Intermittency of point processes in warfare


  1. Yanofsky, C.M.
  2. Bickel, D.R.
Corporate Authors
Defence Research and Development Canada, Centre for Operational Research and Analysis, Ottawa ON (CAN);Ottawa Univ, Ottawa Ont (CAN) Faculty of Medicine
Since instances of criticality are ubiquitous in nature, the intensity of conflicts has been interpreted in terms of self-organized criticality. In this report, interest focused on the statistical properties of series of events in warfare; by investigating the fractal nature of these time series, it is possible in principle to characterize the underlying event-generating process. We applied three methods to explore the scale-invariant behaviour of the time series. With the first two, we examined the tail of each count distribution for evidence of fractal scaling. First, we estimated the density of the logarithm of the counts, and estimated the slope of the graph of the log-counts versus the log-density; second, we fit a truncated power law distribution to the upper-tail cumulative distribution function of the count data using weighted non-linear least squares. Using the third method, we estimated the intermittency (a measure of the propensity of the time series to suddenly increase above typical values) of each time series. In all cases, we applied a bootstrap approach to correct bias and provide levels of confidence. We found that estimates of the scaling exponents of the count distributions were all close to minus one (-1), suggesting that these distributions have wide tails (possibly up to some upper cut-off). For 13 out of 15 data sets, the probability that the scaling exponent is compatible with that of a discrete stable process is 75% or more. In terms of intermittency,
intermittency;violent events;nonlinear systems
Report Number
DRDC-RDDC-2014-C321 — Contract Report
Date of publication
01 Dec 2014
Number of Pages
Electronic Document(PDF)

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