How Citation Boosts Promote Scientific Paradigm Shifts and Nobel Prizes

Abstract

Nobel Prizes are commonly seen to be among the most prestigious achievements of our times. Based on mining several million citations, we quantitatively analyze the processes driving paradigm shifts in science. We find that groundbreaking discoveries of Nobel Prize Laureates and other famous scientists are not only acknowledged by many citations of their landmark papers. Surprisingly, they also boost the citation rates of their previous publications. Given that innovations must outcompete the rich-gets-richer effect for scientific citations, it turns out that they can make their way only through citation cascades. A quantitative analysis reveals how and why they happen. Science appears to behave like a self-organized critical system, in which citation cascades of all sizes occur, from continuous scientific progress all the way up to scientific revolutions, which change the way we see our world. Measuring the "boosting effect" of landmark papers, our analysis reveals how new ideas and new players can make their way and finally triumph in a world dominated by established paradigms. The underlying "boost factor" is also useful to discover scientific breakthroughs and talents much earlier than through classical citation analysis, which by now has become a widespread method to measure scientific excellence, influencing scientific careers and the distribution of research funds. Our findings reveal patterns of collective social behavior, which are also interesting from an attention economics perspective. Understanding the origin of scientific authority may therefore ultimately help to explain how social influence comes about and why the value of goods depends so strongly on the attention they attract.

Full text

How Citation Boosts Promote Scientific Paradigm Shifts
and Nobel Prizes
Amin Mazloumian
1
, Young-Ho Eom
2
, Dirk Helbing
1
, Sergi Lozano
1
, Santo Fortunato
2
*
1ETH Zu
¨rich, Zu
¨rich, Switzerland, 2Complex Networks and Systems Lagrange Laboratory, Institute for Scientific Interchange (ISI), Torino, Italy
Abstract
Nobel Prizes are commonly seen to be among the most prestigious achievements of our times. Based on mining several
million citations, we quantitatively analyze the processes driving paradigm shifts in science. We find that groundbreaking
discoveries of Nobel Prize Laureates and other famous scientists are not only acknowledged by many citations of their
landmark papers. Surprisingly, they also boost the citation rates of their previous publications. Given that innovations must
outcompete the rich-gets-richer effect for scientific citations, it turns out that they can make their way only through citation
cascades. A quantitative analysis reveals how and why they happen. Science appears to behave like a self-organized critical
system, in which citation cascades of all sizes occur, from continuous scientific progress all the way up to scientific
revolutions, which change the way we see our world. Measuring the ‘‘boosting effect’’ of landmark papers, our analysis
reveals how new ideas and new players can make their way and finally triumph in a world dominated by established
paradigms. The underlying ‘‘boost factor’’ is also useful to discover scientific breakthroughs and talents much earlier than
through classical citation analysis, which by now has become a widespread method to measure scientific excellence,
influencing scientific careers and the distribution of research funds. Our findings reveal patterns of collective social behavior,
which are also interesting from an attention economics perspective. Understanding the origin of scientific authority may
therefore ultimately help to explain how social influence comes about and why the value of goods depends so strongly on
the attention they attract.
Citation: Mazloumian A, Eom Y-H, Helbing D, Lozano S, Fortunato S (2011) How Citation Boosts Promote Scientific Paradigm Shifts and Nobel Prizes. PLoS
ONE 6(5): e18975. doi:10.1371/journal.pone.0018975
Editor: Yamir Moreno, University of Zaragoza, Spain
Received January 5, 2011; Accepted March 14, 2011; Published May 4, 2011
Copyright: ß2011 Mazloumian et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: A.M., S.L. and D.H. were partially supported by the Future and Emerging Technologies programme FP7-COSI-ICT of the European Commission through
the project QLectives (grant no.: 231200). Y.-H. E. and S. F. gratefully acknowledge ICTeCollective, grant 238597 of the European Commission. The funders had no
role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. No additional external funding was received for this study.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: fortunato@isi.it
Introduction
Ground-breaking papers are extreme events [1] in science.
They can transform the way in which researchers do science in
terms of the subjects they choose, the methods they use, and the
way they present their results. The related spreading of ideas has
been described as an epidemic percolation process in a social
network [2]. However, the impact of most innovations is limited.
There are only a few ideas, which gain attention all over the world
and across disciplinary boundaries [3]. Typical examples are
elementary particle physics, the theory of evolution, superconduc-
tivity, neural networks, chaos theory, systems biology, na-
noscience, or network theory.
It is still a puzzle, however, how a new idea and its proponent
can be successful, given that they must beat the rich-gets-richer
dynamics of already established ideas and scientists. According to
the Matthew effect [4–7], famous scientists receive an amount of
credit that may sometimes appear disproportionate to their actual
contributions, to the detriment of younger or less known scholars.
This implies a great authority of a small number of scientists,
which is reflected by the big attention received by their work and
ideas, and of the scholars working with them [8].
Therefore, how can a previously unknown scientist establish at
all a high scientific reputation and authority, if those who get a lot
of citations receive even more over time? Here we shed light on
this puzzle. The following results for 124 Nobel Prize Laureates in
chemistry, economics, medicine and physics suggest that innova-
tors can gain reputation and innovations can successfully spread,
mainly because a scientist’s body of work overall enjoys a greater
impact after the publication of a landmark paper. Not only do
colleagues notice the ground-breaking paper, but the latter also
attracts the attention to older publications of the same author (see
Fig. 1). Consequently, future papers have an impact on past papers,
as their relevance is newly weighted.
We focus here on citations as indicator of scientific impact [9–
13], studying data from the ISI Web of Science, but the use of click
streams [14] would be conceivable as well. It is well-known that
the relative number of citations correlates with research quality
[15–17]. Citations are now regularly used in university rankings
[18], in academic recruitments and for the distribution of funds
among scholars and scientific institutions [19].
Results
We evaluated data for 124 Nobel Prize Laureates that were
awarded in the last two decades (1990–2009), which include an
impressive number of about 2million citations. For all of them
and other internationally established experts as well, we find
peaks in the changes of their citation rates (Figs. 2 and 3).
Moreover, it is always possible to attribute to these peaks
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landmark papers (Fig. 4), which have reached hundreds of
citations over the period of a decade. Such landmark papers are
rare even in the lives of the most excellent scientists, but some
authors have several such peaks.
Technically, we detect a groundbreaking article apublished at
time t~taby comparing the citation rates before and after tafor
the earlier papers. The analysis proceeds as follows: Given a year t
and a time window w, we take all papers of the studied author that
were published since the beginning of his/her career until year t.
The citation rate Rvt,wmeasures the average number of citations
received per paper per year in the period from t{wz1to t.
Similarly, the citation rate Rwt,wmeasures the average number of
citations received by the same publications per paper per year
between tz1and tzw(or 2009,iftzwexceeds 2009). The ratio
Rw(t)~Rwt,w=Rvt,w, which we call the ‘‘boost factor’’, is a
variable that detects critical events in the life of a scientist: sudden
increases in the citation rates (as illustrated by Fig. 1) show up as
peaks in the time-dependent plot of Rw(t).
In our analysis we used the generalized boost factor R’w(t),
which reduces the influence of random variations in the citation
rates (see Materials and Methods).
Figure 2 shows typical plots of the boost factors R’w(t)of four
Nobel Prize Laureates. Interestingly, peaks are even found, when
those papers, which mostly contribute to them, are excluded from
the analysis (see insets of Fig. 2). That is, the observed increases in
the citation rates are not just due to the landmark papers
themselves, but rather to a collective effect, namely an increase in
the citation rates of previously published papers. This results from
the greater visibility that the body of work of the corresponding
scientist receives after the publication of a landmark paper and
establishes an increased scientific impact (‘‘authority’’). From the
perspective of attention economics [20], it may be interpreted as a
herding effect resulting from the way in which relevant
information is collectively discovered in an information-rich
environment. Interestingly, we have found that older papers
receiving a boost are not always works related to the topic of the
landmark paper.
Traditional citation analysis does not reveal such crucial events
in the life of a scientist very well. Figure 3 shows the time history of
three classical citation indices: the average number of citations per
paper Sc(t)T, the cumulative number C(t)of citations, and the
Hirsch index [21] (h-index) H(t)in year t. For comparison, the
evolution of the boost factor R’w(t)is depicted as well. All indices
were divided by their maximum value, in order to normalize them
and to use the same scale for all. The profiles of the classical
indices are rather smooth in most cases, and it is often very hard to
see any significant effects of landmark papers. However, this is not
surprising, as the boost factor is designed to capture abrupt
variations in the citation rates, while both C(t)and H(t)reflect the
overall production of a scientist and are therefore less sensitive to
extreme events.
To gain a better understanding of our findings, Figs. 4 and 5
present a statistical analysis of the boosts observed for Nobel Prize
Laureates. Figure 4 demonstrates that pronounced peaks are
indeed related to highly cited papers. Furthermore, Fig. 5 analyzes
the size distribution of peaks. The distribution looks like a power
law for all choices of the parameters wand k(at least within the
relevant range of small values). This suggests that the bursts are
produced by citation cascades as they would occur in a self-
organized critical system [22]. In fact, power laws were found to
result from human interactions also in other contexts [23–25].
The mechanism underlying citation cascades is the discovery of
new ideas, which colleagues refer to in the references of their
papers. Moreover, according to the rich-gets-richer effect,
successful papers are more often cited, also to raise their own
success. Innovations may even cause scientists to change their
research direction or approach. Apparently, such feedback effects
can create citation cascades, which are ultimately triggered by
landmark papers.
Finally, it is important to check whether the boost factor is able
to distinguish exceptional scientists from average ones. Since any
criteria used to define ‘‘normal scientists’’ may be questioned, we
have assembled a set of scientists taken at random. Scientists were
chosen among those who published at least one paper in the year
2000. We selected 400 names for each of four fields: Medicine,
Physics, Chemistry and Economy. After discarding those with no
citations, we ended up with 1361 scientists. In Fig. 6 we draw on a
bidimensional plane each scientist of our random sample (empty
circles), together with the Nobel Prize Laureates considered (full
circles). The two dimensions are the value of the boost factor and
the average number of citations of a scientist. A cluster analysis
separates the populations in the proportions of 79% to 21%. The
separation is significant but there is an overlap of the two datasets,
mainly because of two reasons. First, by picking a large number of
scientists at random, as we did, there is a finite probability to
choose also outstanding scholars. We have verified that this is the
case. Therefore, some of the empty circles deserve to sit on the
top-right part of the diagram, like many Nobel Prize Laureates.
Figure 1. Illustration of the boosting effect. Typical citation
trajectories of papers, here for Nobel Prize Laureate John Bennett
Fenn, who received the award in chemistry in 2002 for the
development of the electrospray ionization technique used to
analyze biological macromolecules. The original article, entitled
Electrospray ionization for mass spectrometry of large biomolecules,
coauthored by M. Mann, C. K. Meng, S. F. Wong and C. M.
Whitehouse, was published in Science in 1989 and is the most cited
work of Fenn, with currently over 3,000 citations. The diagram reports
the growth in time of the total number of citations received by this
landmark paper (blue solid line) and by six older papers. The diagram
indicates that the number of citations of the landmark paper has
literally exploded in the first years after its appearance. However,
after its publication in 1989, a number of other papers also enjoyed a
much higher citation rate. Thus, a sizeable part of previous scientific
work has reached a big impact after the publication of the landmark
paper. We found that the occurrence of this boosting effect is
characteristic for successful scientific careers.
doi:10.1371/journal.pone.0018975.g001
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Figure 3. Dynamics of the boost factor R’w(t)versus traditional citation variables. Each panel displays the time histories of four variables: the boost
factor R’w(t), the average number of citations per paper Sc(t)T, the cumulative number of citations C(t),andtheH-indexearned until year t[21]. The panels refer
to the same Nobel Laureates as displayed in Fig. 2. The classical indices have relativelysmooth profiles, i.e. they are not very sensitive to extreme events in the life of
a scientist like the publication of landmark papers. An advantage of the boost factor is that its peaks allow one to identify scientific breakthroughs earlier.
doi:10.1371/journal.pone.0018975.g003
Figure 2. Typical time evolutions of the boost factor. Temporal dependence of R’w(t)for Nobel Laureates [here for (a) Mario R. Capecchi (Medicine,
2007), (b) John C. Mather (Physics, 2006), (c) Roger Y. Tsien (Chemistry, 2008) and (d) Roger B. Myerson (Economics, 2007)]. Sharp peaks indicate citation boosts
in favor of older papers, triggered by the publication and recognition of a landmark paper. Insets: The peaks even persist (though somewhat smaller), if in the
determination of the citation counts cp,t, the landmark paper is skipped (which is defined as the paper that produces the largest reduction in the peak size,
when excluded from the computation of the boost factor). We conclude that the observed citation boosts are mostly due to a collective effect involving several
publications rather than due to the high citation rate of the landmark paper itself.
doi:10.1371/journal.pone.0018975.g002
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The second reason is that we are considering scholars from
different disciplines, which generally have different citation
frequencies. This affects particularly the average number of
citations of a scientist, but also the value of the boost factor. In this
way, the position in the diagram is affected by the specific research
topic, and the distribution of the points in the diagram of Fig. 6 is a
superposition of field-specific distributions. Nevertheless, the two
datasets, though overlapping, are clearly distinct. Adding further
dimensions could considerably improve the result. In this respect,
the boost factor can be used together with other measures to better
specify the performance of scientists.
Discussion
In summary, groundbreaking scientific papers have a
boosting effect on previous publications of their authors,
bringing them to the attention of the scientific community and
establishing their ‘‘authority’’. We have provided the first
quantitative characterization of this phenomenon by introduc-
ing a new variable, the ‘‘boost factor’’, which is sensitive to
sudden changes in the citation rates. The fact that landmark
papers trigger the collective discovery of older papers amplifies
their impact and tends to generate pronounced spikes long
before the paper receives full recognition. The boosting factor
can therefore serve to discover new breakthroughs and talents
more quickly than classical citation indices. It may also help to
assemble good research teams, which have a pivotal role in
modern science [27–29].
The power law behavior observed in the distribution of peak
sizes suggests that science progresses through phase transitions
[30] with citation avalanches on all scales–from small cascades
Figure 5. Cumulative probability distribution of peak heights in the boost factor curves of Nobel Prize Laureates. The four panels
correspond to different choices of the parameters kand w. The power law fits (lines) are performed with the maximum likelihood method [26]. The
exponents for the direct distribution (of which the cumulative distribution is the integral) are: 3:63+0:16 (top left), 2:93+0:16 (bottom left), 1:63+0:05
(top right), 1:41+0:05 (bottomright). The best fits have the following lower cutoffs and values of the Kolmogorov-Smirnov (KS) statistics: 1:06,0:0289 (top
left), 1:15,0:0264 (bottom left), 13:1,0:038 (top right), 24:7,0:0462 (bottom right). The KS values support the power law ansatz for the shape of the curves.
Still, we point out that on the left plots the data span just one decade in the variable, so one has to be careful about the existence of power laws here.
doi:10.1371/journal.pone.0018975.g005
Figure 4. Correlation between papers and the local maxima
(‘‘peaks’’) of R’w(t).We first determined the ranks of all papers of an
author based on the total number of citations received until the year
2009 inclusively. We then determined the rank of that particular
publication, which had the greatest contribution to the peak. This was
done by measuring the reduction in the height of the peak, when the
paper was excluded from the calculation of the boost factor (as in the
insets of Fig. 2). The distribution of the ranks of ‘‘landmark papers’’ is
dominated by low values, implying that they are indeed among the top
publications of their authors.
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reflecting quasi-continuous scientific progress all the way up to
scientific revolutions, which fundamentally change our perception
of the world. While this provides new evidence for sudden
paradigm shifts [31], our results also give a better idea of why and
how they happen.
It is noteworthy that similar feedback effects may determine
the social influence of politicians, or prices of stocks and
products (and, thereby, the value of companies). In fact, despite
the long history of research on these subjects, such phenomena
are still not fully understood. There is evidence, however, that
the power of a person or the value of a company increase with
the level of attention they enjoy. Consequently, our study of
scientific impact is likely to shed new light on these scientific
puzzles as well.
Materials and Methods
The basic goal is to improve the signal-to-noise ratio in the
citation rates, in order to detect sudden changes in them. An
effective method to reduce the influence of papers with largely
fluctuating citation rates is to weight highly cited papers more.
This can be achieved by raising the number of cites to the power
k, where kw1. Therefore, our formula to compute R’w(t)looks as
follows:
R’w(t)~PpPtzw
t0~tz1(cp,t0)k
PpPt
t0~t{wz1(cp,t0)k:ð1Þ
Here, cp,t0is the number of cites received by paper pin year t0.
The sum over pincludes all papers published before the year t;w
is the time window selected to compute the boosting effect. For
k~1we recover the original definition of Rw(t)(see main text).
For the analysis presented in the paper we have used k~4and
w~5, but our conclusions are not very sensitive to the choice of
smaller values of kand w.
Acknowledgments
We acknowledge the use of ISI Web of Science data of Thomson Reuters
for our citation analysis.
Author Contributions
Conceived and designed the experiments: AM YHE DH SL SF. Performed
the experiments: AM YHE SL. Analyzed the data: AM YHE SL. Wrote
the paper: SF DH.
References
1. Albeverio S, Jentsch V, Kantz H, eds. Extreme Events in Nature and Society.
Berlin, Germany: Springer.
2. Bettencourt LM, Cintro´n-Arias A, Kaiser DI, Castillo-Cha´vez C (2006) The
power of a good idea: Quantitative modeling of the spread of ideas from
epidemiological models. Physica A 364: 513–536.
3. Davenport TH, Beck JC (2001) The Attention Economy : Understanding the
New Currency of Business. Boston, USA: Harvard Business School Press.
4. Merton RK (1968) The Matthew effect in science: The reward and
communication systems of science are considered. Science 159: 56–63.
5. Merton RK (1988) The Matthew effect in science, ii: Cumulative advantage and
the symbolism of intellectual property. ISIS 79: 606–623.
6. Scharnhorst A (1997) Characteristics and impact of the matthew effect for
countries. Scientometrics 40: 407–422.
7. Petersen AM, Jung WS, Yang JS, Stanley HE (2011) Quantitative and empirical
demonstration of the Matthew effect in a study of career longevity. Proc Natl
Acad Sci USA 108: 18–23.
8. Malmgren RD, Ottino JM, Nunes Amaral LA (2010) The role of mentorship in
protege performance. Nature 465: 622–626.
9. Garfield E (1955) Citation Indexes for Science: A New Dimension in
Documentation through Association of Ideas. Science 122: 108–111.
10. Garfield E (1979) Citation Indexing. Its Theory and Applications in Science,
Technology, and Humanities. New York, USA: Wiley.
11. Egghe L, Rousseau R (1990) Introduction to Informetrics: Quantitative Methods
in Library, Documentation and Information Science. Amsterdam, The Nether-
lands: Elsevier.
12. Amsterdamska O, Leydesdorff L (1989) Citations: indicators of significance.
Scientometrics 15: 449–471.
13. Petersen AM, Wang F, Stanley HE (2010) Methods for measuri ng the citations
and productivity of scientists across time and discipline. Phys Rev E 81: 036114.
14. Bollen J, de Sompel HV, Smith JA, Luce R (2005) Toward alternative metrics of
journal impact: A comparison of download and citation data. Information
Processing & Management 41: 1419–1440.
15. Trajtenberg M (1990) A penny for your quotes: Patent citations and the value of
innovations. RAND Journal of Economics 21: 172–187.
16. Aksnes DW (2006) Citation rates and perceptions of scientific contribution. J Am
Soc Inf Sci Technol 57: 169–185.
17. Moed HF (2005) Citation Analysis in Research Evaluation. Berlin, Germany:
Springer.
18. Van Raan AJF (2005) Fatal attraction: Conceptual and methodological
problems in the ranking of universities by bibliometric methods. Scientometrics
62: 133–143.
19. Boyack KW, Bo¨rner K (2003) Indicator-assisted evaluation and funding of
research: visualizing the influence of grants on the number and citation counts of
research papers. J Am Soc Inf Sci Technol 54: 447–461.
20. Wu F, Huberman BA (2007) Novelty and collective attention. Proc Natl Acad
Sci USA 104: 17599–17601.
21. Hirsch JE (2005) An index to quantify an individual’s scientific research output.
Proc Natl Acad Sci USA 102: 16569–16572.
22. Bak P, Tang C, Wiesenfeld K (1987) Self-organized criticality: An expla nation of
the 1/f noise. Phys Rev Lett 59: 381–384.
Figure 6. Two-dimensional representation of our collection of
Nobel Prize Laureates and a set of 1361 scientists, which were
randomly selected. On the x-axis we report the average number of
citations of a scientist, on the y-axis his/her boost factor. It can be seen
that, on average, Nobel Prize winners clearly perform better. However a
Nobel Prize is not solely determined by the average number of citations
and the boost factor, but also by further factors. These may be the
degree of innovation or quality, which are hard to quantify.
doi:10.1371/journal.pone.0018975.g006
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PLoS ONE | www.plosone.org 5 May 2011 | Volume 6 | Issue 5 | e18975

23. Baraba´si AL (2005) The origin of bursts and heavy tails in human dynamics.
Nature 435: 207–211.
24. Oliveira JG, Baraba´ si AL (2005) Human dynamics: The correspondence
patterns of Darwin and Einstein. Nature 437: 1251.
25. Malmgren RD, Stouffer DB, Campanharo ASLO, Amaral LAN (2009) On
Universality in Human Correspondence Activity. Science 325: 1696–1700.
26. Clauset A, Shalizi CR, Newman MEJ (2007) Power-law distributions in
empirical data. SIAM Reviews 51: 661–703.
27. Guimera` R, Uzzi B, Spiro J, Amaral LAN (2005) Team Assembly Mechanisms
Determine Collaboration Network Structure and Team Performance. Science
308: 697–702.
28. Wuchty S, Jones BF, Uzzi B (2007) The Increasing Dominance of Teams in
Production of Knowledge. Science 316: 1036–1039.
29. Jones BF, Wuchty S, Uzzi B (2008) Multi-University Research Teams: Shifting
Impact, Geography, and Stratification in Science. Science 322: 1259–1262.
30. Stanley HE (1987) Introduction to Phase Transitions and Critical Phenomena.
New York, USA: Oxford University Press.
31. Kuhn TS (1962) The Structure of Scientific Revolutions. Chicago, USA:
University of Chicago Press.
Citation Boosts and Nobel Prizes
PLoS ONE | www.plosone.org 6 May 2011 | Volume 6 | Issue 5 | e18975