Get the publication Pareto front

Enter a public Google Scholar profile URL or user code to explore its journal articles and preprints in freshness vs impact space, and show its Pareto front.

Google Scholar profile:

Direct link here:

Red dots are publications on the Pareto front (purple if preprint only); blue dots are the remaining publications (navy blue if preprint only). A dark border indicates that the profile author is the first listed author (note that this does not detect co-first authorship or equal-contribution statements; it only checks the first author listed by Google Scholar).

Pareto front

The Pareto front is the set of options for which no objective can be improved without worsening at least one other objective. It is named after Italian economist Vilfredo Pareto; the set now called the Pareto front was explicitly described as the Paretian frontier by Francis Bator in 1958, who defined it as the set of positions from which nobody can be made better off without making somebody else worse off (Bator 1958). Here, a publication lies on the front when no other publication is both newer and more highly cited. The front therefore highlights papers that offer the strongest trade-offs between freshness and impact. In statistics and multi-objective analysis, this is important because it avoids collapsing competing criteria into a single arbitrary score and makes efficient alternatives visible for comparison and interpretation.

Kolkata index

The Kolkata index is a measure of how citations are distributed across articles. It is derived from the Lorenz curve. In this example, in which we are in the space of publications and citations, a value k means that the most highly cited (1 − k) fraction of publications receives k of all citations. It generalises the Pareto principle by estimating the split from the data rather than assuming the familiar 80%/20% rule. The measure was introduced as the k-index by Asim Ghosh, Nachiketa Chattopadhyay and Bikas K. Chakrabarti in 2014 (Ghosh 2014). In this tool, publications take the place of people and citations take the place of wealth. The index therefore summarises how concentrated a profile’s citation impact is and permits comparisons between profiles with different numbers of publications and total citations.

Janus gap

The Janus gap, or impact renewal gap, is a temporal-impact measure proposed here to show where an author’s accumulated citation impact lies relative to the temporal centre of their journal publication record. For N journal articles, let y_i be the publication year of article i and c_i its number of citations. Provided that at least one article has been cited, the Janus gap J is defined as: J The first term is the citation-weighted mean publication year, and the second is the ordinary mean publication year. Their difference is expressed in years: a positive Janus gap means that the citation-weighted centre of the profile lies later than the centre of its publication record, indicating an impact that leans more towards newer work; a negative value means that it lies earlier, indicating an impact that leans more towards older, legacy work; and a value around zero means that the two temporal centres are closely aligned. The name refers to Janus, the Roman god traditionally represented with two faces looking in opposite directions, one towards the past and the other towards the future. In the same way, the sign of the Janus gap shows which direction the profile’s accumulated impact faces. Unlike the Pareto front and the Kolkata index, the Janus gap is not an established bibliometric indicator.

Interpreting the Janus gap: because the measure is based on accumulated citations, older publications have had more time to receive citations, and negative values are therefore expected for many profiles. The Janus gap should be understood as the temporal position of a profile’s accumulated impact, rather than as an age-adjusted measure of current research momentum.