science by other nations (including China, South Korea, India, and Brazil) has been even more rapid (1, 2) . The share of international collaborations has also increased, as has the share of citations to papers with foreign authors (1, 2) . This spread of knowledge production has not been unexpected. It was anticipated long ago that improved communication technologies would make it easier to learn about new discoveries regardless of location and that this would lead to the pursuit of creative work in more diverse places (3) .
While this perspective suggests a diminishing influence for location in scientific work, location may in fact continue to have considerable import in science. This is because learning about which new ideas exist may not have been an important benefit of location for quite some time and because location likely still impacts the fertility of creative work in other important ways (4) .
One potential remaining influence of location stems from the fact that when new ideas are first discovered, they are often raw and poorly understood. The ideas only gradually mature into useful advances after a community of scientists tries them out and develops them. But such work is hard, harder than work that builds on well-established ideas. Thus, when a scientist seeks to build on a recent advance, it is beneficial to be surrounded by a community of scholars with whom to debate about which new ideas to try out and how (3) (4) (5) (6) (7) (8) . Daily interactions with colleagues, the training environment, and ready access to potential collaborators are therefore especially important in scientific work that is closer to the edge of the scientific frontier in the sense that it builds on recent advances. Because such local factors influence the fertility of the debates that seek to unlock the mysteries of new ideas, the tendency to work with new ideas can be expected to vary by location. This mechanism -and thus the import of location -may even be increasingly influential. For increases in training times, specialization, and teamwork indicate that reaching the edge of the frontier now involves even more work than before (10). Therefore, even as the pursuit of science spreads to more diverse places, location may well continue to have an important influence on what kind of science is pursued -through the impact that location may have on the ability to work with novel ideas. Identifying where barriers to knowledge adoption still exist is thus crucial for understanding the role of location in knowledge production and for designing policies that can help eliminate the remaining barriers.
We calculate each nation's propensity to publish biomedical work that is close to the edge of the scientific frontier in the sense that it builds on relatively recent ideas. The results reveal each nation's position on the scientific frontier: what share of its contributions to biomedical science build on relatively new ideas vs. well-established ideas. We refer to the constructed measure as the edge factor. Whereas the familiar impact factor measures scientific influence (11, 12) , the edge factor measures an aspect of novelty of scientific work -the tendency to build on ideas close to the edge of the scientific frontier. These measures capture distinct aspects of science and are complementary tools in policy evaluation and design (13). A feature shared by them is that for each entity both measures quantify the average of a characteristic.
Our empirical analysis is focused on biomedicine because it is an important area of science and because of the availability of the Pubmed/MEDLINE database on over 24 million biomedical research papers. We use text analysis to determine the ideas that each paper built upon and also the vintage of those ideas (see Methods and Materials) . Location of each contribution is assigned based on the affiliation of the first author of the paper. We select countries as the unit of analysis because borders continue to influence scientist interactions and because many important science policy decisions are set at the national level. The results show that the United States and South Korea have the most advanced positions on the scientific frontier: scientists working in these nations build on cutting-edge ideas more often than do scientists in other locations. The propensity for novel science is well above average also in Singapore and Taiwan. Countries that come after these four countries have approximately average propensity for novel science. Such countries include China, Canada, most western European countries (including the United Kingdom and Germany), Australia, and South Africa. Other countries (including Turkey, India, Brazil, and Iran) come further behindscientists in these countries have clearly below average propensities for novel work. Confidence intervals and results for alternative specifications (shown in Table S4 ) indicate that in most cases these results are robust (the one exception is Saudi Arabia, for which results from alternative specifications suggest a below average tendency for novel work). Countries examined here thus have quite different propensities for work with newer ideas in biomedicine. This indicates that location continues to exert considerable influence on what kind of science is pursued.
Furthermore, even developed nations are not on an equal footing in the pursuit of novel scientific work: in some developed nations scientists take advantage of opportunities created by the arrival of new ideas much more often than do scientists in other nations. Figure 2 shows the change in the edge factor for each nation from the 1990s to present.
South Korea, Taiwan, and China have leapfrogged most developed nations. Whereas the United States is still among the leaders, the relative positions of Switzerland and the United Kingdom are less advanced now than they were in the 1990s. Overall some convergence appears to have taken place as the lagging nations are no longer as far behind the leaders, suggesting that the world of ideas may have become somewhat flatter. Analysis of the edge factor by 5-year time periods (shown in Table S5 ) indicates that most changes that occur are persistent. The changes thus reflect systematic changes in capabilities rather than merely year-to-year random variations.
In our approach, we compare each contribution only to other contributions that use ideas from the same idea category and are linked to the same research area (the 127 idea categories include "Amino Acid, Peptide, or Protein" and "Pharmacologic Substance"; the 125 research areas include "Biochemistry" and "Neoplasms"; see Tables S1 and S2 for the full lists). Table 1 shows the edge factor separately for four groupings of idea categories: "Clinical and Anatomy", "Drugs and Chemicals", "Basic Science and Research Tools", and "Miscellaneous", and for three groupings of research areas: "Applied", "Basic Science", and "Other (Both Applied and Basic Science)". For most nations the edge factor is similar across these groupings, suggesting that the pursuit of novel work is generally dependent on capabilities that some countries possess but others lack. One important exception is China. China's contributions linked to the idea category grouping "Basic Science and Research Tools" now have the second highest propensity for novel work (after Singapore), but its contributions linked to idea category groupings "Clinical and Anatomy" and "Drugs and Chemicals" are well below average in terms of their novelty. This result serves to highlight an important feature of our approach: it can be used to reveal not just whether a nation is facing barriers in new idea adoption but where in the idea space those barriers lie.
While our results show that differences persist even among developed nations in their propensity to work with new ideas, the results do not reveal the specific mechanisms driving these differences. One potential driver of these cross-locational differences stems from the difficulty of working with new ideas. Because novel science is harder than conventional science, novel science is more dependent on interactions with colleagues. The fertility of these scientist interactions depends on factors such as the extent of complementary tacit knowledge that is embedded in people and is transferred to others in meetings (5, 16) . Cross-national variation in the extent and depth of human capital investments can thus lead to cross-national variation in the tendency to adopt new ideas (17).
Willingness to try out new ideas can vary by location also due to differences in scientist demographics. For example, given that early-career scientists are the most likely to work with new ideas (9), and given that the increase in the extent of science in China is so recent and thus many of its scientists are early on their careers, the novelty of science in China may be driven in part by the youth of its scientists. Cross-national differences in new idea adoption and China's remarkably ability to leapfrog in this regard may also be driven in part by differences in incentives to pursue novel work: it has long been understood that nations without vested interests in existing technologies have an elevated incentive to explore new ideas (18, 19) . Some of the variation in new idea adoption can also be driven by variation in where the ideas are first born, and by remaining delays in the spread of awareness about which new ideas exist.
Our results are consistent with findings from recent related work that measured the complexity of each country's production structure based on its exports and found large differences in the capabilities of nations (20). Their analysis was motivated by the idea that a nation's capabilities determine the input varieties that can be fruitfully used in production. Our work, by contrast, is motivated by the idea that capabilities determine whether a nation's scientists can take advantage of the opportunities created by the arrival of new ideas. Moreover, whereas in this related work the complexity of goods production is measured indirectly based on exports, the edge factor is calculated directly based on the measured idea inputs. Common to these analyses is the belief that the capabilities of a nation affect which inputs it uses and both analyses are aimed at constructing new measures that reflect those capabilities.
Our finding that nations continue to differ in their ability to pursue novel science is in line with cross-country comparisons of scientific impact as measured by citations (1, 2) . The ability to take advantage of scientific opportunities continues to vary across locations in spite of the "death of distance" phenomenon, because locational differences in capabilities persist (21-24). But some aspects of our results also differ from the results obtained through traditional analyses of scientific productivity. Data on the tendency to produce highly cited papers point to the United States as a leader that remains far ahead of most western European nations and even further ahead of South Korea, Taiwan and China (1, 2, (25) (26) (27) . Our analysis on the use of new ideas, by contrast, suggests that South Korea, Taiwan and China have caught up with western Europe and are now close to the United States in terms of their tendency to work with cutting-edge ideas.
Moreover, we find that China is now a leader in favoring newer ideas when working with new basic science ideas and research tools. The finding that some countries are among the leaders in terms of their edge factor but lag in terms of their impact is not surprising (28). For work on an idea early -when the idea is still raw -may well have less impact than work that builds on more established ideas which properties are better understood. The early work on the idea is still crucial: it helps the idea develop and thus makes more significant advances possible. Moreover, countries investing heavily in novel science can reap significant benefits also for themselves from their focus: early work on an idea can help the country develop capabilities that enable it to take advantage of the later, more fertile, opportunities linked to the same idea.
Because the edge factor captures an aspect of science that is distinct from impact, it has potential applications also beyond cross-national comparisons. This is important because the obsession with impact -decried even by an editor of Science (34) -may have led to less healthy science: the rise of citation metrics coincided with a decline in the novelty of biomedicine (31).
A singular focus on citation counts can lead to stagnant science because impact factors underreward scientists who try out new ideas, thereby stifling work that helps ideas mature and makes more meaningful advances possible (14,15). By using measures like the edge factor in conjunction with impact-based metrics, university administrators and funding agencies can strike a better balance between rewarding innovative but risky work that develops ideas early on and rewarding work that takes advantage of the ideas in their more mature stages.
6. Thomas S. Kuhn, Objectivity, Value Judgment and Theory Choice; (in Thomas S. Kuhn, ed., The Essential Tension, University of Chicago Press, Chicago, pp. 320-339, 1977) 7. Abbott P. Usher, A History of Mechanical Inventions (McGraw-Hill, New York, 1929) . 8. One indication that work that tries out new ideas is indeed harder than more conventional science is that the trying out of new ideas is linked with larger team size (9). 108-111 (1955) .
12. Eugene Garfield, Citation Analyses as a Tool in Journal Evaluation, Science 178, 471-478 (1972) .
13. Optimal science policy requires that both influence and novelty are rewarded. One reason why rewarding influence alone is not enough is that rewarding novelty directly helps solve a coordination problem that is inherent in the formation of a vibrant scientific community to a new area of investigation (14, 15) . Moreover, useful work that tries out a new idea need not be influential in the traditional sense; such work can have scientific value -in terms of helping unlock the mysteries of the new idea -even when it merely demonstrates which research paths do not work. 17. Of course, not all fruitful interactions are limited by location, as is evidenced by the fact that a quarter of science now involves international collaborations (1, 2) . However, the rise of long-distance collaborations can also be a source of cross-national differences in new idea 28. Prior work too has found novelty and impact to correlate only imperfectly (15, 29, 30) .
Novelty has been the focus in also several additional recent analyses (31) (32) (33) 9, 24 Scatter points are colored to indicate edge factors that are well above average (red), about average (grey), and well below average (blue). An edge factor above 100 indicates an above average tendency for work that builds on relatively new ideas (a contribution is considered novel if it is in the top 5% by the age of the newest idea it builds upon; the comparison group for each contribution is all other papers published in the same year and linked to the same (idea category, research area) pair). 
Our source for the research area of each article is the broad subject terms that are assigned by the National Library of Medicine for journals in the MEDLINE database (https://wwwcf.nlm.nih.gov/serials/journals/index.cfm). We show further below how articles in the MEDLINE database are distributed across the journal categories in this database (see section A.4).
As our source for information on which words and word sequences represent meaningful concepts in biomedicine and which concepts are synonyms, we use the 2017 version of the Unified Medical Language System (UMLS) metathesaurus (https://www.nlm.nih.gov/research/umls/). The UMLS metathesaurus links over 5 million terms that appear in one or more of over 150 medical vocabularies.
In addition to determining the synonyms for each term, the UMLS database assigns each term to one or more of 127 semantic types (https://semanticnetwork.nlm.nih.gov). We use the semantic type of each term to determine the idea category represented by the term (see section A.5.4).
Further below we list examples of ideas and idea categories captured by this approach (see section A.5.4).
When we determine the vintage of each idea (section A.5.2), we use the sample of all papers in the MEDLINE database.
By contrast, when we calculate for each location its propensity to publish novel work, we limit the sample of papers in several ways. First, we limit the analysis to original research papers, thereby excluding editorials, reviews, etc. However, in a robustness analysis, we include all papers in the sample. Second, we limit the analysis to papers published during 1988-2016. This is because the coverage for affiliation data in the MEDLINE database begins in 1988. Third, we limit the analysis to papers for which the available text on the title and the abstract of the article in the database includes at least 200 characters and no more than 5000 characters. However, in a robustness analysis, we conduct the analysis without this character limit.
The number of articles that are included in our main specification is shown by publication year in Figure S1 .
We assign each paper to a country based on the affiliation string for the first author of the paper. We limit the analysis to first authors because for most papers published before 2014 the affiliation information in MEDLINE is limited to the first author of each paper. Figure S2 shows by publication year the share of papers that we were able to match to a country. The decrease in the rate of matched papers in recent years is due to the fact that for those years some of the affiliation strings in MEDLINE include the affiliation string for multiple authors.
The form of such entries makes it more difficult to match those papers to a country.
For ease of exposition we limit the number of locations by combining some countries that publish a smaller number of biomedical publications to regions. Figure S3 shows the share of papers by location (country or region) and time period.
We use the journal categories (Broad Subject Terms) to represent the research area of each paper. On average, each original research article published during 2015-2016 is linked to 1.49 journal categories. Table S1 shows the distribution of links from papers to journal categories during this time period. Further below we discuss papers with multiple links or with no links to journal categories are handled (see section A.5.3).
In our main specification, all journal categories are included in the analysis. In secondary analyses, we conduct three separate analyses -each limits the analysis to one of the following three groups of journal categories: "Applied", "Basic Science", and "Other (Both Applied and Basic Science)".
To conduct these secondary analyses, we assign each journal category to one of these three journal category groups. Here we make use of the MeSH keywords affixed to each MEDLINE article and the "A-C-H" model (31) that classifies papers along the translational axis based on the MeSH keywords. Specifically, using the MeSH codes we first determine each paper's position on the translational axis as specified by the A-C-H model:
• We thus construct three separate indicator variables ("H status", "A status", "C status"). In the A-C-H model, papers with "H status" have an applied aspect to them, and papers with either "A status" or "C status" have a basic science aspect to them. More than one of these indicator variables will be positive for papers that have both an applied and a basic science aspect to them.
For each journal category, we next calculate the average of each of these three dummy variables ("H status", "A status", "C status") among all papers linked to that journal category. Denoting these variables as "Average H status", "Average A status", and "Average C status", we use them to classify journal categories to three journal category groups as follows:
• Journal categories that satisfy conditions "Average H status > Average C status" and "Average H status > 0.2" are assigned to journal category group "Applied". • Journal categories that satisfy "Average H status < Average C status" and "Average A status < 0.8" and "Average C status > 0.5" are assigned to journal category group "Basic Science". (We thus exclude journal categories that focus heavily on veterinary medicine from this category even though such journal categories are located early along the translational axis in the A-C-H model; this happens in the A-C-H model because the model does not distinguish between veterinary medicine and animal studies as pre-cursor to human medicine). • The remaining journal categories are assigned to journal group category "Other (Both Applied and Basic Science)".
The result of this approach for determining the journal category group of each journal category is shown in the last column of Table S1 .
We employ text analysis to discern which ideas each research paper built upon. We treat each of the 5+ million terms in the comprehensive United Medical Language System (UMLS) metathesaurus as representing ideas. To identify which of these ideas each research paper in the MEDLINE database built upon, we search the title and abstract of each publication for all the terms in the UMLS metathesaurus.
Thus, the first step in the text analysis is to determine for each article in the MEDLINE database which UMLS terms appear in it. Further below we also show a list of examples of ideas identified by this approach (section A.5.4).
The vintage of the idea represented by a UMLS term is determined based on how long ago the UMLS term was first mentioned in a biomedical research paper. We interpret the mention of a relatively new term as indicative of work that builds on ideas close to the edge of the scientific frontier. We refer to the year of first appearance of a term as the cohort year of the term. In a robustness analysis, we set the cohort year of each term as the earliest year the UMLS term or any of its synonyms appears in the MEDLINE data (synonyms are determined based on the synonym information in the UMLS metathesaurus).
Because of the sparsity of publications in MEDLINE with a publication year before 1946, the cohort year of ideas (i.e. the year of first appearance) does not reflect the ideas' true vintage well for ideas that are new to biomedicine before 1950. Thus, we exclude from the analysis all terms with cohort before 1950.
Further below we show examples of cohort years assigned to terms using this approach (see section A.5.4).
In determining the novelty of biomedical work, we seek to control for the idea category of each idea (we also control for the the research area of the paper). Thus, we aim to compare the use of novel ideas against the use of more established ideas from the same idea category. The rationale for seeking to control for the idea category is the following: how recent ideas should be considered novel depends on what type of an idea it is. For example, a paper that employs a 10year old research tool may represent novel work but the same need not be true for a paper that examines a gene of the same vintage.
To control for the idea category in the present analysis, we take advantage of the fact that the UMLS metathesaurus classifies terms to 127 categories (these categories are listed further below). We treat each of these UMLS categories as representing an idea category.
We make use of these idea categories as follows. After determining which UMLS terms are mentioned in each paper, we determine which UMLS categories are represented by these terms. We then treat a paper that mentions terms from K different idea categories as K separate contributions. The underlying assumption in this approach is that work that mentions at least one idea from an idea category advances our understanding of how ideas from that idea category work. Thus, work that mentions ideas from multiple categories advances our understanding on multiple dimensions. Table S2 shows the number of links to each idea category from papers published during 2015-2016. As was mentioned above in section A.5.2, we only include in the analysis those terms that have cohort year 1950 or later.
In our main analysis, we calculate the overall edge factor based on links to any of the 127 idea categories. In a secondary analysis, we calculate the edge factor separately for each of the following four groupings of idea categories: "Clinical and Anatomy", "Drugs and Chemicals", "Basic Science and Research Tools", and "Miscellaneous". We link each UMLS category to one of these four idea category groups. The last column of Table S2 shows which idea category belongs to which idea category group.
What kind of work should be considered novel is likely to depend also on the research area. For example, use of a 10-year old research tool may be novel work in public health research but not in biotechnology research. To address this issue, we also determine the links from papers to research areas. We use the National Library of Medicine (NLM) journal categories as proxies for research areas (these journal categories were listed in section A.4, Table S1 )
Thus, after determining the ideas mentioned in each paper, we determine which idea categories are linked to these ideas as well as which research areas are linked to the journal where the paper is published. We define a contribution as an (idea category, research area) pair linked to a paper.
In our approach, a paper is considered to contribute to our understanding of all the (idea category, research area) pairs linked to it. A paper can make multiple contributions, depending on how many (idea category, research area) pairs are linked to it. A paper that mentions ideas from K idea categories, and is published in a journal that is linked to J journal categories, is treated as K*J separate contributions.
Note that a paper that mentions multiple ideas from an idea category results in the same number contributions as a paper that mentions only one idea from the idea category.
The number of links listed in the second column of Table S1 is the number of links to (idea category, research area) pairs associated with each research area. Similarly,tThe number of links listed in the second column of Table S2 is the number of links to (idea category, research area) pairs associated with each idea category. On average, each paper published during 2015-2016 is linked to linked to 6.26 (idea category, research area) pairs. Therefore, in our approach each paper is, on average, counted as 6.26 contributions.
When determining whether a contribution represents novel work, we only consider the age of the newest term linked to the (idea category, research area) pair from the paper in question.
Researcher's choice is between using any new ideas or only well-established ideas from this idea category. This is discussed in more detail next.
Above we defined a contribution as a link from a paper to an (idea category, research area) pair; these links are inferred from the UMLS terms that appear in the title and abstract of the paper. The novelty of each contribution is determined in three steps.
Step 1. Age of each UMLS term that links a paper to the (idea category, research area) pair. First, for each contribution associated with a paper, we determine the age of each term that links the paper to the (idea category, research area) pair in question. Age of each term is calculated by subtracting the cohort year of the term from the publication year of the paper.
Step 2. Age of the newest UMLS term that links a paper to the (idea category, research area) pair. Second, for each contribution we determine the age of the newest term that links the paper to the (idea category, research area) pair. We refer to the cohort year of the newest term that links a paper to the (idea category, research area) pair as the cohort year of the contribution.
Step 3. Novelty of the contribution relative to other contributions to the (idea category, research area) pair among papers published in the same year. The relative novelty of a contribution is then determined by comparing the vintage of the contribution to the vintages of all the other contributions linked to the same (idea category, research area) pair, among papers published in the same year. The interpretation is that a paper that links to an idea category reflects a choice faced by a scientist: one can choose work with at least one relatively new idea from this idea category, or one can choose to work with only well-established ideas from this idea category. The comparison is also limited by research area because whether the use of an idea represents novel work is expected to depend on the context where it is used. The reason for limiting the comparison to papers published in the same year is obvious: because the rate of scientific progress need not be the same over time, the use of a 10-year old research tool may represent novel work in one year but not in some other year.
Having determined all contributions linked to an (idea category, research area) pair among papers published in the same year, we order the contributions based on their vintage (age of the newest term linked to that (idea category, research area) pair from each paper). We then construct an indicator variable that captures the relative novelty of each contribution: in our baseline specification, contributions that are in the top 5% based on their vintage are considered novel work (the indicator variable is 1 for such contributions and 0 otherwise). In robustness analyses, we construct the indicator variable using alternative choices for the cutoff percentile (top 1%, top 5%, or top 20%) Figure S4 shows Contributions with a cohort between these extremes are sometimes novel and other times not. This is because novelty is calculated by comparing the vintage of a contribution to the vintage of other contributions linked to the same (idea category, research area) pair. Hence, the cutoff cohort for novel contributions varies across (idea category, research area) pairs. Table S3 shows examples of ideas, as represented by UMLS terms, captured by our approach. The table also shows the idea category of each term. Some terms appear multiple times because these terms are linked to multiple UMLS categories by the UMLS metathesaurus. As in related prior work (15), the list of terms shows that the approach used here captures ideas that are widely recognized to have been important inputs in biomedical work in recent decades (for expositional reasons the list is focused on popular ideas -there are of course also many unpopular, less important ideas that are captured by our approach) and that for most terms the cohort year assigned to the term reflects the era when the idea represented by the term entered biomedicine.
A.6.1 Novelty of a nation's contributions linked to a specific each (idea category, research area) pair
Having determined the contributions of each paper (i.e. which (idea category, research area) pairs are linked to from each paper) and which contributions are novel (i.e. which contributions have the top 5% status based on their vintage), we next normalize the novelty variable within contributions to each (idea category, research area) pair so that the average of the normalized novelty variable is 100 within each (idea category, research area) pair. In implementing the normalization, we combine data from multiple years. For example, in our main specification we combine data from 2015-2016.
Location-level novelty scores for each (idea category, research area) pair. Using the normalized contribution-level novelty variable, we then calculate for each location its propensity for novel work within each (idea category, research area) pair. That is, for each location we calculate the mean of the normalized novelty variable based on all of the location's contributions linked to a specific (idea category, research area) pair. We refer to each such average of the novelty variables as the edge factor of the location for the specific (idea category, research area) pair. An edge factor above (below) 100 indicates an above (below) average tendency for work that builds on relatively novel ideas. In our main specification, these edge factors are calculated based on papers published during 2015-1016.
Having determined the relative novelty of each location's contributions separately for each (idea category, research area) pair -the location's edge factor for that (idea category, research area) pair -we construct the overall edge factor for each nation as a weighted sum of these (idea category, research area) pair specific edge scores.
Weights. In our main specification, we use as weights the frequency at which each (idea category, research area) pair is encountered in biomedicine. In other words, the weight of an edge factor for an (idea category, research area) pair is the total number of papers linked to it from any location during the time period. A justification for selecting these weights is that those (idea category, research area) pairs that are encountered more often in biomedicine are, by revealed preference, considered more important by scientists. The ability to pursue cutting-edge work in an often-encountered (idea category, research area) pair is thus arguably more valuable than is the ability to pursue cutting-edge work in a rarely encountered (idea category, research area) pair. The implicit assumption in this approach is that, even though it is not yet known which (idea category, research area) pairs will be the most important sources of future progress in biomedicine, the past is the best predictor of the future.
Because the overall scientific frontier position for a nation (the edge factor) is calculated as a weighted sum over its position across all (idea category, research area) pairs, the resulting measure for the nation reflects its overall capability across all of biomedicine, as opposed to only the nation's capabilities in areas where it has concentrated most of its own activities. Accordingly, the edge factor is high only if the country has significant capabilities across different areas of biomedicine; expertise in a narrow subset of biomedicine is not enough.
However, in a secondary analysis we show that the results are robust to the case when the edge factor is calculated using as weights each country's own number of papers that link to a given (idea category, research area) pair. Hence, the results from this alternative specification reflect the novelty of the work actually pursued by the nation -emphasizing more the novelty of the nation's work in areas where it publishes a lot -rather than the nation's capabilities across all of biomedicine.
Cells with missing observations. Not all locations have publications linked to every (idea category, research area) pair. In our main specification, we handle such cells with missing observations by replacing the nation's edge factor for that cell with the nation's weighted average across the other cells (those (idea category, research area) pairs for which the location does have publications linked to it). The weights used in this calculation are the same weights as discussed above.
In an alternative specification, we replace cells with missing edge scores with 0 (the worst possible edge score). In another alternative specification, we replace cells with missing edge scores with 100 (by definition the average novelty score for every (idea category, research area) pair). In both cases the results are similar to the results for the main specification (see section A.8).
Comparison with Closest Prior Work. The analysis has two main differences with the closest prior work (15). First, there is a shift in substantive focus -from ranking journals to ranking nations. Second, the present analysis is conducted at the contribution-level, with contribution defined as a link from a paper to an (idea category, research area) pair, whereas the analysis in (15) is conducted at the paper-level. That is, here the novelty score for an entity is calculated first at the contribution-level separately for each (idea category, research area) pair and the overall novelty score for the entity is then calculated as a weighted sum across these each (idea category, research area) pairs. By contrast, in the prior work (15) the novelty score for an entity was calculated at the paper-level either without controlling for either the idea category or the research area, or by only controlling for the research in a manner that essentially uses as weights the entity's own involvement in the research area (in this prior work the research area was determined based on the appearance of 6-digit MeSH terms; the entity of interest in this prior work was a journal, here it is a nation).
The advantage of the approach pursued in the present analysis is thus not only that the present approach controls for the idea category but also that the present approach uses as weights the (idea category, research area) pair's overall importance in biomedicine (as measured by the total number of contributions linked to it). This yields a better reflection of an entity's capabilities in biomedicine compared to the case when the weights represent the distribution of the entity's own involvement across different areas of biomedicine.
Novel Idea Inputs vs. Novel Combinations of Idea Inputs. As in the closest prior work (15), the focus here is on the novelty of idea inputs, as opposed to the novelty of the combination of idea inputs. Novelty of combinations is a focus in several recent analyses (29-33). Both foci come with their advantages (15). The focus on the use of new ideas makes it possible to include on a larger number of ideas in the analysis than is computationally feasible in an analysis of combinatorial novelty. Analysis of the use of new ideas is also important because the trying out of new ideas is so central to scientific progress. For without new ideas science eventually stagnates -combinatorial novelty alone cannot overcome it. Table S4 shows the results from a variety of alternative specifications. For ease of comparison, the results from the main specification are reported again in column (1d).
Confidence intervals reported column (1e) are constructed using a bootstrap method. We first generate each of 1000 artificial samples by re-sampling with replacement from the (idea category, research area) pairs until the total weighted number of observations (i.e. contributions) in each constructed sample is at least as large as the total weighted number of observations is in the original sample. Next, we calculate the edge factor for each nation in each constructed artificial sample. We then eliminate the largest 2.5% and the smallest 2.5% of the values in the edge factor distribution for each nation among these constructed bootstrapped samples. The extremes of remaining edge factor values form the 95% confidence interval for the edge factor of each nation.
The calculated confidence intervals indicate that scientists in the four top nations are clearly above average in their propensity to use new ideas, that scientists in most developed nations have approximately an average propensity to use new ideas, and that scientists in developing nations have a below average propensity to use new ideas.
The analysis reported in column (2) differs from the main specification in terms of how those (idea category, research area) pairs are treated for which a nation has no contributions linked to it: now the edge factor for such (idea category, research area) pairs are replaced with 0, reflecting the most pessimistic scenario about the nation's capabilities for that (idea category, research area) pair. By contrast, in the main specification these missing observations are replaced with the average edge score for the nation for (idea category, research area) pairs for which the nation does have observations.
Comparison of the main results (column 1c) against the results in column (2) shows that while the edge factor decreases somewhat for the smaller nations (as expected), the results remain qualitatively unchanged.
The analysis reported in column (3) differs from the main specification in how the weights for the edge factor for each (idea category, research area pair) are calculated. Here, for each country the weight for an (idea category, research area) pair is the country's own total number of research publications linked to the same (idea category, research area) pair. Thus, the overall edge factor is the same as the average of the nation's novelty scores across all of its contributions. By contrast, in the main specification weight for each (idea category, research area) pair is the same for all nations: it is the total number of papers linked to that (idea category, research area) pair.
Comparison of the main results (column 1) against the results reported in column (3) shows that the results are robust to this alternative specification.
The analyses reported in columns (4-6) differ from the main specification in that the dummy variable indicating novelty of a contribution is now constructed using top 20%, top 10% and top 1% cutoffs. By contrast, in the main specification this dummy variable is constructed using the top 5% cutoff.
Comparison of the main results (column 1) against results reported in columns (4) (5) (6) indicates that while the main results are qualitatively robust -leaders do better than laggards regardless of the measure -the relative position of the United States improves as one moves to a narrower cutoff (from 5% to 1%) and China's relative position improves when one moves to a wider cutoff (from 5% to 10% and 10% to 20%). A possible explanation is that countries may differ in terms of how many of their institutions are on the very edge of the frontier ("the bleeding edge"), so that some countries to fare better when novelty is calculated based on a narrower measure. For example, the U.S. may have many of the very top institutions in the world (in terms of their tendency to work with new ideas) but most of its institutions may be further down in the pack. In another country, such as China, institutions may be more homogenous in terms of the scientists' tendency to work with new ideas. The differences may also be driven by variation in where the new ideas are first born (the United States may be disproportionately the origin of new ideasand thus receive a disproportionate share of the very first mentions of new terms -but scientists working in China may be relatively more eager to build on the new ideas).
The analysis reported in column (7) differs from the main specification in that now the cohort of each UMLS term is the year of the earliest mention of that term or any of its synonyms, with synonyms specified by the UMLS. In contrast, in the main specification the cohort year is the year of the earliest mention of the term itself.
Comparison of the main results (column 1) against the results reported in column (7) shows that the conclusions from the main specification are robust in this way as well.
The analysis reported in column (8) differs from the main specification in that the analysis now includes all publications in MEDLINE as opposed to only regular research articles. The analysis reported in column (9) in turn differs from the main specification in that the analysis now includes also publications for which the text information on the title and abstract is less than 200 characters or more than 5000 characters -in the main specification such publications were excluded from the analysis.
Comparison of the main results (column 1) against the results reported in columns (8) and (9) show that the results are robust also to these alternative specifications. 
CLINICAL AND ANATOMY (1st of 4 idea category groups) A UMLS term that is linked to multiple UMLS categories is treated as multiple separate observations; each such link represents one observation. All (UMLS term, UMLS category) pairs are first ranked based on the number of times the UMLS term is the newest term in a paper among all terms that belong to the same UMLS category.
We present 4 separate lists, one for each of the following four groups of idea categories that we use in the paper (Table S2 shows how the 127 UMLS categories map into these 4 category groups): "Clinical and Anatomy", "Drugs and Chemicals", "Basic Science and Research Tools", and "Miscellaneous"
The rankings are constructed separately for each of these 4 idea category groups and for each decade, with the decade determined based on the cohort year of the UMLS term. The cohort year of a UMLS term is the year the term is first mentioned in the MEDLINE database. For each UMLS term the table also lists the earliest cohort of any of the term's synonyms that appear in the UMLS metathesaurus.
For each decade we only present the top 25 UMLS terms. The analysis in the paper is based on all UMLS terms, not only the UMLS terms presented here. The focus on on a narrow set of popular UMLS terms here is for expositional convenience only.
Explanations for the columns:
Column (1): Decade of cohort; calculated based on the first number in column (6).
Column (2): Rank within decade of cohort; calculated based on column (3) and the first number in column (6).
Column (3): Number of times the UMLS term appears in a paper and is the newest term in the paper from that idea category. Calculated based on papers published during 2010-2016. Column (4): Cumulative share of earliest mentions, calculated based on column (3) separately for each decade of cohort.. Column (5): The UMLS term. Column (6): Cohort of term, set as the earliest year the term is mentioned in MEDLINE. The number in parenthesis is the earliest cohort of any synonym of the term (including the term itself). Column (7): The UMLS category of the term; in our analysis this represents the idea category of the term.
The UMLS term lists for the 4 idea category groups appear in this order below: "Clinical and Anatomy", "Drugs and Chemicals", "Basic Science and Research Tools", and "Miscellaneous". 