temporal Aggregation -- References -- Appendix 5.A Nonparametric Kernel Density Estimation…”

Tabla de Contenidos: “…Machine generated contents note: Preface List of Abbreviations 1 Introduction 1.1 Forward Problem 1.2 Inverse Problem 1.3 Issues in Inverse Problem Solving 1.4 Linear, Nonlinear and Linearized Problems 2 Signal and System as Vectors 2.1 Vector Space 2.1.1 Vector Space and Subspace 2.1.2 Basis, Norm and Inner Product 2.1.3 Hilbert Space 2.2 Vector Calculus 2.2.1 Gradient 2.2.2 Divergence 2.2.3 Curl 2.2.4 Curve 2.2.5 Curvature 2.3 Taylor's Expansion 2.4 Linear System of Equations 2.4.1 Linear System and Transform 2.4.2 Vector Space of Matrix 2.4.3 Least Square Solution 2.4.4 Singular Value Decomposition (SVD) 2.4.5 Pseudo-inverse 2.5 Fourier Transform 2.5.1 Series Expansion 2.5.2 Fourier Transform 2.5.3 Discrete Fourier Transform (DFT) 2.5.4 Fast Fourier Transform (FFT) 2.5.5 Two-dimensional Fourier Transform References 3 Basics for Forward Problem 3.1 Understanding PDE using Images as Examples 3.2 Heat Equation 3.2.1 Formulation of Heat Equation 3.2.2 One-dimensional Heat Equation 3.2.3 Two-dimensional Heat Equation and Isotropic Diffusion 3.2.4 Boundary Conditions 3.3 Wave Equation 3.4 Laplace and Poisson Equations 3.4.1 Boundary Value Problem 3.4.2 Laplace Equation in a Circle 3.4.3 Laplace Equation in Three-dimensional Domain 3.4.4 Representation Formula for Poisson Equation References 4 Analysis for Inverse Problem 4.1 Examples of Inverse Problems in Medical Imaging 4.1.1 Electrical Property Imaging 4.1.2 Mechanical Property Imaging 4.1.3 Image Restoration 4.2 Basic Analysis 4.2.1 Sobolev Space 4.2.2 Some Important Estimates 4.2.3 Helmholtz Decomposition 4.3 Variational Problems 4.3.1 Lax-Milgram Theorem 4.3.2 Ritz Approach 4.3.3 Euler-Lagrange Equations 4.3.4 Regularity Theory and Asymptotic Analysis 4.4 Tikhonov Regularization and Spectral Analysis 4.4.1 Overview of Tikhonov Regularization 4.4.2 Bounded Linear Operators in Banach Space 4.4.3 Regularization in Hilbert Space or Banach Space 4.5 Basics of Real Analysis 4.5.1 Riemann Integrable 4.5.2 Measure Space 4.5.3 Lebesgue Measurable Function 4.5.4 Pointwise, Uniform, Norm Convergence and Convergence in Measure 4.5.5 Differentiation Theory References 5 Numerical Methods 5.1 Iterative Method for Nonlinear Problem 5.2 Numerical Computation of One-dimensional Heat equation 5.2.1 Explicit Scheme 5.2.2 Implicit Scheme 5.2.3 Crank-Nicolson Method 5.3 Numerical Solution of Linear System of Equations 5.3.1 Direct Method using LU Factorization 5.3.2 Iterative Method using Matrix Splitting 5.3.3 Iterative Method using Steepest Descent Minimization 5.3.4 Conjugate Gradient (CG) Method 5.4 Finite Difference Method (FDM) 5.4.1 Poisson Equation 5.4.2 Elliptic Equation 5.5 Finite Element Method (FEM) 5.5.1 One-dimensional Model 5.5.2 Two-dimensional Model 5.5.3 Numerical Examples References 6 CT, MRI and Image Processing Problems 6.1 X-ray CT 6.1.1 Inverse Problem 6.1.2 Basic Principle and Nonlinear Effects 6.1.3 Inverse Radon Transform 6.1.4 Artifacts in CT 6.2 MRI 6.2.1 Basic Principle 6.2.2 K-space Data 6.2.3 Image Reconstruction 6.3 Image Restoration 6.3.1 Role of p in (6.35) 6.3.2 Total Variation Restoration 6.3.3 Anisotropic Edge-preserving Diffusion 6.3.4 Sparse Sensing 6.4 Segmentation 6.4.1 Active Contour Method 6.4.2 Level Set Method 6.4.3 Motion Tracking for Echocardiography References 7 Electrical Impedance Tomography 7.1 Introduction 7.2 Measurement Method and Data 7.2.1 Conductivity and Resistance 7.2.2 Permittivity and Capacitance 7.2.3 Phasor and Impedance 7.2.4 Admittivity and Trans-impedance 7.2.5 Electrode Contact Impedance 7.2.6 EIT System 7.2.7 Data Collection Protocol and Data Set 7.2.8 Linearity between Current and Voltage 7.3 Representation of Physical Phenomena 7.3.1 Derivation of Elliptic PDE 7.3.2 Elliptic PDE for Four-electrode Method 7.3.3 Elliptic PDE for Two-electrode Method 7.3.4 Min-max Property of Complex Potential 7.4 Forward Problem and Model 7.4.1 Continuous Neumann-to-Dirichlet Data 7.4.2 Discrete Neumann-to-Dirichlet Data 7.4.3 Nonlinearity between Admittivity and Voltage 7.5 Uniqueness Theory and Direct Reconstruction Method 7.5.1 Calderon's Approach 7.5.2 Uniqueness and Three-dimensional Reconstruction: Infinite Measurements 7.5.3 Nachmann's D-bar Method in Two Dimension 7.6 Backprojection Algorithm 7.7 Sensitivity and Sensitivity Matrix 7.7.1 Perturbation and Sensitivity 7.7.2 Sensitivity Matrix 7.7.3 Linearization 7.7.4 Quality of Sensitivity Matrix 7.8 Inverse Problem of EIT 7.8.1 Inverse Problem of RC Circuit 7.8.2 Formulation of EIT Inverse Problem 7.8.3 Ill-posedness of EIT Inverse Problem 7.9 Static Imaging 7.9.1 Iterative Data Fitting Method 7.9.2 Static Imaging using 4-channel EIT System 7.9.3 Regularization 7.9.4 Technical Difficulty of Static Imaging 7.10 Time-difference Imaging 7.10.1 Data Sets for Time-difference Imaging 7.10.2 Equivalent Homogeneous Admittivity 7.10.3 Linear Time-difference Algorithm using Sensitivity Matrix 7.10.4 Interpretation of Time-difference Image 7.11 Frequency-difference Imaging 7.11.1 Data Sets for Frequency-difference Imaging 7.11.2 Simple Difference Ft,ω2− Ft,ω1 7.11.3 Weighted Difference Ft,ω2− [alpha] Ft,ω1 7.11.4 Linear Frequency-difference Algorithm using Sensitivity Matrix 7.11.5 Interpretation of Frequency-difference Image References 8 Anomaly Estimation and Layer Potential Techniques 8.1 Harmonic Analysis and Potential Theory 8.1.1 Layer Potentials and Boundary Value Problems for Laplace Equation 8.1.2 Regularity for Solution of Elliptic Equation along Boundary of Inhomogeneity 8.2 Anomaly Estimation using EIT 8.2.1 Size Estimation Method 8.2.2 Location Search Method 8.3 Anomaly Estimation using Planar Probe 8.3.1 Mathematical Formulation 8.3.2 Representation Formula References 9 Magnetic Resonance Electrical Impedance Tomography 9.1 Data Collection using MRI 9.1.1 Measurement of Bz 9.1.2 Noise in Measured Bz Data 9.1.3 Measurement of B = (Bx,By,Bz) 9.2 Forward Problem and Model Construction 9.2.1 Relation between J , Bz and σ 9.2.2 Three Key Observations 9.2.3 Data Bz Traces σ∇u © e z-directional Change of σ 9.2.4 Mathematical Analysis toward MREIT Model 9.3 Inverse Problem Formulation using B or J 9.4 Inverse Problem Formulation using Bz 9.4.1 Model with Two Linearly Independent Currents 9.4.2 Uniqueness 9.4.3 Defected Bz Data in a Local Region 9.5 Image Reconstruction Algorithm 9.5.1 J-substitution Algorithm 9.5.2 Harmonic Bz Algorithm 9.5.3 Gradient Bz Decomposition and Variational Bz Algorithm 9.5.4 Local Harmonic Bz Algorithm 9.5.5 Sensitivity Matrix Based Algorithm 9.5.6 Anisotropic Conductivity Reconstruction Algorithm 9.5.7 Other Algorithms 9.6 Validation and Interpretation 9.6.1 Image Reconstruction Procedure using Harmonic Bz Algorithm 9.6.2 Conductivity Phantom Imaging 9.6.3 Animal Imaging 9.6.4 Human Imaging 9.7 Applications References 10 Magnetic Resonance Elastography 10.1 Representation of Physical Phenomena 10.1.1 Overview of Hooke's Law 10.1.2 Strain Tensor in Lagrangian Coordinates 10.2 Forward Problem and Model 10.3 Inverse Problem in MRE 10.4 Reconstruction Algorithms 10.4.1 Reconstruction of [mu] with the Assumption of Local Homogeneity 10.4.2 Reconstruction of [mu] without the Assumption of Local Homogeneity 10.4.3 Anisotropic Elastic Moduli Reconstruction 10.5 Technical Issues in MRE References…”

Tabla de Contenidos: “…5.7.4 Finite Dimensional Statistical Inference 232 -- 6 Convex Optimization 235 -- 6.1 Linear Programming 237 -- 6.2 Quadratic Programming 238 -- 6.3 Semidefinite Programming 239 -- 6.4 Geometric Programming 239 -- 6.5 Lagrange Duality 241 -- 6.6 Optimization Algorithm 242 -- 6.6.1 Interior Point Methods 242 -- 6.6.2 Stochastic Methods 243 -- 6.7 Robust Optimization 244 -- 6.8 Multiobjective Optimization 248 -- 6.9 Optimization for Radio Resource Management 249 -- 6.10 Examples and Applications 250 -- 6.10.1 Spectral Efficiency for Multiple Input Multiple Output Ultra-Wideband Communication System 250 -- 6.10.2 Wideband Waveform Design for Single Input Single Output Communication System with Noncoherent Receiver 256 -- 6.10.3 Wideband Waveform Design for Multiple Input Single Output Cognitive Radio 262 -- 6.10.4 Wideband Beamforming Design 268 -- 6.10.5 Layering as Optimization Decomposition for Cognitive Radio Network 272 -- 6.11 Summary 282 -- 7 Machine Learning 283 -- 7.1 Unsupervised Learning 288 -- 7.1.1 Centroid-Based Clustering 288 -- 7.1.2 k-Nearest Neighbors 289 -- 7.1.3 Principal Component Analysis 289 -- 7.1.4 Independent Component Analysis 290 -- 7.1.5 Nonnegative Matrix Factorization 291 -- 7.1.6 Self-Organizing Map 292 -- 7.2 Supervised Learning 293 -- 7.2.1 Linear Regression 293 -- 7.2.2 Logistic Regression 294 -- 7.2.3 Artificial Neural Network 294 -- 7.2.4 Decision Tree Learning 294 -- 7.2.5 Naive Bayes Classifier 295 -- 7.2.6 Support Vector Machines 295 -- 7.3 Semisupervised Learning 298 -- 7.3.1 Constrained Clustering 298 -- 7.3.2 Co-Training 298 -- 7.3.3 Graph-Based Methods 299 -- 7.4 Transductive Inference 299 -- 7.5 Transfer Learning 299 -- 7.6 Active Learning 299 -- 7.7 Reinforcement Learning 300 -- 7.7.1 Q-Learning 300 -- 7.7.2 Markov Decision Process 301 -- 7.7.3 Partially Observable MDPs 302 -- 7.8 Kernel-Based Learning 303 -- 7.9 Dimensionality Reduction 304 -- 7.9.1 Kernel Principal Component Analysis 305 -- 7.9.2 Multidimensional Scaling 307.…”

Tabla de Contenidos: “…Intro -- Advances in Remote Sensing Technology and the Three Poles -- Contents -- About the Editors -- Notes on Contributors -- Foreword -- Preface -- List of Acronyms -- Section I Earth Observation (EO) and Remote Sensing (RS) Applications in Polar Studies -- 1 The Three Poles: Advances in Remote Sensing in Relation to Spheres of the Planet Earth -- 1.1 Introduction -- 1.1.1 Earth as a System and Components of the Earth System -- 1.1.2 Role of the "Three Poles" and the Three Poles Regions in the Earth System -- 1.1.2.1 Defining the Three Poles, Three Poles Regions, and Their Geographical Extent -- 1.1.2.2 Interaction Among Components of the Earth System and Role of the Three Poles -- 1.1.3 Advancement of RS Technologies in Relation to Their Application in the Three Poles Regions -- 1.1.3.1 Remote Sensing Technology Advancements -- 1.1.3.2 Role of Remote Sensing (RS) in Mapping/Monitoring/Quantitative Analysis of Sub-Systems of Our Planet in the Three Poles Regions -- 1.2 Aim of the Book and Its Five Sections -- 1.3 Overview of the Contributing Chapters Covering Research About Different Aspects of the Sub-Systems of Our Planet in the Three Poles Regions -- 1.4 Summary and Recommendations -- References -- 2 Continuous Satellite Missions, Data Availability, and Nature of Future Satellite Missions with Implications to Polar Regions -- 2.1 Introduction -- 2.1.1 Types of Orbit -- 2.1.1.1 High Earth Orbit (HEO) -- 2.1.1.2 Medium Earth Orbit (MEO) -- 2.1.1.3 Semi-Synchronous Orbit -- 2.1.1.4 Molniya Orbit -- 2.1.1.5 Low Earth Orbit (LEO) -- 2.1.1.6 Polar Orbit and Sun-Synchronous Orbit -- 2.1.1.7 Lagrange's Point -- 2.2 Satellite Missions and Data Availability -- 2.3 Future Satellite Missions -- 2.4 Applicability of Satellite Products in Three Poles Regions -- 2.5 Challenges and Limitations -- 2.6 Summary -- Acknowledgments -- References…”

“…He also examines the roles played by DeMoivre, James Bernoulli, and Lagrange, and he provides an accessible exposition of the work of R.A. …”

“…Les images peuvent être distinctes et successives ou bien arrangées en scènes à l'intérieur d'un rouleau ou d'un panneau plus vaste : l'idée est toujours qu'en parcourant l'ensemble, on peut comprendre l'histoire. …”

“…Sa couleur, la façon dont elle est arrangée ou dérangée, ornée ou tondue, sont des signes qu'on perçoit d'emblée ou qu'il faut interpréter. …”

“…This edition also contains four new appendices on D'Alembert's principle and Lagrange's equations, derivation of Hamilton’s principle, Noether’s theorem, and conic sections…”