**2.1. Patent data**

As an indicator representing the relationship between science and technology, the number of cited scientific documents per patent (it is known as "science linkage") has been widely used. It is relatively straightforward to introduce science linkage, since it does not require identification of each scientific paper cited in patents and match to a specific record in databases of academic papers, such as Web of Science (WoS) and Scopus. However, science linkage only provides information on vicinity of science from technology, not vicinity of technology from science. Along with the research utilizing science linkage as an index as described above, the nature of patent-paper citations itself has been studied. Such studies needed identification of bibliography of papers which appeared in patent documents. For example, Branstetter and Ogura [4] used data of patent-paper citations provided by CHI Research and analyzed the relationship between probabilities of occurring patent-paper citations and some variables obtained from both patents and papers for California. Such research had been relatively scarce, since they required a large-scale data set with identified paper data. However, in recent years, Ahmadpoor and Jones analyzed a large citation network, which consisted of patent-patent, paper-paper, and patent-paper citations, based on a large data set of US patents and scientific papers indexed in the Web of Science database provided by Clarivate Analytics and comprehensive patentpaper citation data [5]. They dealt with both patent-patent and paper-paper citations symmetrically and handled patent-paper citations like it bordered between these two networks and then uncovered differences in various aspects of them. Fukuzawa and Ida [6] analyzed the features of patent-paper citations from the paper side for 100 top researchers who were awarded the twenty-first-century COE. They found some important characteristics of patent-paper citations, such as the time lag of the former was longer than the latter, and the more the papers were cited

While these findings are important for practical use of patent-paper citations, there are almost no existing studies on the development of impact indicators of papers cited in patents.

On the other hand, the demand for methods of analysis and empirical indicator data of "papers cited in patents" in practical context has been expanded recently. For example, the Fifth Science and Technology Basic Plan which is the current Japanese five-year national plan for the promotion of science and technology between FY 2016 and 2020 requires monitoring of the performance. "Scientific papers cited in patents" is one of the key performance indicators of the plan. However, an effective method for showing performance using patent-paper citations is still unclear; therefore, it is indispensable to develop valid indicators of patent-paper citations. My motivation is to develop impact indicators for scientific papers to show technological impact at meso (institutional sector in a country, research funding, and so on) to macro levels (country), based on the statistical nature of patent-paper citations. In the field of bibliometrics, many indicators have been developed and verified by many researchers (see [7]) and practical uses such as Leiden Ranking and Scimago Journal & Country Rank. Therefore, by developing robust impact indicators based on patent-paper citations symmetrical to existing bibliometric impact indicators, it should be possible to overview both the scientific and technological

Moreover, from the view of patents, there have been many indicators for measuring patent quality (major indicators were written in [8]). For evaluating scientific papers from the aspect

from other papers, the more they tended to be cited from patents.

impacts of researches at the same time.

152 Scientometrics

I used worlds' patent data contained in the 2016 spring edition of the Patstat database produced by European Patent Office (EPO). The database contains patent applications filed until January 2016 and publications published until February 2016.

To avoid overrating the same inventions, patent data were counted by the DOCDB patent family. Only patent families which contain published patents, neither utility models nor design patents, were included in the dataset for securing consistencies of their statistic natures. Patent families are counted by their application year. The application year of the patent family was defined as the earliest filing year of the applications that constituted the family. Patent families which no application belonged to any of technology field defined in [10] were excluded, since percentiles of patent-patent citations were calculated by technology field.
