Are Contributions from Chinese Physicists Undercited?

Evaluating scientific contribution from each country to each discipline has been a trending topic in Scientometrics. In practice, for science policymakers, it is also important to have proper recognition of their own country’s academic position,

especially for the fast-developing countries like China. Often in this kind of study, researchers count the number of publications or received citations of the countries and in the fields of interest and rank them accordingly (King, 2004; Meho & Yang, 2007; Moed & Halevi, 2015).

However, a simple counting of publications and citations might underestimate or overestimate the contribution of a country. How the papers are cited, say by important mile-stone like papers or by insignificant homework-like papers, should make a large difference. In fact, that is exactly the idea behind PageRank algorithm (Brin & Page, 1998) and Leontief Input-Output Analysis (LIOA) of Economics (Leontief, 1941; Miller & Blair, 2009): citation or more generally a linkage from a more influential node, which can be papers, web pages, economic sectors, and scientific fields, should weight more than that from an insignificant node. In the LIOA, economists are interested in the same question. Given an input-output table between economic sectors, which sector is more influential than others. For precisely this purpose, Loentief proposed the LIOA, which regard the economic sectors and the input-output relation among them as an open system, while taking final demanders and labor input as the external sector (Leontief, 1941). In Shen et al. (2016), we extended LIOA into a Modified closed system input–output analysis (MCSIOA) to make the analysis to be applicable to an input-output table of any flow between any nodes beyond economic sectors and to even closed systems.

LIOA starts from the direct input-output coefficient matrix B, where Bji$B_{j}^{i}$means how many units of a product i is needed to produce one unit of product j. Then the idea of LIOA is that for each unit of product j from the final demanders, denoted as Y^j, the economic system needs to produce first Y^j, and then also the raw materials need to produce Y^j, thus BY^j, and then also the raw materials to produce BY^j, thus BBY^j = B²Y^j and so on. Overall, one arrives at the famous Leontief inverse input-output matrix X=Yj+BYj+B2Yj+⋯=(1−B)−1Yj==ΔLYj.$X={{Y}^{j}}+B{{Y}^{j}}+{{B}^{2}}{{Y}^{j}}+\cdots ={{\left( 1-B \right)}^{-1}}{{Y}^{j}}=\overset{\Delta }{\mathop{=}}\,L{{Y}^{j}}.$Depending on the structure of L, some sectors Y^j might lead to a large X, even when it is needed by the final demanders only a small amount. In terms of scientific influence, this is like to say that if a field A cites heavily a field B and the field B also cites heavily a field C, then the field A should be considered strongly influenced by the field C.

MCSIOA (Shen et al., 2016) follows the same spirit but works on closed systems where there is not a natural external sector like the final demanders in LIOA. Therefore, instead of a matrix inverse, which requires an external sector, MCSIOA uses the largest matrix eigenvalue and the corresponding eigenvector (called the largest eigen pair for simplicity), which is applicable to closed systems and also takes into account higher-order effects of the matrix. To see why the largest eigen pair includes higher-order effects, one can use the power method calculation of it: starting from a random initial vector X₀, the iterative multiplication X_n = BX_n−₁ leads to eventually the largest eigenvalue pair. we also refer the readers to Shen et al. (2016) for further details, which will also be briefly explained in the section of Data and Method.

In this work, we will apply MCSIOA to an input-output table between the subfields of physics from major countries. We will regard the overall influence of each sector calculated by MCSIOA as the net influence and use the number of citations as the direct influence of each sector, and then compare the net and the direct influence. When a country is ranked higher according to the net influence than the one according to the direct influence, then we say publications from that country have been undercited. We say publications from a country are overcited if the net influence rank is lower than the rank according to the direct citation counts.

We are fully aware that the above approach is just one possible way to measure the net influence. Simply counting of citations is a limited influence measure, but it is easy to understand and easy to implement. The use of MCSIOA, on the other hand, requires further justification. However, from the above explanation of its spirit and also from its success in economics application and the previous Scientometric study, we think it provides a reasonable measure of the net influence by taking not only the direct but also the indirect connections into consideration.

The rest of this manuscript is organized as follow, the data and method are in section 2. In section 3, we illustrate the main results. Conclusions and discussions will be in section 4.

The data we use in this work is provided to us by the American Physical Society (APS) and it includes all papers published in APS journals between 1977 and 2013. There are a total of 404,496 papers and 6,039,964 citations. All papers have been classified according to the Physics and Astronomy Classification Scheme (PACS) codes, which is a classification system of subfields of physics. We chose the first and third-level PACS code for our analysis. There are F = 1,281 subfields in total.

Totally 165 countries and regions are identified from 337,768 authors’ address. For non-USA addresses, the last part of the address string is usually a country name. For that, we match this last part to a list of countries. For the USA addresses, there is often not a country name in the address strings, we then match the state names to a list of states in the USA. In very rare cases, we find a match of the last part of the address string in both lists and in those cases, we check each of them manually. We use the full count when assigning papers to countries. As illustrated in Figure 1, for each citation between a citing paper A and a cited paper B, we identify the corresponding fields f ^A, f ^B and country c ^A, c^B, which can be more than one, and then add this citation to the citation count from fA×cA${{f}^{A\times {{c}^{A}}}}$to fB×cB,${{f}^{B\times {{c}^{B}}}},$

Figure 1

We then keep the countries/regions with more than 1,000 publications in our record and group other countries and call it “others”. In the end, there are C = 45 countries/regions in our record.

Once we have the input-output matrix x=(xji)(C⋅F)×(C⋅F),$x={{\left( x_{j}^{i} \right)}_{\left( C\cdot F \right)\times \left( C\cdot F \right)}},$where each element xji$x_{j}^{i}$representing the number of citations from j to i, we define the direct input-output coefficient matrix F

and perform the MCSIOA that is the net influence of sector j is (Shen et al., 2016).

where λMAX−j$\lambda _{MAX}^{-j}$are the largest eigenvalue of F^{(− j)}, which is the matrix after removing the jth row and column of F. It is called IOF in (Shen et al., 2016). We then rank all sectors according to respectively their total number of received citations Xj=∑kxkj${{X}^{j}}=\sum\nolimits_{k}{x_{k}^{j}}$and their IOF SIOj$S_{IO}^{j}$and compare the two ranks to determine sector j is overcited or undercited.

The idea behind the definition of SIOj$S_{IO}^{j}$can be seen from the following two facts. Firstly, the largest eigenvalue of F takes into account both direct and indirect connections in F. Secondly, the largest eigenvalue of the original F matrix is 1, and it can be regarded as the production efficiency of F, meaning that all the input when supplied according to the right combination, the corresponding eigenvector. Therefore, the largest eigenvalue F^{(− j)} also captures both direct and indirect connections, and it means the percentage of production efficiency of the system after the sector j removed, due to which some unmatched supplies will be wasted. Therefore, if the sector j is well-connected to the rest of the system and rest of the system deeply relies on sector j, then the percentage of production efficiency of the rest of the system will be low. Our previous study (Shen et al., 2016) have shown that indeed influential sectors do lead to large SIOj.$S_{IO}^{j}.$

The difference between net influence and the direct influence and the direct influence means that indirect citation does not follow a similar pattern of direct citations. For example, if most of the citations are from the same sector (country × field), then the dissipation power of the sector is lower, and then the net influence will also be lower. Or the net influence is lower when most of the citations come from low impact papers. On the other hand, if most citations from other sectors and from high impact papers, the net influence will be higher.

In this work, using the IOF calculated from the general input-output analysis (Shen et al., 2016) as a measure of net influence and the direct citation counts as a measure of the direct influence, we discuss the question of whether or not publications from physicists from a country, especially China, have been undercited. We find that 75% percent of German subfields are undercited and 74% for the USA, while China has 40% percent undercited subfields. We also provide a list of such highly undercited or overcited subfields for each country.

Our discovery that there are more overcited subfields than undercited subfields for China implies that often the paper citing papers from Chinese physicists are often with low influence themselves. We have not looked into whether or not it is indeed the case. Doing so will require a paper-level application of the PageRank algorithm or input-output analysis. This will be the topic of future studies.

The data we analyzed in this work is only on physics and only from the APS journals. The method is applicable and should be applied to other disciplines or even all the disciplines together. After all, evaluating and recognizing properly scientific contributions of our own countries properly can be meaningful not only to science policymakers and educators but also to individual researchers and even citizens.

The definition of overciting or under-citing in this work is based on the comparison between direct citation ranks and the IOF rank. We admit that this is not the only way to define overciting or under-citing.