Quantifying collective dynamics and emergent behaviors in complex systems

Abstract

Nature is not simple as it is often described in the textbooks, yet not all intractable either. Captivated by its nature, not too complex to drive away but enough so to tantalize our curiosity in deep down, many scientists could not resist but devote themselves to studies of complex system. As such devoted writing, this Thesis presents characteristics of complex systems and catches glimpses of its principles. Two different approaches have been conventionally taken for scholars of different areas when facing complex systems. On the one hand, physicists, or natural scientists, have avoided interactions and interdependencies as much as possible, and instead, have achieved the immaculate ivory tower. Unfortunately, for physicists, interactions and interdependencies, the essential features of complex systems, give rise to all the fascinating collective dynamics and emergent behaviors, for which we have extended our domain little by little. On the other hand, humanists have taken on the qualitative description to tackle such complexities and have given up the quantitative approaches. Analysis of extremely complex systems, such as psychology, sociology, linguistics, and even biology to some extent, has, therefore, often been limited to qualitative or descriptive methods. However quantitative approaches provide a precise way to formulate hypotheses mathematically, to allow statistical testing, to classify given models, and to compare with alternatives in a rigorous and transparent way. As our understanding of these systems has advanced and as many novel mathematical tools for the analysis of such complex systems have been developed by pioneers, we have witnessed that it has become possible to approach these questions in a rigorous and mathematical way. At the same time, unprecedented computation power and large-scale quantitative data have become available. For example, patterns of human mobility, social interactions and language use were once studied with manually col...