The citation normalization of publication p from faculty Embedded Image leverages the universal log-normal properties of citation statistics (61), yielding a stationary, normally distributed citation measure zi,pN(0, 1) (fig. S5) that is well suited for identifying longitudinal patterns of citation impact in research careers (25, 35).

To be specific, we disaggregated the articles by publication year and removed the time-dependent trend in the location and scale of the underlying log-normal citation distribution by definingEmbedded Image(4)where Embedded Imageis the mean and σt≡σ[ln(1 + cs,t)] is the SD of the citation distribution, after adding 1 to each citation tally (to avoid the divergence of ln 0 associated with uncited publications) and applying the natural logarithm. We calculated μt and σt within the subset of publications for a given year t and discipline s (BIO or CS). The SD σt ≈ 1.4 is approximately constant across time and the two disciplines we analyzed.

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