Do Successful Researchers Reach the Self-Organized Critical Point?

Article Type

Research Article

Publication Title

Physics Switzerland

Abstract

The index of success of the researchers is now mostly measured using the Hirsch index (h). Our recent precise demonstration, that statistically (Formula presented.), where (Formula presented.) and (Formula presented.) denote, respectively, the total number of publications and total citations for the researcher, suggests that average number of citations per paper ((Formula presented.)), and hence h, are statistical numbers (Dunbar numbers) depending on the community or network to which the researcher belongs. We show here, extending our earlier observations, that the indications of success are not reflected by the total citations (Formula presented.), rather by the inequalities among citations from publications to publications. Specifically, we show that for highly successful authors, the yearly variations in the Gini index (g, giving the average inequality of citations for the publications) and the Kolkata index (k, giving the fraction of total citations received by the top (Formula presented.) fraction of publications; (Formula presented.) corresponds to Pareto’s 80/20 law) approach each other to (Formula presented.), signaling a precursor for the arrival of (or departure from) the self-organized critical (SOC) state of his/her publication statistics. Analyzing the citation statistics (from Google Scholar) of thirty successful scientists throughout their recorded publication history, we find that the g and k for the highly successful among them (mostly Nobel laureates, highest rank Stanford cite-scorers, and a few others) reach and hover just above (and then) below that (Formula presented.) mark, while for others they remain below that mark. We also find that all the lower (than the SOC mark 0.82) values of k and g fit a linear relationship, (Formula presented.), with (Formula presented.), as suggested by an approximate Landau-type expansion of the Lorenz function, and this also indicates (Formula presented.) for the (extrapolated) SOC precursor mark.

First Page

46

Last Page

59

DOI

10.3390/physics6010004

Publication Date

3-1-2024

Comments

Open Access; Gold Open Access; Green Open Access

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