Page 154 - Becoming Metric Wise

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Publication and Citation Analysis

Because these overlapping multisets are not easy to see we provide a
full explanation.

m

H 5 b; c; f ; f ; g , obtained from b-a; c-a; f -a; f -b; g-b
1
H 5 b; f ; f ; f ; g; d; e; h; i; j; h; i; j , is obtained from b-c-a;

m

2
f -b-a; f -c-a; f -g-b; g-b-a; dðeÞ-c-a; hði; jÞ-f -b;
hði; jÞ-f -a
H 5 f ; f ; g; h; i; j; h; i; j; h; i; j , is obtained from f -b-c-a;
m

3
f -g-b-a;g-b-c-a; hði; jÞ-f -g-b; hði; jÞ-f -c-a;
hði; jÞ-f -b-a
m
H 5 ff ; h; i; j; h; i; jg, is obtained from f -g-b-c-a;
4
hði; jÞ-f -b-c-a

m
and finally: H 5 h; i; j is obtained from: hði; jÞ-f -g-b-c-a
5
This illustrates the use of multisets.
The oldest example we know of a scientometric article that shows
explicitly how to calculate influences of several generations is (Rousseau,
1987). In that article we explained an algorithm, based on the so-called
Gozinto theorem, to calculate the influence of backward generations on a
target article. Generations are considered as sets, but an element is used in
the calculation as often as it is cited. The article further used the idea of
weighting citations based on their location in the article and the fre-
quency of occurrence.
5.14 DELAYED RECOGNITION AND SLEEPING BEAUTIES
The term sleeping beauty (van Raan, 2004b) refers to a paper whose
importance is not recognized for several years after publication (it is
asleep) and then suddenly (kissed by a prince?) receives recognition and
accrues many citations (they live happily ever after?). Although the term
sleeping beauty in this context dates from the early 21st century, the phe-
nomenon of delayed recognition or premature discovery has been
observed much earlier (Garfield, 1980, 1989). Van Raan proposed three
dimensions along which delayed recognition can be measured: the
length of the sleep, the depth of the sleep, i.e., the average number of
citations per year during the sleeping period, and the intensity of being
awake referring to the number of citations received after the awakening
time. Braun et al. (2010) focused on the role of the prince. Articles
playing the role of the prince are among the first citing articles, are
themselves at least fairly cited and have a considerable relative number
of cocitations with the sleeping beauty. In a few cases the “kiss” was