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)20001997200119981999
Age (Ai)25143
Citations (Ci)40773112
Diffusion Speed (Ci/Ai)20.0015.403.002.750.67
Rank (i)12345
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