Overview

This course explores the features of complexity science. Our world is connected by an abundance of complex systems. Across all levels of organizations from physical, biological world to the social world, we may think of the connectivity between individual elements and how they interact and influence each other. For example, how humans transmit pandemics within a group, how cars interact in the traffic system and how networks connect in governmental organizations. Although these systems are diverse and different, they have surprisingly huge features in common. In the past several decades, the study of complexity science has been increasing. It is widely acknowledged that an innovative, integrated and analytical way of thinking is essential for understanding the complex issues in the human societies. In this course, we will aim to give everyone a comprehensive introduction of the complex systems, to talk about the resilience, robustness and sustainability of the systems and to learn basic mathematical methods for complex system analysis, for example regime shifts and tipping points, the agent-based modelling, the dynamic and network theories. Most importantly, we will implement the theories into practical applications of cities and health to help students gain practice in complex systems way of thinking. This course is co-developed by Associate Professor Cheong Siew Ann, Professor Stephen Lansing and Professor Peter Sloot between 2014 and 2020 at the Complexity Institute, Nanyang Technological University, Singapore.

Syllabus

Course Overview and Week 1: Introduction to Complex Systems

This week provides an overview of complex systems, explaining the evolution of complexity science, its applications in society, and the importance of gaining a basic understanding of the field. As complexity science is not a spectator sport, the module emphasizes that students must go beyond learning models and methods from lectures. You will be required to try these out to develop a practical feel for what they mean and what they can do. Accordingly, this week utilizes Jupyter Notebooks to facilitate two specific exercises, the Nagel-Schreckenberg model of vehicular traffic and the Game of Life.

Week 2: Robustness, Resilience, and Sustainability

In this week, you will get a comprehensive understanding of robustness, resilience and sustainability. You will learn the self-organized criticality in the complexity system and self-similarity including the fractals, power law, universality and phase transition diagram. This week includes a case study of the subak system in Bali, which will help you further understand the tragedy of the commons. Lastly, you will get introduced to the resilience of a swarm.

Week 3: Regime Shifts and Tipping Points

In this week, you will get a basic understanding of tipping point and regime shifts, and their applications in forecasting. You will understand the phase transition diagram, criticality and landau theory. Additionally, you will review examples on early warnings and forecasting in earthquakes and stock markets.

Week 4: Introduction to Agent-Based Modeling

In this week, you will learn about Agent-Based Modeling: what it is, how it works, why it is used and how to use it. Then, you will try a Jupyter Notebook exercise on Schelling’s Segregation Model. You will also learn how to build an ABM using qualitative data from observations and interviews and then validate and calibrate an ABM through examples. In the end, you'll review how to use ABM for policy assessment.

Week 5: Introduction to Static Complex Network

In this week, you will get a comprehensive understanding of what a complex network is and how to measure on networks in terms of nodes and paths. You will get introduced to different types of random network and small-world networks that will help you have a better understanding. You will also discuss the robustness of a network, percolation transitions and real-world examples.Lastly, you will review complex networks and their attributes before looking at different network models.