and one-half appeared as institutional differences
within a given field (e.g., university patents in
materials science had lower D than firms’ patents
in materials science).
We next considered the institutional “hand-off”
across the boundary where D ¼ 1. For D ¼ 1
patents, 78% were assigned to firms, yet 80% of
D ¼ 1 papers had university authors (Fig. 4B).
The prevalence of hand-offs from university
papers to business patents is consistent with
long-standing conceptions that consider university outputs as public goods upon which marketplace invention can draw (1). Thus, although
university patenting is particularly closely related to science (Fig. 4A) and can thus play a direct
role in technology transfer (35, 36), the lion’s
share of D ¼ 1 patents still comes from firms.
Related, other patents typically connected to the
patent-paper frontier through these D ¼ 1 firm
patents (fig. S6).
Figure 4C examines the role of the same individual in spanning the paper-patent boundary. We define these cases by matching the
inventor names for the patent with the author
names for the paper that the patent cites (see
supplementary materials for further discussion). For D ¼ 1 university patents, 55.4% cited
a paper written by an individual with the same
name. A high percentage also appeared for
government patents, but the percentage fell to
14.3% for D ¼ 1 corporate patents. In Stokes’s
theoretical characterization of “Pasteur’s quadrant” (2), where the same individual may be
engaged in advancing both understanding and
use, universities and government laboratories
appear to be especially common homes for such
individuals, who in turn appear highly productive.
Figure S7 and table S10 show that both the paper
and the patent produced by such an individual
were especially likely to be home runs in their
Contrary to conceptions in which technological and scientific progress operate in independent spheres, we find majority connectivity between
the corpus of patented inventions and the corpus
of scientific papers. However, these connections
are typically indirect, and both scientific fields
and patenting technology classes vary enormously
in their connectivity and proximity to the other
domain. These findings are consistent with and
can help quantify some features of the “linear
model” of science, which imagines that scientists
typically work to advance understanding but that
such advances may underlie practical applications, often in indirect or unexpected ways. The
prevalence of private-sector patents linking back
to the output of universities and government laboratories is further consistent with institutional
views of the linear model. Although these features of the linear model appear to receive strong
support, our data do not address potentially “
nonlinear” reverse linkages where technological advances, including new equipment and tools, may
also drive scientific progress (7, 11, 17).
The distance metric further reveals facts that
are consistent with and help quantify the fruitful,
creative interplay between understanding and
application (2, 19, 21). Patented inventions that
draw directly on scientific advances were espe-
cially impactful compared to other patents. More-
over, papers directly cited by patents were also
the highest-impact papers within the scientific
domain. These facts are consistent with a sharp
complementarity between understanding and use
and are also reflected at the individual level; an
individual scientist/inventor, especially in univer-
sity and government laboratory settings, often
personally spanned the boundary, working to
advance both the scientific and technological
frontiers and managing to hit “home runs” in
Beyond loose classifications of “basic” or “ap-
plied” research and related terminologies (6, 7),
the distance metric provides a quantifiable typol-
ogy to describe R&D outputs and the nature of
their impacts. The typology can characterize the
research outputs of not only fields but also
journals, funders, research institutions, and in-
dividuals themselves. Indices based on the D
metric may thus present useful tools for under-
standing and evaluating types of research, in-
stitutional priorities, funding outcomes, and
individual careers. While the distance metric
in our application uses a directed graph, from
patented invention to scientific advance, one
may also deploy the metric on knowledge net-
works built using other link definitions. For ex-
ample, full text analyses might allow one to
characterize “necessary” precursor knowledge
as opposed to the standard of “relevant” pre-
cursor knowledge that appears to be indicated
by citation networks (see supplementary ma-
terials discussion). One might also build a metric
that runs from scientific advances back to prior
patented technologies, given appropriate reference
information. And one might consider inventions
or other applications outside patents. Such studies
would further enrich our understanding of the
interplay between scientific advance and tech-
nological progress to engage additional theo-
ries (11, 17).
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We gratefully acknowledge support from the Alfred P. Sloan
Foundation under award G-2015-14014 and support from
the Northwestern Institute on Complex Systems. We thank
workshop participants at the National Academy of Sciences,
the European Policy for Intellectual Property Association,
the Northwestern Institute for Complex Research, the
Institute for Policy Research, P. Azoulay, A. Jaffe, A. Marco,
M. Trajtenberg, and B. Uzzi for helpful comments. We are
especially grateful to R. Gaetani for help with patent data.
The Web of Science data are available via Thomson Reuters.
The patent data sets are available publicly as discussed in the
supplementary materials. The constructed D metric variables
are available from the authors: firstname.lastname@example.org.
edu (corresponding author) and mohammad.ahmadpoor@
Materials and Methods
Figs. S1 to S9
Tables S1 to S10
9 February 2017; accepted 10 July 2017