# Biomedical Convergence Facilitated by the Emergence of Technological and
Informatic Capabilities

Dong Yanga, Department of Management of Complex Systems, Ernest and Julio
Gallo Management Program, School of Engineering, University of California,
Merced, California 95343, USA  Ioannis Pavlidis  Computational Physiology
Laboratory, University of Houston, Houston, Texas 77204, USA  Alexander
Michael Petersena, Department of Management of Complex Systems, Ernest and
Julio Gallo Management Program, School of Engineering, University of
California, Merced, California 95343, USA

11footnotetext:  These authors contributed equally; Send correspondence to:
<EMAIL_ADDRESS>
We analyzed Medical Subject Headings (MeSH) from 21.6 million research
articles indexed by PubMed to map this vast space of entities and their
relations, providing insights into the origins and future of biomedical
convergence. Detailed analysis of MeSH co-occurrence networks identifies three
robust knowledge clusters: the vast universe of microscopic biological
entities and structures; systems, disease and diagnostics; and emergent
biological and social phenomena underlying the complex problems driving the
health, behavioral and brain science frontiers. These domains integrated from
the 1990s onward by way of technological and informatic capabilities that
introduced highly controllable, scalable and permutable research processes and
invaluable imaging techniques for illuminating fundamental structure-function-
behavior questions. Article-level analysis confirms a positive relationship
between team size and topical diversity, and shows convergence to be
increasing in prominence but with recent saturation. Together, our results
invite additional policy support for cross-disciplinary team assembly to
harness transdisciplinary convergence.

The codification of knowledge facilitates more efficient search across the
vast space of possible creative inputs accessible to scientists
fleming2001recombinant  – conceived in research as strategic configurations of
established and new entities, relationships, tools, equipment, methods,
processes, observation, theory, etc. Organization of knowledge into an
ontology facilitates additional understanding of its structure, dynamics and
future trajectories borner2010atlas ; borner2015atlas ; borner2021atlas , as
such knowledge maps borner2003visualizing ; fleming2004science ;
borner2012design ; shi2015weaving  improve scientists’ ability to establish
and recall complex relationships saket2015map . The pervasive drive to
document entities and their relationships in detailed *-omics atlases will
thereby help scholars manage the increasing volume and pace of knowledge
production pan2016memory ; petersen_citationinflation_2018  and accelerate
breakthrough discovery rzhetsky2015choosing ; helbing2012accelerating  by
helping scholars manage the uncertainty associated with exploration
kuhn1959essential ; march1991exploration .

Against this backdrop, we developed network-based methods for assessing the
evolution of biomedical innovation. As the field of biology transitions from
its descriptive roots into a health innovation frontier, research increasingly
combines tacit inputs involving trial, error and practice (e.g. manual
laboratory techniques) with explicit inputs that are highly transmissible and
modifiable (e.g. pre-assembled computer algorithms). Consequently, the theory
of recombinant innovation fleming2001recombinant  provides a powerful
framework for understanding the potency, and uncertainty, embodied by
combinatorial approaches to search, refinement, experiment and discovery.
Likewise, the triple-helix model of innovation leydesdorff1996emergence ;
etzkowitz2000dynamics ; petersen2016triple  establishes the importance of
catalysts for bringing potent opportunities – i.e., challenging problems
demanding novel solutions met with a diverse supply of research approaches –
to fruition. The catalysts in the present context are techno-informatic
capabilities, characterized by highly controllable, scalable and permutable
research processes for exploring and testing the exponentially vast number of
biological interactions.

In order to prime the pump, national innovation systems have increased
investment into transdisciplinary convergence science NSFConvergenceAccel , a
paradigm prescribed by its originators as “the coming together of insights and
approaches from originally distinct fields” NRC:2014 ; eyre2017convergence  –
as opposed to subfield integration characteristic of interdisciplinary
approaches colon2008chemical ; pan2012evolution ; Leahey_Sociological_2014 .
Stimulation of potent triple-helix configurations aims to support the
emergence of new hybrid disciplines sharp2011promoting , for addressing
complex global challenges helbing2013globally . Recombinant innovation is
fundamental to the convergence science value proposition, as integrating
diverse teams of experts hedges against uncertainty underlying the exploration
process fleming2004perfecting  and provides a testable mechanism Petersen:2018
; HBP_2020  for explaining the propensity of larger teams producing higher
impact science Wuchty:2007 . By way of example, the advantage of cross-
disciplinary integration was evident in full force during the genomics
revolution, wherein traditional biologists and computer scientists leveraged
familiar operational language to overcome relatively large epistemic and
cultural distances between their traditionally distinct fields Petersen:2018 .
Recent work lends further support to cross-disciplinarity
fleming2004perfecting ; Petersen:2018  as the more impactful convergence mode
for exploring across long disciplinary distances HBP_2020 , as compared to
expansive learning approaches Engestrom:2010  pursued by mono-disciplinary
teams.

It is generally appreciated that techno-informatic capabilities will transform
many research domains, in addition to biomedicine. Yet even in the case of the
latter, we lack high-resolution maps for understanding the rich history and
future potential of cross-domain integration. Hence, to identify and map the
anatomy of biomedical convergence, we analyzed millions of intra-article
keyword combinations using the high-resolution Medical Subject Heading (MeSH)
classification system MESH ; MESHMap , a controlled thesaurus maintained by
the U.S. National Library of Medicine (NLM) and implemented within the
$\sim$30 million articles indexed by PubMed. By visualizing MeSH co-occurrence
networks and measuring inter-article MeSH diversity over the last half
century, we identified the dominant knowledge configurations underlying
contemporary convergence. Notably, we document how Technology (captured by
MeSH branch J) and Informatics (MeSH Branch L) emerged as convergence bridges,
transforming non-invasive imaging, high-throughput anomaly detection, and big
data integration – all key tools that are critical to addressing challenges at
the frontiers of health, behavioral and brain science HBP_2020 .

Figure 1:  Biomedical Knowledge Network. (A) Explicit network structure
defined by the Medical Subject Heading (MeSH) tree implemented by the US
National Library of Medicine across the PubMed index. Visualized is the quasi-
hierarchical MeSH-MeSH network composed from the six traditional biomedical
branches. (B) Network visualization of the “Anatomy” subtree (branch A). Nodes
are individual MeSH and links are prescribed by the NLM MeSH Tree; nodes sized
and shaded according to node degree. (C) Serial refinement of the MeSH
appearing within each PubMed article: the set of MeSH $\vec{m}_{p}$ for each
article $p$ are refined to just the Major “keywords” (indicated within PubMed
by an asterisk $*$); these Major MeSH $\vec{m}^{*}_{p}$ are readily mapped to
their parent MeSH at the 2nd-level ($L_{2}$) and 1st-level ($L_{1}$). (D)
Historical MeSH co-occurrence frequencies for articles and reviews at the
$L_{1}$ and $L_{2}$ levels; MeSH branches indicated by color-scale border
segments (note the different color schema than in panel A). MeSH clusters are
determined by a modularity maximizing algorithm Blondel:2008  and indicated by
the gray-scale border segments; hierarchical structure indicates the minimum
spanning tree representation of each co-occurrence matrix; entities are sorted
within cluster in decreasing order of prevalence, calculated as the sum of co-
occurrences with all other MeSH.

## Quantitative Framework

Related ontology and diversity research. Prior scientific ontology studies use
journal and article classification systems of varying granularity and
specificity levels. A common objective is to measure disciplinary diversity by
using classification systems as proxies for research topic subject areas, and
measuring category-category correlations wagner2011approaches ; yegros2015does
. Some studies utilize broadly defined categories, such as the journal-level
“Subject Category” descriptors implemented within Web of Science
porter2007measuring ; porter2009science ; rotolo2013does , or article-level
systems used within multi-disciplinary journals such PNAS boyack2004mapping
and PLOS ONE petersen2019megajournal . Another stream of research utilizes
more high-resolution article-level classification systems, such as keywords
Leahey_Sociological_2014 , International Patent Classification (IPC) and US
Patent Office Classification (USPC) codes fleming2001recombinant ;
fleming2007breakthroughs ; youn2015invention ; verhoeven2016measuring , MeSH
boyack2004mapping ; boyack2011clustering ; MESHMap ; foster2015tradition ;
shi2015weaving ; petersen2016triple  and Physics and Astronomy Classification
Scheme (PACS) codes pan2012evolution . Other approaches include topic mapping
based on co-word analysis mane2004mapping  and hybrid approaches integrating
keywords and cited references to group research into knowledge clusters
borner2012design .

The MeSH tree. We operationalize the representation of the biomedical
knowledge network using article-level MeSH annotations, which can be
considered as keywords with varying specificity that are interrelated within a
quasi-hierarchical tree illustrated in Fig. 1(A). The official MeSH tree is
maintained by the NLM and consists of 16 branches designated by the characters
A, B, C, D, E, F, G, H, I, J, K, L, M, N, V, Z (see
https://meshb.nlm.nih.gov/treeView to explore the tree). The six branches A,
B, C, D, E, G represent core biological entities, concepts and methods;
whereas the branches F, J, L, N represent peripheral domains comprised also of
entities, concepts and methods.

Previous studies focused on MeSH belonging to specific branch subsets, such as
C, D and E MESHMap ; petersen2016triple . Here we exclude MeSH from the H, I,
K, M, V, Z branches, as these are comprised of non-technical MeSH such as H
(“Disciplines and Occupations”) and V (“Publication Characteristics”) – see
Fig. S1 for a schematic representation of the quasi-hierarchical MeSH tree. To
illustrate branch substructure, Fig. 1(B) shows the explicit MeSH-MeSH
relations endowed in the MeSH tree for branch A (“Anatomy”). This particular
branch is dominated by biophysical structures and their attributes – i.e.,
representing one half of the structure-function dichotomy, with branch G
(“Phenomena and Processes”) representing the other half.

Article-level Data. Our comprehensive analysis is based upon the 2020 PubMed
index consisting of more than 30 million index entries, with 93% of these
classified as “Journal Article” or “Review”. We then pruned this dataset of
articles lacking Major MeSH and focused on the sample spanning 1970-2018,
resulting in 21.6 million publications (for additional details see Methods).
Regarding notation, in what follows we use subscript $p$ to indicate article-
level information such as publication year, indicated by $y_{p}$; the number
of coauthors, $k_{p}$; and the set of MeSH “keywords”, represented as a vector
$\vec{m}_{p}$ with 29,638 elements, each representing a distinct MeSH term. An
article with the sample average of 4 Major MeSH terms corresponds to
$\sum_{i}\vec{m}_{p,i}=4$.

Projecting MeSH onto 10 Subject Areas (SA). We analyzed all MeSH belonging to
the 10 core and peripheral branches. We refer to these broad knowledge domains
as Subject Areas (SA). These SA represent a basis set for classifying MeSH
according to their first-level parent branches (denoted by $L_{1}$). The MeSH
tree is quasi-hierarchical (containing a relatively small number of loops),
with 12 hierarchical levels per branch MESHMap . Hence, based upon this
explicit relational tree structure, we can map any MeSH occurring at the third
level or greater to its corresponding second-level ($L_{2}$) MeSH term, for
which there are 104 types.

Figure 1(C) illustrates the full process for producing $\vec{SA}_{p}$, which
begins with first pruning out minor MeSH terms and auxiliary qualifiers,
leaving just Major MeSH terms that represent the article’s core SA
decomposition. By way of example, the MeSH term “Obesity” has four Tree Number
locators corresponding to three SA (C, E and G): C18.654.726.500;
C23.888.144.699.500; E01.370.600.115.100.160.120.699.500;
G07.100.100.160.120.699.500 (see Fig. S1). Hence, the $L_{2}$ representation
of this single MeSH term is then given by {C18, C23, E01, G07} (which are each
distinct MeSH terms among the 29,638). We catalogue these MeSH using a $L_{2}$
count vector, denoted by $\vec{SA}^{(2)}$, which contains 104 elements.
Further projecting this set to its $L_{1}$ representation yields {C, C, E, G},
represented by $\vec{SA}^{(1)}$={0,0,2,0,1,0,1,0,0,0}. This example highlights
the nuanced organizational structure of the MeSH tree, where terms can span
multiple SA and contexts, thereby giving rise to relatively small yet non-
trivial cross-branch connectivity within the explicit MeSH knowledge network –
see Fig. S2 for a network visualization of the explicit MeSH-MeSH relations
within core biological SA. Combining multiple MeSH into $\vec{SA}_{p}$ yields
a quantitative signature of each article’s SA composition.

Figure 2:  Structure and Dynamics of MeSH-MeSH Co-occurrence. (A) Top 10 most
frequent destemmed keywords from Chemistry and Physiology or Medicine Nobel
Prize rational statements, sized proportional to their prevalence,
illustrating the transition from structural to mechanistic orientation of
grand scientific pursuits. (B,C) MeSH branches are indicated by axis labels
with corresponding color-scale border segments; MeSH clusters determined by
the Louvain modularity maximizing algorithm Blondel:2008  are indicated by the
outer gray-scale border segments. MeSH are ordered within cluster in
decreasing order of prominence corresponding to total number of article
instances for a given period, as indicated by the numerical scales. (B)
$L_{1}$ co-occurrence matrices show sequential dynamics across 4 non-
overlapping periods; linear color-scale. (C) $L_{2}$ co-occurrence;
logarithmic color-scale. (D) Co-occurrence cluster size dynamics by year and
resolution level: $L_{1}$ (left) and $L_{2}$ (right).

## Results

MeSH Co-Occurrence at the $L_{1}$ and $L_{2}$ levels. We assessed the entire
space of MeSH combinations by tallying SA co-occurrences among the present
(non-zero) elements contained in $\vec{SA}^{(1)}_{p}$ and
$\vec{SA}^{(2)}_{p}$. Continuing with the example above, consider the SA
counts {C, C, E, G}, which could arise from an article with a single Major
MeSH annotation of “Obesity”, or an article with four Major MeSH mapping
individually to the same set of SA; we do not distinguish between these two
cases. We then tabulate the SA co-occurrences by counting for all unique SA-SA
dyad types. In such a case, we tabulate three co-occurrence types: CE, CG and
EG. When aggregating co-occurrence tallies across articles, we combine
normalized tallies – e.g. by assigning 1/3 weight to the CE, CG and EG matrix
elements in the example above – so that each article contributes a total
weight of 1 to the co-occurrence matrix ${\bf M}^{(1)}$ (and similarly for
${\bf M}^{(2)}$ constructed at $L_{2}$). In this way, the total sum across
matrix elements of ${\bf M}$ is proportional to the total number of articles
analyzed in the sample; see the Methods section Major MeSH Descriptors for
further details.

To begin, Fig. 1(D) shows co-occurrence frequencies recorded in the symmetric
matrices ${\bf M}^{(1)}_{1970-2018}$ and ${\bf M}^{(2)}_{1970-2018}$,
calculated across articles published between 1970-2018. Each matrix indicates
the SA name along the right border, accompanied by a consistent color
indicating the corresponding $L_{1}$ branch, useful for guiding visual
inspection. We grouped SA into knowledge clusters using the Louvain modularity
maximizing algorithm Blondel:2008 , indicated by the gray-scale border
segments along the upper and left matrix borders. The top border contains
hierarchical clustering trees indicating the minimum spanning tree
representation of each matrix. To further aid visual inspection, we maintain
the gray-scale cluster shades across the aggregate matrices shown in Figs. 1
as well as the time-disaggregated matrices visualized in Fig. 2.

As such, we analyzed MeSH co-occurrences at both the $L_{1}$ and $L_{2}$
levels, thereby producing knowledge network maps with complementary degrees of
granularity. The main result for $L_{1}$ is the two-SA substructure observed
for ${\bf M}^{(1)}_{1970-2018}$. This substructure confirms that D, C, A, E, B
and G form a core biomedical cluster, with the peripheral application domains
N, F, J and L forming a second cluster.

At higher resolution, the $L_{2}$ matrix ${\bf M}^{(2)}_{1970-2018}$ features
three mixed clusters. The first cluster is comprised of a wide array of
$L_{2}$ MeSH pertaining to complex human phenomena related to behavior,
physiology and health. Importantly, this cluster also includes L01
(“Information Science”) and J01 (“Technology, Industry, and Agriculture”).
Because these are two focal domains in our analysis, we refer to their MeSH
scope notes to provide additional context. According to MeSH scope notes,
“Technology” refers to “the science and application of techniques” (J01), and
more specifically “the application of scientific knowledge to practical
purposes in any field [including] methods, techniques, and instrumentation”
(J01.897). Likewise, MeSH scope notes describe “Information Science” (L01) as
“The field of knowledge, theory, and technology dealing with the collection of
facts and figures, and the processes and methods involved in their
manipulation, storage, dissemination, publication, and retrieval.”

The second cluster is comprised of diagnostic methods associated with
particular diseases and the systems they affect, as represented by MeSH
primarily from branches A (“Anatomy”), C (“Chemicals and Drugs”) and E
(“Analytical, Diagnostic and Therapeutic Techniques, and Equipment”). The
third cluster is comprised of biological entities and the phenomena that
relate them, from cells to chemicals and the multi-scale processes that
connect inputs, outputs and characteristics of their reaction environments.

Historical co-occurrence trends. The last half-century of biomedical research
has witnessed incredible transition from a descriptive field – focused around
identifying molecules, higher-order structures, reaction pathways and
mediators – into a field seeking to identify holistic mechanisms underlying
systemic abnormalities in an effort to develop pointed therapies. This
transition is illustrated through the Nobel Prizes awarded for Chemistry and
Physiology or Medicine, which up until the 1970s and 1980s predominantly
awarded research documenting key structural entities and reactions. Based upon
this early work, subsequent Nobel research has transitioned to addressing
challenges at the nexus of the medical innovation triple helix – where
societal demand and industrial supply for acute solutions are facilitated by
technological capabilities petersen2016triple .

To illustrate this point, Fig. 2(A) shows the top ten stemmed keywords from
Nobel Prize “rationale” statements, identifying prominent contextual themes
across the last half century. Indeed the 1980s brought forth novel imaging,
laboratory control and synthesis technologies, fundamental in the 1990s to map
the genetic blueprints encoding biological structure Petersen:2018 .
Polymerase chain reaction (PCR), among other high-throughput techniques,
accelerated science to the realm of highly controllable, scalable and
permutable processes that hitherto have been primarily restricted to
traditional computational domains. Since then, the last twenty years has been
marked by the rapid development of bioengineering capabilities, such as CRISPR
gene editing tools doudna2014new  and powerful demonstration of stem cell
pluripotency takahashi2007induction , which allow scientists to more precisely
understand emergent structure-function relations, opening the door for
synthetic biology applications benner2005synthetic  that (re)design biological
systems church2014regenesis  or even develop altogether new building blocks
hoshika2019hachimoji .

To visualize this history unfold, we disaggregated the MeSH co-occurrence data
into four non-overlapping periods: 1970-1989, 1990-1999, 2000-2009 and
2010-2018. For each period we tabulate the co-occurrence matrix, denoted by
${\bf M}^{(1)}_{y}$ (${\bf M}^{(2)}_{y}$), where $y$ denotes a given period.
Figure 2(B) illustrates the structural dynamics at the $L_{1}$ level,
identifying branch E and J as vacillating domains switching between the two
dominant clusters. The first $L_{1}$ cluster is characterized by D, A, G and B
– largely descriptive SA, with the exception of “Phenomena and Processes” (G).
The second cluster is comprised of N, F and L – peripheral SA which are
increasingly convergent with the traditional SA, as indicated by extreme off-
diagonal elements representing cross-domain integration.

At higher resolution, Fig. 2(C) shows the structural evolution of ${\bf
M}^{(2)}_{y}$, which is characterized by two relatively stable clusters and a
more diverse and vacillating intermediate cluster. Note that MeSH are sorted
within each cluster in decreasing order of prevalence, calculated as the sum
of co-occurrence values across a given row of ${\bf M}^{(2)}_{y}$. Notably,
“Information Science” (L01) and “Technology, Industry, and Agriculture” (J01)
are located in this intermediate cluster during the 1970-1989 period, where
they play less dominant roles as indicated by their ranks within the cluster.
However, over time their prominence within this cluster increases; by
2010-2018, J01 joined the biological agents and reactions cluster,
characterized by the core “Amino Acids, Peptides, and Proteins” (D12),
“Chemical Actions and Uses” (D27), “Eukaryota” (B01) and “Organic Chemicals”
(D02). Close inspection reveals J01 having relatively strong co-occurrence
with “Inorganic Chemicals” (D01), “Investigative Techniques” (E05), “Health
Care Quality, Access, and Evaluation” (N06) and “Biomedical and Dental
Materials” (D25) – indicative of a highly convergent applications nexus
facilitated by technological capabilities.

Close inspection further reveals a similar transformation for L01, which rose
to prominence from the 1980s onward, as genomics and other panoramic omics
revolutions increased the demand for informatic solutions to map, characterize
and associate entities into a functional atlas. This role did not merely
manifest from increased technological capabilities associated with “Diagnosis”
(E01) and “Investigative Techniques” (E05), but also involved the integration
of powerful “Mathematical Concepts” (G17), in particular “Algorithms”
(G17.035) to optimize classification and AI methods for “Deep Learning”
(G17.485.500). Such methods are critical for capitalizing on new data-driven
opportunities in Health Care (represented broadly by N04, N05, N06) for
understanding “Behavior and Behavior Mechanisms” (F01).

Figure 3:  Prominent convergence bridges. (A) For each MeSH, we analyzed the
time series of bridge rank, $R_{i,t}$, a normalized ranking based upon the
knowledge bridge score ($\beta_{i}$) defined in Eq. (1). Smaller rank values
($R_{i,t}$) correspond to larger $\beta_{i}$ values, representing MeSH that
are highly co-occurrent with MeSH belonging to other knowledge clusters.
Plotted are smoothed time series to facilitate visual inspection. Notably, J01
and L01 are rapidly emerging convergence bridges arising from the highly
generalizable, scalable and codifiable nature of techno-informatic tools and
algorithms facilitating novel non-invasive imaging, high-throughput analysis,
measurement, and data integration. Other MeSH shown here identify the emerging
convergence nexus of Health Care (N04, N05) and Behavior (F01). (B) MeSH
neighborhood subnetworks for J01 and L01 each show the ten most frequently co-
occurring MeSH for the indicated period – sorted clockwise, starting from the
top, with nodes sized proportional to ${\bf M}^{(2)}_{ij}$; each MeSH’s SA is
indicated by its node/label color. Links are plotted with thickness and shade
proportional to ${\bf M}^{(2)}_{jj^{\prime}}$, thereby indicating the cross-
domain linkages among prominent neighbors that are facilitated by $i$. Each
node includes its MeSH identifier and a knowledge cluster identifier, the
latter indicated by a gray scale gradient. For example, MeSH J01 “Technology,
Industry, and Agriculture” (which is a member of C3 for the first three
periods and subsequently transitioning to C1 in the most recent period) is
highly connected to MeSH from all other clusters (C1-C3), in particular to L01
until its disassociation in the most recent period 2010-2018; interestingly,
L01 “Information Science” diverged from J01 as early as the first period
1970-1989, subsequently becoming more strongly coupled with members of branch
E and G. See Figs. S3-S4 for extended analysis of bridge ranks and
neighborhood subnetworks for the remaining convergence bridges

Biomedical convergence identified by the emergence of cross-cluster bridges.
To identify MeSH serving as bridges that link different knowledge clusters, we
developed a metric which quantifies the degree to which individual nodes
connect distinct clusters in a connected weighted network. This metric is
motivated by the bridge centrality index jensen2016detecting . We develop this
approach with ${\bf M}^{(2)}_{t}$ in mind, which is a complete network as
opposed to a sparse network (See Methods section Calculation of the cross-
cluster bridge score for further details). Applying this method to ${\bf
M}^{(2)}_{t}$ yields a knowledge bridge score for each MeSH and year, denoted
by $\beta_{i,t}$, which is large if a MeSH is highly connected to clusters
other than its own.

Figure 3 shows the rank dynamics $R_{i,t}$ (where larger $\beta_{i,t}$
correspond to smaller rank $R_{i}$) for 8 MeSH that are distinguished by
either persistent growth or sustained prominence as knowledge bridges over the
entire study period. Notably, L01 features steady growth following its
emergence in the early 1980s, whereas J01 features an oscillating upward
trend. We also observe a divergence between “Behavior and Behavior Mechanisms”
(F01) and “Psychological Phenomena” (F02), with the latter becoming
increasingly insular over the last 20 years. The emergence of health care
bridges relating to “Health Services Administration” (N04), “Health Care
Quality, Access, and Evaluation” (N05) and situational behavior analysis (F01)
is another disruptive trend from the last decade – consistent with the ramp-up
of several international Human Brain Projects Markram:2012 ; Grillner:2016  in
2013, thereby championing the brain research nexus as the next frontier
HBP_2020 .

Figure 4:  Increasing prevalence of cross-domain knowledge integration. (A)
Fraction of articles, $f_{X}(t)$, featuring at least half of Major MeSH in
ABCDEG and at least a quarter in J, L or J+L. (B) $f_{D,p}$ measures article-
level SA diversity, based on weighted pairwise SA-SA combinations defined in
Eq. (S2). Average $f_{D,p}$ diversity value and standard deviation (error bar)
calculated for non-overlapping 3-year windows over the period 1970–2018; the
global average diversity value (0.47) is indicated by the horizontal dashed
line. The mean value $\langle f_{D}(t)\rangle$ has increased from 0.38 to
0.53, representing 39.5% growth, over the entire 49-year sample period. (C)
Increased knowledge diversity correlates with the emergence of team science,
where the most rapid increase is among the larger teams with 11-50 coauthors.
Solo-author research has only recently reached the average diversity value
indicated by the horizontal dashed line. (D) Heterogenous trends by
longstanding core (Cell), elite multi-disciplinary (Nature, PNAS, Science) and
biomedical (Lancet, NEJM, JAMA) journals. NEJM and JAMA show the largest
consistent increase over time; Nature and PNAS exhibit the largest increase in
the last decade. Each curve represents the third-order polynomial trend, with
shaded colored areas indicating the 99% CI for each trend line.

Convergence factors – SA composition, prevalence, team size and scientific
impact. The value proposition envisioned by convergence science originators
NRC:2014  was novel configurations of experts strategically assembled to
address a dimension of the underlying problem that would be otherwise
inaccessible by mono-disciplinary strategies. The convergent union between
biology and computing experts in the genomics revolution provides a rich
example Petersen:2018 . Hence, it follows that convergent research strategies
are more likely to prevail in team science endeavors, and provides a testable
mechanism for the propensity for larger teams to produce higher-impact science
Wuchty:2007 .

Indeed, the importance of informatic (L) and technological (J) capabilities to
modern biomedical research cannot be understated. To illustrate the emergence
of these bio-technological and bio-informatic modes, indicated by $X$, we
calculated the fraction of articles by year that contain a significant
component belonging to SA J and/or L. To ensure that the articles are
otherwise focused on traditional biomedical SA, we estimate the number of
cross-domain articles by focusing on the subset of PubMed articles featuring a
half or more of their MeSH in the core categories ABCDEG. We then assign the
indicator $X$ to those articles which also contain at least a quarter of their
MeSH belonging to L, J, or L+J in combination, and report the quantity of
articles featuring $X$ as the fraction $f_{X}(t)$ of the total articles by
year.

Figure 4(A) indicates a burst of activity around the early 1990s for research
containing both L and J in combination – much greater than the $f_{X}(t)$
calculated for either SA alone. This particular configuration of ABCDEG
$\times$ J $\times$ L represents a formidable nexus featuring the combination
of high-throughput equipment to produce and churn through massive biomedical
data. For comparison, Fig. S5(A) applies the same method to all MeSH (i.e.,
not distinguishing between Major and Minor MeSH), thereby including the more
peripheral MeSH capturing the idiosyncratic research details. This second
perspective indicates a more steady integration over time of J and L
capabilities at the SA periphery, with the strongest upturn in J+L in the
early 2000s, which has since saturated. Hence, if the 1990s brought forth the
revolution in biomedical research, and the 2000s witnessed the further
penetration of this paradigm shift, there appears to be a recent stagnation
owing primarily to L which has permeated other convergence zones Roco:2013 ,
such as computational social science lazer_computational_2009  and the science
of science Fortunato_2017_Science .

To further explore the evolution of cross-domain SA configurations at the
article level, we developed a Blau-like diversity measure, denoted by
$f_{D,p}$, and based upon SA-SA co-occurrence. This measure accounts for two
distinct diversity types – both categorical variation and concentration
disparity harrison2007s . Our method takes as input the categorical count
vector $\vec{SA}_{p}$ and applies the outer tensor product,
$\vec{SA}_{p}\otimes\vec{SA}_{p}$, yielding a weighted matrix ${\bf D}_{p}$
that captures dyadic SA-SA co-occurrence; see SI Appendix Eqs. (S1)-(S2) for
further elaboration. To summarize, if an article’s MeSH descriptors are
contained in just a single SA, then there will be only one single non-zero
value contained in ${\bf D}_{p}$, which will occur along the matrix diagonal.
Conversely, if the article features several SA, then off-diagonal elements
represent cross-domain combinations. Hence, $f_{D,p}$ measures the relative
fraction of off-diagonal to diagonal elements – with $f_{D,p}=0$ corresponding
to minimal diversity. Because more evenly distributed SA counts will yield
relatively larger off-diagonal values, and hence larger $f_{D,p}$ value, it is
both a measure of variation and disparity harrison2007s . Morever,
$f_{D,p}\in[0,1)$ is a bounded statistic with clear interpretation of the
lower and upper bounds.

We computed $f_{D,p}$ based upon $\vec{SA}^{(2)}_{p}$ counts tallied for each
publications in our PubMed sample (i.e. using the $L_{2}$ MeSH representation
of an article). Figure 4(B) shows the evolution of the mean diversity value
$\langle f_{D}(t)\rangle$ calculated for articles grouped by publication year,
and shows a steady increase in SA diversity over the last half century.
Analysis of the entire distribution of values, $P(f_{D,p,t})$, also exhibits a
systematic positive shift across the range of $f_{D,p}$ values, and so the
increase in the mean value is not just the result of an uper tail effect in
the aggregate distribution. Rather, we observe a marked decrease in the
prevalence of mono-SA articles characterized by $f_{D,p}=0$ in the lower
distribution tail – see Fig. S5(B). This result is analog to the reduced
frequency of single-authored research observed over the same period
Wuchty:2007 , indicative of the intense burden to integrate distant knowledge
domains, a challenge that contributes to the disappearance of the
“renaissance” solo genius Heller:2015 ; simonton_after_2013 .

To assess how team size mediates article-level SA diversity, we disaggregated
the data into four team-size groups: solo-author (coauthor number $a_{p}=1$);
small-sized team ($1<a_{p}\leq 5$); medium team ($5<a_{p}\leq 10$); and large
team ($10<a_{p}\leq 50$). Figure 4(C) shows the dominant trends in average
diversity time series $\langle f_{D}(t)\rangle$ for each team size group, from
1970 to present. To facilitate visual comparison of the dominant trends, shown
are each time series fit using a third-order polynomial: $\langle
f_{D}(t)\rangle\equiv a+b(t-1990)+c(t-1990)^{2}+d(t-1990)^{3}$. Notably, the
curve for solo-author team shows a significant systematic shift towards lower
SA diversity values. From the mid-1980s onward, the curves are ordered
according to team size group, with the largest teams achieving SA diversity
levels far in excess of the unconditional average for the entire period,
$\langle f_{D}\rangle=0.47$ (indicated by the horizontal dashed line in each
figure sub-panel). As a robustness check, Fig. S5(C) shows the journal-level
relation between article-level SA diversity and mean journal team size for the
60 biomedical journals appearing in the set of top-100 journals ranked by 2018
Clarivate Analytics JCR Impact Factor, indicating a higher range of SA
diversity associated with larger teams.

The wide variation in journal-level $\langle f_{D}\rangle_{j}$ indicates that
support for convergence science is a feature of the distinct communities of
expertise. While it is beyond the present study, we speculate that the
multidisciplinary composition of a journal’s editorial board is likely to be a
strong factor underlying the prevalence of convergence science featured in a
particular journal. Among the most prestigious journals shown in Fig. 4(D),
several feature recent decline in $\langle f_{D}(t)\rangle$ over the last two
decades, including Cell and the Lancet; contrariwise, the medical journals
NEJM and JAMA are consistently trending upwards. To further illustrate the
dynamics at the journal level, Fig. S5(D) shows the top-10 journals in terms
of their largest growth in $\langle f_{D}(t)\rangle$ over the study period,
featuring prominent journals in multiple domain areas including cancer,
microbiology, medicine and psychology. Despite such consistent growth trends
for some journals, this is not a universal feature. See Table S1 for prominent
journals ranked according to their average SA diversity value $\langle
f_{D}\rangle_{j,1970-2018}$.

## Discussion

With each new discovery – some large, others incremental – there is also a
need to find its place in the order of things – some adding new layers to our
understanding, and others filling in gaps. Classification systems are designed
to manage the increasing volume of knowledge, so that it can be readily
recorded, searched, explored and exploited in the pursuit to create new
knowledge. From the Decimal Classification system (developed by expert
committees and used in libraries around the world) to the Wikipedia category
structure (a crowdsourced representation of our collective knowledge UDCWiki1
; UDCWiki2 ; UDCWiki3 ), we are surrounded by ontologies that attempt to
organize our common understanding. Likewise, the MeSH system aims to organize
biomedical knowledge into a networked hierarchy that relates objects, methods,
theory and other contextual metadata; notably, the traditional PACS system has
recently been revamped into PhySH by adopting a similar concept-based
hierarchy that is better suited for integrating the multiple sub-disciplines
and facets that define the domain of physics PhySH2019 .

We exploited the MeSH ontology structure to develop a dynamic and high-
resolution map of cross-domain integration, which contributes to prior efforts
to visualize the biomedical knowledge network MESHMap ; petersen2016triple ;
shi2015weaving . In particular, we developed methods to visualize MeSH co-
occurrence and quantify cross-domain diversity. Macro-level analysis of MeSH
co-occurrence networks identifies three robust knowledge clusters: the vast
universe of microscopic biological entities and structures; systems, disease
and diagnostics; and biological and social phenomena capturing emergent
properties, processes and functions. Research at the health, behavioral and
brain science frontiers typically integrate these knowledge domains, signaling
the emergence and future potential of convergence science NRC:2005 ;
sharp2011promoting ; Roco:2013 ; NRC:2014 ; ConvergenceElephant_2014 ;
eyre2017convergence ; HBP_2020 . The convergence nexus of Health Care (N),
Behavior and Behavior Mechanisms (F01) and Information Science (L01) is a
prime example, making way for transdisciplinary brain science HBP_2020  to map
and model brain circuits Jorgenson:2015  that are fundamental to addressing
the grand challenge regarding the “global burden of mental disorders”
Kessler:2009 ; dzau2018reimagining . We reinforced these macro trends by
micro-level analysis of article-level MeSH diversity, which increased by 40%
over the entire study period from 1970 to 2018 – see Fig. 4(B). This shift can
be partly explained by a reduction in the prevalence of mono-domain research,
analog to the simultaneous reduction of solo-authored research Wuchty:2007 .

Comprehensive analysis of the knowledge network can also identify periods of
disruption. By assessing the dynamics of MeSH usage across the entire PubMed
index, we identified periods in which MeSH increasingly fluctuate between
knowledge clusters (see Fig. S6). To identify the particular MeSH that bridge
different knowledge communities we developed a cross-cluster bridge metric in
Eq. (1). Figure 3 shows the emergence of technology (J01) and informatics
(L01) as prominent convergence bridges, reflecting the highly generalizable,
scalable and codifiable characteristic of techno-informatic tools and
algorithms that accelerate scientific discovery by facilitating high-
throughput, measurement, data integration and analysis. Figure 4(A) further
indicates the prevalence of this potent combination, which rapidly emerged in
the early 1990s during the genomics revolution. Notably, this endeavor
highlights the role of cross-disciplinary collaboration between scholars from
traditional biology and computer science departments, which provided an early
example of successful convergence, likely owing to the consortium science
model whereby teams of teams organize with a common goal to share benefits
equitably within and beyond institutional boundaries Petersen:2018 . In
related work, we show that research integrating subject areas that span
relatively larger disciplinary distances is more impactful when executed by
cross-disciplinary teams as opposed to mono-disciplinary teams HBP_2020 . We
provide complementary support, showing that medium and large-scale teams have
a notable advantage integrating multiple research domains – see Fig. 4(C).
Viewed from a different bureaucratic perspective, we observe variable levels
and growth rates of convergence in journals, possibly owing to the multi-
disciplinary composition (or lack thereof) of journal editorial boards.

In summary, techno-informatic capabilities are increasingly essential to the
biomedical frontier. As illustrated by Fig. 4(A), these distinct inputs are
increasingly found as complements rather than substitutes – for the period
2000-2018 we estimate that $\langle f_{\times}\rangle\approx$8.2% of research
articles relied on techno-informatic capabilities in tandem (J+L); this
frequency corresponds to a 291% growth over the J+L convergence levels in
1980. If the future relies on harnessing the combined power of human and
machine intelligence, then the development of human-in-the-loop and Man-
Machine Systems (J01.897.441) “in which the functions of the man and the
machine are interrelated and necessary for the operation of the system” will
require transdisciplinary domains such as bio-mechatronics to flourish by
harnessing convergence li2016guest . For this reason, scientists are
increasingly in need of knowledge maps to navigate the realm of possibilities
and to thereby which conceptual bridges to cross and which to avoid.

## Methods

Subject Area (SA) classification using MeSH. We used the 2020 MeSH
classification tree, which includes 29,638 descriptors that are organized in a
tree-like structure denoting their hierarchical relations. MeSH descriptors
are assigned to biomedical publications through an indexing process performed
by examiners at the US National Library of Medicine (NLM). With on average 12
MeSH per article, this ontology facilitates topic mapping and topic co-
occurrence analysis at multiple levels of specificity petersen2016triple . We
restrict our analysis to the “Major Topic Headings” for each article, which
are indicated in each PubMed article page by an asterisk ∗ next to the MeSH
term; these Major MeSH account for roughly 1 in 3 MeSH descriptors, and so
with on average 4 Major MeSH these annotations are sufficient to identify the
article’s core content. As such, we use these publication-level MeSH to
determine the topical Subject Areas (SAs), as indicated by the 10 pre-defined
science-oriented MeSH branches (A, B, C, D, E, F, G, J, L, N).

Major MeSH Descriptors: refinement to 1st and 2nd branch level representation.
For each publication $p$, we extracted the set of Major MeSH terms (as
indicated by an asterisk in PubMed records) and represent them by the vector
$\vec{m}_{p}$ containing 29,638 elements, each representing a distinct MeSH
term. We then map each MeSH term to its corresponding tree location, which
specifies its classification among the 10 science-oriented MeSH branches. To
be specific, we define a generic operator $O_{M}$ which takes the vector
$\vec{m}_{p}$ and maps these counts to a combined count vector
$\vec{SA}^{(2)}_{p}$ with 104 elements representing all $L_{2}$ MeSH:
$O^{(2)}_{M}(\vec{m}_{p})=\vec{SA}^{(2)}_{p}$. Similarly, we define the
operator $O_{M}^{(1)}(\vec{SA}^{(2)}_{p})=\vec{SA}^{(1)}_{p}$, which maps the
$L_{2}$ MeSH counts to their $L_{1}$ branches.

In order to count co-occurrences, we take each $\vec{SA}$ and denote the
binary SA vector $B_{p}={\tt Sign}(\vec{SA})$, which reduces each element
value to either 0 or 1. For an article with $M_{p}$ non-zero elements, we then
count all ${M_{p}\choose{2}}$ pairwise permutations which we record in a
normalized co-occurrence matrix, given by ${\bf M}^{(1)}_{p}$ (${\bf
M}^{(2)}_{p}$) for the $L_{1}$ ($L_{2}$) representation. Each matrix is
normalized to unity such that the total of all subelements $\sum_{i,j}{\bf
M}_{p,ij}=1$. This normalization step ensures that each publication
contributes an equal share to the annual co-occurrence matrix, given by ${\bf
M}^{(1)}_{y}=\sum_{p\in y}{\bf M}^{(1)}_{p}=N(y)$, where $N(y)$ is the total
number of articles analyzed from year $y$ (with similar definition for the
$L_{2}$ level).

Calculation of the cross-cluster bridge score. Motivated by the bridge
centrality index jensen2016detecting , we define the knowledge bridge score
$\beta_{i}$ of node $i$, given by

$\beta_{i}=\sum_{C_{I},C_{J}\in C\ {\tt and}\ C_{I}\neq C_{J}}D_{IJ}W_{iJ}\ ,$
(1)

which first requires identifying nodes belonging to distinct clusters,
calculated here using the Louvain algorithm Blondel:2008 . Here $C$ represents
the set of connected clusters in the giant component of an undirected network,
and $C_{J}$ represents a cluster that is different from the cluster $C_{I}$
containing a given node $i$. We define $D_{IJ}$ to be the distance between
cluster $C_{I}$ and $C_{J}$, measured as the inverse of the sum of weights of
edges between the clusters, represented as $D_{IJ}=W_{IJ}^{-1}=(\sum_{i\in
C_{I}{\tt and}j\in C_{J}}W_{ij})^{-1}$. Similarly, $W_{iJ}$ is the sum of
weights of edges between node $i$ and all other nodes belonging to cluster
$C_{J}$. For our purposes, we define the link weights as empirical co-
occurrence values, $W\equiv{\bf M}^{(2)}_{t}$. Hence, individual MeSH terms
(nodes) that play key roles in bridging knowledge clusters have high
$\beta_{i}$ values; contrariwise, nodes that are only connected to nodes
belonging to their own cluster have $\beta=0$.

Since ${\bf M}^{(2)}_{t}$ tallies are proportional to the total number $N(t)$
of articles published in year $t$, which are generally increasing, we instead
focus on the rank associated with each $\beta_{i}$ score, denoted by
$r_{\beta,i}$. Figure S3 shows the rank dynamics of the MeSH in each cluster
exhibiting significant growth or decline over the study period. To address how
to compare ranks of nodes from clusters of varying size (measured as the total
number of nodes within the cluster $I$, denoted by $|C_{I}|$), then we define
the normalized Bridge rank score as $R_{i}=r_{\beta,i}/|C_{I}|$, as plotted in
Figure 3.

Based upon each time series $R_{i,t}$ calculated at the 1-year time
resolution, we identified emerging bridges using the following criteria: (i)
The node is on average ranked in the top-20 of its own cluster; (ii) the time
series is at least half as long as the entire observation period from 1970 to
2018; (ii) There is a significant positive or negative trend, as determined by
linear regression, such that the trend coefficient P-value is smaller than
0.01; (iv) the trend coefficient magnitude is sufficiently large, in magnitude
$>$ 0.1. These criteria identify 8 emerging knowledge bridges: E05, F01, F02,
G07, J01, L01, N04 and N05.

Data Availability: All data analyzed here are openly available from PubMed
API, the MeSH tree prescribed by the NLM (see
https://meshb.nlm.nih.gov/treeView) and the 2018 Web of Science JCR list of
Impact Factors.

## Acknowledgments

IP acknowledges funding from the Eckhard- Pfeiffer Distinguished Professorship
Fund; IP and AMP acknowledge support from NSF grant 1738163 entitled ‘From
Genomics to Brain Science’. AMP acknowledges financial support from a Hellman
Fellow award that was critical to completing this project. Any opinions,
findings, and conclusions or recommendations expressed in this paper are those
of the authors and do not necessarily reflect the views of the funding
agencies.

## Author Contributions

DY analyzed and visualized the data; IP performed research and participated in
the writing of the manuscript; AMP performed the research, drafted the
manuscript, collected, analyzed, and visualized the data.

## Additional Information

Supplementary Information accompanies this paper.

Competing financial interests The authors declare no competing financial
interests.

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Supplementary Information – Appendix Text, Figure S1-S6 & Table S1

Biomedical Convergence Facilitated by the Emergence of Technological and
Informatic Capabilities

Dong Yang1, Ioannis Pavlidis2, Alexander M. Petersen1

1Department of Management of Complex Systems, Ernest and Julio Gallo
Management Program, School of Engineering, University of California, Merced,
California 95343, USA;
2Computational Physiology Laboratory, University of Houston, Houston, Texas
77204, USA

Appendix Text

##  S1 MeSH cluster dynamics indicate periods of knowledge network
reorganization.

The knowledge network dynamics, in particular bursts of cluster size variation
exhibited in Figure 2(D), allude to paradigm shifts mediated by scientific
discovery. To identify particularly disruptive periods in the knowledge
network, we developed a network method for identifying fluctuations of
individual MeSH constituents across clusters by tracking the entry and exit of
constituents between sequential 1-year periods.

To systematically track relations between MeSH branches, at either the $L_{1}$
or $L_{2}$ level, this straightforward method requires a flexible system for
labeling clusters. To this end we designed a cluster-tagging method that first
relies on identifying the stable subclusters, or cliques. In the present case,
these cliques correspond to MeSH that are always observed in the same cluster
together – in particular within co-occurrence clusters calculated at the
1-year level.

Figure S6(A) shows the MeSH cliques for the $L_{1}$ and $L_{2}$ levels. For
example, an interesting cross-SA clique observed at the $L_{2}$ level is the
dyad formed by “Technology, Industry, and Agriculture” (J01) and “Biomedical
and Dental Materials” (D25); another mono-SA clique is the one formed by seven
$L_{2}$ branches (D01, D02, D03, D04, D09, D10, D27), all from the $L_{1}$
D-branch. Hence, these stationary cliques are motifs that uniquely identify an
arbitrary cluster $C_{x}$ according to its constituent cliques.

By way of example, Fig. S6(B) shows the cluster $C_{c}$ which contains the
D-clique described above in two subsequent years. Consequently, an arbitrary
MeSH denoted by $i$ belonging to $C_{c}$ in year $t$ and $t+1$ is stationary
with respect to the cliques. Alternatively, consider an arbitrary MeSH $j$
which was a member of $C_{a}$ (identified by two particular cliques) and
$C_{e}$ in the next year (identified by two cliques, one from $C_{a}$ and one
altogether new one). In this case, the MeSH $j$ (indicated by orange) has
partially switched clusters. Finally, consider an arbitrary MeSH $k$
(indicated by red) which was a member of $C_{b}$ (identified by a single
clique) and $C_{d}$ in the next year (identified by a completely different
clique); this case corresponds to minimal continuity (maximal discontinuity)
with respect to cluster member cliques.

To quantify aggregate cluster dynamics, we assign each MeSH (represented
generically by the index $m$) a set of labels $Q_{m,t}=\\{q_{1},...,q_{n}\\}$
corresponding to each of the $n$ unique cliques present, as indicated by $q$,
for a given year $t$. We then calculate the Jaccard distance $\Delta
J_{m}=1-|Q_{m,t}\cap Q_{m,t+1}|/|Q_{m,t}\cup Q_{m,t+1}|$. Hence, $\Delta
J_{m}=0$ corresponds to maximal continuity (since $|Q_{m,t}\cap
Q_{m,t+1}|=|Q_{m,t}\cup Q_{m,t+1}|$). Conversely, $\Delta J_{m}=1$ corresponds
to maximal discontinuity (since $|Q_{m,t}\cap Q_{m,t+1}|=0$). When there is a
partial shift in cluster member cliques, then we obtain intermediate values,
$0<\Delta J_{m}<1$.

Figure S6(C) indicates the periods with the highest levels of MeSH network
reorganization, characterized by $\Delta J_{m}>0$ values (indicated by orange
and red curves). These results are consistent for both the e $L_{1}$ and
$L_{2}$ resolution levels. MeSH data aggregated at the $L_{1}$ level indicates
a period of heightened MeSH cluster dynamics starting in the roughly 2000 and
continuing in bursts up to present. Additional inspection at the $L_{2}$ level
indicates periodic fluctuations occurring over time, but again with heightened
turbulence in the early 1980s, and in the years around 2010. We interpret
these heightened periods of MeSH cluster discontinuity as indicators of
individual MeSH that emerge as cross-cluster knowledge bridges that integrate
distinct knowledge domains, a hallmark of biomedical convergence in topical SA
space. As such, the objective of this method is to the objective of which is
to identify and justify disruptive periods analyzed in detail in the following
sections.

##  S2 Techno-informatic capabilities facilitate biomedical convergence around
brain, behavior and health science.

Concurrent co-occurrence of MeSH pairs (denoted by $j$ and $j^{\prime}$) that
are close neighbors of a given MeSH (i.e., the ego node, $i$) is indicative of
recombinant knowledge domains mediated by $i$. To analyze this triadic closure
phenomena as it relates to cross-domain convergence, we explored dynamic
patterns occurring in the subset of ${\bf M}^{(2)}_{jj^{\prime}}$ values among
the most prominent co-occurring neighbors of a given MeSH. In particular, we
focused on the co-occurrence dynamics for each of the convergence bridges
identified in Fig. 3.

For each convergence bridge MeSH, we then selected the ten most frequently co-
occurring MeSH for the denoted period. Figure S4 shows the subset of ${\bf
M}^{(2)}$ values visualized as a subnetwork. For a given period, the top ten
co-occurring neighbors ($j$) are sorted in clockwise fashion starting from the
top, with nodes sized proportional to ${\bf M}^{(2)}_{ij}$. To facilitate
visual inspection, each MeSH’s SA is indicated by its node/label color. Links
are plotted with thickness and shade proportional to ${\bf
M}^{(2)}_{jj^{\prime}}$, thereby indicating the cross-domain linkages among
prominent neighbors that are facilitated by $i$. Each node includes its MeSH
identifier and a knowledge cluster identifier, the latter indicated by a gray
scale gradient.

The most significant feature of each convergence bridge are as follows:
“Investigative Techniques” (E05) integrate all clusters with high SA
diversity. “Behavior and Behavior Mechanisms” (F01) integrates health,
“Physiological Phenomena”, “Eukaryotes” and “Pathological Conditions, Signs
and Symptoms” domains. F01 and “Psychological Phenomena” (F02) increasingly
incorporate “Information Science” (L01) and “Investigative Techniques”.
“Physiological Phenomena” (G07), which exhibits a high co-occurrence with
“Food and Beverages” research, representing the increasingly lucrative domain
of human health science, also exhibits high diversity of cross-SA and cross-
cluster. “Technology, Industry, and Agriculture” (J01) increasingly integrates
from the 1990s onward with the “Chemical and Drugs” domain, highlighting the
role of academic-industry-government cross-industry triple-helix
etzkowitz2000dynamics ; leydesdorff1996emergence  underlying the
pharmaceutical industry. L01 integrates with “Mathematical Concepts” to
facilitate research investigating “Behavior and Behavior Mechanisms” by
leveraging technology providing non-invasive “Investigative Techniques’. And
both “Health Services Administration” (N04) and “Health Care Quality, Access,
and Evaluation” (N05), which have become highly coupled mirrors of each other,
have in the last decade incorporated “Information Science” methods for
clinical diagnosis and classification of “Pathological Conditions, Signs and
Symptoms” and overall health care program assessment.

##  S3 Outer-product method for measuring categorical diversity and disparity.

We leverage a generic tensor-product method that takes as input a weighted
vector and yields a scalar diversity measure based upon categorical mixing.
While the result of our approach is nearly identical to the Blau index (also
referred to as the Gini-Simpson index), our diversity measure is motivated by
way of dyadic co-occurrence rather than the standard formulation motivated
around repeated sampling. Within the present context, the weighted vector of
category counts is the SA decomposition of an article, given by
$\vec{SA}_{p}^{(1)}$ or $\vec{SA}_{p}^{(2)}$. The resulting metric,
represented by $f_{D,p}$, quantifies the degree of cross-domain co-occurrence
and is a bounded statistic in the range $[0,1)$.

Calculating $f_{D,p}$ begins with the outer-product
$\vec{SA}_{p}\otimes\vec{SA}_{p}$, where $\otimes$ is the outer tensor
product. The resulting matrix represents dyadic combinations of categories as
opposed to permutations (i.e., capturing the subtle difference between an
undirected and directed network). While we did not explore it further, this
matrix formulation may also give rise to higher-order measures of diversity
associated with the eigenvalues of the outer-product matrix.

We normalize the resulting outer-product matrix so that our analysis is not
systematically biased by increase in the number of MeSH per paper over time;
see petersen2016triple  for secular growth in the number of MeSH per article,
reflecting growth of the MeSH ontology accompanied by growth in the length and
breadth of published research. All steps together, the normalized co-
occurrence matrix ${\bf D}_{p}$ is given by

$\displaystyle{\bf
D}_{p}\equiv\frac{U(\vec{SA}_{p}\otimes\vec{SA}_{p})}{||U(\vec{SA}_{p}\otimes\vec{SA}_{p})||}\
.$ (S1)

Without loss of generality, this definition involves $U({\bf G})$, an operator
yielding the upper-diagonal elements of the arbitrary matrix ${\bf G}$ (i.e.,
representing the undirected co-occurrence network among subcategories);
$||...||$ indicates the matrix total calculated by summing across all matrix
elements. The subtle difference between the Blau index arises from $U({\bf
G})$, which is imposed to capture the difference between combinations rather
than permutations (or directed versus undirected network). Hence, this
perspective offers a new pathway to this fundamental diversity measure by way
of co-occurrence rather than repeated sampling.

Hence, ${\bf D}_{p}(\vec{SA}_{p})$ tabulates the weighted product across all
undirected SA-SA pairs. We then define the co-occurrence diversity as the
scalar quantity given by

$\displaystyle f_{D,p}=1-\mathrm{Tr}({\bf D}_{p})\in[0,1)\ ,$ (S2)

where $\mathrm{Tr}$ is the matrix trace, corresponding to the sum of diagonal
elements in ${\bf D}_{p}$. Hence, $f_{D,p}$ is the tally of off-diagonal
elements in ${\bf D}$. Articles featuring a single SA have value $f_{D,p}=0$,
whereas articles featuring multiple SA have values in the range $0<f_{D,p}<1$.
Regarding the upper limit, when all vector elements have equal values then
$f_{D,p}=(d-1)/(d+1)$, where $d$ is the dimension of the categorical vector
(for the Blau index the upper limit is instead d-1/d). In the present case
$d=10$ and so the maximum $f_{D,p}$ value is 9/11. The average article
diversity by publication year, denoted by $\langle f_{D}(t)\rangle$, is
representative of a characteristic article since $f_{D,p}\in[0,1)$ is bounded.

By way of example, consider a decomposition across only 6 SA, and the
particular case of an article with 4 MeSH belonging to 3 different SA, e.g.
$\vec{SA}_{p}=\\{1,2,0,0,1,0\\}$. Calculation of the co-occurrence matrix
${\bf D}_{p}(\vec{SA}_{p})$ in Eq. (S1) yields

${\bf D}_{p}(\vec{SA}_{p})=$
$\left(\begin{array}[]{cccccc}\frac{1}{11}&\frac{2}{11}&0&0&\frac{1}{11}&0\\\
\\\ 0&\frac{4}{11}&0&0&\frac{2}{11}&0\\\ \\\ 0&0&0&0&0&0\\\ \\\ 0&0&0&0&0&0\\\
\\\ 0&0&0&0&\frac{1}{11}&0\\\ \\\ 0&0&0&0&0&0\\\ \end{array}\right)$

with $||U(\vec{SA}_{p}\otimes\vec{SA})||=11$. The categorical diversity is the
total across the off-diagonal elements, $f_{D,p}=5/11$.

For comparison, consider the representation of an article with the same number
of metadata entities that all fall into just the second category,
$\vec{SA}_{p}=\\{0,4,0,0,0,0\\}$. In which case

${\bf D}_{p}(\vec{SA}_{p})=$ $\left(\begin{array}[]{cccccc}0&0&0&0&0&0\\\ \\\
0&1&0&0&0&0\\\ \\\ 0&0&0&0&0&0\\\ \\\ 0&0&0&0&0&0\\\ \\\ 0&0&0&0&0&0\\\ \\\
0&0&0&0&0&0\\\ \end{array}\right)$

and so $f_{D,p}=1-1=0$.

What does this measure measure? Notably, $f_{D,p}$ accounts for both
categorical differences (Shannon-like) and concentration disparity (Gini-like)
harrison2007s . One the first hand, articles with more variation in SA
categories will correspond to larger $f_{D,p}$ values, as the number of non-
zero off-diagonal elements is proportional to ${{M_{p}}\choose{2}}\sim
M_{p}^{2}$, where $M_{p}$ is the number of distinct SA present, which
contributes to larger $f_{D,p}$; and on the second hand, the off-diagonal
elements will be relatively larger in combination if the count values
contained in $SA_{2}$ are more evenly distributed, i.e., are not highly
concentrated in just one category.

Figure S1: Schematic representation of the quasi-hierarchical MeSH tree. We
restrict this illustration to MeSH belonging to the core biomedical branches
$\alpha=\\{A,B,C,D,E,G\\}$. The location of each MeSH $m$ is given by the set
of locations of the parent nodes directly above it. For example the MeSH
“Overnutrition” with Tree Number C18.654.726 is located at the third level,
and has daughter MeSH “Obesity” which has four Tree Numbers corresponding to
three distinct branches (C, E and G): C18.654.726.500, C23.888.144.699.500,
E01.370.600.115.100.160.120.699.500, G07.100.100.160.120.699.500. Hence, this
particular MeSH maps onto three $L_{1}$ branches represented by
$\vec{SA}^{(1)}=$ {0,0,2,0,1,0,1,0,0,0}.  Figure S2: Structure and
interconnectivity of the MeSH knowledge network.(A) Network visualization of
the MeSH branches $\alpha_{i}=\\{A,B,C,D,E,G\\}$. Size and color of nodes is
proportional to the in-degree of the MeSH term (from higher tree levels). The
color of the link is associated with the branch classification of the parent
node. (B) MeSH network with most prominent nodes labeled for visual
inspection. (C) The network of links that span different tree branches,
$\alpha_{i}\leftrightarrow\alpha_{j}$.  Figure S3:  MeSH with high bridge rank
and significant trends – by knowledge cluster. Evolution of knowledge bridge
ranks for individual MeSH that feature either sustained high bridge rank or
significant positive (indicated by green) or negative (indicated by red) rank
change over the entire period of analysis.  Figure S4:  Temporal network
dynamics for 8 convergence bridges. Each row illustrates a MeSH term ($i$)
identified as a convergence bridge. Each network is calculated using data from
the indicated period, and shows the ten most frequently co-occurring MeSH –
sorted clockwise, starting from the top, with nodes sized proportional to
${\bf M}^{(2)}_{ij}$; each MeSH’s SA is indicated by its node/label color.
Links are plotted with thickness and shade proportional to ${\bf
M}^{(2)}_{jj^{\prime}}$, thereby indicating the cross-domain linkages among
prominent neighbors that are facilitated by $i$. Each node includes its MeSH
identifier and a knowledge cluster identifier, the latter indicated by a gray
scale gradient. For example, MeSH J01 “Technology, Industry, and Agriculture”
(which is a member of $C3$ for the first three periods and subsequently
transitioning to $C1$ in the most recent period) is highly connected to MeSH
from all other clusters (C1-C3), in particular to L01 until its disassociation
in the most recent period 2010-2018; interestingly, L01 “Information Science”
diverged from $J01$ as early as the first period 1970-1989, subsequently
becoming more strongly coupled with members of branch E and G.  Figure S5:
Cross-domain knowledge integration – supporting analysis. (A) Analog to Fig.
4(A) but calculated using all MeSH (i.e., analyzing MeSH independent of
Major/Minor status). (B) Probability distribution $P(f_{D,p})$ for each of the
3-year subsamples analyzed in Fig. 4(B). One notable shift is the decreased
prevalence of mono-domain articles ($f_{D,p}=0$) which is a large but not sole
contributor to the increasing trend in average value, $\langle
f_{D}(t)\rangle$ (shown as horizontal vertical dashed lines). Nevertheless,
the right tail of the distribution is well defined and does not increase
dramatically in range (i.e., the max diversity value is persistently around
the value 0.9). The peak around value 1/3 (1/2) corresponds to articles with
MeSH contributing equally to two (three) distinct SA and represents the first
(second) mode of cross-domain convergence. (C) Robustness check for Fig. 4(C),
showing positive relationship between average team size and cross-domain SA
diversity calculated at the journal level (ANOVA p-val.= 0.017; shaded region
is 99% CI). (D) Ten biomedical journals featuring the highest growth in
average $f_{D,p}$ values over 1970-2018.  Figure S6:  Method for quantifying
fluctuations of individual MeSH across knowledge clusters. Reorganization of
co-occurrence networks are indicative of paradigmatic disruption and cross-
domain bridge formation. Stable subclusters are groups of MeSH that always
appear together in annual-level co-occurrence matrix Louvain clustering – see
Fig. 2(C). These cliques are used as an unique identification system for
calculating the cluster continuity $\Delta J_{m}$ of a given MeSH term $m$
over sequential 1-year periods. (A) Cliques for the period 1970-2018
calculated for the $L_{1}$ (left) and $L_{2}$ (right) levels. (B) Schematic of
the identification system for tracking cluster dynamics of individual $m$. For
example, comparing MeSH $i$ for the sequential year $t$ and $t+1$ periods, $i$
stayed in the cluster $C_{c}$ (identified as having the D-clique comprised of
seven $L_{2}$ MeSH from the D-branch) and so there is maximal continuity of
the cliques defining its surrounding cluster. Contrariwise, MeSH $k$
transitioned from a cluster in $t$ defined by a single clique that differs
from the clique defining its cluster in $t+1$; hence, this case corresponds to
minimal continuity. The case of MeSH $j$ is inbetween these extreme cases,
whereby $j$ transitions from a cluster in $t$ that shares a common clique as
the cluster in $t+1$, but with differing second member clique. (C) Frequency
distribution of continuity values $\Delta J_{m}$ by year. Years with low MeSH
cluster continuity feature higher frequencies of MeSH that switch knowledge
clusters entirely (red) or partially (orange); conversely, periods with high
cluster continuity, in which all $m$ stay in the same cluster, corresponds to
the gray curve approaching unity. The period with the highest levels of
knowledge cluster discontinuity started in the early-2000s and peaked around
2010. Discontinuity peaks indicate the emergence of individual MeSH serving as
cross-cluster bridges.  Table S1:  Top-20 Convergent Journals. Biomedical
journals in the top-100 2018 JCR Impact Factor, ranked according to average
categorical SA diversity over the period 1970 to 2018.

Journal ($j$) | Average SA diversity
---|---
| $\langle f_{D}\rangle_{j,1970-2018}$
Circ. Res. | 0.556
J. Clin. Oncol. | 0.549
J. Am. Coll. Cardiol. | 0.511
Acta. Neuropathol. | 0.509
Nat. Genet. | 0.506
Gut | 0.493
PNAS | 0.483
Science | 0.481
Ann. Intern. Med. | 0.474
N. Engl. J. Med. | 0.466
Cell | 0.466
Nature | 0.464
Eur. Heart J. | 0.462
BMJ | 0.459
Endocr. Rev. | 0.456
Lancet | 0.452
Clin. Microbiol. Rev. | 0.436
Physiol. Rev. | 0.434
Annu. Rev. Immunol. | 0.400
CA. Cancer J. Clin. | 0.389