# The Boundary-Spanning Mechanisms of Nobel Prize Winning Papers

Yakub Sebastian  College of Engineering, IT & Environment, Charles Darwin
University, Australia  Corresponding author: Yakub Sebastian,
<EMAIL_ADDRESS>Chaomei Chen  College of Computing & Informatics,
Drexel University, USA

###### Abstract

The breakthrough potentials of research papers can be explained by their
boundary-spanning qualities. Here, for the first time, we apply the structural
variation analysis (SVA) model and its affiliated metrics to investigate the
extent to which such qualities characterize a group of Nobel Prize winning
papers. We find that these papers share remarkable boundary-spanning traits,
marked by exceptional abilities to connect disparate and topically-diverse
clusters of research papers. Further, their publications exert structural
variations on the scale that significantly alters the betweenness centrality
distributions of existing intellectual space. Overall, SVA not only provides a
set of leading indicators for describing future Nobel Prize winning papers,
but also broadens our understanding of the similar prize-winning properties
that may have been overlooked among other regular publications.

##  1 Introduction

###  1.1 Background

The prospect of discovering methods and metrics for explaining and predicting
breakthrough scientific papers, such as the Nobel Prize winning papers,
continues to fuel some of the most consequential studies into the science of
science research (Zuckerman, 1967; Garfield and Malin, 1968; Ashton and
Oppenheim, 1978; Chen et al., 2009; Chen, 2012; Uzzi et al., 2013; Mukherjee
et al., 2017; Ma and Uzzi, 2018; Schneider and Costas, 2017; Clauset et al.,
2017; Li et al., 2019a; Min et al., 2021). On one hand, predicting significant
scientific achievements is a challenging enterprise as an increasing number of
studies have revealed the unpredictable nature of scientific success
(Mallapaty, 2018). On the other hand, recent advances in digital libraries and
scientific publication indexing services such as Dimensions, Lens.org, and
Microsoft Academic Graph (in addition to the Web of Science and Scopus)
provide us with an unprecedented level of digital access to hundreds of
millions of scientific publications and metadata (Hook et al., 2020; Kanakia
et al., 2020). These resources present new opportunities for developing the
next-generation computational methods for explaining and predicting
breakthroughs in science (Wang and Liu, 2020).

In this paper, we propose structural variation analysis as a promising
computational model that explains a major underlying mechanism of the
intellectual impacts of Nobel Prize winning papers, especially in terms of
their boundary-spanning qualities. Our method sheds light on the distinctive
quality of these papers from the standpoint of Structural Variation Theory
(Chen et al., 2009). We premise the work on the assumption that connecting
otherwise disparate clusters of knowledge is a key mechanism behind
transformative scientific discoveries, which also shares the vision of
literature-based discovery research pioneered by Swanson (Swanson, 1986). The
approach is advantageous as it renders scientific impact measurable,
explainable, and actionable through a rich set of structural variation metrics
computed from large bibliographic networks, as will be demonstrated in this
paper.

###  1.2 Motivation

Nobel Prize is considered by many as the epitome of scientific achievements
(Inhaber and Przednowek, 1976; Fortunato et al., 2018). The towering prestige
of the Nobel Prize within the scientific community and the extraordinary
esteem conferred to their laureates motivated a number of important studies
into the mechanisms behind winning the award (Zuckerman, 1967; Wagner et al.,
2015; Revesz, 2015). But measuring and explaining the scientific impact of
Nobel Prize winning papers is not easy (Ashton and Oppenheim, 1978; Hu and
Rousseau, 2017; Kosmulski, 2020; Turki et al., 2020; Bjørk, 2020). There are
limitations in solely relying on citation counts, journal impact factors, or
other summative metrics as they do not provide clear theoretical and
mechanistic explanations on what makes certain scientific breakthroughs more
important than the others.

The Structural Variation Theory, in contrast, provides a useful theoretical
framework that explains Nobel Prize winning papers by their shared boundary-
spanning mechanisms. There is a growing body of evidence that support this
conceptual view. Nobel laureates possess the exceptional intellectual agility
that allowed them to transcend own specialities and appropriate fresh concepts
from other disciplines that enable intellectual quantum leaps (Archer, 2007).
Uzzi et al. (2013) found that the propensity of a paper to be highly cited was
correlated with its ability to make highly novel combinations of prior
knowledge. And recently Fortunato et al. (2018) suggested that researchers
should include ‘a balanced mixture of new and established elements’ as a key
ingredient in making a successful scientific career.

The theory is operationalized as the Structural Variation Analysis (SVA)
module in CiteSpace111http://cluster.cis.drexel.edu/~cchen/citespace/, a
widely used free application for visualizing and analyzing trends and patterns
in scientific literature (Chen, 2006, 2012). A number of SVA metrics have been
proposed to measure different dimensions of a paper’s breakthrough properties.
However, their value as potentially leading indicators of future Nobel Prize
winning papers have not been systematically studied (Chen, 2012; Chen and
Song, 2017; Hou et al., 2020; Chen, 2020). Chen et al. (2009) previously
studied two cases of Nobel Prize in Physiology or Medicine in their
introduction of Structural Variation Theory, i.e. the discovery of the
bacterium Helicobacter pylori and its role in peptic ulcer disease (Marshall
and Warren, 1984) and the discovery of principles for introducing specific
gene modification in mice by the use of embryonic stem cells (Evans and
Kaufman, 1981). But their investigation was limited to measuring the
structural and temporal properties of the winning papers. Note that these
properties are lagging indicators of success because they can only be
calculated from the citation patterns of a paper, which may take many years to
accumulate. In contrast, it is highly desirable to have a new set of leading
indicators that allow the breakthrough potentials of a paper to be measured
immediately upon its publication.

There is also a unique challenge associated with consolidating the impact
metrics of a Nobel Prize. The award is often shared by more than one
laureates, suggesting the presence of several related breakthrough papers.
Because these papers may be published many years or decades between each other
(Li et al., 2019a, b), they add an additional layer of complexity when
measuring the breakthrough characteristics for a single Nobel Prize.

###  1.3 Contributions

Two research problems are addressed in this paper:

  1. 1.

Do Nobel Prize winning papers exert exceptional boundary-spanning mechanisms
upon their underlying intellectual structures as postulated by the Structural
Variation Theory? If yes, what SVA metrics best signals the boundary-spanning
mechanisms of these papers and why?

  2. 2.

What strategy should be used to consolidate the breakthrough characteristics
when multiple winning papers are associated with a Nobel Prize?

In answering these questions we make the following research contributions.
First, within the constraint of our selected case studies, we demonstrate that
Nobel Prize winning papers exhibit highly distinguishable boundary-spanning
properties. We empirically show two SVA metrics, Centrality Divergence and
Entropy, as strongly salient measures of the structural variations exerted by
these papers. Our results provide fresh insights into mechanisms that may be
at work behind transformative research. For cases where there are multiple
winning papers, we propose synthesizing an artificial pseudopaper as a way to
consolidate their structural variation potentials. Finally, we also provide
some practical advice when using CiteSpace’s SVA module in search of promising
breakthrough papers.

The rest of this paper is organized as follows. Section 2 reviews related
work, followed by descriptions of our selected Nobel Prize cases in Section 3.
Methods and results are presented in Section 4 and Section 5, respectively. We
discuss the significance of the results in Section 6 and highlight their
limitations in Section 7. Finally, Section 8 concludes the paper.

##  2 Related Work

###  2.1 The mechanisms of scientific breakthroughs

There is a rich tapestry of prior work that aim to provide mechanistic
explanations for scientific breakthroughs (Popper, 1963; Kuhn, 1962). Here, we
cast our work against more recent developments in this research, especially
those that concern Nobel Prize papers. Uzzi et al. (2013) found that the
probability of a research paper to be highly cited (‘high impact’ or ‘hit’
papers) doubled if it made highly novel combinations of prior knowledge apart
from strengthening well-established, conventional associations. Although their
finding supports the correlation between boundary-spanning properties of a
paper and its future high impact, it offers no specific insights for papers
associated with the Nobel Prizes. Ye et al. (2013) investigated the
relationships between prior awards and the citation count of landmark papers
of the Nobel Prize in Physiology or Medicine. The study, which covered prizes
awarded between 1983 and 2012, found that citation ranking and impact factor
did not always positively correlate with the chance of winning Nobel Prizes.
In a similar vein, Mukherjee et al. (2017) also studied how the combinations
of prior work can be correlated to the future impact of a paper as measured by
its citation count. They found that among papers indexed in the Web of Science
and in the U.S. Patent Office database, high impact papers were more likely to
include those that cited younger references. The work, however, did not
specifically account for the mechanisms behind Prize-winning papers.

Another group of works incorporated a diverse set of success indicators to
predict future Nobel Prize winners. Revesz (2015) proposed a combination of
total citation counts and the h-index as a new citation index measure. Using
this measure, they found that Nobel laureates tend to author fewer but highly
cited papers, applicable to at least five Nobel laureates in physics. For the
Nobel Prize in Economics, Chan et al. (2018) discovered that winning the John
Bates Clark Medal was a predictive factor for winning the Nobel prize. Li et
al. (2020) traced the career patterns of all Nobel Prize laureates from 1900
to 2016 and found that although significant alterations in the co-authorship
structure and dramatic changes in the post-Nobel research directions were
unique to most laureates, nothing was remarkable about their pre-Nobel career
trajectories in comparison to those of non-laureates. Gingras and Wallace
(2010) conducted a vast bibliometric analysis of five hundred most cited and
influential chemists and physicists indexed in the Web of Science from 1900 to
2006. These included the nominees and laureates of Nobel Prize in physics and
chemistry. Their results suggested significant difficulties in explaining the
publications of Nobel Prize winners when relying on measures such as citation-
based ranking and Freeman’s degree centrality. Savov et al. (2020) used LDA
topic modelling and SVM classifier to predict when breakthrough will occur. A
novel feature, innovation score, was introduced to measure how far ahead or
behind time are the topics contained in a particular paper. They found the
correlations between high citation counts and high innovation scores. The
study is limited to papers published in the WWW and SIGIR conference
proceedings.

###  2.2 Network properties and structural variations

Certain properties of bibliographic network surrounding a paper may offer
valuable clues to their scientific potentials. For instance, Wagner et al.
(2015) modelled the research networks of the laureates of Nobel Prize in
Physiology or Medicine between 1969 and 2011. Levels of productivity, impact,
co-authorship and collaborative patterns were then calculated from these
networks. Consistent with Revesz (2015), they found that the laureates
produced fewer but highly cited papers. The authors also examined the average
degree, density, modularity, and communities of co-authorship networks to find
that Nobel laureates demonstrated distinctive abilities for performing
scientific brokering roles that close existing structural holes within the
networks. This is in line with the central premise of the structural variation
theory. Ma and Uzzi (2018) constructed a large scientific prize network that
also included Nobel laureates. Analysis done on the network revealed the
interlocking of small, elite subdisciplinary areas formed by previously
awarded prizes. By regressing the number of scientific prizes won by each
winner on a set of variables, the authors found that the propensity of winning
scientific prizes could be explained by a person’s university prestige, high
h-index, and by the fact that they belonged to a prize-winning genealogical
network. More recently, Ioannidis et al. (2020) investigated if papers
associated with Nobel Prizes in physics, medicine or chemistry between 1995
and 2017 were heavily clustered only in a handful disciplines. They found that
only 5 out 114 fields of science accounted for more than half of the studied
Nobel Prizes. The winning papers originated from clusters with high-citation
density, although no variable was suggested as being predictive of these
winners.

Our work is most related to the work by Min et al. (2021). The authors
computed a paper’s scientific breakthrough potential by measuring the
structural variations observable from the network of its citing papers. Their
proposed metrics include average clustering coefficient, average degree,
maximum closeness centrality, maximum eigenvector centrality, and number of
connected components in the network. For evaluation, 116 Nobel Prize winning
papers in all fields were collected with techniques introduced by Shen and
Barabási (2014) and Min et al. (2018). By comparing these against a group of
control papers (i.e. regular papers with comparable citation counts), they
found that Nobel Prize winning papers had a higher number of connected network
components, indicative of some forms of boundary-spanning mechanisms.
Nevertheless, Min et al’s method fundamentally differs from ours in that their
structural variations are computed from the network structure of a Nobel
paper’s citing papers. In order to work, it requires that the first layer of
citing papers accumulate over time after a Nobel paper’s publication (Min et
al., 2021). As such, the authors’ metrics are lagging indicators of scientific
breakthrough. In contrast, we are proposing a set of SVA metrics as leading
indicators of breakthrough that can be computed at the time of a paper’s
publication. It does not need to wait for the paper’s citation structure to
emerge, which takes time. Our SVA method is derived directly from the
structural variation theory and has a clear theoretical underpinning. The
theoretical bases of Min et al.’s structural variation metrics, however, are
somewhat unclear. Finally, we differ in that we base on selection of Nobel
Prize winning papers on a dataset systematically curated by Li et al. (2019b),
which facilitates transparency and reproducibility.

Finally, let us mention a few other works in this area. Winnink et al. (2019)
proposed a search algorithm that measures four characteristics of breakthrough
papers (including several Nobel Prize winning papers): application-oriented
research impact, cross-disciplinary research impact, researchers-inflow
impact, and discoverers-intra-group impact. Similar to Min et al. (2021),
computing these measures requires that a paper’s emerging citation patterns be
available. Schneider and Costas (2017) developed methods for detecting
potential breakthrough papers that depend on first categorising every paper
into one of four citation-based typologies: lowly cited publications,
moderately cited publications, highly cited publications, and outstanding
publications. This method also requires the availability of a paper’s citation
data.

###  2.3 Previous applications of SVA

SVA has previously been used in various scientometric investigations. Chen
(2012) studied the statistical correlation between early SVA metrics (i.e.
modularity change rate, cluster linkage, and centrality divergence) with the
likelihood of a paper to become highly cited. The SVA model was also applied
to identify important papers in the field of regenerative medicine (Chen et
al., 2012). Hou et al. (2020) used the modularity change rate as the basis for
calculating four types of scholarly impact of individual researchers and most
recently Chen (2020) employed SVA for analysing the transformative potentials
of COVID-19 literature.

##  3 Case Studies

In this work, we focus on the latest collection of Nobel Prize winning papers
that were systematically curated by Li et al. (2019b).222Available for
download from
https://dataverse.harvard.edu/dataset.xhtml?persistentId=doi:10.7910/DVN/6NJ5RN
The dataset covers key publications of 92.4% of all Nobel laureates from 1900
to 2016. We limit this study to 3 cases of the Nobel Prize in Physiology or
Medicine, even though our method is consistently applicable to other Nobel
Prize categories. The selected cases are Nobel Prizes winners in 2012, 2014,
and 2016. The first two cases (2012, 2014) were selected on the basis that
their landmark papers are the youngest in Li et al.’s dataset. We reason that
younger papers provide richer bibliographic data for analysis from decades
worth of baseline literature. The third case (2016) was selected for its
unique characteristics, to be explained shortly.

###  3.1 Case 1: Nobel Prize in Physiology or Medicine 2012

John B. Gurdon and Shinya Yamanaka were jointly awarded the Nobel Prize in
Physiology or Medicine 2012 for the discovery that mature cells can be
reprogrammed to be pluripotent stem cells.333Press release. NobelPrize.org.
Nobel Media AB 2020. Viewed on Sun. 22 Nov 2020.
https://www.nobelprize.org/prizes/medicine/2012/press-release/ The discovery
occurred in two phases. First, in a landmark experiment Gurdon (1962a)
successfully transplanted mature, fully differentiated intestinal cell nuclei
into the egg cell of a frog. The egg cell then developed into a normal
tadpole, demonstrating for the first time the reversibility of cell
specialisation process, which is the cornerstone for future cell reprogramming
techniques.

More than 40 years later, in 2006, Shinya Yamanaka and colleague discovered a
combination of four genes that can be used to induce pluripotent stem cells
(or iPSCs) from mature cells called fibroblasts in laboratory environments
(Takahashi and Yamanaka, 2006; Takahashi et al., 2007). It was a major
scientific breakthrough given the fact that iPSCs can be prepared from mature
human cells and used for developing all kinds of body cells. The field of
regenerative medicine was born. Together, the works of Gurdon and Yamanaka not
only give new insights into the development of cells and organisms, but also
provide scientists with formidable tools for creating radically new forms of
medical treatments.

Four papers were selected as directly associated with this prize (Li et al.,
2019b). The selection was made by inspecting bibliographic information from
the Nobel Prize official website, the laureates’ Nobel Prize lectures and
online CVs, and by applying a few other criteria. Two of the papers are
attributed to Gurdon (Gurdon, 1962b, a), while the remaining to Yamanaka and
his colleagues (Takahashi and Yamanaka, 2006; Takahashi et al., 2007). All
papers are highly cited in recognition of their scientific contributions. At
the time when we collected their bibliographic data, (Gurdon, 1962b) was cited
321 times, (Gurdon, 1962a) 701 times, (Takahashi and Yamanaka, 2006) 16,123
times, and (Takahashi et al., 2007) 12,866 times.

###  3.2 Case 2: Nobel Prize in Physiology or Medicine 2014

The Nobel Prize in Physiology or Medicine 2014 is shared among John O’Keefe,
May-Britt Moser and Edvard I. Moser for their discoveries of cells responsible
for the positioning system in the brain.444Press release. NobelPrize.org.
Nobel Media AB 2020. Viewed on Mon. 23 Nov 2020.
https://www.nobelprize.org/prizes/medicine/2014/press-release/ Their works
answer the long mystery of how the brain maps its surrounding space and
navigates through complex environments. Similar to Case 1, the scientific
breakthrough occurred in two phases. First, O’Keefe discovered the first
component of brain positioning system called the ‘place cells’ (O’Keefe and
Dostrovsky, 1971). These are specialised nerve cells responsible for forming
spatial maps. Subsequently in 2005 May-Britt and Edvard Moser discovered the
‘grid cells’, which is the second crucial component in the brain’s positioning
system (Hafting et al., 2005). Grid cells are responsible for creating a
coordinate system, which is crucial for precise positioning and pathfinding.
The discoveries of both types of cells opens a new way for understanding how
an ensemble of brain cells perform higher cognitive functions that include
thinking, memory, and planning. Two breakthrough papers,(O’Keefe and
Dostrovsky, 1971) and (Hafting et al., 2005), are attributed to this prize (Li
et al., 2019b).

###  3.3 Case 3: Nobel Prize in Physiology or Medicine 2016

Yoshinori Ohsumi received the Nobel Prize in Physiology or Medicine 2016 for
his discovery of the mechanisms for autophagy.555Press release.
NobelPrize.org. Nobel Media AB 2020. Viewed on Mon. 23 Nov 2020.
https://www.nobelprize.org/prizes/medicine/2016/press-release/ Autophagy is
the process by which cells degrade and recycle their own cellular components.
It is a key cellular process that helps eliminate intracellular viruses and
bacteria. Because damages in the autophagy machinery have been associated with
multiple diseases, new drugs can be designed to fix the autophagy process.
Prior to Ohsumi’s groundbreaking work, little was known as to how autophagy
takes place. There are two winning papers for this prize. In the first, Ohsumi
proved the existence of autophagy in yeast cells by introducing a novel cell
engineering technique that disrupts the degradation process in the yeast cells
(Takeshige et al., 1992). The disruption led to the accumulation of
autophagosomes in the cell vacuole, which was observable under a microscope.
The autophagosomes provide the direct evidence for autophagy process in cells.
In the second paper, Ohsumi further postulated that genes instrumental to
autophagy must have been activated when the autophagosomes accumulated in the
cell vacuole (Tsukada and Ohsumi, 1993). To find out, he exposed the yeast
cells a specific chemical that allowed fifteen autophagy-specific genes to be
isolated. This succession of findings complete his extraordinary discovery.

As mentioned above, the breakthrough papers for this case possess peculiar
characteristics that make it an interesting case study. Both Ohsumi’s papers
have been noted as exemplary of under-cited influential landmark papers (Hu
and Rousseau, 2017). This means that the paper should been more frequently
cited that they actually are and there is little explanation as to why and how
such papers could satisfy the conventional breakthrough criteria. Therefore,
our aim is to provide an alternative explanation for their intellectual impact
using SVA.

##  4 Method

###  4.1 Structural variation analysis (SVA)

The theoretical foundation and central premise of the structural variation
theory are well-documented and will not be further elaborated in this paper
(Chen et al., 2009; Chen, 2012). SVA operationalizes the theory by providing
tools and metrics for measuring the intellectual impact of a paper in terms of
the amount of structural changes it exerted on its underlying co-citation
network. Note that SVA particularly focuses on detecting boundary-spanning
mechanisms in scientific literature, such that papers that establish more
novel links between previously disconnected clusters in a co-citation network
are more likely to be scientifically impactful than others. The detection of
other types of discovery mechanisms is beyond its design scope. We mentioned
previously that SVA is available as a module in the CiteSpace software (Chen,
2006).

Detecting SVA signals of a paper depends on two factors: (1) the SVA metrics
used and (2) the SVA network modelling. Prior studies indicated that different
SVA metrics have varying strength of correlation with the eventual impact of a
paper (Chen, 2012). Importantly, their performance as leading indicators for
Nobel Prize winning papers have never been studied before. The network from
which SVA metrics are calculated must be configured in ways that could amplify
SVA signals. For example, widening the temporal coverage of SVA baseline
network can bring up richer structures in the network. In the following
sections we describe the SVA metrics in mathematical terms and also recommend
a promising network modelling strategy .

###  4.2 SVA metrics

We study seven SVA metrics: (a) modularity change rate, (b) cluster linkage,
(c) centrality divergence, (d) harmonic mean of (a)-(c), (e) within-cluster
link, (f) between-cluster link, and (g) entropy. Here the mathematical
properties of the metrics are briefly explained. Readers should refer to
(Chen, 2012, 2020) for more details. Below is the list the common notations
and definitions used throughout the metric formulations.

Notation | Definition
---|---
$G(V,E)$ | Network $G$ is a document co-citation network;
|  $v\in V$ are nodes representing cited references;
|  $e\in E$ are links between nodes that are cited together at least once.
Paper $a$ | Paper that is the target of SVA.
$\tau_{a}$ | The year paper $a$ is published.
$Y_{(t,a)}$ |  $t$-year(s) of publication immediately prior to $\tau_{a}$.
$G_{s}$ | Baseline network $G$ generated from a set of articles $s$ published in the period $Y_{(t,a)}$.
$G_{a}$ |  $G_{s}$ plus novel co-citation links introduced by paper $a$.
$Q(G,C)$ | Overall modularity of $G$ obtained by an arbitrary partitioning $C$.
$K$ | Total number of clusters in a network.
$C_{B}(v,G)$ | Betweenness centrality of node $v$ in network $G$.

####  4.2.1 Modularity change rate ($\Delta M$), cluster linkage ($CL$), and
centrality divergence ($C_{KL}$)

These are the most established SVA metrics (Chen, 2012). The $\Delta$M of
paper $a$ measures the relative structural change of a network as a result of
additional information added by paper $a$ onto its baseline network. $\Delta
M$ is mathematically defined as follows (Chen, 2012; Hou et al., 2020):

$\Delta M(a)=\frac{Q(G_{s},C)-Q(G_{a},C))}{Q(G_{s},C)}$ (1)

The higher the $\Delta M$ score, the greater the extent of relative structural
changes exerted by paper $a$ upon its baseline network. To obtain $C$ and $Q$,
the Louvain community detection algorithm is used (Blondel et al., 2008).

The Cluster Linkage ($CL$) metric measures the overall structural change
exercised upon a network by paper $a$ in terms of novel connections added
between clusters. $CL$ ignores within-cluster links. Equation 2 explains how
the $Linkage$ score of a network $G$ with partition $C$ is calculated, where
$n$ is the total number of nodes in $G$, $\lambda_{ij}$ is an edge function
between nodes $v_{i}$ and $v_{j}$, and $\epsilon_{ij}$ is an adjustable weight
of the between-cluster link between both nodes.

$\begin{split}Linkage(G,C)=\frac{\sum_{i\neq
j}^{n}\lambda_{ij}\epsilon_{ij}}{K}\\\ \lambda_{ij}=\begin{cases}0,v_{i}\in
c_{j}\\\ 1,v_{i}\notin c_{j}\end{cases}\end{split}$ (2)

The $CL$ score of paper $a$ is then calculated as a weighted ratio between the
increase/decrease in Linkage score if a network owing to novel between-cluster
links added by $a$ in $G_{a}$, in comparison to the original Linkage score of
$G_{s}$ before the links are added. This is shown in Equation 3. $CR$ denotes
the number of cited references in paper $a$ that contributed to making novel
between-cluster links, whereas $NR$ is the total number of references it
cited. This means that, all other things being equal, the $\frac{CR}{NR}$
weighting scheme allows $CL$ to reward a paper with a high percentage of
boundary-spanning references.

$CL(a)=\bigg{(}\frac{Linkage(G_{a},C)-Linkage(G_{s},C)}{Linkage(G_{s},C)}\bigg{)}\times
100\times\bigg{(}\frac{CR}{NR}\bigg{)}$ (3)

The third metric, Centrality Divergence ($C_{KL}$), captures the structural
variations induced by paper $a$ in terms of the divergence of the distribution
of betweenness centrality of nodes in the baseline network. Unlike $\Delta$M
and $CL$, $C_{KL}$does not depend on the partitioning of a network and is
formulated as follows:

$C_{KL}(G_{s},a)={\sum}_{i=0}^{n}p_{i}\cdot\textrm{log}\bigg{(}\frac{p_{i}}{q_{i}}\bigg{)}$
(4)

where $p_{i}=C_{B}(v_{i},G_{s})$ and $q_{i}=C_{B}(v_{i},G_{a})$. The degree of
structural changes measured by $C_{KL}$ is defined in terms of the Kullback-
Leibler Divergence (Chen, 2012).

Previous research have suggested that different SVA metrics are sensitive to
different kinds of global structural variations. For predicting future
citation counts of papers in four research domains (terrorism, mass
extinction, complex network analysis, and knowledge domain visualization) Chen
(2012) found that on overall $CL$ was the best predictor. He also found
$C_{KL}$ to be particularly useful for capturing boundary-spanning
characteristics of a paper at interdisciplinary levels. On the other hand,
$\Delta$M was useful for characterising the evolution of individual authors’
scholarly impacts over time from a structural variation theory point of view
(Hou et al., 2020).

####  4.2.2 Within-cluster link ($\alpha$)and between-cluster link ($\beta$)

Chen and Song (2017) introduced within-cluster and between-cluster links as
additional measures of structural variation. The within-cluster link
($\alpha$) metric calculates the rate of novel within-cluster links added by
paper $a$ divided by the number of all within-cluster links:

$\alpha(a)=\frac{\textrm{no. of novel within-cluster links introduced by
}a}{\textrm{no. of all within-cluster links}}$ (5)

The between-cluster link ($\beta$) metric is calculated in the same way as
$\alpha$, except that it only focuses on novel between-cluster links that
connect nodes from disparate clusters. The $\beta$ score of paper $a$ is
computed as follows:

$\beta(a)=\frac{\textrm{no. of novel between-cluster links introduced by
}a}{\textrm{no. of all between-cluster links}}$ (6)

####  4.2.3 Entropy ($E$)

A citing paper’s entropy ($E$) is calculated as a standard information entropy
of the proportion of its cited references over the clusters of the underlying
co-citation network. Entropy is calculated below:

$E(a)=-{\sum_{i=1}^{n}p(a,i)\cdot\textrm{log}\big{(}p(a,i)\big{)}}$ (7)

where $p(a,i)=\frac{\textrm{no. of references in }a\textrm{ that belong to
cluster }i}{\textrm{no. of references in }a}$ and $n$ is the total number of
clusters in a merged network. Given its mathematical definition, a citing
paper with the maximum entropy would have its cited references evenly
distributed across all clusters. In contrast, a paper with the least entropy
(0) would have all its references residing in a single cluster.

####  4.2.4 Harmonic ($H$)

The harmonic score of paper $a$ $\big{(}H(a)\big{)}$ is the harmonic mean of
three structural variation metric scores, i.e. $\Delta M(a)$, $CL(a)$, and
$C_{KL}(a)$ (Chen, 2020). It summarizes the impact of a paper from three
different aspects of structural variations. We calculate $H(a)$ as follows:

$H(a)=\frac{3\cdot\Delta M(a)\cdot CL(a)\cdot C_{KL}(a)}{\Delta M(a)\cdot
CL(a)+\Delta M(a)\cdot C_{KL}(a)+CL(a)\cdot C_{KL}(a)}$ (8)

###  4.3 Network modelling

Beside the choice of SVA metrics, another factor that significantly influences
the outcomes of structural variation analysis is the network configurations.
This section explain our approach. We follow the standard practice of SVA
analysis that recommends document co-citation network as the primary network
representation (Chen, 2012; Hou et al., 2020; Chen, 2020). There are two non-
trivial network modelling components to be addressed here: (1) the method for
acquiring relevant literature that forms the basis for constructing a co-
citation network, and (2) finding suitable network configurations.

####  4.3.1 Cascading citation expansion

Adequately identifying the most representative body of scholarly publications
determines the quality of the resultant network and its subsequent SVA
analyses. For this purpose, we used the Cascading Citation Expansion (CCE)
method proposed by Chen and Song (2019), which offers a flexible method to
improve the quality of data retrieved for systematic scientometric reviews.
Our selected Nobel Prize winning papers served as the initial seed of CCE
expansion.

The CCE procedures are as follows. Bibliographic records associated with the
three cases of Nobel Prize awards were downloaded from Dimensions (Hook et
al., 2018) 666Digital Science. (2018-2021) Dimensions [Software] available
from https://app.dimensions.ai. Accessed in July 2020, under licence
agreement. in July 2020 using the CCE function in CiteSpace. The CCE process
started with a set of seed publications (i.e. the previously identified Nobel
Prize winning papers) and retrieved publications cited by the seed
publications as a step backward expansion, as well as publications that cited
the seed publications as a one step forward expansion. In practice, users may
specify multiple steps of expansion in each direction to meet their needs.
Refer to (Chen and Song, 2019) for more details of the CCE expansion process.

To obtain the dataset used in our study, we applied a 1-step backward and
1-step forward expansion from the seed publications (see Section 3). For each
seed paper, its DOI was used as a a start. If the DOI is missing, then we
would use the Dimensions publication ID, such as pub.1076143041, instead.
Below is a list of all seed papers with their corresponding DOI and Microsoft
Academic Graph ID (MAGID) numbers.

  1. 1.

Case 1, Seed 1 ($S_{1,1}$): (Gurdon, 1962b). Times cited: 321.
DOI 10.1016/0012-1606(62)90043-X. MAGID 2094753906.

  2. 2.

Case 1, Seed 2 ($S_{1,2}$): (Gurdon, 1962a). Times cited: 701.
PubmedID 13951335. MAGID 2153824299.

  3. 3.

Case 1, Seed 3 ($S_{1,3}$): (Takahashi and Yamanaka, 2006). Times cited:
16,123.
DOI 10.1016/j.cell.2006.07.024. MAGID 2125987139.

  4. 4.

Case 1, Seed 4 ($S_{1,4}$): (Takahashi et al., 2007). Times cited: 12,866.
DOI 10.1016/j.cell.2007.11.019. MAGID 2138977668.

  5. 5.

Case 2, Seed 1 ($S_{2,1}$): (O’Keefe and Dostrovsky, 1971). Times cited:
3,385.
DOI 10.1016/0006-8993(71)90358-1. MAGID 2052515926.

  6. 6.

Case 2, Seed 2 ($S_{2,2}$): (Hafting et al., 2005). Times cited: 2,050.
DOI 10.1038/nature03721. MAGID 1970792572.

  7. 7.

Case 3, Seed 1 ($S_{3,1}$): (Takeshige et al., 1992). Times cited: 787.
10.1083/jcb.119.2.301. MAGID 2126801593.

  8. 8.

Case 3, Seed 2 ($S_{3,2}$): (Tsukada and Ohsumi, 1993). Times cited: 1,135.
10.1016/0014-5793(93)80398-E. MAGID 2011580247.

Table 1 shows the basic bibliographic profiles of each dataset retrieved with
the Cascading Citation Expansion (CCE) technique. The column Unique Records
denotes the combined non-duplicate bibliographic records retrieved using CCE
for each Nobel Prize case, seeded with previously identified seed
publications. The percentages indicate the amount of valid DOIs and References
in the records. At the time of retrieval, abstracts were not yet available
from Dimensions.

Table 1: Profile of bibliographic records retrieved for each Nobel Prize case.

Case Unique Records Range DOI References Date of Retrieval 1 45,628 1952 -
2020 99.40% 99.19% 7/16/2020 2 14,885 1948 - 2020 99.70% 99.68% 7/16/2020 3
16,330 1951 - 2018 97.97% 96.50% 7/13/2020

####  4.3.2 Network parameters

The retrieved datasets above were then used to construct document co-citation
networks. These network must be configured to improve the ability to capture
SVA signals (Chen, 2012). One may a priori assume that larger networks are
more likely to include novel co-citation links. However, indefinitely
increasing the network sizes could be counter-productive. A higher level of
noise can be introduced into the increasingly larger network. Also, the
performance of metrics such as $\Delta M$ may be more influenced by the
specific locations the novel links are added, instead of by the size of the
network (Chen, 2012). Finally, from a practical standpoint, constraining the
network size has the benefit of keeping reasonable SVA running time in
CiteSpace.

We explain the key parameters for configuring co-citation networks for SVA.
First, the basic parameters were applied to all current cases. These are Link
Retaining Factor (LRF), Maximum Links Per Node (Max Links), Look Back Years
(LBY), and parameter $e$. We set LRF to 3, which retains the number of
strongest links up to three times the number of nodes in a network. Max Links
was set to 10, ensuring that at most ten strongest links are retained by a
node. Both parameters have been empirically shown to increase the clarity of a
network’s visualization. LBY and $e$ were set to -1 (i..e unlimited look back
years) and 0.00, respectively. LBY affects the number of cited references to
be included for each citing paper, whereas $e$ controls the number of top
cited references appearing in the network. Both settings ensure that these
parameters are free from subjective preferences of the analyst.

We focus our present study on the following parameters:

  1. 1.

Scaling factor ($k$). Parameter $k$ modifies the $g$-index of the network. The
$g$-index is the largest number that equals the average number of citations of
the most highly cited $g$ publications (Egghe, 2006). Setting higher $k$
values produces larger networks, vice versa. We set this initially to 5.

  2. 2.

Publication time frame. This parameter controls the time frame of an SVA
analysis relative to a target paper. It corresponds to the notation $Y_{t,a}$
in Section 4. For all case studies, we set publication time frame to 5 years
prior to the publication year of a Nobel Prize winning paper. This means that
if the paper was published in 2007 then the publication time frame spans from
2002 to 2007.

  3. 3.

Sliding window. This parameter dictates the number of years required to build
the baseline network, which is necessary for computing most of our SVA
metrics. This parameter was set to 5 years for all cases to maintain
consistency. This implies that if the seed paper was published in 2007, the
baseline network for calculating its SVA metrics will be constructed from all
papers published five years prior to 2007 (i.e. from 2002 to 2006).

###  4.4 Artificial breakthrough papers

We mentioned at the introduction to this paper that one of our key research
contributions is a method for consolidating the structural variation effects
of multiple seed papers associated with the same Nobel Prize. For this, we
propose artificially creating a pseudopaper that encapsulates all novel links
made by the associated seed papers. Given two seed papers $s_{1}$ and $s_{2}$
published in $\tau_{s_{1}}$ and a later year $\tau_{s_{2}}$, respectively, we
propose the following algorithm:

  1. 1.

Create a pseudopaper $Ps(s_{1}\oplus s_{2})$ to replace both seed papers.

  2. 2.

Let $Ps(s_{1}\oplus s_{2})$ cite all references cited by $s_{1}$ and $s_{2}$,
with duplicated references removed.

  3. 3.

Remove $s_{1}$ and $s_{2}$ from the co-citation network in year $\tau_{s_{1}}$
and $\tau_{s_{2}}$, respectively.

  4. 4.

Place $Ps(s_{1}\oplus s_{2})$ in the co-citation network of year
$\tau_{s_{2}}$. The pseudopaper should not be placed in year $\tau_{s_{1}}$
because it may cite references that only appear in $\tau_{s_{2}}$.

  5. 5.

Remove without replacement any citation to $s_{1}$ in year $\tau_{s_{1}}$, and
replace any to citation to either $s_{1}$ or $s_{2}$ in year $\tau_{s_{2}}$
with a citation to $Ps(s_{1}\oplus s_{2})$.

  6. 6.

Run SVA.

##  5 Results

This section presents the results of our SVA analyses on the selected cases of
Nobel Prize in Physiology or Medicine winners. To promote transparency and
reproducibility of our results, the CCE datasets are available from a shared
repository provided at the end of this article. In the results, we will refer
to the target Nobel Prize winning papers as seed papers (denoted by notation
$S_{x,y}$). Recall that they were used for seeding the Cascading Citation
Expansion process described in Section 4. For example, paper $S_{1,1}$ denotes
the first seed paper identified for Case 1 (Gurdon, 1962b), $S_{1,2}$ the
second seed paper for Case 1 (Gurdon, 1962a), $S_{2,1}$ the first seed paper
for Case 2, and so on. Any other paper is the non-Nobel Prize winning paper.
Refer to the previous section for a complete list of all the seed papers.

###  5.1 SVA on Case 1

The co-citation network for $S_{1,1}$ and $S_{1,2}$ (Gurdon’s papers) was
constructed from the publications between 1957 and 1962. The dataset, obtained
with CCE method, included 51 papers and 786 unique cited references. Fig. 1
visualizes the co-citation network. The numbered labels stand for various
clusters detected from the network. The red dash lines represent novel co-
citation links introduced by $S_{1,1}$. One could observe in the network that
Gurdon’s first landmark paper $S_{1,1}$ drew many new connections that span
across various parts of the network’s core largest connected component. His
second paper, $S_{1,2}$, did not appear in the network, suggesting that it did
not add novel links. This is supported by the fact that nearly forty-percent
of its references were already covered by $S_{1,1}$. As a result, there were
also not many important structural holes left in the network to be bridged by
$S_{1,2}$.

Figure 1: Boundary-spanning mechanism exhibited by Gurdon’s landmark
publication in 1962 ($S_{1,1}$).

The initial SVA outcome is highly encouraging. Table 2 shows the SVA scores of
seed $S_{1,1}$ compared with other top cited papers in the result set. In this
relatively small network (47 nodes, 157 links), only 6 papers made novel co-
citation links. $S_{1,1}$ topped nearly all SVA metrics (except $\beta$ where
it performed equally with the other papers), clearly indicating strong impacts
exerted by its publication on the underlying intellectual structure. Its high
entropy score suggests that the paper cited a highly diverse set of references
in various clusters. Its $CL$ score greatly stands out, which also indicates
that $S_{1,1}$ introduced many novel co-citation links that connected
disparate clusters. Finally, the seed paper also emerged at the top of the $H$
metric, suggesting its prominence along the most established SVA metrics
($\Delta M$, $CL$, $C_{KL}$).

Table 2: Case 1. The SVA scores of top-6 most cited papers in the network
(1957-1962). SVA score ranges: $\Delta$M:0.0 - 64.69, CL:-15.00 - 145.71,
$C_{KL}$:0.0 - 0.58, H:0.0 - 1.72, $\alpha$:0.0 - 0.5, $\beta$:0.0 - 1.0, E:
0.0 - 1.01. The subscript next to each SVA score of the seed paper indicates
the paper’s relative rank according to that metric, sorted in a descending
order. $S_{1,1}$ denotes the seed paper (Gurdon, 1962b) and the asterisk *
represents a tie with other papers.

Citation $\Delta$M CL $C_{KL}$ H $\alpha$ $\beta$ E DOI 321 ($S_{1,1}$)
$64.69_{1}$ $145.71_{1}$ $0.58_{1}$ $1.72_{1}$ $0.5_{1}$ $1_{*}$ $1.01_{1}$
10.1016/0012-1606(62)90043-x 68 0 -3.43 0.14 0 0 1 0.69
10.1016/0012-1606(62)90006-4 59 0 -15 0.15 0 0 1 0.69
10.1016/0012-1606(62)90004-0 45 21.28 11.54 0.22 0.67 0 1 0.5
10.1016/0012-1606(62)90037-4 43 0 0 0 0 0 0 0 10.1007/bf00577042 29 29.87 2.86
0.17 0.54 0 1 0.56 10.1002/jcp.1030600404

Figure 2: The co-citation network surrounding the publication of $S_{1,3}$ and
$S_{1,4}$ (2001 - 2007). The purple and red dash lines are co-citation links
made by one of the Yamanaka’s competitors (Yu et al., 2007). The numbered
cluster labels were generated using CiteSpace’s implementation of Latent
Semantic Indexing.

Four decades passed between Gurdon’s landmark papers and Yamanaka’s
groundbreaking works, during which the intellectual structures would have
changed considerably. Consequently, SVA was run on $S_{1,3}$ and $S_{1,4}$
independently from from $S_{1,1}$ and $S_{1,2}$ to precisely demonstrate the
structural changes effected by Yamanaka’s discovery against the state-of-the-
art in the field. The publication analysis time frame spans from 2001 to 2007,
calculated as five years prior to the publication the earlier seed
($S_{1,3}$). The merged network consisted of 454 nodes and 2,373 links, with
2,126 papers making novel co-citation links. The network is visualized in Fig.
2 and the SVA results are given in Table 3. Both seed papers are the most
cited papers in the result set. For comparison, we plotted novel co-citation
links made by the third most cited paper in the result, namely the paper by Yu
et al. (2007). The purple lines indicate the existing (non-novel) links found
in the paper, whereas the red dash lines represent newly introduced novel
links. A further examination on this competing paper revealed that it is in a
close competition to Yamanaka’s work as the authors also successfully isolated
four protein transcription factors for reprogramming human somatic cells to
pluripotent stem cells in the same year as Yamanaka. Then, in Fig. 3 we show
novel links introduced by $S_{1,3}$ and $S_{1,4}$. It is easy to see that, in
contrast to Yu et al. (2007) who contributed relatively few novel links,
Yamanaka’s papers added a much higher number of novel links that span across
the far reaches of the network. Comparing the two later figures also suggests
that the structural variations exerted by $S_{1,3}$ are likely to be more
significant that that of $S_{1,4}$ not only because the former added a lot
more novel links than the latter but also because the links span the
boundaries of multiple clusters in the network.

Figure 3: Novel co-citation links introduced by $S_{1,3}$ and $S_{1,4}$. (A)
depicts novel links introduced by $S_{1,3}$ (Takahashi and Yamanaka, 2006),
and B shows novel links added by $S_{1,4}$ (Takahashi et al., 2007). Note that
the underlying network is identical to that is shown in Fig 2. Table 3: Case
1. The SVA scores of top-10 most cited papers in the network (2001-2007). SVA
score ranges: The ranges of the obtained SVA metric scores are: $\Delta$M:0.0
- 89.36, CL:-76.24 - 494.69, $C_{KL}$:0.0 - 0.87, H:0.0 - 2.54, $\alpha$:0.0 -
1.0, $\beta$:0.0 - 1.0, E: 0.0 - 2.10. The subscript next to an SVA score of
each seed paper indicates the paper’s relative rank according to that metric,
sorted in a descending order.

Citation $\Delta$M CL $C_{KL}$ H $\alpha$ $\beta$ E DOI 16123 ($S_{1,3}$)
$65.89_{36}$ $267.53_{3}$ $0.82_{2}$ $2.42_{2}$ $0.6_{291}$ $0.99_{591}$
$2.1_{1}$ 10.1016/j.cell.2006.07.024 12866 ($S_{1,4}$) $4.18_{548}$
-$51.89_{1596}$ $0.01_{487}$ $0.03_{319}$ $0.53_{347}$ $0.77_{831}$
$0.95_{356}$ 10.1016/j.cell.2007.11.019 7257 0 -21.4 0 0 0 0.33 1.1
10.1126/science.1151526 3836 0 -8 0 0 0.49 0 0 10.1038/nature05874 3702 8.25
-7.01 0.35 0.96 0.25 1 0.67 10.1016/j.cell.2006.02.041 3309 0 -42.86 0 0 0.52
0 0 10.1038/nature05934 2132 7.96 -20.48 0.02 0.05 0.29 0.93 0.96
10.1038/nature05944 1844 0 0 0 0 0 0 0 10.1126/science.1141319 1829 0 -5.71 0
0 0 1 0.69 10.1002/dvg.20335 1781 25.92 -7.77 0.35 0.98 0.2 1 1 10.1038/ng1760

Table 3 shows the SVA metrics of both seed papers. Consistent with the
previous visualizations, $S_{1,3}$ performed better than $S_{1,4}$ as it
ranked first by metric E, second in $C_{KL}$ and H, and third according to
$CL$. Its high entropy score accounts for the highly diverse set of clusters
that it connected (see again Fig. 3). In contrast, $S_{1,4}$ did not feature
prominently by any SVA standard. Overall, however, the structural variations
induced by Yamanaka’s breakthrough papers appear less striking than that of
Gurdon’s paper. There could be several possible explanations for these. First,
due to the intense competition among regenerative cell biologists and the
rapid proliferation of publications in this research discipline, there were
perhaps fewer significant structural holes to span over. Second, it is
plausible that the breakthrough components are so distributed among Yamanaka’s
two papers that SVA signals can only marginally be detected from each paper
when observed independently. Therefore, a method that consolidates these
breakthrough elements into a single paper may overcome this limitation. Akin
to Gurdon’s case, it is may be that the poor SVA signal from $S_{1,4}$ can be
explained by the fact that some of its otherwise novel links have already been
made in $S_{1,3}$. We have observed that at least 30% references in $S_{1,4}$
had already been cited by $S_{1,3}$.

###  5.2 SVA on Case 2

Similar to the first case, in this Nobel Prize case a significant number of
years lapsed between seed papers $S_{2,1}$ (O’Keefe and Dostrovsky, 1971) and
$S_{2,2}$ (Hafting et al., 2005). Hence, we ran SVA independently on each seed
paper. The results for $S_{2,1}$ in Table 4 indicate that the paper wrought
remarkable structural changes upon its baseline network as it topped all SVA
metrics, except for $CL$ and $\beta$ which ranked it at fifteenth and third
places, respectively. The underlying network consisted of 89 nodes and 399
links, with a total of 38 citing papers made novel co-citation links. Fig. 4
visualizes the novel links introduced by $S_{2,1}$ to the network (1966 -
1971). They span over the boundaries of Cluster #0 and Cluster #2. The
identical cluster labels indicate the close affinity of both clusters’
research topics. This result provides a clear evidence of boundary-spanning
mechanisms at work behind O’Keefe’s landmark paper.

Table 4: Case 2. The SVA scores of top-10 most cited papers in the network
(1966-1971). SVA score ranges: $\Delta$M:0.0 - 75.41, CL:-48.05 - 0.00,
$C_{KL}$:0.0 - 0.54, H:0.0 - 1.58, $\alpha$:0.0 - 1.0, $\beta$:0.0 - 1.0, E:
0.0 - 1.3. The subscript next to an SVA score of each seed paper indicates the
paper’s relative rank according to that metric, sorted in a descending order.

Citation $\Delta$M CL $C_{KL}$ H $\alpha$ $\beta$ E DOI 3385 ($S_{2,1}$)
$75.41_{1}$ -$48.05_{15}$ $0.54_{1}$ $1.58_{1}$ $1_{1}$ $0.89_{3}$ $1.33_{1}$
10.1016/0006-8993(71)90358-1 356 3.7 -1.61 0.02 0.06 0.21 0.52 0.61
10.1007/bf00142518 294 0 0 0 0 0 0 0.69 10.1016/0028-3932(71)90005-4 291 0 0 0
0 0 0 0.69 10.1016/0006-8993(71)90303-9 200 0 -17.86 0.01 0 0.4 0 0
10.1007/bf00234246 195 0 0 0 0 0 0 0 10.1113/jphysiol.1971.sp009681 154 0 -25
0 0 0.5 0 0 10.1113/jphysiol.1971.sp009508 135 0 -11.34 0.02 0 0 1 0.69
10.1016/0031-9384(71)90172-7 132 0 0 0 0 0 0 0 10.1016/0031-9384(71)90235-6
131 0 0 0 0 0 0 0 10.1016/0042-6989(71)90005-8

Figure 4: Boundary-spanning mechanism exhibited by O’Keefe’s landmark
publication in 1971 ($S_{2,1}$).

The SVA result for $S_{2,2}$, i.e. May-Britt and Edvard Moser’s discovery
paper (Hafting et al., 2005) is presented in Table 5. Similar to Yamanaka’s
papers, there is less clear-cut evidence for its structural variations from
the metric point of view. Despite being the most cited paper in the result
set, $S_{2,2}$ ranked no. 1 only in $C_{KL}$ and fourth by $CL$. $H$ was not
useful due to zero $\Delta M$ and this time $E$ did not give a particularly
strong signal. Instead, one may observed in this result that Quiroga et al.
(2005) (DOI:10.1038/nature03687) scored highly for $\Delta M$ where it ranked
no. 1. The paper successfully discovered that neurons are activated
differently by extremely different pictures of people, places, or objects,
itself an important discovery. This may suggest another great potential of SVA
as a discovery tool. It can be used to find other impactful papers that should
have received a better recognition from the scientific community.

Table 5: Case 2. The SVA scores of top-10 citing papers in the network
(2000-2005). SVA score ranges: $\Delta$M:0.0 - 62.54, CL:-93.62 - 54.84,
$C_{KL}$:0.0 - 0.25, H:0.0 - 0.67, $\alpha$:0.0 - 1.0, $\beta$:0.0 - 1.0, E:
0.0 - 1.43. The subscript next to an SVA score of each seed paper indicates
the paper’s relative rank according to that metric, sorted in a descending
order.

Citation $\Delta$M CL $C_{KL}$ H $\alpha$ $\beta$ E DOI 2050 ($S_{2,2}$)
$0_{48}$ $36.42_{4}$ $0.25_{1}$ $0_{42}$ $0.44_{84}$ $0.89_{127}$ $1.32_{8}$
10.1038/nature03721 1181 0 -2.89 0 0 0 1 0.64 10.1016/j.neuron.2005.05.002
1174 0 -4.3 0 0 0.45 0.6 0.6 10.1038/nrn1607 940 62.54 -13.82 0.01 0.02 1 1
1.04 10.1038/nature03687 680 0 0 0 0 0 0 0.56 10.1152/jn.00697.2004 673 0
-5.85 0.03 0 0.53 1 0.41 10.1113/jphysiol.2004.078915 649 0 -10.07 0.02 0 0.67
1 0.5 10.1016/j.neuron.2005.02.028 637 0 -8.93 0.01 0 0 1 0.64
10.1371/journal.pbio.0030402 584 0 -4.8 0.07 0 0.59 0.92 0.76
10.1111/j.1469-7580.2005.00421.x 502 0 93.62 0.14 0 0.47 0.9 1.16
10.1002/hipo.20113

The underlying network for $S_{2,2}$ are shown in part (A) of Fig. 5, which
covered 197 nodes and 1,137 links. There were 277 citing papers that made
novel co-citation links. There are six major clusters in the network that
overlapped with each other. The novel links added by $S_{2,2}$ are illustrated
in Fig. 5 part (B). The highly dense links cover 5 out of the 6 major
clusters. The existing links (purple links) are concentrated on the largest
cluster (Cluster #0), which is the center of the network, where most research
works were traditionally concentrated. Importantly, we can see that the novel
links (red dash lines) significantly extended the boundaries of the existing
links to include pyramidal cells and entorhinal cortex research topics, which
are located at the extremities of the network.

Figure 5: The co-citation network surrounding $S_{2,2}$ (2000 - 2005). The
clusters were labeled with cited publications’ keywords. (A) shows the
underlying network. (B) illustrates the novel links introduced by $S_{2,2}$.

###  5.3 SVA on Case 3

The two winning papers contributing to this award (Takeshige et al., 1992;
Tsukada and Ohsumi, 1993) were published by Ohsumi and his colleagues at
nearly the same time. Hence, we covered both papers in a single SVA analysis.
Table 6 shows that neither $S_{3,1}$ nor $S_{3,2}$ ranked highly by any SVA
metric. In addition, both papers were not the most cited among their cohort,
making our result consistent with a previous study that considered Ohsumi’s
papers as the so-called under-cited influential papers (Hu and Rousseau,
2017). This atypical characteristic poses a unique challenge for SVA that we
will attempt to solve presently.

Table 6: Case 3. The SVA scores of the top-10 citing papers in the network
(1987-1993). SVA score ranges: $\Delta$M:0.0 - 80.62, CL:0.0 - 49.42,
$C_{KL}$:0.0 - 0.27, H:0.0 - 0.70, $\alpha$:0.0 - 1.0, $\beta$:0.0 - 1.0, E:
0.0 - 1.55. The subscript next to an SVA score of each seed paper indicates
the paper’s relative rank according to that metric, sorted in a descending
order.

Citation $\Delta$M CL $C_{KL}$ H $\alpha$ $\beta$ E DOI 2463 0 -17.31 0 0 0.19
0 0 10.1038/362318a0 1482 0 0 0 0 0 0 0 10.1016/0092-8674(93)90376-2 1477 0
-8.54 0 0 0.57 0 0 10.1083/jcb.116.5.1071 1135 ($S_{3,2}$) $0_{220}$
-$16.67_{197}$ $0_{118}$ $0_{125}$ $1_{19}$ $0_{183}$ $0_{220}$
10.1016/0014-5793(93)80398-e 787 ($S_{3,1}$) $53.29_{17}$ -$12.16_{168}$
$0.03_{45}$ $0.09_{16}$ $0_{96}$ $1_{12}$ $1.04_{29}$ 10.1083/jcb.119.2.301
769 0 -11.77 0.02 0 0.47 0.71 0.34 10.1038/355409a0 669 0 0 0 0 0 0 0
10.1091/mbc.3.12.1389 614 0 0 0 0 0 0 0 10.1172/jci115849 569 0 0 0 0 0 0 0.69
10.1111/1523-1747.ep12359590 534 0 -2.15 0.04 0 1 0 0
10.1002/j.1460-2075.1993.tb05813.x

There are 225 nodes and 1,225 links in the merged network, as shown in Fig. 6.
There were 305 citing papers that made novel co-citation links. It is
interesting to find that although the boundary-spanning property of $S_{3,1}$
is obvious from the visualization (i.e the paper connected two opposing
clusters on the far sides of the network), the paper’s SVA scores were
relatively unremarkable compared to other papers. Fine-tuning the network
parameters may be necessary to better uncover its structural variations.
Alternatively, the boundary-spanning mechanisms of both seed papers may need
to be further consolidated. Altogether, this demonstrates the non-trivial
challenge in extrapolating a uniform SVA configuration across different
scenarios.

Figure 6: The co-citation network surrounding Ohsumi’s breakthrough papers
(1987 - 1993), showing novel links added by $S_{3,1}$ (Takeshige et al.,
1992). Cluster labels were generated with log-likelihood ratio and the node
sizes correspond to the degree of betweenness centrality of a cited reference.
Figure 7: Comparing the structural variations induced by Ohsumi’s papers
against the most cited paper in our SVA result set (Söllner et al., 1993) (see
Table 6). (A) outlines the novel links induced by $S_{3,2}$ (Tsukada and
Ohsumi, 1993). (B) compares the novel links induced by Söllner et al. (1993).
The underlying network is identical to that in Fig. 6.

For Ohsumi’s second landmark paper ($S_{3,2}$), the network visualization in
Fig. 7 part (A) shows the relatively fewer novel links it added. Fig. 7 part
(B) allows us to visually compare $S_{3,1}$ and $S_{3,2}$ against the most
highly cited paper in the current result (Söllner et al., 1993). One can tell
that, unlike Ohsumi, Sollner et al. did not make a significant number of new
connections despite being more highly cited. This is evident from the fewer
red dash lines compare to the purple ones. This highlights the discrepancy
between a conventional measure of impact such as total citation count and what
could be considered as groundbreaking from the standpoint of the Nobel Prize
committee. Here SVA provides a promising alternative that better explains the
breakthrough qualities of a paper.

###  5.4 SVA performance with artificial pseudopapers

We summarize the performance of all SVA metrics for the three Nobel Prize
cases in Table 7. The marginal performances in independently detecting SVA
signals of $S_{1,3}$ and $S_{1,4}$ (Case 1), $S_{2,2}$ (Case 2), and all seed
papers in Case 3 prompted us to consider a different approach to measure
structural variations. In this section, we present the results obtained from
applying our proposed pseudopaper strategy. Still in Table 7, we can observe
that consolidating the underperfoming seed papers into a pseudopaper
dramatically improved many key SVA signals. For Case 1, Ps($S_{1,3}\oplus
S_{1,4}$) topped the $CL$, $C_{KL}$, $H$, and $E$. This improvement is
significant considering that only $E$ could previously detect the structural
variations induced by $S_{1,3}$. On the contrary, a pseudopaper did not
greatly benefit Gurdon’s publications. $S_{1,1}$ has already performed well in
virtually all SVA metrics on its own accord. Adding $S_{1,2}$ made no
difference as this second paper did not contribute novel links to the network
as mentioned earlier.

Table 7: Summary performance of SVA metrics for Cases 1 - 3. The pseudopaper
strategy amplifies SVA signals that are otherwise hard to detect from the
original seed papers. $Ps(s_{1}\oplus s_{2})$ denotes a pseudopaper generated
from seed papers $s_{1}$ and $s_{2}$. Where applied, $\rho_{s}$ represents a
collection of non-seed paper(s) published by the Nobel laureates of $s$ in the
same year as seed paper $s$’s publication.

Seeds Citation $\Delta$M CL $C_{KL}$ H $\alpha$ $\beta$ E $S_{1,1}$ $321_{1}$
$64.69_{1}$ $145.71_{1}$ $0.58_{1}$ $1.72_{1}$ $0.5_{1}$ $1_{*}$ $1.01_{1}$
$S_{1,2}$ $701_{n/a}$ n/a n/a n/a n/a n/a n/a n/a Ps($S_{1,1}\oplus S_{1,2}$)
$1022_{1}$ $64.69_{1}$ $68.52_{1}$ $0.54_{1}$ $1.63_{1}$ $0.25_{1}$ $1_{*}$
$1.01_{1}$ $S_{1,3}$ $16123_{1}$ $65.89_{36}$ $267.53_{3}$ $0.82_{2}$
$2.42_{2}$ $0.6_{291}$ $0.99_{591}$ $2.1_{1}$ $S_{1,4}$ $2866_{2}$
$4.18_{548}$ -$51.89_{1596}$ $0.01_{487}$ $0.03_{319}$ $0.53_{347}$
$0.77_{831}$ $0.95_{356}$ Ps($S_{1,3}\oplus S_{1,4}$) $28989_{1}$ $57.19_{53}$
$807.52_{1}$ $1.21_{1}$ $3.57_{1}$ $0.72_{113}$ $0.99_{513}$ $2.02_{1}$
$S_{2,1}$ $3385_{1}$ $75.41_{1}$ -$48.05_{15}$ $0.54_{1}$ $1.58_{1}$ $1_{1}$
$0.89_{3}$ $1.33_{1}$ $S_{2,2}$ $2050_{1}$ $0_{48}$ $36.42_{4}$ $0.25_{1}$
$0_{42}$ $0.44_{84}$ $0.89_{127}$ $1.32_{8}$ Ps($S_{2,2}\oplus\rho_{S_{2,2}}$)
$2167_{1}$ $2.34_{37}$ $1361.17_{1}$ $0.42_{1}$ $1.08_{1}$ $0.45_{82}$
$0.9_{121}$ $1.45_{1}$ $S_{3,1}$ $787_{5}$ $53.29_{17}$ -$12.16_{168}$
$0.03_{45}$ $0.09_{16}$ $0_{96}$ $1_{12}$ $1.04_{29}$ $S_{3,_{2}}$ $1135_{4}$
$0_{220}$ -$16.67_{197}$ $0_{118}$ $0_{125}$ $1_{19}$ $0_{183}$ $0_{220}$
Ps($S_{3,1}\oplus S_{3,2}$) $1922_{2}$ $66.42_{4}$ -$48.55_{123}$ $0.07_{28}$
$0.2_{12}$ $0.67_{6}$ $1_{3}$ $1.35_{6}$ Ps($S_{3,1}\oplus S_{3,2}$) ($k$=25)
$1922_{2}$ $79.45_{2}$ -$66.06_{183}$ $0.08_{1}$ $0.23_{1}$ $0.57_{27}$
$0.97_{139}$ $1.61_{2}$

A similar better performance was obtained for Case 2 as its pseudopaper
Ps($S_{2,2}\oplus\rho_{S_{2,2}}$) ranked first according to $CL$, $C_{KL}$,
$H$, and $E$. Without the pseudopaper approach, $S_{2,2}$ only stood out by
$C_{KL}$. The new notation $\rho_{2,2}$ denotes a regular, non-winning paper
that was paired with seed paper $S_{2,2}$. We will explain the selection of
$\rho_{2,2}$ shortly at the end of this section. It is important to note that
in addition to improving the overall SVA detection results, a pseudopaper
preserved the top SVA metrics of the underlying seed papers (i.e. $E$ in Case
1 and $C_{KL}$ in Case 2). We intentionally excluded O’Keefe;s paper
($S_{2,1}$) from the current pseudopaper analysis due to its previous good SVA
performance.

Unfortunately for Case 3, strong SVA signals of seed papers remained elusive
even after the application of the pseudopaper strategy (Table 7, second last
row). So, as suggested previously, further fine-tuning SVA parameters such as
the scaling factor $k$ may be the necessary next step in this case. Increasing
$k$ from 5 to 25 successfully improved the SVA detection performance for
pseudopaper Ps($S_{3,1}\oplus S_{3,2}$) such that it now ranked first
according to $C_{KL}$ and $H$. We also found that with $k=25$ the $\Delta M$
and $E$ scores improved dramatically. We detail the performance of Ohsumi’s
pseudopaper Ps($S_{3,1}\oplus S_{3,2}$) ($k$=25) against the other top cited
papers in Table 8. Table 9 shows the step-wise effects of increasing scaling
factor $k$ in Case 3 (Ohsumi’s case).

Table 8: Case 3. SVA metric scores of the top-10 most cited papers in the
network containing $Ps(S_{3,1}\oplus S_{3,2})$) (denoted by $\star$) with
scaling factor 25 ($k=25$; 1988-1993). A total of 208 citing papers made novel
co-citation links. SVA score ranges: $\Delta$M:0.0 - 80.09 — CL:0.0 - 66.06 —
$C_{KL}$:0.0 - 0.08 — H:0.0 - 0.23 — $\alpha$:0.0 - 1.0 — $\beta$:0.0 - 1.0 —
E: 0.0 - 1.68.

Citation $\Delta$M CL $C_{KL}$ H $\alpha$ $\beta$ E DOI 2463 0 -20.43 0.01 0
0.49 0.86 0.57 10.1038/362318a0 $\star$1922 $79.45_{2}$ -$66.06_{183}$
$0.08_{1}$ $0.23_{1}$ $0.57_{27}$ $0.97_{139}$ $1.61_{2}$ N/A 1727 0 -3.55 0 0
0 1 0.69 10.1016/0092-8674(93)90384-3 1482 0 -11.11 0 0 0.33 0 0
10.1016/0092-8674(93)90376-2 696 0 -0.67 0 0 1 0 0
10.1111/j.1469-8137.1993.tb03796.x 569 0 0 0 0 0 0 0
10.1111/1523-1747.ep12359590 534 0 -2.14 0 0 0 1 0.69
10.1002/j.1460-2075.1993.tb05813.x 518 67.81 -13.7 0.01 0.02 0 0.85 1.21
10.1073/pnas.90.7.2559 495 0 -5.53 0 0 0 1 0.69 10.1073/pnas.90.7.2812 495 0
-1.36 0 0 0 1 0.69 10.1128/mmbr.57.2.402-414.1993

Table 9: The effects of varying scaling factor $k$ on detecting structural
variation signals from pseudopaper $Ps(S_{3,1}\oplus S_{3,2})$ in Case 3. The
numbers in parentheses indicate to the pseudopaper’s ranks by the
corresponding metrics.

$k$ $\Delta$M CL $C_{KL}$ H $\alpha$ $\beta$ E 5 66.42 (5) -48.55 (123) 0.07
(28) 0.20 (12) 0.67 (6) 1.00 (3) 1.35 (6) 10 75.83 (3) -54.01 (157) 0.08 (19)
0.24 (10) 0.8 (15) 1.00 (9) 1.52 (3) 15 74.20 (7) -59.89 (166) 0.09 (1) 0.26
(1) 0.86 (13) 1.00 (6) 1.61 (3) 20 79.28 (3) -61.90 (173) 0.08 (2) 0.25 (1)
0.71 (14) 0.97 (130) 1.61 (2) 25 79.45 (2) -66.06 (183) 0.08 (1) 0.23 (1) 0.57
(27) 0.97 (139) 1.61 (2)

Further, we visually demonstrate the positive SVA effect of increasing a
network’s scaling factor. Contrasting parts (A) and (B) in Fig. 8 suggests
that the coverage of pseudopaper $Ps(S_{3,1}\oplus S_{3,2})$’s novel links was
expanded significantly when $k$ was set to 25. They reached out to new, far
away cluster such as the protein biogenesis cluster (Cluster #5 in part (B) of
the figure). This could have resulted in the increased centrality divergence
and entropy values of the pseudopaper (Table 7). The expanded reach of the
novel links is expected because increasing $k$ from 5 to 25 introduced nearly
three times more nodes and links into the network. The harmonic mean of the
modularity and the weighted mean silhouette of the network also substantially
improved from 0.2808 to 0.3767, suggesting an enhanced network quality. Having
said that, setting large scaling factors is computationally expensive in
CiteSpace and should be employed with care.

Figure 8: Increasing the scaling factor of co-citation network in Case 3 (1988
- 1993) enriches the intellectual representation of the network and broadens
the coverage of a pseudopaper’s novel links. (A) depicts the novel links added
by $Ps(S_{3,1}\oplus S_{3,2})$ ($k=5$). (B) shows the novel links added by the
same pseudopaper for $k=25$.

The increased scaling factor the network also brought in a new potentially
breakthrough paper that was not found previously. A paper by Bennett and
Scheller (1993), located on the third last row of Table 8 (DOI
10.1073/pnas.90.7.2559), proposed a new synaptic vesicle docking and fusion
model. Their model may lead to better understanding about the molecular
mechanisms in neurotransmitter release, which is important to learning and
memory in higher organisms. The relatively high $E$ (1.21) and $\Delta M$
(67.81) scores of this paper may signify its boundary-spanning characteristic
and high scientific value. In fact, we found that its co-author, Richard H.
Scheller, was the recipient of the 1997 NAS Award in Molecular Biology for his
work in ‘performing elegant experiments to resolve the molecular components
responsible for controlling neurotransmitter vesicle release and chemical
communication within the nervous
system’.777https://en.wikipedia.org/wiki/NAS_Award_in_Molecular_Biology Note
that several NAS Award recipients went on to receive Nobel Prizes in
Physiology or Medicine. This is another example of how SVA could provide us
with a better understanding of the tremendous values offered by many other
papers that are not necessarily recognized with a Nobel Prize.

Finally, let us make a few notes regarding the selection of $\rho_{S_{2,2}}$
for the purpose of synthesizing $Ps$($S_{2,2}\oplus\rho_{S_{2,2}}$) in Case 2.
Because the discovery by May-Britt and Edvard Moser was only associated with a
single winning paper, in lieu of a second winning paper we decided to
incorporate other papers published by these laureates in the same year as that
of $S_{2,2,}$. The replacement paper $\rho_{S_{2,2}}$ was limited to only 1
paper to maintain consistency with the pseudopapers for the other two cases.
We also searched candidates for $\rho_{S_{2,2}}$ from the same CCE dataset
seeded with $S_{2,2}$ to maximize the relevance of the selected paper.
Additional heuristics for shortlisting $\rho_{S_{2,2}}$ candidates are: (i)
currently listed as candidate winning papers in the source Nobel Prize dataset
(Li et al., 2019b), (ii) co-authored by both May-Britt and Edvard Moser, (iii)
does not belong to the competing research group led by John O’Keefe, and (iv)
demonstrated considerably SVA signals according to $C_{KL}$, $H$, and $E$ (we
chose these metrics given their good performance so far). Three candidates
emerged from criteria (i)-(iii), namely (Steffenach et al., 2005), (Leutgeb et
al., 2005a), and (Leutgeb et al., 2005b). Using criterion (iv) as a
tiebreaker, we selected (Leutgeb et al., 2005b) as $\rho_{S_{2,2}}$.

##  6 Discussions

Our work demonstrates, for the first time, the promising performance of SVA
metrics in explaining the boundary-spanning mechanisms behind selected Nobel
Prize winning papers. Various SVA metrics capture the impact of award-winning
papers in terms of what boundaries they bridged exactly. As leading indicators
of intellectual impacts, a Nobel Prize paper’s winning potential can detected
using SVA at the time of its publication. This is in contrast with other
competing metrics that can only be computed from a paper’s citation data,
which may take years to accumulate (Min et al., 2018, 2021). Our method is
transparent, highly reproducible, and requires only minimal adjustments to the
standard SVA procedures and parameters in CiteSpace.

Perhaps more importantly, since papers that may never land on a Nobel Prize
are far more than those that did, our methodology is valuable to identify
papers that share the same boundary-spanning properties despite the fact that
they may not be awarded a Nobel Prize for one reason or another. This is
already demonstrated in our results for Case 2 and Case 3 involving (Quiroga
et al., 2005) and (Bennett and Scheller, 1993), respectively. The method’s
potentially wide-ranging applicability is important to increase our
understanding of the nature of research excellence.

###  6.1 Nobel Prize and SVA

The Nobel Prize winning papers selected for this study were distinguished by
exceptional boundary-spanning characteristics, which are very well captured by
the centrality divergence ($C_{KL}$), entropy ($E$), and the harmonic ($H$)
metrics. We also show that our artificial pseudopaper approach allows the
potential structural variations made by a Nobel Prize discovery to be more
amenable to detection by SVA metrics. This technique will be useful in
scenarios where the original winning papers tend to emit weak SVA signals.

These initial SVA results seem to suggest that certain Nobel Prize winning
papers are more sensitive to the mechanism that SVA is looking for. In
particular, seed papers $S_{1,1}$ (Case 1) and $S_{2,1}$ (Case 2) are highly
amenable to SVA detection and topped nearly all the available SVA metrics, no
matter how we configured their underlying networks. The effects may be further
exaggerated by the lack of competition within a relatively old co-citation
network, where novel connections were rare (see Table 2 and Table 4).
Together, these make it easier to distinguish the boundary-spanning quality of
these papers.

As for the other seed papers, the initial underperformance of SVA metrics
under their individual assessment suggests that the scientific community may
have perceived the impact of a seed paper differently, or that history played
it out differently. In other words, it cannot be ruled out that some Nobel
Prize winning papers may not play the most fundamental scientific role and
that one may have overestimated their role in relation to the discovery. There
could be other papers which could have better played the role in their place
but are not recognized by Li et al’s study (Li et al., 2019b). Due to the non-
trivial nature of nominating and selecting the actual Nobel Prize winners, we
also recognize that there could be other selection criteria and other
mechanisms of scientific discovery that cannot be fully accounted by the
structural variation theory.

###  6.2 Interpreting SVA metrics

The general behaviours of $\Delta M$, $CL$, and $C_{KL}$ have been discussed
elsewhere. For example, the strong betweenness centrality divergence induced
by a paper (i.e. high $C_{KL}$ score) was found to be a valuable early sign of
its transformative potential at the interdisciplinary levels (Chen, 2012).
Likewise in this study $C_{KL}$ emerged as the clear winner, adding further
evidence to its usefulness. The significance of $C_{KL}$ metric suggests that
not all novel co-citation links contribute equally to the overall impact of a
paper and that the scientific community may tend to favor papers that draw new
links in ways that significantly alter the distribution of betweenness
centrality scores of nodes in a network. This makes sense given that
betweenness centrality characterizes a boundary-spanning mechanism; a node of
a high betweenness centrality evidently bridges two bodies of scientific
knowledge. We also note that the reported lower performance of $\Delta M$ is
consistent with earlier studies (Chen, 2012) and may suggest some limitations
of metrics that rely on modularity-based network partitioning.

Metric $E$ and $H$ are relatively newer SVA metrics and their good performance
in this study is highly encouraging. $E$ can be considered as a diversity
metric that favors the breadth over the depth in terms of the
coverage/distribution of cited references over clusters. The metric offers a
major advantage in terms of its simplicity and connection to the widely known
Shannon’s information entropy (Chen, 2020; Lin, 1991). Its good performance in
relation to the Nobel Prize winning papers may further strengthen the
prevailing association between the ability to draw novel links between diverse
ideas and the propensity of making lasting scientific impacts (Uzzi et al.,
2013; Fortunato et al., 2018). However, the novelty or the uncertainties of
some critical ties may be reduced over time as more studies get published.
This is a good candidate for further investigations. The promising performance
of $H$ suggests the workability of an aggregation-oriented approach to
measuring structural variations. It may anticipate a category of breakthrough
papers that may not necessarily stand out by a single metric but are
exceptional when several metrics are taken together.

Previously, $CL$ was found to correlate well with the future citation counts
of research papers (Chen, 2012). Accordingly, in the current study, its
usefulness is limited to seed papers that garnered exceptionally high citation
counts. For under-cited influential papers such as Ohsumi’s, $CL$ is not a
good boundary-spanning indicator. In this case, $CL$ produced negative scores,
which is quite an unexpected behavior. We reserve this issue for future
investigations.

Finally, we offer a few explanations as to why the artificial pseudopaper
technique might have worked. In scenarios where two seed papers were published
in proximity to each other, it is possible that the first seed already filled
up the intellectual gaps to such extent that there is nothing left to fill by
the second seed. As mentioned earlier, this ‘self-eclipse’ phenomenon seems to
characterize the relationship between $S_{1,3}$ and $S_{1,4}$. Consequently, a
pseudopaper could have strengthened the overall impact of both papers,
especially when they should be naturally evaluated in conjunction with each
other. This further suggests that research excellence may be more
appropriately recognized in a way that transcends the scope of individual
publications. The same conceptual consolidation technique may also be
beneficial because it overcomes the limitations in scenarios where novel links
are so dispersed over a few winning papers that a single paper does not
exhibit structural variation strong enough for detection (e.g. Ohsumi’s papers
in Case 3). It might also help in situations where a Nobel laureate might have
drawn crucial novel associations through another less popular paper (e.g. the
inclusion of a non-prize winning paper by May-Britt and Edvard Moser provided
help for this case).

###  6.3 Useful SVA strategies

Our experience suggests several new strategies in using SVA with CiteSpace. We
observed that increasing the $k$ value quickly enlarges the network, resulting
in untenable SVA running time. Therefore, we recommend that anyone interested
in using SVA first prioritize the sliding windows before optimizing other
configuration parameters such as $k$. The width of the sliding window should
be increased gradually (by default is 2) while maintaining a low scaling
factor (e.g. 5). This allows a richer structure of the network to emerge while
keeping reasonable SVA running time (i.e. within hours instead of days).
Besides, we also found that the quality of SVA detection does not always
change monotonically with the increase or decrease in sliding window value.
So, we suggest that researchers first explore and select the most ‘optimal’
sliding window under a small, fixed $k$ value. The optimum sliding window size
may vary by case. Once a ‘promising’ window width is determined, use it with
increasingly larger $k$ values to obtain better SVA detection. The workability
of this approach was previously demonstrated in improving SVA scores of
pseudopaper $Ps(S_{3,1}\oplus S_{3,2}$) by setting larger $k=25$.

##  7 Limitations and Future Work

We provided cases of boundary-spanning mechanisms that are supported at a
higher level of abstraction. We have not addressed in detail the novel
conceptual links made by each seed paper at the cluster level. Doing so is
necessary to further understand the exact nature of their boundary-spanning
mechanisms. The conceptual role played by the seed paper itself is probably
the most important one and is unfortunately beyond the expected scope of
CiteSpace’s SVA. Also, given the inherent limitation associated with most case
study-based research, the present findings are only indicative of the
boundary-spanning properties of Nobel Prize winners in general.

The Cascading Citation Expansion is a highly systematic method that
capitalizes on the conscious and highly selective citing behaviours to gather
the most relevant literature base (Chen and Song, 2019). It is not immediately
evident that seeding the CCE process with pre-selected Nobel Prize winning
papers could have produced networks that inadvertently amplified the SVA
signals of the seed papers. The difficulties in detecting SVA signals of some
seeds in the initial part of our experiments may in fact suggest that such
biases, if any, have a limited impact on the ensuing analyses. A future work
may include empirically testing this assumption by seeding CCE with a non-
winning paper that has close topical relevance to the winning paper.

Focusing citation contexts and brokerage links between concepts in concept
trees from the connected clusters is a promising research direction (Chen,
2020). Future studies should also focus on conducting a larger scale SVA
analysis on a higher number of Nobel Prize winning papers to further ascertain
the current findings. Another exciting direction is to compare with SVA
analysis of Nobel Prize nominees, which is gradually made available through
the Nobel Prize Nomination
Archive.888https://www.nobelprize.org/nomination/archive/

##  8 Conclusion

The boundary-spanning mechanisms of a select group of Nobel Prize winning
papers are demonstrated through a series of experiments with SVA. They are
strongly characterized by the ability to draw novel co-citation links from
topically-diverse clusters in ways that led to significant alterations of the
betweenness centrality distributions in the underlying co-citation network.
Through this work, we not only isolated key SVA leading indicators that are
representative of the Nobel Prize papers’s qualities but also proposed new
techniques for improving SVA signal detection. Overall, our findings support
the structural variation theory as a promising scientific breakthrough theory.

## Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any
commercial or financial relationships that could be construed as a potential
conflict of interest.

## Author Contributions

YS and CC conceived and designed the study. CC collected the data. YS
conducted the experiments. YS and CC analyzed and interpreted the results. YS
and CC wrote the paper.

## Acknowledgments

This paper was written using data obtained in July 2020 from Digital Science’s
Dimensions platform, available at https://app.dimensions.ai. Access was
granted to subscription-only data sources under licence agreement.

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