, Volume 115, Issue 2, pp 1051–1070 | Cite as

Analysing the variation tendencies of the numbers of yearly citations for sleeping beauties in science by using derivative analysis

  • Hui FangEmail author


To comprehensively characterize the citation histories of sleeping beauties (SBs), this paper presents a derivative analysis of SB citation curves. Derivative analysis can differentiate among periods with different variation tendencies (ascending, declining or unchanged) in the number of yearly citations; these variation tendencies can be identified from successive (positive, negative or zero) derivatives. To overcome the interference caused by fluctuations in the citation curves, a smoothing method is first applied. A sleeping period appears in a citation curve as a horizontal region with a low citation count. During an awakening period, the derivatives of the curve are positive and may include a few zeros. Some SBs experience a rapid increase in yearly citations once awakened and have a short awakening period, whereas for others, the number of yearly citations increases steadily over a long awakening period. Different SBs can also show different forms based on the change in the number of yearly citations after they reach their peak, and these forms can also be distinguished through derivative analysis. Derivative analysis can be used alone to identify SBs and determine their awakening times or in combination with other methods of identifying SBs to improve their performance by assisting in the identification of abnormal SBs. Derivative analysis enables the “beauty coefficient’’ method (Ke et al. in Proc Natl Acad Sci USA 112(24):7426–7431, 2015) to determine awakening times that do not vary over time, thereby making Ke et al.’s method immune to interference due to citation fluctuations. It also allows one to determine multiple awakening times for a single SB.


Sleeping beauty Citation history Derivative analysis Variation tendency Smoothing method 



The author is grateful to Professor Jianjun Sun and to the two anonymous reviewers for helpful comments on earlier versions of this article.


  1. Aichouchi, A. E., & Gorry, P. (2017). Bundle of sleeping-beauties: The case of Paul Hagenmüller and solid-state chemistry. In 16th International conference on scientometrics and informetrics (pp. 1786–1787). China: Wuhan.Google Scholar
  2. Antoniou, A. (2005). Digital signal processing: Signal, systems, and filters. New York: McGraw-Hill.Google Scholar
  3. Axelrod, R., & Hamilton, W. D. (1981). The evolution of cooperation. Science, 211(4489), 1390–1396.MathSciNetCrossRefzbMATHGoogle Scholar
  4. Braun, T., Glänzel, W., & Schubert, A. (2010). On sleeping beauties, princes and other tales of citation distributions. Research Evaluation, 19(3), 195–202.CrossRefGoogle Scholar
  5. Buchsbaum, G. (1980). A spatial processor model for object colour perception. Journal of the Franklin Institute, 310(1), 1–26.CrossRefGoogle Scholar
  6. Cole, S. (1970). Professional standing and the reception of scientific discoveries. American Journal of Sociology, 76(2), 286–306.CrossRefGoogle Scholar
  7. Costas, R., van Leeuwen, T. N., & van Raan, A. F. J. (2010). Is scientific literature subject to a ‘‘sell-bydate’’? A general methodology to analyze the ‘‘durability’’ of scientific documents. Journal of the American Society for Information Science and Technology, 61(2), 329–339.CrossRefGoogle Scholar
  8. De Rujula, A., Georgi, H., Glashow, S. L. (1977). Molecular charmonium - A new spectroscopy. Physical Review Letters, 38(7), 317–321.CrossRefGoogle Scholar
  9. Dieckmann, U., & Law, R. (1996). The dynamical theory of coevolution: A derivation from stochastic ecological processes. Journal of Mathematical Biology, 34(5–6), 579–612.MathSciNetCrossRefzbMATHGoogle Scholar
  10. Du, J., & Wu, Y. (2016). A bibliometric framework for identifying “princes” who wake up the “sleeping beauty” in challenge-type scientific discoveries. Journal of Data and Information Science, 1(1), 50–68.Google Scholar
  11. Du, J., & Wu, Y. (2017). A parameter-free index for identifying under-cited sleeping beauties in science. In 16th International conference on scientometrics and informetrics (pp. 148–157). China: Wuhan.Google Scholar
  12. Fiala, D., Subelj, L., Zitnik, S., & Bajec, M. (2015). Do PageRank-based author rankings outperform simple citation counts? Journal of Informetrics, 9(2), 334–348.CrossRefGoogle Scholar
  13. Gadrey, J., Gallouj, F., & Weinstein, O. (1995). New modes of innovation: How services benefit industry. International Journal of Service Industry Management, 6(3), 4–16.CrossRefGoogle Scholar
  14. Garfield, E. (1980). Premature discovery or delayed recognition-why? Current Contents, 21, 5–10.Google Scholar
  15. Garfield, E. (1989). Delayed recognition in scientific discovery: Citation frequency analysis aids the search for case histories. Current Contents, 23, 3–9.Google Scholar
  16. Garfield, E. (1990). More delayed recognition. 2. From inhibin to scanning electron-microscopy. Current Contents, 9, 3–9.Google Scholar
  17. Geritz, S. A. H., Kisdi, E., Meszena, G., Metz, J. A. J. (1998). Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evolutionary Ecology, 12(1), 35–57.CrossRefGoogle Scholar
  18. Glänzel, W., & Garfield, E. (2004). The myth of delayed recognition. Scientist, 18(11), 8–9.Google Scholar
  19. Glänzel, W., Schlemmer, B., & Thijs, B. (2003). Better late than never? On the chance to become highly cited only beyond the standard bibliometric time horizon. Scientometrics, 58(3), 571–586.CrossRefGoogle Scholar
  20. Gorry, P., & Aichouchi, A. E. (2017). Sleeping beauty awakened by self-citation of a review: A case study of Judah Folkman hypothesis on angiogenesis. In 16th International conference on scientometrics and informetrics (pp. 778–786). China: Wuhan.Google Scholar
  21. Gorry, P., & Ragouet, P. (2016). “Sleeping beauty’’ and her restless sleep: Charles Dotter and the birth of interventional radiology. Scientometrics, 107(2), 773–784.CrossRefGoogle Scholar
  22. Hartley, J., & Ho, Y.-S. (2017). Who woke the sleeping beauties in psychology? Scientometrics, 112(2), 1065–1068.CrossRefGoogle Scholar
  23. Ho, Y.-S., & Hartley, J. (2017). Sleeping beauties in psychology. Scientometrics, 110(1), 301–305.CrossRefGoogle Scholar
  24. Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53(282), 457–481.MathSciNetCrossRefzbMATHGoogle Scholar
  25. Ke, Q., Ferrara, E., Radicchi, F., & Flammini, A. (2015). Defining and identifying sleeping beauties in science. Proceedings of the National Academy of Sciences of the United States of America, 112(24), 7426–7431.CrossRefGoogle Scholar
  26. Lachance, C., & Larivière, V. (2014). On the citation lifecycle of papers with delayed recognition. Journal of Informetrics, 8(4), 863–872.CrossRefGoogle Scholar
  27. Li, J. (2014). Citation curves of “all-elements-sleeping-beauties”: “Flash in the pan” first and then “delayed recognition”. Scientometrics, 100(2), 595–601.CrossRefGoogle Scholar
  28. Li, J., & Shi, D. (2016). Sleeping beauties in genius work: When were they awakened? Journal of the Association for Information Science and Technology, 67(2), 432–440.MathSciNetCrossRefGoogle Scholar
  29. Li, J., Shi, D., Zhao, S. X., & Ye, F. Y. (2014). A study of the ‘‘heartbeat spectra’’ for ‘‘sleeping beauties’’. Journal of Informetrics, 8(3), 493–502.CrossRefGoogle Scholar
  30. Li, J., & Ye, F. Y. (2012). The phenomenon of all-elements-sleeping-beauties in scientific literature. Scientometrics, 92(3), 795–799.CrossRefGoogle Scholar
  31. Li, J., & Ye, F. Y. (2016). Distinguishing sleeping beauties in science. Scientometrics, 108(2), 821–828.CrossRefGoogle Scholar
  32. Ogino, T. & Aoki, M. (1980). Mechanism of Yellow Luminescence in GAN. Japanese Journal of Applied Physics, 19(12), 2395–2406.CrossRefGoogle Scholar
  33. Ohba, N., & Nakao, K. (2012). Sleeping beauties in ophthalmology. Scientometrics, 93(2), 253–264.CrossRefGoogle Scholar
  34. Rabiner, L. R. (1972). Linear program design of finite impulse response (FIR) digital filters. IEEE Transactions on Audio and Electroacoustics, AU, 20(4), 280–288.CrossRefGoogle Scholar
  35. Reichstein, T., & Shoppee, C. W. (1949). Chromatography of steroids and other colourless substances by the method of fractional elution. Discussions of the Faraday Society, 7, 305–311.CrossRefGoogle Scholar
  36. Savitzky, A., & Golay, M. J. E. (1964). Smoothing and differentiation of data by simplified least squares procedures. Analytical Chemistry, 36(8), 1627–1639.CrossRefGoogle Scholar
  37. Smith, J. M. (1976). Evolution and the theory of games: In situations characterized by conflict of interest, the best strategy to adopt depends on what others are doing. American Scientist, 64(1), 41–45.Google Scholar
  38. Smith, J. M., & Price, G. R. (1973). The logic of animal conflict. Nature, 246(5427), 15–18.CrossRefzbMATHGoogle Scholar
  39. Sun, J., Min, C., & Li, J. (2016). A vector for measuring obsolescence of scientific articles. Scientometrics, 107(2), 745–757.CrossRefGoogle Scholar
  40. Szabo, G., & Fath, G. (2007). Evolutionary games on graphs. Physics Reports-Review Section of Physics Letters, 446(4–6), 97–216.MathSciNetGoogle Scholar
  41. Takeda, K., & Shiraishi, K. (1994). Theoretical possibility of stage corrugation in Si and Ge analogs of graphite. Physical Review B, 50(20), 14916–14922.CrossRefGoogle Scholar
  42. Taylor, P. D., & Jonker, L. B. (1978). Evolutionary stable strategies and game dynamics. Mathematical Biosciences, 40(1–2), 145–156.MathSciNetCrossRefzbMATHGoogle Scholar
  43. Teixeira, A. A. C., Vieira, P. C., & Abreu, A. P. (2017). Sleeping beauties and their princes in innovation studies. Scientometrics, 110(2), 541–580.CrossRefGoogle Scholar
  44. van Calster, Ben. (2012). It takes time: A remarkable example of delayed recognition. Journal of American Society for Information Science and Technology, 63(11), 2341–2344.CrossRefGoogle Scholar
  45. van Raan, A. F. J. (2004). Sleeping beauties in science. Scientometrics, 59(3), 467–472.CrossRefGoogle Scholar
  46. van Raan, A. F. J. (2015). Dormitory of physical and engineering sciences: Sleeping beauties may be sleeping innovations. PLoS ONE, 10(10), e0139786.CrossRefGoogle Scholar
  47. van Raan, A. F. J. (2017). Sleeping beauties cited in patents: Is there also a dormitory of inventions? Scientometrics, 110(3), 1123–1156.CrossRefGoogle Scholar
  48. Yannuzzi, L. A., Sorenson, J., Spaide, R. F., Lipson, B. (1990). Idiopathic polypoidal choroidal vasculopathy (IPCV). Retina—The Journal of Retinal and Vitreous Diseases, 10(1), 1–8.Google Scholar
  49. Ye, F. Y., & Bornmann, L. (2017). “Smart girls” versus “sleeping beauties” in the sciences: The identification of instant and delayed recognition by using the citation angle. Journal of the Association for Information Science and Technology. Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Analytical Chemistry for Life Science, School of Electronic Science and EngineeringNanjing UniversityNanjingChina

Personalised recommendations