# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## career years h-index by diffusion speed

The career years h-index by diffusion speed (Mahbuba and Rousseau 2013) is similar to the other career years h-indices, but rescales the citation counts per year for the time ellapsed since the year of publication. One could also calculate it for a fixed time window, but here we are using career length at the time of calcuation. One creates a list of years ranked by diffusion speed estimated for all citations for all publications from that year. This list is then processed in the same manner as a typical h-type index, namely the career years h-index by diffusion speed is the largest value h for which at least h years have a diffusion speed of h.

$$\text{career years }h\text{ by diffusion speed}=\underset{i}{\max}\left(i\leq \frac{C_i}{A_i}\right).$$

Because the diffusion speed will often not be an integer, the authors recommend interpolating between this and the next largest value, as with the real h-index, in order to more accurately estimate the metric.

$$h_{int}=\frac{\left(h+1\right)\frac{C_h}{A_h}-h\frac{C_{h+1}}{A_{h+1}}}{1-\frac{C_{h+1}}{A_{h+1}}+\frac{C_h}{A_h}}.$$

### Example

Years are ordered by diffusion speed per year, from highest to lowest.

Year (yi) Age (Ai) Citations (Ci) Diffusion Speed (Ci/Ai) Rank (i) 2000 1997 2001 1998 1999 2 5 1 4 3 40 77 3 11 2 20.00 15.40 3.00 2.75 0.67 1 2 3 4 5 h = 3

The largest rank where i ≤ Ci/Ai is 3. The interpolated rank betweeen this and the next largest value is 3.00.

### History

YearCareer years hint by diffusion speed
19971.0000
19982.0000
19992.0000
20002.9000
20013.0000
20024.7500
20035.0000
20045.7319
20056.3137
20066.7479
20077.0000
20088.1667
20098.4455
20109.3750
201110.2326
201210.1910
201310.2258
201410.1818
201510.7011
201610.6875
201710.5017

## References

• Mahbuba, D., and R. Rousseau (2013) Year-based h-type indicators. Scientometrics 96(3):785–797.