Abstract
In a previous study of patent classifications in nine material technologies for photovoltaic cells, Leydesdorff et al. (Scientometrics 102(1):629–651, 2015) reported cyclical patterns in the longitudinal development of Rao–Stirling diversity. We suggested that these cyclical patterns can be used to indicate technological life-cycles. Upon decomposition, however, the cycles are exclusively due to increases and decreases in the variety of the classifications, and not to disparity or technological distance, measured as (1 − cosine). A single frequency component can accordingly be shown in the periodogram. Furthermore, the cyclical patterns are associated with the numbers of inventors in the respective technologies. Sometimes increased variety leads to a boost in the number of inventors, but in early phases—when the technology is still under construction—it can also be the other way round. Since the development of the cycles thus seems independent of technological distances among the patents, the visualization in terms of patent maps, can be considered as addressing an analytically different set of research questions.
Highlights
In a previous study of nine material technologies for photovoltaic (PV) cells, Leydesdorff et al (2015) found a cyclic pattern in Rao–Stirling diversity (Rao 1982; Stirling 2007) using the cosine for technological proximity (Jaffe 1986) and relative frequencies among patent classifications as variety
Rao–Stirling diversity combines two of the three aspects of interdisciplinarity distinguished by Rafols and Meyer (2010): variety and disparity. [The third aspect, balance or coherence, was further developed by Rafols et al (2012) for interdisciplinary units and by Leydesdorff and Rafols (2011) for developments at the field level.] Leydesdorff et al
Footnote 2 continued Note that for i = j—that is the diagonal—cosine(i,i) = 1, and the disparity (1 - cos) = 0P. This term does not contribute to the Rao–Stirling diversity in our case, and variety is equal to i61⁄4j pipj
Summary
In a previous study of nine material technologies for photovoltaic (PV) cells, Leydesdorff et al (2015) found a cyclic pattern in Rao–Stirling diversity (Rao 1982; Stirling 2007) using the cosine for technological proximity (Jaffe 1986) and relative frequencies among patent classifications as variety. The cyclic patterns could be recognized by an expert in these technologies as a reflection of the development of technological life-cycles. In this communication, I decompose the cyclic pattern in the diversity in terms of variety and disparity, respectively. The cyclic pattern in the classifications is reflected in the number of inventors, but with a potential delay. Because some patents are tagged in more than a single category, the 6030 tags (in the third column of Table 1) are based on a smaller number of patents
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