Selected Models for Dynamics of Research Organizations and Research Production

  • Nikolay K. VitanovEmail author
Part of the Qualitative and Quantitative Analysis of Scientific and Scholarly Communication book series (QQASSC)


The understanding of dynamics of research organizations and research production is very important for their successful management. In the text below, selected deterministic and probability models of research dynamics are discussed. The idea of the selection is to cover mainly the areas of publications dynamics, citations dynamics, and aging of scientific information. From the class of deterministic models we discuss models connected to research publications (SI-model, Goffmann–Newill model, model of Price for growth of knowledge), deterministic model connected to dynamics of citations (nucleation model of growth dynamics of citations), deterministic models connected to research dynamics (logistic curve models, model of competition between systems of ideas, reproduction–transport equation model of evolution of scientific subfields), and a model of science as a component of the economic growth of a country. From the class of probability models we discuss a probability model connected to research publications (based on the Yule process), probability models connected to dynamics of citations (Poisson and mixed Poisson models, models of aging of scientific information (death stochastic process model and birth stochastic process model connected to Waring distribution)). The truncated Waring distribution and the multivariate Waring distribution are described, and a variational approach to scientific production is discussed. Several probability models of production/citation process (Paretian and Poisson distribution models of the h-index) as well as GIGP model distribution of bibliometric data are presented. A stochastic model of scientific productivity based on a master equation is described, and a probability model for the importance of the human factor in science is discussed. The chapter ends by providing information about some models and distributions connected to informetrics: limited dependent variable models for data analysis and the generalized Zipf distribution and its connection to the Waring distribution and Yule distribution.


Poisson Process Research Publication Epidemic Model Negative Binomial Distribution Citation Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    D. de Solla Price. Little Science, Big Science. (Columbia University Press, New York, 1963)Google Scholar
  2. 2.
    D.P. Wallace, The relationship between journal productivity and obsolescence. J. Am. Soc. Inf. Sci. 37, 136–145 (1986)CrossRefGoogle Scholar
  3. 3.
    L. Egghe, On the influence of growth on obsolescence. Scientometrics 27, 195–214 (1993)CrossRefGoogle Scholar
  4. 4.
    W. Glänzel, U. Schoepflin, A bibliometric study on ageing and reception process of scientific literature. J. Inf. Sci. 21, 37–53 (1995)CrossRefGoogle Scholar
  5. 5.
    W. Goffman, V.A. Newill, Generalization of epidemic theory. An application to the transmission of ideas. Nature 204(4955), 225–228 (1964)CrossRefGoogle Scholar
  6. 6.
    P. Nyhius, Logistic curves, in CIPR encyclopedia of production engineering, ed. by L. Laperriere, G. Reinhart (Springer, Berlin, 2014), pp. 759–762CrossRefGoogle Scholar
  7. 7.
    A. Fernandez-Cano, M. Torralbo, M. Vallejo, Reconsidering Price’s model of scientific growth: an overview. Scientometrics 61, 301–321 (2004)CrossRefGoogle Scholar
  8. 8.
    V. Volterra, Population growth, equilibria, and extinction under specified breeding conditions: a development and extension of the theory of the logistic curve, in The Golden Age of Theoretical Ecology: 1923–1940, ed. by F.M. Scudo, J.E. Ziegler (Springer, Berlin, 1978), pp. 18–27CrossRefGoogle Scholar
  9. 9.
    C.-Y. Wong, L. Wang, Trajectories of science and technology and their co-evolution in BRICS: Insigths from publication and patent analysis. J. Inf. 9, 90–101 (2015)CrossRefGoogle Scholar
  10. 10.
    L. Egghe, I.K. Ravichandra, Rao. Classification of growth models based on growth rates and its applications. Scientometrics 25, 5–46 (1992)CrossRefGoogle Scholar
  11. 11.
    P.S. Meyer, Bi-logistic growth. Technol. Forecast. Soc. Chang. 47, 89–102 (1994)CrossRefGoogle Scholar
  12. 12.
    M. Ausloos, On religion and language evolutions seen through mathematical and agent based models, in Proceedings of the First Interdisciplinary CHESS Interactions Conference, ed. by C. Rangacharyulu, E. Haven (World Scientific, Singapore, 2010), pp. 157–182CrossRefGoogle Scholar
  13. 13.
    P.S. Meyer, J.W. Yung, J.H. Ausubel, A primer on logistic growth and substitution: the mathematics of the Loglet Lab software. Technol. Forecast. Soc. Chang. 61, 247–271 (1999)CrossRefGoogle Scholar
  14. 14.
    H.W. Menard, Science: Growth and Change (Harvard University Press, Cambridge, MA, 1971)CrossRefGoogle Scholar
  15. 15.
    G.N. Gilbert, Measuring the growth of science: a review of indicators of scientific growth. Scientometrics 1, 9–34 (1978)CrossRefGoogle Scholar
  16. 16.
    D. Wolfram, C.M. Chu, X. Lu, Growth of knowledge: bibliometric analysis using online database data, in Informetrics 89/90, ed. by L. Egghe, R. Rousseau (Elsevier, Amsterdam, 1990), pp. 355–372Google Scholar
  17. 17.
    G.O. Ware, A general statistical model for estimating future demand levels of data-base utilization within an information retrieval organization. J. Am. Soc. Inf. Sci. 24, 261–264 (1973)CrossRefGoogle Scholar
  18. 18.
    N. Bailey, Some stochastic models for small epidemics in large populations. Appl. Stat. 13, 9–19 (1964)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 19.
    M.S. Bartlet, Stochastic Population Models in Ecology and Epidemiology (Wiley, New York, 1960)Google Scholar
  20. 20.
    W. Goffman, An epidemic process in an open population. Nature 205, 831–832 (1965)zbMATHCrossRefGoogle Scholar
  21. 21.
    D. Mollison, Dependence of epidemic and population velocities on basic parameters. Math. Biosci. 107, 255–287 (1991)zbMATHCrossRefGoogle Scholar
  22. 22.
    F.C. Hoppensteadt, Mathematical Theories of Populations: Demographics, Genetics and Epidemics (SIAM, Philadelphia, PA, 1975)Google Scholar
  23. 23.
    K. Cooke, P. van den Driessche, X. Zou, Interaction of maturation delay and nonlinear birth in population and epidemic models. J. Math. Biol. 39, 332–352 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    H.W. Hethcote, The mathematics of infectious diseases. SIAM Rev. 42, 599–653 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    V. Colizza, A. Barnat, M. Barthelemy, A. Vespigniani, The modeling of global epidemics: stochastic dynamics and predictability. Bull. Math. Biol. 68, 1893–1921 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 26.
    R.M. May, Simple mathematical models with very complicated dynamics. Nature 261(5560), 459–467 (1976)CrossRefGoogle Scholar
  27. 27.
    H. Caswell, Matrix Population Models (Wiley, New York, 2001)Google Scholar
  28. 28.
    R.D. Holt, Population dynamics in two-patch environments: some anomalous consequences of an optimal habitat distribution. Theoretical Population Biology 28, 181–208 (1985)MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    M.P. Hassell, H.N. Comins, R.M. May, Spatial structure and chaos in insect population dynamics. Nature 353(6341), 255–258 (1991)CrossRefGoogle Scholar
  30. 30.
    Z. Ma, J. Li, Basic knowledge and developing tendencies in epidemic dynamics, in Mathematics for Life Sciences and Medicine, ed. by Y. Takeuchi, Y. Iwasa, K. Sato (Springer, Berlin, 2007), pp. 5–49Google Scholar
  31. 31.
    N.K. Vitanov, M. Ausloos, Knowledge epidemic and population dynamics models for describing idea diffusion, in Models for Science Dynamics, ed. by A. Scharnhorst, K. Börner, P. van den Besselar (Springer, Berlin, 2012), pp. 69–125CrossRefGoogle Scholar
  32. 32.
    C. Antonelli, The Economics of Localized Technological Change and Industrial Dynamics (Kluwer, Dordrecht, 1995)CrossRefGoogle Scholar
  33. 33.
    P. Anderson, Perspective: complexity theory and organization science. Organ. Sci. 10, 216–232 (1999)CrossRefGoogle Scholar
  34. 34.
    M.A. Nowak, Five rules for the evolution of cooperation. Science 314(5805), 1560–1563 (2006)CrossRefGoogle Scholar
  35. 35.
    W. Weidlich, G. Haag, Concepts and Models of a Quantitative Sociology: The Dynamics of Interacting Populations (Springer, Berlin, 1983)zbMATHCrossRefGoogle Scholar
  36. 36.
    D. Strang, Adding social structure to diffusion models. Sociol. Methods Res. 19, 324–353 (1991)CrossRefGoogle Scholar
  37. 37.
    P.A. Geroski, Models of technology diffusion. Res. Policy 29, 603–625 (2000)CrossRefGoogle Scholar
  38. 38.
    C. Castellano, S. Fortunato, V. Loreto, Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591–646 (2009)CrossRefGoogle Scholar
  39. 39.
    N.K. Vitanov, Z.I. Dimitrova, Application of the method of simplest equation for obtaining exact traveling-wave solutions for two classes of model PDEs from ecology and population dynamics. Commun. Nonlinear Sci. Numer. Simul. 15, 2836–2845 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  40. 40.
    R. Baptista, The diffusion of process innovations: a selective review. Int. J. Econ. Bus. 6, 107–129 (1999)CrossRefGoogle Scholar
  41. 41.
    I.Z. Kiss, M. Broom, P.G. Craze, I. Rafols, Can epidemic models describe the diffusion of topics across disciplines? J. Inf. 4, 74–82 (2010)CrossRefGoogle Scholar
  42. 42.
    H.G. Landau, A. Rapoport, Contribution to the mathematical theory of contagion and spread of information. I: spread through a thoroughly mixed population. Bull. Math. Biophys. 15, 173–183 (1953)MathSciNetCrossRefGoogle Scholar
  43. 43.
    W. Goffman, Mathematical approach to the spread of scientific ideas—the history of mast cell research. Nature 212, 449–452 (1966)CrossRefGoogle Scholar
  44. 44.
    A. Lotka, Elements of Physical Biology (Williams and Wilkins, Baltomore, 1925)zbMATHGoogle Scholar
  45. 45.
    V. Volterra, Variations and fluctuations of the number of individuals in animal species living together. Journal du Conseil/Conseil Permanent International pour l’Exploration de la Mer 3, 3–52 (1928)CrossRefGoogle Scholar
  46. 46.
    F.J. Ayala, M.E. Gilpin, J.G. Ehrenfeld, Competition between species: theoretical models and experimental tests. Theor. Popul. Biol. 4, 331–356 (1973)MathSciNetCrossRefGoogle Scholar
  47. 47.
    M.E. Gilpin, F.J. Ayala, Global models of growth and competition. PNAS 70, 3590–3593 (1973)zbMATHCrossRefGoogle Scholar
  48. 48.
    R.D. Holt, J. Pickering, Infectious disease and species coexistence: a model of Lotka-Volterra form. Am. Nat. 126, 196–211 (1985)CrossRefGoogle Scholar
  49. 49.
    Y. Takeuchi, Global Dynamical Properties of Lotka-Volterra Systems (World Scientific, Singapore, 1996)zbMATHCrossRefGoogle Scholar
  50. 50.
    A. Castiaux, Radical innovation in established organizations: being a knowledge predator. J. Eng. Technol. Manag. 24, 36–52 (2007)CrossRefGoogle Scholar
  51. 51.
    K. Dietz, Epidemics and rumors: a survey. J. R. Stat. Soc. A 130, 505–528 (1967)MathSciNetCrossRefGoogle Scholar
  52. 52.
    S. Solomon, P. Richmond, Power laws of wealth, market order volumes and market returns. Phys. A 299, 188–197 (2001)zbMATHCrossRefGoogle Scholar
  53. 53.
    S. Solomon, P. Richmond, Stable power laws in variable economics. Lotka—Volterra implies Pareto—Zipf. Eur. Phys. J. B 27, 257–261 (2002)Google Scholar
  54. 54.
    W.O. Kermack, A.G. McKendrick, A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. A 115, 700–721 (1927)zbMATHCrossRefGoogle Scholar
  55. 55.
    M. Nowakowska, Epidemical spread of scientific objects: an attempt of empirical approach to some problems of meta—science. Theory Decis. 3, 262–297 (1973)CrossRefGoogle Scholar
  56. 56.
    D.J. Daley, Concerning the spread of news in a population of individuals who never forget. Bull. Math. Biophys. 29, 373–376 (1967)CrossRefGoogle Scholar
  57. 57.
    A.D. Barbour, S. Utev, Approximating the Reed-Frost epidemic process. Stoch. Process. Appl. 113, 173–197 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  58. 58.
    H. Abbey, An examination of the Reed-Frost theory of epidemics. Hum. Biol. 24, 201–233 (1952)Google Scholar
  59. 59.
    J.A. Jacquez, A note on chain-binomial models of epidemic spread: what is wrong with the Reed-Frost formulation? Math. Biosci. 87, 73–82 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  60. 60.
    W. Goffman, V.A. Newill, Communication and epidemic process. Proc. R. Soc. Lond. Ser. A 298, 316–334 (1967)zbMATHCrossRefGoogle Scholar
  61. 61.
    G. Harmon, Remembering William Goffman: mathematical information science pioneer. Inf. Process. Manag. 44, 1634–1647 (2008)CrossRefGoogle Scholar
  62. 62.
    M. Cohen, A. Blaivas, A model for the growth of mathematical specialties. Scientometrics 3, 265–273 (1981)CrossRefGoogle Scholar
  63. 63.
    B.M. Gupta, L. Sharma, C.R. Karisiddappa, Modelling the growth of papers in a scientific speciality. Scientometrics 33, 187–201 (1995)CrossRefGoogle Scholar
  64. 64.
    M. Kochen, Stability and growth of knowledge. Am. Doc. 20, 186–197 (1969)CrossRefGoogle Scholar
  65. 65.
    A.N. Tabah, Literature dynamics: studies on growth, diffusion and epidemics. Annu. Rev. Inf. Sci. Technol. 34, 249–286 (1999)Google Scholar
  66. 66.
    B.M. Gupta, P. Sharma, C.R. Karisiddappa, Growth of research literature in scientific specialities. A modeling perspective. Scientometrics 40, 507–528 (1997)CrossRefGoogle Scholar
  67. 67.
    B.M. Gupta, S. Kumar, S.L. Sangam, C.R. Karisiddappa, Modeling the growth of world social science literature. Scientometrics 53, 161–164 (2002)CrossRefGoogle Scholar
  68. 68.
    L.M.A. Bettencourt, A. Cintron-Arias, D.I. Kaiser, C. Castillo-Chavez, The power of a good idea: quantitative modeling of the spread of ideas from epidemiological models. Phys. A 364, 513–536 (2002)CrossRefGoogle Scholar
  69. 69.
    L.M.A. Bettencourt, D.I. Kaiser, J. Kaur, C. Castillo-Chavez, D.E. Wojick, Population modeling of the emergence and development of scientific fields. Scientometrics 75, 495–518 (2008)CrossRefGoogle Scholar
  70. 70.
    M. Szydlowski, A. Krawiez, Growth cycles of knowledge. Scientometrics 78, 99–111 (2009)CrossRefGoogle Scholar
  71. 71.
    D.J. de Solla Price, The exponential curve of science. Discovery 17, 240–243 (1956)Google Scholar
  72. 72.
    K. Sangwal, Progressive nucleation mechanism and its application to the growth of journals, articles and authors in scientific fields. J. Inf. 5, 529–536 (2011)CrossRefGoogle Scholar
  73. 73.
    K. Sangwal, On the growth of citations of publication output of individual authors. J. Inf. 5, 554–564 (2011)CrossRefGoogle Scholar
  74. 74.
    K. Sangwal, Progressive nucleation mechanism of the growth behavior of items and its application to cumulative papers and citations of individual authors. Scientometrics 92, 643–655 (2012)CrossRefGoogle Scholar
  75. 75.
    K. Sangwal, Growth dynamics of citations of cumulative papers of individual authors according to progressive nucleation mechanism: concept of citation acceleration. Inf. Process. Manag. 49, 757–772 (2013)CrossRefGoogle Scholar
  76. 76.
    D. Kashchiev, Nucleation: Basic theory with applications (Butterworth-Heinemann, Oxford, 2000)Google Scholar
  77. 77.
    E.H. Kerner, Further considerations on the statistical mechanics of biological associations. Bull. Math. Biophys. 21, 217–253 (1959)MathSciNetCrossRefGoogle Scholar
  78. 78.
    J.C. Allen, Mathematical model of species interactions in time and space. Am. Nat. 109, 319–342 (1975)CrossRefGoogle Scholar
  79. 79.
    A. Okubo, Diffusion and Ecological Problems: Mathematical Models (Springer, Berlin, 1980)zbMATHGoogle Scholar
  80. 80.
    W.G. Willson, A.M. de Roos, Spatial instabilities within the diffusive Lotka—Volterra system: individual—based simulation results. Theor. Popul. Biol. 43, 91–127 (1993)zbMATHCrossRefGoogle Scholar
  81. 81.
    Y.F. le Coadic, Information system and the spread of scientific ideas. R&D Manag. 4, 97–111 (1974)CrossRefGoogle Scholar
  82. 82.
    E. Bruckner, W. Ebeling, A. Scharnhorst, The application of evolution models in scientometrics. Scientometrics 18, 21–41 (1990)CrossRefGoogle Scholar
  83. 83.
    N.K. Vitanov, I.P. Jordanov, Z.I. Dimitrova, On nonlinear population waves. Appl. Math. Comput. 215, 2950–2964 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  84. 84.
    N.K. Vitanov, I.P. Jordanov, Z.I. Dimitrova, On nonlinear dynamics of interacting populations: coupled kink waves in a system of two populations. Commun. Nonlinear Sci. Numer. Simul. 14, 2379–2388 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  85. 85.
    N.K. Vitanov, Z.I. Dimitrova, M. Ausloos, Verhulst-Lotka-Volterra (VLV) model of ideological struggle. Phys. A 389, 4970–4980 (2010)zbMATHCrossRefGoogle Scholar
  86. 86.
    N.K. Vitanov, M. Ausloos, G. Rotundo, Discrete model of ideological struggle accounting for migration. Adv. Complex Syst. 15, Article No. 1250049 (2012)Google Scholar
  87. 87.
    W. Ebeling, A. Scharnhorst, Evolutionary models of innovation dynamics, in Traffic and Granular Flow’99. Social, Traffic and Granular Dynamics, ed. by D. Helbing, H.J. Herrman, M. Schekenberg, D.E. Wolf (Springer, Berlin, 2000), pp. 43–56Google Scholar
  88. 88.
    E. Borensztein, J. De Gregorio, J.-W. Lee, How does foreigh direct investment affect economic growth? J. Int. Econ. 45, 115–135 (1998)CrossRefGoogle Scholar
  89. 89.
    J. Dedrick, V. Gurbaxani, K.L. Kraemer, Information technology and economic performance: a critical review of the empirical evidence. ACM Comput. Surv. 35, 1–28 (2003)CrossRefGoogle Scholar
  90. 90.
    S.W. Popper, C. Wagner, New foundations of growth: The U.S. innovation system today and tomorrow. RAND MR-1338.0/1-OSTP (2001)Google Scholar
  91. 91.
    E. Mansfield, Industrial Research and Technological Innovation: An Econometric Analysis (Norton, New York, 1968)Google Scholar
  92. 92.
    A.I. Yablonskii, Mathematical Methods in the Study of Science (Nauka, Moscow, 1986). (in Russian)Google Scholar
  93. 93.
    C.W. Cobb, P.H. Douglas, A theory of production. Am. Econ. Rev. 18(Supplement), 139–165 (1928)Google Scholar
  94. 94.
    A. Aulin, The Impact of Science on Economic Growth and its Cycles (Springer, Berlin, 1998)zbMATHCrossRefGoogle Scholar
  95. 95.
    Q.L. Burell, Predictive aspects of some bibliometric processes, in Informetrics 87/88, ed. by L. Egghe, R. Rousseau (Elsevier, Amsterdam, 1988), pp. 43–63Google Scholar
  96. 96.
    Q.L. Burrell, A note on ageing in a library circulation model. J. Doc. 41, 100–115 (1985)CrossRefGoogle Scholar
  97. 97.
    D.R. Cox, Some statistical methods connected with series of events (with discussion). J. R. Stat. Soc. B 17, 129–164 (1955)zbMATHGoogle Scholar
  98. 98.
    J. Grandell, Doubly stochastic Poisson processes, vol. 529, Lecture Notes in Mathematics (Springer, Berlin, 1976)zbMATHGoogle Scholar
  99. 99.
    H.S. Sichel, On a distribution representing sentence-length in written prose. J. R. Stat. Soc. A 137, 25–34 (1974)CrossRefGoogle Scholar
  100. 100.
    H.S. Sichel, Repeat-buying and the generalized inverse Gaussian-Poisson distribution. Appl. Stat. 31, 193–204 (1982)CrossRefGoogle Scholar
  101. 101.
    J.O. Irvin, The generalized Waring distribution. Part I. J. R. Stat. Soc. A 138, 18–21 (1975)Google Scholar
  102. 102.
    J.O. Irvin, The generalized Waring distribution. Part II. J. R. Stat. Soc. A 138, 204–227 (1975)CrossRefGoogle Scholar
  103. 103.
    J.O. Irvin, The generalized Waring distribution. Part III. J. R. Stat. Soc. A 138, 374–384 (1975)CrossRefGoogle Scholar
  104. 104.
    A.I. Yablonsky, Mathematical Models in Science Studies (Nauka, Moscow, 1986). (in Russian)Google Scholar
  105. 105.
    G.U. Yule, A mathematical theory of evolution, based on the conclusions of Dr. J.C. Willis, F.R.S. Philos. Trans. R. Soc. B 213, 21–87 (1925)CrossRefGoogle Scholar
  106. 106.
    H.A. Simon, C.P. Bonini, The size distribution of business firms. Am. Econ. Rev. 48, 607–617 (1958)Google Scholar
  107. 107.
    M. Brown, S. Ross, R. Shorrock, Evacualtion of a Yule process with immigration. J. Appl. Probab. 12, 807–811 (1975)MathSciNetzbMATHCrossRefGoogle Scholar
  108. 108.
    N. O’Connell, Yule process approximation for the skeleton of a branching process. J. Appl. Probab. 30, 725–729 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  109. 109.
    D.J. Aldous, Stochastic models and descriptive statistics for phylogenetic trees, from Yule to today. Stat. Sci. 16, 23–34 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  110. 110.
    S. Redner, How popular is your paper? An empirical study of the citation distribution. Eur. Phys. J. B 4, 131–134 (1998)CrossRefGoogle Scholar
  111. 111.
    S. Redner, Citation statistics from 110 years of physical review. Phys. Today 58, 49–54 (2005)CrossRefGoogle Scholar
  112. 112.
    C.C. Sarli, E.K. Dubinsky, K.L. Holmes, Beyond citation analysis: a model for assessment of research impact. J. Med. Libr. Assoc. 98, 17–23 (2010)CrossRefGoogle Scholar
  113. 113.
    M.Y. Wang, G. Yu, D.R. Yu, Minimg typical features for highly cited papers. Scientometrics 87, 695–706 (2011)CrossRefGoogle Scholar
  114. 114.
    M. Wang, G. Yu, S. An, D. Yu, Discovery of factors influencing citation impact based on a soft fuzzy rough set model. Scientometrics 93, 635–644 (2012)CrossRefGoogle Scholar
  115. 115.
    Q.L. Burrell, Stochastic modeling of the first-citation distribution. Scientometrics 52, 3–12 (2001)CrossRefGoogle Scholar
  116. 116.
    L. Egghe, I.K. Ravichandra Rao, Citation age data and the obsolescence function: fits and explanations. Inf. Process. Manag. 28, 201–217 (1992)CrossRefGoogle Scholar
  117. 117.
    R. Rousseau, Double exponential models for first-citation processes. Scientometrics 30, 213–227 (1994)CrossRefGoogle Scholar
  118. 118.
    L. Egghe, A heuristic study of the first-citation distribution. Scientometrics 48, 345–359 (2000)CrossRefGoogle Scholar
  119. 119.
    D.R. Cox, V.I. Isham, Point Processes (Chapman & Hall, London, 1980)zbMATHGoogle Scholar
  120. 120.
    J.F.C. Kingman, Poisson processes (Clarendon Press, Oxford, 1992)zbMATHGoogle Scholar
  121. 121.
    T. Mikosch, Non-life Insurance Mathematics. An Introduction with the Poisson Process (Springer, Berlin, 2009)zbMATHCrossRefGoogle Scholar
  122. 122.
    H.C. Tijms, A First Course in Stochastic Models (Wiley, Chichester, 2003)zbMATHCrossRefGoogle Scholar
  123. 123.
    S. Nadarajan, S. Kotz, Models for citations behavior. Scientometrics 72, 291–305 (2007)CrossRefGoogle Scholar
  124. 124.
    S.M. Ross, Stochastic Processes (Wiley, New York, 1996)zbMATHGoogle Scholar
  125. 125.
    Q.L. Burrell, The \(n\)-th citation distribution and obsolescence. Scientometrics 53, 309–323 (2002)CrossRefGoogle Scholar
  126. 126.
    A.F.J. van Raan, Sleeping beauties in science. Scientometrics 59, 467–472 (2004)CrossRefGoogle Scholar
  127. 127.
    Q.L. Burrell, Are “sleeping beauties” to be expected? Scientometrics 6, 381–389 (2005)CrossRefGoogle Scholar
  128. 128.
    J. Grandell, Mixed Poisson processes (Chapman & Hall, London, 1997)zbMATHCrossRefGoogle Scholar
  129. 129.
    S.A. Klugman, H.H. Panjer, G.E. Wilmot, Loss Models. From Data to Decisions (Wiley, Hoboken, NJ, 2008)zbMATHCrossRefGoogle Scholar
  130. 130.
    M. Bennet, Stochastic Processes in Science, Engineering and Finance (Chapman & Hall, Boca Raton, FL, 2006)Google Scholar
  131. 131.
    R.-D. Reiss, M. Thomas, Statistical Analysis of Extreme Values (Birkhäuser, Basel, 1997)zbMATHCrossRefGoogle Scholar
  132. 132.
    Q.L. Burrell, A simple stochastic model for library loans. J. Doc. 36, 115–132 (1980)CrossRefGoogle Scholar
  133. 133.
    Q.L. Burrell, Predictive aspects of some bibliometric processes, in Infometrics 87/88, ed. by L. Egghe, R. Rousseau (Amsterdam, Elsevier, 1988), pp. 43–63Google Scholar
  134. 134.
    Q.L. Burrell, Using the gamma-Poisson model to predict library circulation. J. Am. Soc. Inf. Sci. 41, 164–170 (1990)CrossRefGoogle Scholar
  135. 135.
    J.M. Hilbe, Negative Binomial Regression (Cambridge University Press, Cambridge, 2007)zbMATHCrossRefGoogle Scholar
  136. 136.
    N.L. Johnson, A.W. Kemp, S. Kotz, Univariate Discrete Distributions (Willey, Hoboken, NJ, 2005)zbMATHCrossRefGoogle Scholar
  137. 137.
    J.H. Pollard, A Handbook of Numerical and Statistical Techniques: With Examples Mainly from the Life Sciences (Cambridge University Press, Cambridge, 1977)zbMATHCrossRefGoogle Scholar
  138. 138.
    M. Greenwood, G.U. Yule, An inquiry into the nature of frequency distributions representative of multiple happenings with particular reference to the occurrence of multiple attacks of disease or repeated accidents. J. R. Stat. Soc. A 83, 255–279 (1920)CrossRefGoogle Scholar
  139. 139.
    J. Mingers, Q.L. Burrell, Modeling citation behavior in management science journals. Inf. Process. Manag. 42, 1451–1464 (2006)CrossRefGoogle Scholar
  140. 140.
    E.S. Vieira, J.A.N.F. Gomes, Citation to scientific articles: its distribution and dependence on the article features. J. Inf. 4, 1–13 (2010)CrossRefGoogle Scholar
  141. 141.
    C. Lachance, V. Lariviere, On the citation lyfecycle of papers with delayed recognition. J. Inf. 8, 863–872 (2014)CrossRefGoogle Scholar
  142. 142.
    A.I. Yablonskii, Models and Methods of Mathematical Study of Science (AN USSR, Moscow (in Russian), 1977)Google Scholar
  143. 143.
    A. Schubert, W. Glänzel, A dynamic look at a class of skew distributions. A model with scientometric application. Scientometrics 6, 149–167 (1984)CrossRefGoogle Scholar
  144. 144.
    W. Glänzel, A. Schubert, Predictive aspects of a stochastic model for citation processes. Inf. Process. Manag. 31, 69–80 (1995)CrossRefGoogle Scholar
  145. 145.
    R. Frank, Brand choice as a probability process. J. Bus. 35, 43–56 (1962)CrossRefGoogle Scholar
  146. 146.
    J.S. Coleman, Introduction to Mathematical Sociology (Collier-Macmillan, London, 1964)Google Scholar
  147. 147.
    H.A. Simon, On a class of skew distribution functions. Biometrica 42, 425–440 (1955)MathSciNetzbMATHCrossRefGoogle Scholar
  148. 148.
    Y. Ijiri, H. Simon, Skew Distributions and the Sizes of Business Firms (North Holland, Amsterdam, 1977)zbMATHGoogle Scholar
  149. 149.
    J. Eeckhout, Gibrath’s law for (all) cities. Am. Econ. Rev. 94, 1429–1451 (2004)CrossRefGoogle Scholar
  150. 150.
    W. Glänzel, Bibliometrics as a Research Field: A Course on Theory and Application of Bibliometric Indicators (Ungarische Akademie der Wissenschaften, Budapest, 2003)Google Scholar
  151. 151.
    W. Glänzel, U. Schoepflin, A stochastic model for the ageing of scientific literature. Scientometrics 30, 49–64 (1994)CrossRefGoogle Scholar
  152. 152.
    S. Shan, G. Yang, L. Jiang, The multivariate Waring distribution and its application. Scientometrics 60, 523–535 (2004)CrossRefGoogle Scholar
  153. 153.
    M. Abramowitz, I.A. Stegun (eds.), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, New York, 1972)zbMATHGoogle Scholar
  154. 154.
    Q.L. Burrell, Age-specific citation rates and the Egghe-Rao function. Inf. Process. Manag. 39, 761–770 (2003)zbMATHCrossRefGoogle Scholar
  155. 155.
    P. Fronczak, A. Fronczak, J.A. Holyst, Publish or perish: Analysis of scientific productivity using maximum entropy principle and fluctuation-dissipation theorem. Phys. Rev. E 75, Art. No.026103 (2007)Google Scholar
  156. 156.
    K.G. Zipf, Human Behaviour and the Principle of Least Effort (Addison-Wesley, Cambridge, MA, 1949)Google Scholar
  157. 157.
    A.I. Yablonsky, On fundamental regularities of the distribution of scientific productivity. Scientometrics 2, 3–34 (1980)CrossRefGoogle Scholar
  158. 158.
    L. Hartman, Technological forecasting, in Multinational Corporate Planning, ed. by G.A. Steiner, W. Cannon (Crowell-Collier Publishing Co., New York, 1966)Google Scholar
  159. 159.
    G.W. Tyler, A thermodynamic model of manpower system. J. Oper. Res. Soc. 40, 137–139 (1989)zbMATHCrossRefGoogle Scholar
  160. 160.
    I.K. Ravichandra Rao, Probability distributions and inequality measures for analysis of circulation data, in Informetrics, ed. by L. Egghe, R. Rousseau (Elsevier, Amsterdam, 1988), pp. 231–248Google Scholar
  161. 161.
    W. Glänzel, On the \(h\)-index—A mathematical approach to a new measure of publication activity and citation impact. Scientometrics 67, 315–321 (2006)CrossRefGoogle Scholar
  162. 162.
    E.J. Gumbel, Statistics of Extremes (Dover, New York, 2004)zbMATHGoogle Scholar
  163. 163.
    W. Glänzel, A. Schubert, Price distribution. An exact formulation of Price’s “Square root law”. Scientometrics 7, 211–219 (1985)CrossRefGoogle Scholar
  164. 164.
    H. Boxenbaum, F. Pivinski, S.J. Ruberg, Publication rates of pharmaceutical scientists: application of the Waring distribution. Drug Metab. Rev. 18, 553–571 (1987)CrossRefGoogle Scholar
  165. 165.
    Q.L. Burrell, A simple model for linked infometric processes. Inf. Process. Manag. 28, 637–645 (1992)CrossRefGoogle Scholar
  166. 166.
    Q.L. Burrell, Hirsch’s \(h\)-index: a stochastic model. J. Inf. 1, 16–25 (2007)CrossRefGoogle Scholar
  167. 167.
    H.S. Sichel, A bibliometric distribution which really works. J. Am. Soc. Inf. Sci. 36, 314–321 (1985)CrossRefGoogle Scholar
  168. 168.
    H.S. Sichel, Anatomy of the generalized inverse Gaussian-Poisson distribution with special application to bibliometric studies. Inf. Process. Manag. 28, 5–17 (1992)CrossRefGoogle Scholar
  169. 169.
    L. Perreault, B. Bobee, R. Rasmussen, Halphen distribution system. Mathematical and statistical properties. J. Hydrol. Eng. 4, 189–199 (1999)Google Scholar
  170. 170.
    H.S. Sichel, Repeat-bying and the generalized inverse Gaussian-Poisson distribution. Appl. Stat. 31, 193–204 (1982)CrossRefGoogle Scholar
  171. 171.
    A.K. Romanov, A.I. Terekhov, The mathematical model of productivity—and age-structured scientific community evolution. Scientometrics 39, 3–17 (1997)CrossRefGoogle Scholar
  172. 172.
    A.K. Romanov, A.I. Terekhov, The mathematical model of the scientific personnel movement taking into account the productivity factor. Scientometrics 33, 221–231 (1995)CrossRefGoogle Scholar
  173. 173.
    P. Vinkler, Correlation between the structure of scientific research, scientometric indicators and GDP in EU and non- EU countries. Scientometrics 74, 237–254 (2008)CrossRefGoogle Scholar
  174. 174.
    L.C. Lee, Y.W. Chuang, Y.Y. Lee, Research output and economic productivity: a Granger causality test. Scientometrics 89, 465–478 (2011)CrossRefGoogle Scholar
  175. 175.
    P.W. Hart, J.T. Sommerfeld, Relationship between growth in gross domestic product (GDP) and growth in the chemical engineering literature in five different countries. Scientometrics 42, 299–311 (1998)CrossRefGoogle Scholar
  176. 176.
    F. de Moya-Anegon, V. Herrero Solana, Science in America Latina: a comparison of bibliometric and scientific-technical indicators. Scientometrics 46, 299–320 (1999)CrossRefGoogle Scholar
  177. 177.
    F. Ye, A quantitative relationship between per capita GDP and scientometric criteria. Scientometrics 71, 407–413 (2007)CrossRefGoogle Scholar
  178. 178.
    J. Sylvan Katz, B.R. Martin, What is research collaboration? Res. Policy 26, 1–18 (1997)CrossRefGoogle Scholar
  179. 179.
    A.F.J. van Raan, Science as an international enterprise. Sci. Public Policy 24, 290–300 (1997)Google Scholar
  180. 180.
    M. Pezzoni, V. Sterzi, F. Lissoni, Career progress in centralized academic systems: Social capital and institutions in France and Italy. Res. Policy 41, 704–719 (2012)CrossRefGoogle Scholar
  181. 181.
    D.B. de Beaver, R. Rosen, Studies in scientific collaboration: Part I-The professional origins of scientific co-authorship. Scientometrics 1, 65–84 (1979)CrossRefGoogle Scholar
  182. 182.
    D.B. de Beaver, R. Rosen, Studies in scientific collaboration: Part II—Scientific co-authorship, research productivity and visibility in the French scientific elite 1799–1830. Scientometrics 1, 133–149 (1979)CrossRefGoogle Scholar
  183. 183.
    D.B. de Beaver, R. Rosen, Studies in scientific collaboration: Part III—Professionalization and the natural history of modern scientific co-authorship. Scientometrics 1, 231–245 (1979)CrossRefGoogle Scholar
  184. 184.
    T. Luukkonen, O. Persson, G. Sivertsen, Understanding patterns of international scientific collaboration. Sci. Technol. Hum. Values 17, 101–126 (1992)CrossRefGoogle Scholar
  185. 185.
    M. Meyar, O. Persson, Nanotechnology—interdisciplinarity, patters of collaboration and differences in application. Scientometrics 42, 195–205 (1998)CrossRefGoogle Scholar
  186. 186.
    A.E. Andersson, O. Persson, Networking scientists. Ann. Reg. Sci. 27, 11–21 (1993)CrossRefGoogle Scholar
  187. 187.
    G. Melin, O. Persson, Hotel cosmopolitan: a bibliometric study of collaboration at some European universities. J. Am. Soc. Inf. Sci. 49, 43–48 (1998)CrossRefGoogle Scholar
  188. 188.
    P. Mählck, O. Persson, Socio-bibliometric mapping of intra-department networks. Scientometrics 49, 81–91 (2000)CrossRefGoogle Scholar
  189. 189.
    T. Lukkonen, R. Tijssen, O. Persson, G. Sivertsen, The measurement of international scientific collaboration. Scientometrics 28, 15–36 (1993)CrossRefGoogle Scholar
  190. 190.
    C.S. Wagner, L. Leydesdorff, Network structure, self-organization, and the growth of international collaboration in science. Res. Policy 34, 1608–1618 (2005)CrossRefGoogle Scholar
  191. 191.
    R. Stichweh, Science in the system of world society. Soc. Sci. Inf. 35, 327–340 (1996)CrossRefGoogle Scholar
  192. 192.
    B. Jamweit, E. Jettestuen, J. Mathiesen, Scaling properties in European research units. PNAS 106, 13160–13163 (2009)CrossRefGoogle Scholar
  193. 193.
    N. Deschacht, T.C.E. Engels, Limited dependent variable models and probabilistic prediction in informetrics, in Measuring Scholarly Impact. Methods and Practice, ed. by Y. Ding, R. Rousseau, D. Wolfram (Springer, Cham, 2014), pp. 193–214Google Scholar
  194. 194.
    H.P. Van Dalen, K. Henkens, Signals in science—the importance of signaling in gaining attention in science. Scientometrics 64, 209–233 (2005)CrossRefGoogle Scholar
  195. 195.
    J.W. Fedderke, The objectivity of national research foundation peer review in South Africa assessed against bibliometric indexes. Scientometrics 97, 177–206 (2013)CrossRefGoogle Scholar
  196. 196.
    L. Rokach, M. Kalech, I. Blank, R. Stern, Who is going to win the next Association for the Advancement of Artificial Intelligence fellowship award? Evaluating researchers by mining bibliographic data. J. Am. Soc. Inf. Sci. Technol. 62, 2456–2470 (2011)CrossRefGoogle Scholar
  197. 197.
    P. Jensen, J.-B. Rouquier, Y. Croissant, Testing bibliometric indicators by their prediction of scientists promotions. Scientometrics 78, 467–47 (2009)CrossRefGoogle Scholar
  198. 198.
    P. Vakkari, Internet use increases the odds of using the public library. J. Doc. 68, 618–638 (2012)CrossRefGoogle Scholar
  199. 199.
    T.C.E. Engels, P. Goos, N. Dexters, E.H.J. Spruyt, Group size, \(h\)-index and efficiency in publishing in top journals explain expert panel assessments of research group quality and productivity. Res. Eval. 22, 224–236 (2013)CrossRefGoogle Scholar
  200. 200.
    S.-C.J. Sin, International coauthorship and citation impact: a bibliometric study of six LIS journals, 1980–2008. J. Am. Soc. Inf. Sci. Technol. 62, 1770–1783 (2011)CrossRefGoogle Scholar
  201. 201.
    A. Abbasi, J. Altmann, L. Hossain, Identifying the effects of co-authorship networks on the performance of scholars: a correlation and regression analysis of performance measures and social network analysis measures. J. Inf. 5, 594–607 (2011)CrossRefGoogle Scholar
  202. 202.
    G.D. Walters, Predicting subsequent citations to articles published in twelve crimepsychology journals: author impact versus journal impact. Scientometrics 69, 499–510 (2006)CrossRefGoogle Scholar
  203. 203.
    L. Bornmann, H.D. Daniel, Selecting scientific excellence through committee peer review—a citation analysis of publications previously published to approval or rejection of post-doctoral research fellowship applicants. Scientometrics 68, 427–440 (2006)CrossRefGoogle Scholar
  204. 204.
    F. Barjak, S. Robinson, International collaboration, mobility, and team diversity in the life sciences: impact on research performance. Soc. Geogr. 3, 23–36 (2008)CrossRefGoogle Scholar
  205. 205.
    S. Shan, On the generalized Zipf distribution. Part I. Inf. Process. Manag. 41, 1369–1386 (2005)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of MechanicsSofiaBulgaria
  2. 2.Max-Planck Institute for the Physics of Complex SystemsDresdenGermany

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