Raoul R. Nigmatullin - Böcker

Reading Randomness I shows readers how to understand and analyze seemingly “noisy” and irregular data. It offers practical methods for comparing and labeling fluctuations, ensuring reproducible results across laboratories, industries, and research fields.The book begins with a narrative tour of how people have understood chance, from ancient divination and games to modern probability, information theory, and computing. In seven chapters, the authors provide step-by-step instructions for extracting reliable patterns from raw measurements. These instructions include removing trends, checking whether a signal has long-term memory, and identifying stable patterns hidden inside apparent randomness. The book also presents new tools for analyzing “trendless” sequences, extending Fourier-style analysis to complicated, multi-period data, and measuring correlations in a way that distinguishes between contributions from the system itself and the environment. Using a reader-friendly approach, the authors explain how “memory” kernels capture slow, history-dependent behavior. Throughout the book, the authors emphasize independent checks, surrogate tests, and instrument-path corrections to ensure that conclusions can be reliably and safely transferred across places and time.With case studies ranging from transcendental numbers and electrical circuits to earthquake records and precious metal price data, this valuable guidebook will appeal to students, researchers, and professionals working with complex data in science, engineering, and finance.

This book is intended as a manual on modern advanced statistical methods for signal processing. The objectives of signal processing are the analysis, synthesis, and modification of signals measured from different natural phenomena, including engineering applications as well. Often the measured signals are affected by noise, distortion and incompleteness, and this makes it difficult to extract significant signal information. The main topic of the book is the extraction of significant information from measured data, with the aim of reducing the data size while keeping the basic information/knowledge about the peculiarities and properties of the analyzed system; to this aim, advanced and recently developed methods in signal analysis and treatment are introduced and described in depth. More in details, the book covers the following new advanced topics (and the corresponding algorithms), including detailed descriptions and discussions: the Eigen-Coordinates (ECs) method, The statistics of the fractional moments, The quantitative "universal" label (QUL) and the universal distribution function for the relative fluctuations (UDFRF), the generalized Prony spectrum, the Non-orthogonal Amplitude Frequency Analysis of the Smoothed Signals (NAFASS), the discrete geometrical invariants (DGI) serving as the common platform for quantitative comparison of different random functions. Although advanced topics are discussed in signal analysis, each subject is introduced gradually, with the use of only the necessary mathematics, and avoiding unnecessary abstractions. Each chapter presents testing and verification examples on real data for each proposed method. In comparison with other books, here it is adopted a more practical approach with numerous real case studies.