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This book is aimed at students in communications and signal processing who want to extend their skills in the energy area. It describes power systems and why these backgrounds are so useful to smart grid, wireless communications being very different to traditional wireline communications.
List of contents
Preface xv
Acknowledgments xix
Some Notation xxi
1 Introduction 1
1.1 Big Data: Basic Concepts 1
1.2 Data Mining with Big Data 9
1.3 A Mathematical Introduction to Big Data 13
1.4 A Mathematical Theory of Big Data 28
1.5 Smart Grid 34
1.6 Big Data and Smart Grid 36
1.7 Reading Guide 37
Bibliographical Remarks 39
Part I Fundamentals of Big Data 41
2 The Mathematical Foundations of Big Data Systems 43
2.1 Big Data Analytics 44
2.2 Big Data: Sense, Collect, Store, and Analyze 45
2.3 Intelligent Algorithms 48
2.4 Signal Processing for Smart Grid 48
2.5 Monitoring and Optimization for Power Grids 48
2.6 Distributed Sensing and Measurement for Power Grids 49
2.7 Real-time Analysis of Streaming Data 50
2.8 Salient Features of Big Data 51
2.9 Big Data for Quantum Systems 54
2.10 Big Data for Financial Systems 55
2.11 Big Data for Atmospheric Systems 73
2.12 Big Data for Sensing Networks 74
2.13 Big Data forWireless Networks 75
2.14 Big Data for Transportation 78
Bibliographical Remarks 78
3 Large Random Matrices: An Introduction 79
3.1 Modeling of Large Dimensional Data as Random Matrices 79
3.2 A Brief of Random MatrixTheory 81
3.3 Change Point of Views: From Vectors to Measures 85
3.4 The Stieltjes Transform of Measures 86
3.5 A Fundamental Result: The Marchenko-Pastur Equation 88
3.6 Linear Eigenvalue Statistics and Limit Laws 89
3.7 Central LimitTheorem for Linear Eigenvalue Statistics 99
3.8 Central LimitTheorem for Random Matrix S.1T 101
3.9 Independence for Random Matrices 103
3.10 Matrix-Valued Gaussian Distribution 110
3.11 Matrix-ValuedWishart Distribution 112
3.12 Moment Method 112
3.13 Stieltjes Transform Method 113
3.14 Concentration of the Spectral Measure for Large Random Matrices 114
3.15 Future Directions 117
Bibliographical Remarks 117
4 Linear Spectral Statistics of the Sample Covariance Matrix 121
4.1 Linear Spectral Statistics 121
4.2 Generalized Marchenko-Pastur Distributions 122
4.3 Estimation of Spectral Density Functions 127
4.4 Limiting Spectral Distribution of Time Series 146
Bibliographical Remarks 154
5 Large Hermitian Random Matrices and Free Random Variables 155
5.1 Large Economic/Financial Systems 156
5.2 Matrix-Valued Probability 157
5.3 Wishart-Levy Free Stable Random Matrices 166
5.4 Basic Concepts for Free Random Variables 168
5.5 The Analytical Spectrum of theWishart-Levy Random Matrix 172
5.6 Basic Properties of the Stieltjes Transform 176
5.7 Basic Theorems for the Stieltjes Transform 179
5.8 Free Probability for Hermitian Random Matrices 185
5.9 Random Vandermonde Matrix 196
5.10 Non-Asymptotic Analysis of State Estimation 200
Bibliographical Remarks 201
6 Large Non-Hermitian Random Matrices and Quatartenionic Free Probability Theory 203
6.1 Quatartenionic Free ProbabilityTheory 204
6.2 R-diagonalMatrices 209
6.3 The Sum of Non-Hermitian Random Matrices 216
6.4 The Product of Non-Hermitian Random Matrices 220
6.5 Singular Value Equivalent Models 226
6.6 The Power of the Non-Hermitian Random Matrix 234
6.7 Power Series of Large Non-Hermitian Random Matrices 239
6.8 Products of R
About the author
Robert Caiming Qiu, Professor, Dept. of ECE, Tennessee Technological University, Cookeville, TN, USA. Professor Qiu was Founder-CEO and President of Wiscom Technologies, Inc., manufacturing and marketing WCDMA chipsets. Wiscom was acquired by Intel in 2003. Prior to Wiscom, he worked for GTE Labs, Inc. (now Verizon), Waltham, MA, and Bell Labs, Lucent, Whippany, NJ. He holds 5 U.S. patents (another two pending) in WCDMA. Professor Qiu has contributed to 3GPP and IEEE standards bodies, and delivered invited seminars to institutions including Princeton University and the U.S. Army Research Lab. Dr. Qiu was made an IEEE Fellow in 2014.
Dr. Paul Antonik, Chief Scientist, Information Directorate, Air Force Research Laboratory, Rome, N.Y., USA. Dr. Antonik serves as the directorate's principal scientific and technical adviser and primary authority for the technical content of the science and technology portfolio, providing principal technical oversight of a broad spectrum of information technologies.
Summary
This book is aimed at students in communications and signal processing who want to extend their skills in the energy area. It describes power systems and why these backgrounds are so useful to smart grid, wireless communications being very different to traditional wireline communications.
