The measurement of “interdisciplinarity” and “synergy” in scientific and extra‐scientific collaborations

Problem solving often requires crossing boundaries, such as those between disciplines. When policy‐makers call for “interdisciplinarity,” however, they often mean “synergy.” Synergy is generated when the whole offers more possibilities than the sum of its parts. An increase in the number of options above the sum of the options in subsets can be measured as redundancy; that is, the number of not‐yet‐realized options. The number of options available to an innovation system for realization can be as decisive for the system's survival as the historically already‐realized innovations. Unlike “interdisciplinarity,” “synergy” can also be generated in sectorial or geographical collaborations. The measurement of “synergy,” however, requires a methodology different from the measurement of “interdisciplinarity.” In this study, we discuss recent advances in the operationalization and measurement of “interdisciplinarity,” and propose a methodology for measuring “synergy” based on information theory. The sharing of meanings attributed to information from different perspectives can increase redundancy. Increasing redundancy reduces the relative uncertainty, for example, in niches. The operationalization of the two concepts—“interdisciplinarity” and “synergy”—as different and partly overlapping indicators allows for distinguishing between the effects and the effectiveness of science‐policy interventions in research priorities.


| INTRODUCTION
The faculties and disciplines have been organized since the Middle Ages, first as structures of higher education (notably: theology, medicine, and law), but since the 19th century increasingly also as frameworks for academic research (Stichweh, 1990). After WW II, the NSF was created (Bush, 1945) and the disciplines became increasingly important for the distribution of funding, peer review, and editorial control (Langford, Burch, & Langford, 1997;Zuckerman & Merton, 1971). In this context, the call for "interdisciplinary" problem-solving from the policy side meets an institutional dynamics of the disciplines which shields the sciences against external steering (Mulkay, 1976). Government priorities and social demands have to be adapted to the imperatives of the disciplines before they can be implemented successfully at the specialty level (Studer & Chubin, 1980). How can the gaps between disciplinary organization and social relevance be bridged to the benefit of both science and society? Gibbons et al. (1994) suggested the emergence of a "Mode-2" type of scientific knowledge production in which the context of application would serve a "Third Mission" in interactions together with the 2 | THEORETICAL SPECIFICATIONS

| Interdisciplinarity
In a paper entitled "A general framework for analysing diversity in science, technology and society," Stirling (2007) distinguished between (a) variety, (b) balance, and (c) disparity as three aspects of interdisciplinarity. Based on an extensive literature review, Stirling (1998) had translated diversity measures used in ecology, economics, and information theory into a framework for the measurement of "interdisciplinarity" in science policy and research evaluation. In ecology, for example, variety and balance are often combined into a so-called "dualconcept" indicator (Junge, 1994) such as the Simpson index: [ P i,j (p i p j )]-or, equivalently, the Hirschman-Herfindahl index [Σ i (p i ) 2 ] as a measure of concentration in economics. 1 If there is no variety, but complete concentration into a single variant, the index is equal to one. In empirical cases, these indexes vary between zero and one. Note that factors bounded between zero and one can always be multiplied and the product can be used as another indicator between zero and one. 2 Rao (1982) added "disparity" as a third dimension to "diversity." Ceteris paribus, grouping into different clusters can be expected to modify diversity. In an ecology, parts of the variety may be "related variety" in potentially different niches (Frenken, Van Oort, & Verburg, 2007). For example, a biochemist and a sociologist are more distanced in terms of their disciplines-as a grouping variable-than a biochemist and a physicist. One can measure disparity in terms of the distances between elements. However, the measurement of disparity is sensitive to the choice of the unit distance or proximity. Bromham et al. (2016, p. 6841), for example, developed an interdisciplinary distance metrics, which contains a disparity value based on co-classifications. For technical reasons, one often uses (1 − cosine ij ) as the distance measure instead of Euclidean distances or Pearson correlations (Ahlgren, Jarneving, & Rousseau, 2003). 3 Network analysts can also use shortest distances (geodesics) in terms of the links in between two nodes.
Elaborating on Rao (1982;cf. Ricotta & Szeidl, 2006), Stirling (2007) proposed the following measure of diversity as a composed indicator of interdisciplinarity: For the least complex case of α = β = 1, 4 this measure Δ (= P i,j p i p j d ij ) is often called Rao-Stirling (RS) diversity. RS is identical to the "integration score" developed and used by Porter, Roessner, Cohen, and Perreault (2006) and Porter, Cohen, David Roessner, andPerreault (2007), cf. Porter &Chubin (1985). Rafols and Meyer (2010, p. 266) provided Figure 1, which has become iconographic for visualizing the distinctions among the three components of "interdisciplinarity." Rafols and Meyer (2010, pp. 268 ff.) added the distinction between diversity and coherence (cf. Rafols, 2014;Rafols, Leydesdorff, O'Hare, Nightingale, & Stirling, 2012, p. 1268. 5 Based on recent literature in ecology (Jost, 2006;Leinster & Cobbold, 2012;cf. Mugabushaka et al., 2016), Zhang, Rousseau, and Glänzel (2016) have distinguished between Rao-Stirling diversity (Δ) and "true" diversity ( 2 D 3 ). As against RS, one can calculate with "true" diversity as a metric: a "true" diversity of two, for example, is precisely twice as diverse as a "true" diversity of one. Furthermore, Zhang et al. (2016Zhang et al. ( , eq. 6 at p. 1260cf. Mugabushaka et al., 2016, p. 602, Table 1) derived that RS diversity (Δ) can be converted into the "true" diversity index 2 D 3 using: A major advantage of "true" diversity is that one can express one diversity as a percentage of another and thus define a measure for above-and below-expected values in the evaluation. Note that "true" diversity is not bounded between zero and one.
Furthermore, Stirling (1998, p. 48) stated that "any integration of variety and balance into dual-concept diversity must necessarily involve the implicit or explicit prioritization of the subordinate properties." In the meantime, however, Nijssen, Rousseau, and Hecke (1998) had shown that the Gini Index can be considered a measure of balance, but not of variety. One can thus operationalize the three components independently of each other, by using the Gini-coefficient as an indicator of (un)balance (Zhang, Sun, Chinchilla-Rodríguez, Chen, & Huang, 2018). Variety can be defined independently as (n c /N), with N being the total number of classes available and n c the number of classes with values larger than zero. Using this decomposition, Leydesdorff, Wagner, and Bornmann (2019) proposed DIV as a diversity indicator combining the three components as follows: The three components are indicated in Equation (3) with brackets. The right-most factor in this equation is similar to the disparity measure used in RS diversity (Equation (1)), albeit normalized differently. The other two factors represent relative variety as (n c /N) and balance measured as (1 − Gini).
Unlike RS, DIV meets Rousseau's (2018) requirement that diversity increases for each of the three components when the other two remain the same. Rousseau (2019) further improved DIV into a "true" diversity measure as follows: As a "true" diversity measure, DIV* is not bounded between zero and one, but again one can calculate with it. In our opinion, DIV* is the current state of the art.

| Synergy
The term synergy originates from the Greek word συνεργία which means "working together." By working together, a whole is sometimes created that is greater than the sum of its parts. In science, for example, synergy may mean that new options have become available because of the collaboration across (e.g., disciplinary, sectorial, or geographic) boundaries. In other words, the F I G U R E 1 Schematic representation of the attributes of diversity, based on Stirling (1998, p. 41). Source: Rafols & Meyer (2010, p. 266)  number of options in the system under study can be increased by making further distinctions. Newly emerging options are vital to innovative systems, even more than past performances. A system may run out of steam and be deadlocked if new options are no longer generated. Future performance of a region or nation is dependent on both entrepreneurial and structural dynamics such as interactions among selection environments (markets, sciences, endowments, etc).
Technically, a larger number of options add to the maximum capacity of a system. Unlike biological systems, the maximum capacity of a cultural system-he H max in information theory-is not a given but can be reconstructed ( Figure 2). New options can be invented as alternative possibilities (Leydesdorff, Johnson, & Ivanova, 2018, Leydesdorff, Wagner, & Bornmann, 2018, p. 1184. For example, new means of transport can be invented. This adds capacity to the system(s) under study.
The maximum capacity of a system H max is equal to the (logarithm of the) number of options (log(N)). H max is composed of the number of realized states (H observed or H obs in Figure 2) and the number of possible, but not realized states (H max − H obs ). Shannon (1948) defined the proportion of non-realized but possible options [(H max − H obs )/H max ] as redundancy (colored green in Figure 2), and the proportion of realized options as relative uncertainty. If redundancy increases, the relative uncertainty decreases.
For example, when a child asks permission from one of its parents, the other parent is latently present in the response. Uncertainty can be reduced when a latent relation is expected to operate in the background, like in this case the relation between the parents (Abramson, 1963, pp. 130f.). In a triad, the correlation in the relations between each two sets can spuriously be co-determined by a third with a plus or a minus sign. In other words, a latent dimension is operating as a selection environment.
The same information can be appreciated differently by other stakeholders, for example, in university-industry-government relations. The appreciations from different perspectives ("the meanings of the information") can be shared and thus generate redundancy; the same information can be involved more than once. Whereas information can be communicated in relations and measured (using Shannon's formulas), meanings can be provided and shared from different perspectives. Sharing can generate an "overlay" among perspectives with a dynamic of redundancy different from that of information processing (Etzkowitz & Leydesdorff, 2000).
First, there is variation in historical events at the bottom as part of the (probabilistic) entropy flow. Unlike this variation, the dynamic among perspectives operates reflexively-as an "overlay"-upon changes in the network of relations. The perspectives operate as selection environments on the variation and the interactions among these selections can feedback as redundancy on the variation. The feedback has an opposite sign. Shannon (1948) defined information H as the statistical term in Gibbs' formula for thermodynamic entropy S = k B * H. In this formula H = − P i p i Ã log 2 p i and k B is the Boltzmann constant. Like entropy, the Boltzmann constant has the dimensionality Joule/Kelvin so that H is a dimensionless statistic, sometimes called "probabilistic entropy." If the logarithm is two-based, H is measured in bits of information. Note that the second law of thermodynamics is equally valid for H, because k B is a constant. Shannon-type information is therefore necessarily positive and adds to the uncertainty (Krippendorff, 2009). Figure 3 shows two overlapping sets of options with the respective information contents H 1 and H 2 . One can consider the overlap as mutual information or transmission (T 12 ). However, counting the information in the overlap twice would be redundant, and thus: The redundancy R 12 is equal in absolute value to T 12 but with the opposite sign. Whereas mutual information T 12 is Shannon-type information and thus necessarily positive, mutual redundancy R 12 is a measure of reduction of uncertainty, and cannot be Shannon-type information because of the (potentially) negative sign (Krippendorff, 2009). The potential sign switch indicates that a receiving system can appreciate (Shannon-type) information and consider the empty "boxes" as redundancy; that is, the opposite of information in terms of positive or negative contributions to the uncertainty. Shannon's co-author Weaver (1949) already envisaged a calculus of redundancy as a supplement to Shannon's theory of information (cf. Bateson, 1972;Leydesdorff, Johnson, & Ivanova, 2018). Figure 3 is extended to three sets in Figure 4. Three configurations are depicted in Figure 4 metaphorically indicating that T 123 (the overlap among the three in the centre) can be positive (A), absent (C), or zero (B). Redundancy is a measure of these absent options, which can nevertheless be declared (Bateson, 1972;Deacon, 2012). Different from the empty spaces outside the three circles, the size of the delineated gap among them in Figure 4C can be measured.
The formula for the combined set H 123 followsanalogously to H 12 above-using summations and subtractions of the numbers of elements in overlaps among sets, as follows: In Equation (6), the tri-lateral overlap in the center (T 123 in the left pane of Figure 4) is included three times in the summation (H 1 + H 2 + H 3 ) and then subtracted three times by (−T 1 −T 2 −T 3 ). It follows that T 123 has to be added once more after the subtractions in order to capture H 123 .
Equation (6) can be reorganized as follows: Since T 123 is added, while T 12 was subtracted in Equation (5), the sign of the last term representing mutual redundancy in three dimensions is opposite to that representing an even number of dimensions. In other words: R 12 = −T 12 and R 123 = T 123 . Alexander Petersen has shown that the sign changes with the addition of each next dimension because of the sub-additivity of the entropy (Leydesdorff, Petersen, & Ivanova, 2017, p. 17). 6 In summary, one can have both positive and negative loops in interactions among three dimensions.
In general, triads are the building blocks of systems (Bianconi et al., 2014;cf. Krackhardt, 1999). All higherorder configurations can be decomposed into triads (L. C. Freeman, 1996). In the case of more than three (sub)sets, one can compare triads among each three in terms of the redundancies generated. Triads may contain redundancy or uncertainty depending on the rotation ( Figure 5; Ivanova & Leydesdorff, 2014).
The number of possible triads among n sets is n * (n − 1) * (n − 2)/(2 * 3). (The denominator [2 * 3] corrects for double counting.) Each node can partake in n − 1 links of which some are parts of triads which generate redundancy and others are not. Both links and nodes can be part of triads. 7

| MUTUAL INFORMATION AND REDUNDANCY IN A SIMPLE TOY MODEL
Let us begin this discussion with a toy model. In this model (Table 1), four variables are attributed to five cases like column vectors of a matrix.
Using Shannon's formula (H i = − P i p i * log 2 p i ), the expected information content of the first vector (v1), for example, can be elaborated as follows: 13 Ã log 2 9 13 − 4 13 Ã log 2 4 13 = 0:890 bits (By convention, 0 * log(0) = 0). One can compute the joint entropy (H 12 ) and mutual information or transmission between the two dimensions of the matrix by following the steps in Table 2.
Column e in Table 2 contains the margin totals of the five rows of the toy model (columns a to d). Using the grand total of the matrix (N = 45) as denominator, relative frequencies are provided in columns f to i. In column k to n, the values in this two-dimensional probability distribution (p ij ) are transformed into the Shannon-type information (−Σ p ij * log 2 p ij ) in bits. It follows from the summation of the cell values that H ij = 3.23 bits (at the bottom of column o). This is the two-dimensional information content of this matrix.
The margin totals in the vertical and horizontal direction provide us with the one-dimensional probabilities: the information values in column e add up to H 1 = 2.19 bits. Analogously on the basis of the values in the bottom row of columns a to d, H 2 = 1.96 bits. Using Equation (5  A matrix contains by definition a two-dimensional distribution; mutual information in two dimensions is necessarily positive (Theil, 1972). For the representation of a three-dimensional distribution, however, one would need three dimensions. We propose to use the triplet values in consecutive columns as vector representations in the x, y, and z dimensions of a three-dimensional vector space. The four vectors in Table 1 can be considered as consecutive triplets: {v1, v2, v3}, {v1, v2, v4}, {v1, v3, v4}, {v2, v3, v4}. One can compute for each triplet a threedimensional H 123.

8
Let us consider, for example, the first triple {v1, v2, v3} in more detail. Table 3 provides this triplet itself in the top-panel. The relative frequencies are provided for the respective dimensionalities in the second row of matrices.
The information values follow in the bottom row.
Using Equation (7)  Analogously, the four other possible triplets as part of the toy model are: T 124 = −0.08; T 134 = −0.23, and T 234 = −0.08. The values for the four triplets can be aggregated for the set (because of the sigma's in the Shannon formulas). We propose to attribute this redundancy as a synergy value to the nodes and links participating in the respective triads (Leydesdorff & Strand, 2013, p. 1895. A routine is available at https://www.leydesdorff. net/software/synergy.triads, which permutes the column vectors of any matrix so that all possible combinations of variables are evaluated in terms of their values of T 123 . For example, v2 participates in the triads {v1, v2, v3}, {v1, v2, v4}, and {v2, v3, v4}, but not in {v1, v3, v4}. Among the triads in which a vector participates some will generate information (T 123 > 0) and others redundancy (T 123 < 0). We define the synergy value of v2 in this   Figure 6. Redundancy values can be attributed both to nodes and links between them. One needs both components for the visualization of the resulting synergy network ( Figure 6).

| EMPIRICAL APPLICATIONS
4.1 | Comparison of synergy with interdisciplinarity using citation relations among journals As a first example of empirical data, we use the aggregated journal-journal citation matrix of 26 journals cited by publications in Scientometrics during 2017 more than a threshold value of 43 times. 9 We chose this example because the disciplinary and interdisciplinary affiliations of journals are mostly intuitive (Table 4). We compare the 26 column vectors of the matrix ("citing") containing the respective numbers of references to publications (in the Web-of-Science domain) during 2017. Figure 7 provides a map of this set of journals on the basis of the cosine-normalized (column) vectors. The structure induced by Blondel et al.'s (2008) algorithm for decomposition is intuitively recognizable as three groups of journals: information-science journals in the direct environment of Scientometrics, multidisciplinary ones (e.g., PNAS, PLOS One, Science, and Nature) on the right side, and policy and management journals on the left side (e.g., Research Policy and Technovation). Table 4 lists the 26 journals in terms of synergy values in the left-most column, and in terms of the two "true" interdisciplinarity indicators 2 D 3 and DIV* in the next two columns.
On the synergy indicator, Science ranks on the sixth position, and Nature follows on the eighth rank. Large journals with a pronouncedly disciplinary identity such as the Am Econ Rev and a number of journals in the management sciences generate more synergy than Science and Nature. Among the library and information science journals, the journal Scientometrics scores highest on synergy (with rank number 13). However, the journal Social Networks occupies the seventh position on the ranking of synergy values.
Pearson correlations and Spearman rank-order correlations among these and a number of the diversity and interdisciplinarity indicators (discussed above) are provided in the lower and upper triangles of Table 5, respectively. The Spearman rank-order correlation between the DIV* and 2 D 3 in this set of 26 journals is $0.86 (p < .01; see Table 5). In other words, the two measures are statistically similar, but individual evaluations based on them can be considerably different (Table 4).
The synergy indicator correlates significantly (p < .01) with all these indicators at levels between r = 0.4 and r = 0.7. However, Table 6 provides a twofactor solution based on the Pearson correlation matrix. The varimax-rotated factor matrix shows that synergy is a specific (second) dimension different from the varietyindicators, which load on factor 1. As could be expected, the Gini-index correlates negatively since Gini is a measure of unbalance (Nijssen et al., 1998).
The difference in the second dimension between the synergy indicator and the interdisciplinarity indicators confirms that although embedded in "interdisciplinarity," "synergy" provides an external factor structuring the correlations among the interdisciplinarity indicators in the background.
Furthermore, each link can be part of n * (n − 1)/2 triads. For n = 26, this amounts to 325 possible values; 55 of them (16.9%) have a negative value. In Table 7 the links are listed in terms of most synergy. Combining the values for nodes and links, one can generate a network; Figure 7 visualizes this network; using VOSviewer, for both the clustering and the layout. (The computer routine provides among other things files "minus.net" and F I G U R E 6 Synergy retention network of the toy model (in bits of information) "minus.vec" in the Pajek format, which enable the user to proceed to the visualization and further analysis of the synergy network.) Figure 8 is rather different from Figure 7 above. The interpretation of this figure raises all kinds of questions. For example, the relations between Scientometrics and the Americn Economic Review in the center of the synergy map are by more than an order of magnitude smaller than the relations between AER and management journals. Specialist journals are not highly positioned on this ranking, with the exception of Social Networks and to a lesser extent Technological Forecasting and Social Change. However, one should keep in mind that this was a single and potentially specific case. The purpose of this exercise was a proof of concept and a comparison of "synergy" with "interdisciplinarity." More cases and refinement of parameter choices are needed before one can draw empirical conclusions.
Unlike most performance indicators, the synergy indictor was not generated in a research evaluation practice, but is theory-based (McGill, 1954;Ulanowicz, 1997;Yeung, 2008;cf. Krippendorff, 2009). Bridging the gap from theory to practice will require more examples. For example, in a next project, it may be interesting to study synergy in translation research ("from bench to bed") because the generation of synergy is an explicit objective in this type of research.

| Synergy in international coauthorship relations among six westernmediterranean countries (2009)
Unlike interdisciplinarity, synergy can also be generated in extra-scientific contexts, such as university-industry relations or in geographical co-locations. Using data collected in another study (Leydesdorff, Wagner, Park, & Adams, 2013), Table 8 shows the internationally coauthored papers among six Western-Mediterranean countries in 2009: France, Italy, Spain, Morocco, Tunisia, and Algeria. Figure 9a shows the affiliations network of international co-authors among these six nations. As expected, France has relations mainly with Italy and Spain (within the EU), but one can expect a different kind of relations with its former colonies in northern Africa. Figure 9b shows the synergy network: the three European nations generate synergy from their collaborations as do the three northern-African nations among them. However, there is no synergy indicated in the network between France and the northern-African countries in 2009, although there was synergy in earlier years. Note that one can also combine, for example, authorship and disciplinary-specific variables. The example shows that "synergy" is different from "interdisciplinarity." Interdisciplinarity can also be considered a specific type of synergy. The synergy indicator can be used for the evaluation of any set of variables, including disciplinary affiliations, geographical address, or demographic characteristics.

| DISCUSSION AND CONCLUDING REMARKS
The objective of this study was to discuss some recent advances that have been made in the operationalization and measurement of "interdisciplinarity" and "synergy." Using information theory, we operationalized synergy, employed it in two empirical examples, and showed how this indicator of "synergy" can be distinguished from "interdisciplinarity." "Trans-disciplinary" is sometimes used as a residual category, which would also cover "synergy." However, the measurement of "trans-disciplinarity" was hitherto not further developed. "Interdisciplinarity" has mainly been elaborated in bibliometrics on the basis of diversity indicators developed in ecology and economics. Stirling (1998Stirling ( , 2007cf. Rao, 1982) proposed to distinguish between variety, balance, and disparity as aspects of "interdisciplinarity" (A. L. Porter, Cohen, David Roessner, & Perreault 2007;Porter, Roessner, Cohen, & Perreault, 2006;Rafols & Meyer, 2007, 2010. Zhang et al. (2016) reformulated the Rao-Stirling measure of interdisciplinarity into the framework of "true" diversity (Jost, 2006). Leydesdorff et al. (2019) proposed to abandon "dual-concept" diversity (Stirling, 1998, p. 48) by using the Gini-index as a measure of imbalance (Nijssen et al., 1998). Rousseau (2019) finalized this series of studies by proposing DIV* as a measure of "true" diversity. Furthermore, one can distinguish "interdisciplinarity" or "synergy" in the "cited" and "citing" directions. Like measures of "novelty," "disruption," and "breakthrough," the measurement of "interdisciplinarity" in bibliometrics has focused on integration of references from different domains into citing literature more than on knowledge diffusion. By citing documents from different knowledge bases, one integrates interdisciplinarily. When a paper is cited in a variety of domains, diffusion can be considered in terms of (inter)disciplinaity (Carley & Porter, 2012;Leydesdorff, Wagner, & Bornmann, 2018).
Recently, Wu et al. (2019) developed an indicator of disruptiveness using the differences between citing and cited patterns over generations of papers as an indicator of change. One of the referees suggested the comparison of disruptiveness with synergy as a subject for further research.  the prevailing uncertainty provides innovators with dynamic opportunities comparable to local niches (Schot & Geels, 2007). Note that reduction of uncertainty at the systems level provides an advantage for reflexive agency insofar as it is perceived. Second, the number of options available to an innovation system for realization can be as decisive for the system's survival as the historically already-realized innovations. Although uncertainty features in all innovation processes (C. , it poses crucial challenges to the governance of innovation. A system with no redundancy is out of options and thus deadlocked. The current paper contains a proof of concept for the synergy indicator. Further research might address questions such as: what is the major difference between synergy and the other concepts in substantive terms? How are the dynamics different? Information-theoretical measures can be rewritten into a dynamic version (Kullback & Leibler, 1951;Leydesdorff, 1991;Theil, 1972). How does synergy evolve?

| NORMATIVE IMPLICATIONS
In our opinion, "synergy" is important for the measurement of the social functions of science. In translation research, for example, the objective is to accelerate the application of new knowledge from basic (e.g., molecular) biology in the clinic ("from bench to bed") or vice versa to articulate demand at the bedside in terms which can be made relevant for research agendas. Mutatis mutandis, university-industry relations can be conceptualized as processes of transfer, application, and incubation. The mediation between supply and demand may also require managerial or governmental interventions. In university-industry-government ("Triple Helix") relations, nonlinear feedbacks can become more important than linear transfer.
By appreciating redundancies, one can shift the focus from the measurement of past performance to the question of the number of available options. Whereas performance indicators are useful for improving the operational management of research, the measurement of synergy can also be relevant for the coupling to other areas of policy making (cf. Rotolo, Rafols, Hopkins, & Leydesdorff, 2017). Synergy refers to options which are possible, but not yet fulfilled, whereas most bibliometric indicators hitherto evaluate past performance; that is, options that have already been realized. More generally, the measurement of redundancy may provide methodologies opening a range of futureoriented indicators.

ACKNOWLEDGMENTS
We are grateful to anonymous referees and the editor of the journal, Caroline Wagner, Marija Rakas, Lutz Bornmann, Gerard de Zeeuw, Daniel S. Hain, Ludo Waltman, and Machiel Keestra for comments on a previous draft.