Reading Randomness I

New Horizons for Understanding Fractal and Fractional Calculus
1. Auflage 2026
ISBN: 978-1-041-34814-6
Verlag: Taylor & Francis

Buch, Englisch, 240 Seiten, Format (B × H): 178 mm x 254 mm

Reihe: Fractional Order Thinking in Exploring the Frontiers of STEM

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.

Zielgruppe

Academic, Postgraduate, Undergraduate Advanced, and Undergraduate Core

Autoren/Hrsg.

Nigmatullin, Raoul R.

Chen, YangQuan

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik Mathematik Mathematische Analysis

Inhaltsverzeichnis

1. An Introduction to Reading Randomness 2. Discrete Geometrical Invariants (DGI) Based Methods 3. NOCFASS (Non-Orthogonal Combined Fourier Analysis of Smoothed Signals) Methods 4. Generalized Correlations Based Methods 5. Generalized Methods Using Fractional Calculi 6. Hereditary Principled Methods 7. Conclusion and Future Opportunities

Über Autor(innen)

Raoul R. Nigmatullin is Professor at the Radioelectronics and Informative Measurements Technics Department, Kazan National Research Technical University, named after A.N. Tupolev. His research interests include dielectric spectroscopy in electrochemistry and new treatment methods in radiometry.

YangQuan Chen, a Clarivate Highly Cited Researcher, is a professor at the School of Engineering, University of California, Merced. His research interests include smart control engineering via digital twins and applied fractional calculus in STEM.