Simplicial Complexes in Complex Systems: In Search for Alternatives

✍ Scribed by Yi Zhao, Slobodan Maletić

• Publisher: World Scientific Publishing
• Year: 2021
• Tongue: English
• Leaves: 149
• Category: Library

✦ Synopsis

For the last few decades researchers from different fields gather their findings and knowledge trying to give a shape to the new science of complex systems. To address this problem, new tools and methods have to be established. A new, or more precisely an alternative, framework for the characterization of complex system was proposed. In this book we will introduce the applicability of applicability of simplicial complexes in the science of complex systems. After introducing the main definitions and properties of simplicial complexes necessary for representation and analysis of complex systems, we will illustrate the usefulness and versatility of tools and concepts related to the simplicial complexes.

✦ Table of Contents

Contents
Preface
1. Introduction
1.1 Complex system
1.2 Complex networks
1.3 Simplicial complexes
Bibliography
2. The World of Simplicial Complexes
2.1 Geometric simplicial complex
2.2 Abstract simplicial complex
2.3 Simplicial complex via relation
2.4 Characterization of simplicial complexes
2.4.1 Q-analysis
2.4.2 Homology
2.5 Summary
Bibliography
3. How Do We Build Simplicial Complexes
3.1 From complex networks (graphs)
3.2 From data in metric space
3.3 From time series
3.4 Summary
Bibliography
4. Several Applications of Simplicial Complexes
4.1 Opinion exchange modeling
4.2 Topological description of the air traffic control network
4.3 Topological properties of dynamical systems
4.4 Instead of summary: Potential contributions to aeronautical science
Bibliography
5. Take-home Messages
5.1 Brief book summary
5.2 Suggestions for further reading
Index