“…What's the biggest mathematical mystery in nature? Fibonacci numbers! The pattern creeps up in the most unexpected places. …”

Tabla de Contenidos: “…-- Preface xv -- 1 Introduction 1 -- 1.1 Vision: “Big Data” 1 -- 1.2 Cognitive Radio: System Concepts 2 -- 1.3 Spectrum Sensing Interface and Data Structures 2 -- 1.4 Mathematical Machinery 4 -- 1.4.1 Convex Optimization 4 -- 1.4.2 Game Theory 6 -- 1.4.3 “Big Data” Modeled as Large Random Matrices 6 -- 1.5 Sample Covariance Matrix 10 -- 1.6 Large Sample Covariance Matrices of Spiked Population Models 11 -- 1.7 Random Matrices and Noncommutative Random Variables 12 -- 1.8 Principal Component Analysis 13 -- 1.9 Generalized Likelihood Ratio Test (GLRT) 13 -- 1.10 Bregman Divergence for Matrix Nearness 13 -- 2 Spectrum Sensing: Basic Techniques 15 -- 2.1 Challenges 15 -- 2.2 Energy Detection: No Prior Information about Deterministic or Stochastic Signal 15 -- 2.2.1 Detection in White Noise: Lowpass Case 16 -- 2.2.2 Time-Domain Representation of the Decision Statistic 19 -- 2.2.3 Spectral Representation of the Decision Statistic 19 -- 2.2.4 Detection and False Alarm Probabilities over AWGN Channels 20 -- 2.2.5 Expansion of Random Process in Orthonormal Series with Uncorrelated Coefficients: The Karhunen-Loeve Expansion 21 -- 2.3 Spectrum Sensing Exploiting Second-Order Statistics 23 -- 2.3.1 Signal Detection Formulation 23 -- 2.3.2 Wide-Sense Stationary Stochastic Process: Continuous-Time 24 -- 2.3.3 Nonstationary Stochastic Process: Continuous-Time 25 -- 2.3.4 Spectrum Correlation-Based Spectrum Sensing for WSS Stochastic Signal: Heuristic Approach 29 -- 2.3.5 Likelihood Ratio Test of Discrete-Time WSS Stochastic Signal 32 -- 2.3.6 Asymptotic Equivalence between Spectrum Correlation and Likelihood Ratio Test 35 -- 2.3.7 Likelihood Ratio Test of Continuous-Time Stochastic Signals in Noise: Selin's Approach 36 -- 2.4 Statistical Pattern Recognition: Exploiting Prior Information about Signal through Machine Learning 39 -- 2.4.1 Karhunen-Loeve Decomposition for Continuous-Time Stochastic Signal 39 -- 2.5 Feature Template Matching 42 -- 2.6 Cyclostationary Detection 47 -- 3 Classical Detection 51.…”

“…Behavioral, cultural, mathematical, and statistical aspects of risk assessment and modelling have been explored, and have been often illustrated using real and simulated data. …”

“…The topics of the Issue include fractional calculus, the mathematical analysis of the properties of the solutions to fractional equations, the extension of classical approaches, or applications of fractional equations to several fields…”

“…In a clear, concise manner, this book presents the mathematical concepts essential to optical coding theory. …”

“…The book not only describes what indicators do (or are designed to do, which is not always the same thing), but also gives precise mathematical formulae so that indicators can be properly understood and evaluated. …”

“…Argues that economics is a cultural phenomenon, rather than a strictly mathematical entity, that is found in mythology, religion, philosophy, psychology, literature, and film. …”

“…Focused on practical techniques in holography at all levels, it avoids any unnecessary mathematical theory…”

“…The objective of this Special Issue is to address and disseminate the latest gait, posture, and activity monitoring systems as well as various mathematical models/methods that characterize mobility functions. …”

“…The goal of this book is to provide a reference for applications of mathematical modelling in social media and related network analysis and offer a theoretically sound background with adequate suggestions for better decision-making. …”

“…The objective of this Special Issue is to address and disseminate the latest gait, posture, and activity monitoring systems as well as various mathematical models/methods that characterize mobility functions. …”

“…The objective of this Special Issue is to address and disseminate the latest gait, posture, and activity monitoring systems as well as various mathematical models/methods that characterize mobility functions. …”