Efficient computational testing of scale-free behavior in real-world systems

Guannan Zhao, Zhenyuan Zhao, Neil F. Johnson

Research output: Contribution to journalArticlepeer-review


With big data becoming available across the physical, life and social sciences, researchers are turning their attention to the question of whether universal statistical signatures emerge across systems. Power-laws are a particularly potent example, since they indicate scale-free or scale invariant behavior and are observed in physical systems near phase transitions. However, the same scale-free property that enables them to unify behaviors across multiple spatiotemporal scales, also means that usual Gaussian-based approaches cannot be used to test their presence. Here we analyze the crucial question of how to implement a power-law test efficiently, given that a key part involves multiple Monte Carlo simulations to obtain an accurate statistical p-value. We present such a computational scheme in detail.

Original languageEnglish (US)
Pages (from-to)77-82
Number of pages6
JournalJournal of Computational Science
StatePublished - Jan 1 2016


  • Collective behavior
  • Complexity
  • Numerical analysis

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Modeling and Simulation


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