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Complex systems and emergence： How theory meets reality

Emergent behaviors of complex systems have fascinated mankind for aeons. It is only in recent decades that extensive efforts have been made to quantitatively study them, resulting in important theories and tools such as chaos theory, random fractal theory, and multiscale analyses. This article aims to convey the best practices in this vast field, emphasizing theory meets reality. As illustrative examples, cyber-security, financial crises, river flow dynamics, and world-wide political conflicts will be briefly discussed. Important future research directions will also be outlined.