Abstract
The detection and characterization of self-organized criticality (SOC), in both real and simulated data, has undergone many significant revisions over the past 25 years. The explosive advances in the many numerical methods available for detecting, discriminating, and ultimately testing, SOC have played a critical role in developing our understanding of how systems experience and exhibit SOC. In this article, methods of detecting SOC are reviewed; from correlations to complexity to critical quantities. A description of the basic autocorrelation method leads into a detailed analysis of application-oriented methods developed in the last 25 years. In the second half of this manuscript space-based, time-based and spatial-temporal methods are reviewed and the prevalence of power laws in nature is described, with an emphasis on event detection and characterization. The search for numerical methods to clearly and unambiguously detect SOC in data often leads us outside the comfort zone of our own disciplines—the answers to these questions are often obtained by studying the advances made in other fields of study. In addition, numerical detection methods often provide the optimum link between simulations and experiments in scientific research. We seek to explore this boundary where the rubber meets the road, to review this expanding field of research of numerical detection of SOC systems over the past 25 years, and to iterate forwards so as to provide some foresight and guidance into developing breakthroughs in this subject over the next quarter of a century.


























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Acknowledgements
The author team acknowledges the hospitality and partial support for two workshops on Self-Organized Criticality and Turbulence at the International Space Science Institute (ISSI) at Bern, Switzerland, during October 15–19, 2012, and September 16–20, 2013. One of us (JMA) was partially supported by a National Science Foundation Career award, NSF AGS-1255024, and NASA contracts NNH12CG10C and NNX13AE03G. One of us (MJA) was partially supported by NASA contract NNX11A099G and NASA contract NG04EA00C of the SDO/AIA instrument to LMSAL. One of us (MKG) was partially supported by EU FP7 grant PIRG07-GA-2010-268245. One of us (VIA) was partially supported by NASA LWS NNX11AO73G grant and by the Program of the Presidium of Russian Academy of Sciences No. 21. The authors acknowledge the comprehensive and dedicated work of an anonymous referee.
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McAteer, R.T.J., Aschwanden, M.J., Dimitropoulou, M. et al. 25 Years of Self-organized Criticality: Numerical Detection Methods. Space Sci Rev 198, 217–266 (2016). https://doi.org/10.1007/s11214-015-0158-7
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DOI: https://doi.org/10.1007/s11214-015-0158-7
