The Physics Papers in 1989–2008
The 1,445,273 physics papers published in 1989–2008 were produced by 6,658,522 authors. Each paper had 4.61 authors. Among them, 1,189,863 (82.33% of the total) were co-authored papers. The total number of authors of the collaboration papers was 6,403,112. That is, each collaborated paper had 5.38 authors in average.
International collaboration papers were of particular importance in assessing national research productivity. 329,447 (22.79%) of the entire papers were of international co-authorship judged by authors' institutional affiliations. The total number of authors of the international collaboration papers was 3,135,587. Each international collaboration paper had 9.52 authors in average. One can see that, although international collaboration papers only accounted for 22.79% of the physics papers, the huge difference between the paper number and author number and the high average author number per paper have anticipated noticeable counting inflation.
Country Ranks by the Five Accounting Procedures
Here we report the rank changes in the top 30 countries by any of the five accounting procedures. As shown in Table 1, slight variation existed when different accounting procedures were applied, but the distribution of country ranks was rather similar in each method. United States ranked first in all of the five rankings; its paper production was approximately 2.3–2.4 times of the second country in quantity (i.e., Germany or Japan, depending on the procedures used). At the other end, Singapore and Hungary could both fall out of the top 30 when a certain procedure was applied. Hungary made it into the top 30 only in procedure A. In contrast, Singapore was able to hit the top 28 in all procedures but A.
Some countries' ranks never changed no matter which accounting procedure was applied, i.e., United States (1), Russia (5), France (6), U.K. (7), Italy (8), India (9), Poland (13), and Czech (25). For the other countries of varied ranks, a closer examination revealed some interesting patterns. First, one can identify several clusters of countries with adjacent ranks. Within each cluster, country ranks varied by procedure, but ranks were interchangeable only within the same cluster. For instance, in the first cluster of Germany, Japan, and China, one can see three different orders of ranks: 2–3–4 (A); 4–2–3 (B; D); 3–2–4(C; E). It should be noted that Japan was ranked as the 2nd in all procedures but A. For the ranking variations in the other clusters, see Table 1. The two larger clusters are located at the lower half of the table, i.e., the cluster of Switzerland to Taiwan; and the cluster of Denmark to Singapore. An interesting observation of each country's rank changes due to procedures used is that the largest difference of ranks did not exceed 3 even in clusters composed of more countries, e.g., Taiwan ranked 15th the highest and 18th the lowest; Argentina ranked between 26th and 29th, and Singapore between 28th and 31st.
Another interesting observation is that, when procedure A was applied, the Western countries usually ranked higher than their peer countries within the same clusters. In contrast, when procedures B-D were applied, those countries of East Asia and those that can be described as “newly industrializing economies” (Central Intelligence Agency, n.d.) or “emergent markets” (CME Group Index Services, 2010) were ranked higher than their Western peers – for example, Japan and China as opposed to Germany (the 1st cluster); South Korea as opposed to Canada and Spain (the 2nd cluster); Brazil and Taiwan as opposed to Switzerland, Netherlands, and Australia (the 3rd cluster); Ukraine and Mexico as opposed to Belgium and Austria (the 4th cluster); Argentina and Singapore as opposed to their cluster peers (the 5th cluster). The more dramatic rank changes can observed in the following countries: South Korea rose from 12 (procedure A) to 10 (procedures B-D); Taiwan rose from 18 (A) to 15 (B; D); Argentina from 29 (A) to 26 (B; D); Singapore from 31 (A) to 28 (B-D). In contrast, Germany, Switzerland, and Switzerland could drop two ranks; Hungary dropped three in all four procedures.
Finally, comparing the results of the five different procedures, one can see that the results from procedures B-D were rather consistent in the direction of rank change. That is, when any of the procedures other than A was applied, a country's country rank could rise, remain the same, or drop. But the direction in terms of rising or dropping was all the same. Curiously, procedures B versus D, as well as procedures C versus E, yielded nearly identical rankings in the top 30 countries except Denmark and Argentina. This curious high similarity awaits further investigation. Given the similarity of the procedures B-D rankings, it seems safe to conclude that, among various accounting procedures, only procedure A made a larger difference to paper number counting.
We further used the paper numbers from procedure A as the basis for calculating the ratio of counting inflation. We divided each country's paper number from procedure A by the numbers from procedures B-D respectively. Results showed that counting inflation ranged from as low as 1.11 (China in procedure B) to as high as 1.84 (Hungary in procedure C) (see Table 1). For the convenience of observation, we used different background colors for ratio values within four equal sections between 1.00 and 2.00 (1.00–1.25; 1.26–1.50; 1.51–1.75; 1.76 and above).
One can see that, except the U.S., all other countries with inflation ratio lower than 1.25 were Asian countries, i.e., Japan, China, India, South Korea, Taiwan, and Singapore. Only Singapore had inflation ratio higher than 1.25 in two accounting procedures. The low inflation suggests that those countries possibly had not involved as much as the other countries in international collaboration.
All the Western countries within the top 10 countries including Russia had inflation ratio ranging between 1.26–1.50. Other Western countries in top 20–30 could have higher inflation. Switzerland, Denmark, Austria, and Hungary had the highest inflation as compared to other countries. The higher inflation ratio indicates that those countries, when participating in international collaboration, more often served supporting or facilitating roles rather than as the lead investigator.
It makes sense to see the degree of inflation echoed the rank rise and rank drop within each cluster of countries. Countries with lower inflation ratio all rose in ranks when procedures B-D were applied. In contrast, countries with relatively higher ratio in each cluster dropped in ranks when procedures B-D were used for paper counts. The wider gaps of counting inflation can be observed in the 3rd cluster (i.e., Switzerland vs. Taiwan) and the 7th cluster (i.e., Denmark and Hungary vs. Singapore).