SIMPLICIAL COMPLEXES IN COMPLEX SYSTEMS. IN SEARCH FOR ALTERNATIVES

• Preface
• Introduction
• The World of Simplicial Complexes
• How Do We Build Simplicial Complexes
• Several Applications of Simplicial Complexes
• Take-home Messages
• Index

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.

Authors
• Prof. Yi Zhao was born in Weihai, People's Republic of China. He received the PhD degree from Hong Kong Polytechnic University, Hong Kong, in 2007. Since 2007, he has been with the Harbin Institute of Technology (Shenzhen), Shenzhen, China, where he is currently a Professor. His research interests include nonlinear dynamics, nonlinear time series analysis, algebraic topology, and complex system modeling. His recent works have been on the application of mathematical methods to a diverse range of problems, including characterization between time series and complex networks, data science, biomathematics, and topological data analysis. In particular, he studies the theoretical foundation of equivalent transformation between complex networks and time series so as to ensure the consistency of dynamics of complex system, thereby providing theoretical evidences for their reciprocal characterization and concrete characterization methods for the applications in practice. In the recent five years, he has published one monograph coauthored with Dr Slobodan Maletic and more than 40 peer-reviewed journal papers. One of his publication is indexed as ESI highly cited papers. In October 2019, he was certified to be the fellow of Institute of Mathematics and Its Application (FIMA), UK.
• Dr Slobodan Maletic graduated theoretical physics at the Faculty of Physics at the University of Belgrade, and currently holds the position of Research Assistant Professor at the "Vinca" Institute of Nuclear Sciences - National Institute of the Republic of Serbia. As the Postdoctoral Fellow, he spent two years at the Centre for Applied Mathematics, Harbin Institute of Technology Shenzhen. His research interests are related to the interdisciplinary applications of algebraic topology, and theoretical physics, with a focus on the development of quantitative and qualitative framework for tackling issues related to complex systems and complex datasets.