# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## profit p-index

The profit indices (Aziz and Rozing 2013) attempt to measure the effect of collaboration on an author's impact. They use a harmonic weighting algorithm and information on author order (assuming that authors in the middle of an author list had the least impact) to estimate effort for each publication. The effort for the ith publication is

$$E_i=\frac{1+\left|A_i+1-2a_i\right|}{\frac{1}{2}A_i^2+A_i\left(1-D_i\right)},$$

where

$$D_i=\begin{matrix} 0 & \text{if }A_i\text{ is even} \\ \frac{1}{2A_i} & \text{if }A_i\text{ is odd} \end{matrix}.$$

The sum of Ei for all publications is the number of “monograph equivalents” (a monograph being defined as a single-authored publication). The profit (p)-index is the relative contribution of collaborators to an individual's total publication record, or

$$p=1-\frac{\sum\limits_{i=1}^{P}{E_i}}{P}.$$

This value ranges from 0 to 1, with 0 indicating no contribution of co-authors (all solo-authored papers) and 1 meaning complete contribution from co-authors (a value of exactly 1 is impossible).

Yearprofit p
19970.5619
19980.5516
19990.5680
20000.5179
20010.4509
20020.4842
20030.5054
20040.5048
20050.4527
20060.4541
20070.4679
20080.4875
20090.4728
20100.5100
20110.5225
20120.5288
20130.5457
20140.5278
20150.5366
20160.5424
20170.5533

## References

• Aziz, N.A., and M.P. Rozing (2013) Profit (p)-Index: The degree to which authors profit from co-authors. PLoS ONE 8(4):e59814.