# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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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 adjusted h- index is calculated by weighting each publications citation count by this effort,

$$C^{*}_i=E_i C_i,$$

reranking the publications based these weighted counts, and calculating the index as

$$h_a=\underset{i}{\max}\left(i \leq E_iC_i\right)=\underset{i}{\max}\left(i \leq C^{*}_i\right).$$

### Example

Publications are ordered by adjusted number of citations, from highest to lowest.

 Citations (Ci) Authors (Ai) Author Position (ai) Author Effort (Ei) Adjusted Citations ($$C^*_i$$) Rank (i) 42 36 9 14 11 2 2 9 1 2 3 1 1 0 0 0 3 3 1 3 2 1 1 4 1 4 4 2 4 4 2 1 1 1 1 3 2 1 1 3 1 1 3 1 3 3 1 1 0.43 0.43 1.00 0.43 0.50 1.00 1.00 0.17 1.00 0.33 0.17 0.50 0.17 0.17 0.50 1.00 18.00 15.43 9.00 6.00 5.50 2.00 2.00 1.50 1.00 0.67 0.50 0.50 0.17 0.00 0.00 0.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ha = 5

The largest rank where $$i \leq C^*_i$$ is 5.

Yearha
19970
19981
19992
20004
20015
20026
20037
20048
200510
200612
200714
200815
200917
201018
201119
201221
201322
201424
201524
201625
201725

## 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.