Aaron Lercher

Citation rates in mathematics: a study of variation by subdiscipline

Variation of citation counts by subdisciplines within a particular discipline is known but rarely systematically studied. This paper compares citation counts for award-winning mathematicians is different subdisciplines of mathematics. Mathematicians were selected for study in groups of rough equivalence with respect to peer evaluation, where this evaluation is given by the awarding of major prizes and grants: Guggenheim fellowships, Sloan fellowships, and National Science Foundation CAREER grants. We find a pattern in which mathematicians working in some subdisciplines have fewer citations than others who won the same award, and this pattern is consistent for all awards. So even after adjustment at the discipline level for different overall citation rates for disciplines, citation counts for different subdisciplines do not match peer evaluation. Demographic and hiring data for mathematics provides a context for a discussion of reasons and interpretations.

Correlation over time for citations to mathematics articles

Explicit definition of the limits of citation analysis demands additional tests for the validity of citation analysis. The stability of citation rankings over time can be regarded as confirming the validity of evaluative citation analysis. This stability over time was investigated for two sets of citation records from the Web of Science (Thomson Reuters, Philadelphia, PA) for articles published in journals classified in Journal Citation Reports as Mathematics. These sets are of all such articles for the 1960s and for the 1970s. This study employs only descriptive statistics and draws no inferences to any larger population. The study found a high correlation from one decade to the next of rankings among sets of most highly cited articles. However, the study found a low correlation for rankings among articles whose ranks were the 500 directly below those of the 500 most cited. This perhaps expected result is discussed in terms of the Glanzel‐Schubert‐Schoepflin stochastic model for citation processes and also in connection with an account of the purposes of evaluative citation analysis. This interpretative context suggests why the limitations of citation analysis may be inherent to citation analysis even when it is done well.

Persistent value of older scientific journal articles

This paper discusses how to translate the well-confirmed phenomenon of increasing citation of older scientific literature into an argument for the persistent citation impact of older scientific journal articles. Since libraries purchase or subscribe to scientific journal articles in packages consisting of journal-years, the citation impact of past journal-years needs to be assessed separately from that of recent years. The simple and flexible (Bouabid in Scientometrics 88:199–211, 2011. doi:10.1007/s11192-011-0370-5) model, as applied to particular journal-years, is applied and assessed.

Testing theories of preferential attachment in random networks of citations

In this article we examine 2 classic stochastic models of the accumulation of citations introduced by H.A. Simon and Derek John de Solla Price. These models each have 2 distinct aspects: growth, which is the introduction of new articles, and preferential attachment, which describes how established articles accumulate new citations. The attachment rules are the subtle portion of these models that supply the interesting explanatory power. Previous treatments included both aspects. Here we separate preferential attachment from the growth aspect of the model. This separation allows us to examine the results of the preferential attachment rules without confounding these with growth in the number of articles available to receive citations. We introduce the method using Markov chains. We show how to overcome the mathematical and computational complexity to obtain results. A comparison of Simons and Prices rules are computed in 3 Journal Citation Reports subject categories using articles published in the 1960s and allowed to accumulate citations to 1980. This comparison cannot be made through analysis of power laws.