Non-cumulative measures of researcher citation impact

The most commonly used publication metrics for individual researchers are the the total number of publications, the total number of citations, and Hirsch's $h$-index. Each of these is cumulative, and hence increases throughout a researcher's career, making it less suitable for evaluation of junior researchers or assessing recent impact. Most other author-level measures in the literature share this cumulative property. By contrast, we aim to study non-cumulative measures that answer the question "in terms of citation impact, what have you done lately?" We single out six measures from the rather sparse literature, including Hirsch's $m$-index, a time-scaled version of the $h$-index. We introduce new measures based on the idea of "citation acceleration". After presenting several axioms for non-cumulative measures, we conclude that one of our new measures has much better theoretical justification. We present a small-scale study of its performance on real data and conclude that it shows substantial promise for future use.