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A parameter to quantify dynamics of a
researcher's scientific activity
S.B. Popov 1#
1 Sternberg Astronomical Institute,
Universitetski pr. 13, 119992 Moscow, Russia
August 8, 2005
Abstract
I propose the coe#cient, t h , and its modification N t which in a simple
way reflect dynamics of scientific activity of an individual researcher. I
determine t h as a time period (from some moment in the past till the
present moment) during which papers responsible for 1/2 of the total
citation index were published. Parameter N t represents averaging of the
citation index over this period: N t = C.I./2th
1 Introduction
The problem of estimation of an impact of a scientist (or a group of them) is an
actual one (see, for example, [1] and references therein). Still, in many countries,
for example in Russia, citation index (C.I. hereafter) or its modifications are not
widely used. Only now, especially in front of a possible reorganization in the
sphere of science, russian scientists and o#cials start to discuss problems related
to quantifying a scientific impact of individual researchers or their groups. The
problem is non­trivial as many components are involved, and it is impossible
to describe fairly quality of a scientist by a single parameter. The total impact
can be more or less given by the C.I. (we do not discuss here such disadvantages
of this parameter as dependence on research topics, influence of promotion of
results, etc.). However, the structure of C.I. of a scientist (if it is mainly deter­
mined by a single paper with very high C.I., or by several of them with medium
C.I., or by numerous papers with very small C.I., etc.) is lost when one one
simple parameter is used. Di#erent modifications can be suggested. Recently,
Hirsch [2] proposed an interesting coe#cient which supplement the standard
C.I. This parameter is sensitive to the structure of C.I., i.e. it can demonstrate
if the index is dominated by few papers or not. However, all these parameters do
not reflect dynamics of scientific activity. Below we propose a simple estimate
which can distinguish if C.I. of a scientist is due to recent or old publications,
so in principle it is possible to estimate how it is probable that the scientist
produce an important result in near future.
# E­mail: polar@sai.msu.ru
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2 Characteristic time
There were many attempts to include dynamics into bibliometric studies (see,
for example, the citation age in [1] which reflects the citation history of a given
paper). It is important to determine a characteristic time interval; not arbitrary,
but individually for each scientist. For example, one can think about a minimum
time (min #t) in a scientific career of a person, when papers responsible for 1/2
of the total C.I. were published (obviously, for scientists who did the main
contribution in one paper or in a set of papers published during a short time
min #t is short, vise versa for those who continuosly published papers of the
same level min #t is comparable with the duration of the career). If one adds
to this min #t another parameter ­ time interval separating the the present
moment t 0 from the end of the period responsible for min #t ­ then we have a
rough figure of scientific activity of a scientists in time. However, I think that
a better parameter can be defined.
Here I discuss a simple way to estimate a characteristic applicable to in­
dividual scientists. Up to my knowledge such a parameter was not discussed
before.
The idea is to define some characteristic time which can demonstrate how
long ago a scientist published papers which give the main contribution to the
C.I. I propose the parameter t h which is defined as follows. It is the time (from
the present moment towards the past) during which papers that are responsible
for 1/2 of the total C.I. were published. Let me examplify it.
Imagine three scientists (see Fig.1). All started careers simultaneously. At
the present moment all three have the same C.I.=5000. One published in 1965
a paper with C.I.=5000, and nothing after that. For him t h = 40 years. The
second published a paper with C.I.=2500 in 1965 and another one with the
same C.I. in 1975. For him we obtain t h = 30 years. The third one also
had published in 1965 a top­cited paper with C.I.=1000, and then every year
published a papers all of which now have C.I.=100. For him t h = 25 years as
1/2 of his C.I. is due to papers published after 1980.
The parameter t h alone is not a very useful thing as it says nothing about
the total impact. But it can be useful to distinguish researchers who's activity
is not in the far past. Clearly, even for the same total C.I. t h is shorter for
those who published papers with large impact later. Especially, t h can be useful
when both young and more senior scientists are under consideration. It appears
indeed capable to ideally complement the standard C.I. or Hirsch's parameter
h.
It is possible to modify t h to include information about the total C.I. And
in the following section I show a possible way to do it.
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1960 1970 1980 1990 2000 2010
Time, years
0
1000
2000
3000
4000
5000
Number
of
citations
Figure 1: A simple illustration of scientific activity of three scientists with the
same total C.I., but with di#erent distribution of important papers over time.
3 Average activity over the characteristic time
After we determine t h we know a characteristic time scale of scientific activity
of a researcher. Now what we can do is to average its C.I. (or better 1/2 of C.I.
as t h is related to half of the total index, and letter h comes from half) ovet t h .
We define
N t = C.I./2t h .
For the three scientists in the example above N t = 62.5, 83.3, and 100
correspondently. For the same total C.I. values of N t are di#erent demonstrating
the fact that the first one was unactive for a long time, and the period of activity
of the third one is closer to the present moment than for the rest two researchers.
For the same C.I. N t can be di#erent up to a factor of a few (or even by an
order of magnitude) if persons have significantly di#erent histories of scientific
activity.
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4 Conclusions
I presented a simple etimate t h of a time scale which demonstrates dynamics of
scientific activity of scientists. Also the parameter N t = C.I./2t h was proposed
as a compromise between integral and dynamical characteristics of scientific
impact. In my opinion t h can be a good additional parameter to the standard
C.I. value.
Acknowledgments
I want to thank Prof. J. Hirsch for comments on the idea of the coe#cient t h ,
and to participants of the project Elementy.Ru for discussion.
References
[1] Redner S., 2004, physics/0407137
[2] Hirsch J.E., 2005, physics/0508025
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