Fig. 3 The Q-model. The Q-model. (A) Distribution of the paper impact c10 across all publications in the data set. The gray line corresponds to a log-normal.

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Fig. 3 The Q-model. The Q-model. (A) Distribution of the paper impact c10 across all publications in the data set. The gray line corresponds to a log-normal function with average μ = 1.93 and SD σ2 = 1.05 (R2 = 0.98). (B) Distribution of the total number of papers published by a scientist (productivity). The gray line is a log-normal with μ = 3.6 and σ2 = 0.57 [weighted Kolmogorov-Smirnov (KS) test, P = 0.70]. (C) Citations of the highest-impact paper, , versus the number of publications N during a scientist’s career. Each gray point of the scatterplot corresponds to a scientist. The circles are the logarithmic binning of the scattered data. The cyan curve represents the prediction of the R-model, assuming that the impact of each paper is extracted randomly from the distribution P(c10) of Fig. 2A. The red curve corresponds to the analytical prediction (see eq. S35) of the Q-model (R2 = 0.97; see section S4.6 and fig. S29 for goodness of the fit). (D) versus . Each gray point in the scatterplot corresponds to a scientist, where is the average logarithm of her paper impact, excluding the most-cited paper . We report in cyan the R-model prediction and in red the analytical prediction (see eq. S36) of the Q-model (R2 = 0.99; see section S4.6 and fig. S29 for goodness of the fit). (E) Cumulative impact distribution of all papers published by three scientists with the same productivity, N ≃ 100, but different Q. (F) Distribution across all publications. For each paper α of scientist i, we have log pα = log c10,iα − log Qi, where . Therefore, the distribution of , except for a common translational factor μp, corresponds to the distribution of log c10,iα − 〈 log c10,i〉, which is a normal with μ = 0 and σ2 = 0.95 (KS test, p = 0.48). (G) Distribution of parameter Q, P(Q), for all scientists. The gray line corresponds to a log-normal function with μ = 0.93 and σ2 = 0.46 (weighted KS test, p = 0.59). (H) Cumulative distribution of the rescaled impact c10,iα/Qi for the three scientists in (E). The black line corresponds to the universal distribution P(p).The collapse is predicted by Eq. 1. Roberta Sinatra et al. Science 2016;354:aaf5239 Published by AAAS