Page 155 - Becoming Metric Wise

146 Becoming Metric-Wise

actually a self-citation. Examples of sleeping beauties in ophthalmology
were studied by Ohba and Nakao (2012) determining the three factors
proposed by Van Raan.
Yet, the original fairy tale does not begin with the sleeping period.
Indeed, the Sleeping Beauty in the story is a lively princess (the article
receives some citations) and then pricks her finger on a spindle and falls
asleep. Li and Ye (2012) found examples of articles that went through all
stages of the story, referring to them as all-elements-sleeping-beauties.
Hence, it might be better to restrict the term sleeping beauty to all-
elements-sleeping-beauties, or for emphasis, real sleeping beauties, and
keep the terms delayed recognition and premature discovery for the situa-
tion studied by van Raan. Li and Ye (2012) refer to the time line of cita-
tions during the sleeping period as the heartbeat spectrum. Such
heartbeat spectra are also studied in Li et al. (2014).
Du and Wu (2016) propose four requirements for a paper to act as a
Prince: (1) to be published near the year in which the Sleeping Beauty
starts to attract a lot of citations; (2) be a highly cited paper itself; (3)
receive a substantial amount of cocitations with the Sleeping Beauty, and
(4) during a certain period around the awakening the annual number of
citations of the Prince is higher than that of the Sleeping Beauty. They
further point out that sometimes there is more than one Prince and the
author of the Sleeping Beauty paper can be the author of the paper that
plays the role of the Prince.
Although being a sleeping beauty sounds like a yes/no situation, it is
clear that delayed recognition is not a clear-cut phenomenon and a sleep-
ing beauty in the eyes of one person may not be one in the eyes of a col-
league. To solve this problem Ke et al. (2015) turned delayed recognition
or being a sleeping beauty into a time-dependent continuous phenome-
non by defining a beauty coefficient at time T, denoted as B(T). Let c(t)
denote the citation curve of an article, i.e., c(t) is the number of citations
received in year t (or generally in period t, as the unit of time can be a
month, or some other time period). The publication year is year t 5 0
and t takes values between 0 and T. Let c m be the maximum number of
received citations, for which we assume that it happened in year t m . The
line connecting (0, c(0)) and (t m , c m ), which we refer to as the recognition
line, denoted as y(t), has equation:

c m 2 cð0Þ
yðtÞ 5 t 1 cð0Þ (5.12)
t m