This book provides a unifying approach to the study of statistical laws, critically evaluating their role in the theoretical understanding of complex systems and the different data-analysis methods used to evaluate them. Statistical laws describe regular patterns observed in diverse scientific domains, ranging from the magnitude of earthquakes (Gutenberg-Richter law) and metabolic rates in organisms (Kleiber's law), to the frequency distribution of words in texts (Zipf's and Herdan-Heaps' laws), and productivity metrics of cities (urban scaling laws). The origins of these laws, their...

This book serves as a comprehensive introduction to nonlinear complex systems through the application of machine learning methods. Artificial intelligence (AI) has affected the foundations of scientific discovery, and can therefore lend itself to developing a better understanding of the unpredictable nature of complex dynamical systems and to predict their future evolution. 

Utilizing Python code, this book teaches and applies machine learning to topics such as chaotic dynamics and time-series analysis, solitons, breathers, chimeras, nonlinear localization, biomolecular...

This textbook provides a comprehensive exploration of anomalous stochastic processes and extreme events, commonly referred to as "black swans," with a particular focus on (multi-)fractal approaches and continuous-time random walks. The authors present a systematic examination of the subject, tracing its inception and providing a multi-directional perspective. By drawing on real-world experiences in finance, physics, and technology, the book underscores the practical relevance of anomalous stochastic processes for practitioners dealing with real-world data from complex systems.

The...

This book presents Analytical and Approximate Methods for Complex Dynamical Systems and introduces ideas of discontinuous mapping treated as complex dynamical systems. Mathematicians of world-recognized Ukrainian scientific schools established by M.Krylov, M.Bogolyubov, Yu.Mitropolskiy, and A.Sharkovsky used to cooperate for writing the collective book whose purpose consists of illustrating a synergy of combining diverse (by idea and technique) constructive analytical and approximate approaches and methods in complex dynamical systems which are herein associated with mathematical models of...

This book examines the problems of causal determinism and limited completeness in systems theory. Furthermore, the author analyzes options for complexity measurements that include systems’ autonomy and variability for causal inference—i.e., the ability to derive causal relationships from data recorded as a function of time. Such complexity measures present limitations in the derivation of absolute causality in complex systems and the recognition of relative and...

This book marks one of the first applications of the Medicine Network discipline to an everyday scenario. It explores situations where patients, often in adolescence, grapple with the decision of whether to commence a treatment, seeking insights into the more plausible future scenarios. Additionally, the specific feedback from biological systems in the human body serves as a potent metaphor for addressing various challenges in the field of Complex Systems.

In recent times, systems thinking and complexity theory have yielded substantial conceptual advancements across various...

This book brings together key findings, insights, and theories at the intersection of two disciplines – city science and complex systems. It features a curated collection of chapters contributed by emerging...

This book explores the identification of influencers in complex networks, bridging theoretical approaches with practical applications across diverse fields. It examines interdisciplinary complex systems, including online social media, biological networks, brain networks, socioeconomic and financial systems, and ecosystems. The research presented aims to benefit scientists in relevant areas and inspire new scientific inquiries, potentially advancing the field of influencer identification.

In this context, 'influencer' serves as an umbrella term for essential, core, or...