Monday, February 24, 2014

So Compressive Sensing Skews Everything

It's not just your worldview, consider Terry Tao's h-index:

"..For another example, consider T. Tao’s Google scholar profile. Since he has 30 053 citations, the rule of thumb predicts his h-index is 93.6. This is far from his actual h-index of 65. Now, his top five citations (joint with E. Candes on compressed sensing) are applied. Removing the papers on this topic leaves 13 942 citations. His new estimate is therefore 63.7 and his revised h-index is 61..."

The h-index was introduced by the physicist J.E. Hirsch in 2005 as measure of a researcher's productivity. We consider the "combinatorial Fermi problem" of estimating h given the citation count. Using the Euler-Gauss identity for integer partitions, we compute confidence intervals. An asymptotic theorem about Durfee squares, due to E.R. Canfield-S. Corteel-C.D. Savage from 1998, is reinterpreted as the rule of thumb h=0.54 x (citations)^{1/2}. We compare these intervals and the rule of thumb to empirical data (primarily using mathematicians).
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