Questions on h-index application to groups (a la Molinari & Molinari)

[Pikas, Christina K.]

A physicist here where I work had these questions that I am, alas, unable to answer :( Help?

1.            In  J.-F. Molinari, A. Molinari, A new methodology for ranking scientific institutions, Scientometrics, 75 (2008) 163-174 and A. Molinari, J.-F. Molinari, Mathematical aspects of a new criterion for ranking scientific institutions based on the h-index, Scientometrics, 75 (2008) 339-356 there is mention of an overall distribution of scaling of h = h_m N^beta with beta determined empirically to be ~0.4. This was also found in another study by A.L. Kinney, National scientific facilities and their science impact on nonbiomedical research, Proceedings of the National Academy of Sciences, 104 (2007) 17943-17947. Now I've not been able to understand what the implication of the exponent 0.4 is for scaling h into a collection number N and an impact factor h_m. The fact that the scaling works so well is almost supernatural but there must be something else underlying the scaling (there is some discussion in W. Glänzel, On the h-index - A mathematical approach to a new measure of publication activity and citation impact, Scientometrics, 67 (2006) 315-321, but I seem to be missing his point).
2.            In Hirsch's original publication (J.E. Hirsch, An index to quantify an individual's scientific research output, Proceedings of the National Academy of Sciences of the United States of America, 102 (2005) 16569-16572.) he talks about both a linear model as well as a stretched exponential model for the distribution of the total number of citations N_cite. He defines a parameter a as N_cite = a h^2 and notes that a ~ 3 to 5 for individual scientists. For something like the journal citings used in Molinari and Molinari, there must be some  underlying distribution in their study of journals as well as in the Kinney study from which one should, in principle, be able to calculate a (the quadratic scaling in h holds well in the data sets we have looked at), but [study team member] was not familiar with this or any work that has looked at it - are you?

Thanks in advance,
Christina


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Christina K Pikas
Librarian
The Johns Hopkins University Applied Physics Laboratory
Christina.Pikas at jhuapl.edu
(240) 228 4812 (DC area)
(443) 778 4812 (Baltimore area)

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