Grammar of Complexity

From Mathematics to a Sustainable World

The book is an introduction, for both graduate students and newcomers to the field of the modern theory of mesoscopic complex systems, time series, hypergraphs and graphs, scaled random walks, and modern information theory. As these are applied for the exploration and characterization of complex systems. Our self-consistent review provides the necessary basis for consistency. We discuss a number of applications such diverse as urban structures and musical compositions.

Contents:

• Perplexity of Complexity
• Preliminaries: Permutations, Partitions, Probabilities and Information
• Theory of Extreme Events
• Statistical Basis of Inequality and Discounting the Future and Inequality
• Elements of Graph Theory. Adjacency, Walks, and Entropies
• Exploring Graph Structures by Random Walks
• We Shape Our Buildings: Thereafter They Shape Us
• Complexity of Musical Harmony

Readership: Graduate student in information theory, complex systems and mathematical modeling.
Key Features:

• The book provides the unique treatment of the modern theory of mesoscopic complex systems, time series, hypergraphs and graphs, scaled random walks, and modern information theory as applied for exploration and characterization of complex systems
• The book shows how the concepts of complexity theory is applicable to the problem fo survival, urban studies, income inequality, musical harmony
• The book might be used as recommended reading for a course