Abstract
Wars, terrorist attacks, as well as natural catastrophes typically result in a large number of casualties, whose distributions have been shown to belong to the class of Pareto’s inverse power laws (IPLs). The number of deaths resulting from terrorist attacks are herein fit by a double Pareto probability density function (PDF). We use the fractional probability calculus to frame our arguments and to parameterize a hypothetical control process to temper a Lévy process through a collective-induced potential. Thus, the PDF is shown to be a consequence of the complexity of the underlying social network. The analytic steady-state solution to the fractional Fokker-Planck equation (FFPE) is fit to a forty-year fatal quarrel (FQ) dataset.
Highlights
Datasets on the distribution of wealth [7], the richness of language [8], the robustness of urban growth [9], the number of deaths due to fatal quarrels [10], the intrinsic flexibility of biological macroevolution [11] and the inherent variability of other nonsimple phenomena are not statistically normal, which is to say that their statistics are not given by the probability density function (PDF) of
Nonsimple problems, are interwoven, subtly, so that generating solutions is closely related to generating results to apparently unrelated problems. What this means in practice is that the most valuable solutions are connected to multiple problems within an organization; the distribution of solutions have the same imbalance in their influence on problems, as individual talents have on the distribution of income among people
The asymptotic fatal quarrel variability (FQV) PDF has a slope in agreement with the studies involving terrorism where non-G7 countries are targets α = 2.5 (≈ ν + 1), and the FQV inverse power laws (IPLs) is in agreement with the value obtained for North America by Becerra et al [32]
Summary
This essay is about distinguishing between simple and nonsimple We do this for the same reasons that the term nonlinearity was introduced over a half century ago to describe dynamics that are not linear) phenomena, networks and systems, as well as why catastrophes such as fatal quarrels cannot be understood using simple models. Properties such as the time intervals between successive beats of the heart, or between successive breaths, and the length of successive strides in walking typically have fluctuations with PDFs with heavy tails [1] The latter type of size distributions are indicative of nonsimple underlying processes.
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