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This book demonstrates how mathematical methods and techniques can be used in synergy and create a new way of looking at complex systems. It becomes clear nowadays that the standard (graph-based) network approach, in which observable events and transportation hubs are represented by nodes and relations between them are represented by edges, fails to describe the important properties of complex systems, capture the dependence between their scales, and anticipate their future developments. Therefore, authors in this book discuss the new generalized theories capable to describe...

This book explores recent developments in theoretical research and data analysis of real-world complex systems, organized in three parts, namely

Entropy, information, and complexity functions

Multistability, oscillations, and rhythmic synchronization

Diffusions, rotation, and convection in fluids

The collection of works devoted to the memory of Professor Valentin Afraimovich provides a deep insight into the recent developments in complexity science by introducing new concepts, methods, and applications in nonlinear dynamical systems covering...

This book introduces and studies a number of stochastic models of subsistence, communication, social evolution and political transition that will allow the reader to grasp the role of uncertainty as a fundamental property of our irreversible world. At the same time, it aims to bring about a more interdisciplinary and quantitative approach across very diverse fields of research in the humanities and social sciences.

Through the examples treated in this work - including anthropology, demography, migration, geopolitics, management, and bioecology, among other things - evidence is...

Cities are considered to be among the largest and most complex artificial networks created by human beings. This monograph uses methods from spectral graph theory and statistical physics to lay the theoretical foundations for studying compact urban topology.