# On fundamental regularities of the distribution of scientific productivity

- 129 Downloads
- 56 Citations

## Abstract

This paper presents a methodologicl and mathematical study of the main regularities related to the distribution of scientific productivity. An analysis of the se regularities is given from the point of view of two approaches, the frequency and the rank approaches, to the problem of scientific productivity. The connection between these approaches is studied and a number of mathematical formulas that are both of theoretical significance for the understanding of information data basis formation mechanisms and of practical one, in particular, for the estimate of Bradford's law parameters, are deduced. The relation between the scientific productivity distributions under consideration and the stable non-Gaussian distributions is analyzed. The formation of the corresponding regularities of scientific productivity is regarded as a consequence of probability process combined with deterministic one.

## Keywords

Data Basis Formation Mechanism Basis Formation Productivity Distribution Scientific Productivity## Preview

Unable to display preview. Download preview PDF.

## Notes and references

- 1.J. VLACHÝ, Frequency distributions of scientific performance. A bibliography of Lotka's law and related fenomena,
*Scientometrics*, 1 (1978) 109–131.Google Scholar - 2.For the growth statistics see:.Google Scholar
- 3.J. J. HUBERT, Bibliometric models for journal productivity,
*Social Indicators Research*, 4 (1977) 441–473.Google Scholar - 4.A. I. YABLONSKI, Models and Methods of Mathematical Studies of Science (a scientific-analytical review), Moscow, 1977.Google Scholar
- 5.B. MANDELBROT, New methods in statistical economies,
*Journal of Political Economy*, 71 (1963) 421–440.Google Scholar - 6.A. J. LOTKA, The frequency distribution of scientific productivity,
*Journal of the Washington Academy of Science*, 16 (1926) 317–323.Google Scholar - 7.J. VLACHÝ, Variable factors in scientific communities (Observations on Lotka's law),
*Theorie a metoda*, Praha, IV/I, 1972.Google Scholar - 8.B. N. PETROV, G. M. ULANOV, S. V. UL'YANOV, E. M. KHAZEN, Information-Semantic Problems in Organization and Control, Moscow, 1977.Google Scholar
- 9.A. I. YABLONSKY, Statistical models of scientific activity. In:
*Systems Research Yearbook — 1975*, Moscow, 1976.Google Scholar - 10.P. D. ALLISON, D. de S. PRICE, B. C. GRIFFITH, M. J. MORAVCSIK, J. A. STEWART, Lotka's law: a problem in its interpretation and application,
*Social Studies of Science*, 6 (1976), No. 2, 269–276.Google Scholar - 11.Even if one considers only the scientific output measured, for instance, not by publications but by the number of new ideas, according to
*Crane's*results concerning the spreading of innovations in agriculture (See: D. CRANE,*Invisible Colleges. Diffusion of Knowledge in Scientific Communities*, Chicago, 1972), the distribution of the number of innovations advanced by various scientists is also governed by Lotka's law. The author of the law*A. J. Lotka*who analyzed no only the chemical abstract journal but*F. Auerbach's Geschichtstafeln der Physik*for 1600–1900 and obtained an agreement between the corresponding distributions of scientific output (as judged by publications and discoveries) noted the same.Google Scholar - 12.A. J. YABLONSKY. Models and Methods of Mathematical Studies of Science (a scientific-analytical review), Moscow, 1977.Google Scholar
- 13.See. A. J. YABLONSKY,
*op. cit.*, note 9, Statistical models of scientific activity. In:*Systems Research Yearbook — 1975*, Moscow, 1976, for details of randomization of branching processes.Google Scholar - 14.A. I. YABLONSKY, Structure and dynamics of modern science (certain methodological problems). In:
*Systems Research Yearbook — 1976*, Moscow, 1977.Google Scholar - 15.D. de S. PRICE, Networks of scientific papers,
*Science*, 149 (1965) No. 3683, 510–515.Google Scholar - 16.D. Dieks, H. Chang, Difference in impact of scientific publications: Some indices derived from a citation analysis,
*Social Studies of Science*, 6 (1976) No. 2.Google Scholar - 17.Note also the sociological studies of the scientific effect that were conducted, for instance, by D.
*Crane*by means of questionnaire distribution among the members of the “invisible college” in one of the problematic fields of rural sociology (the distribution of innovations in agriculture), in order to determine the influence of other scientists on the results of representatives of the given “college” [See: D. CRANE, Social structure in a grop of scientists: a test of the “Invisible College” hypothesis,*American Sociological Review*, 34 (June 1969) No. 3, 335–352]. Of interest is that the distribution of “influencing” scientists with respect to the number of them being chosen by the examination participants is also governed (qualitatively) by a law similar to that of Lotka: the small number of scientists was given by many participants and vice versa, the basic number of “influencing” scientists was mentioned only once.Google Scholar - 18.D. Dicks, H. Chang,
*op cit.*, note 16. Difference in impact of scientific publications: Some indices derived from a citation analysis,*Social Studies of Science*, 6 (1976) No. 2.Google Scholar - 19.. p. 261.Google Scholar
- 20.e.g. J. R. COLE Patterns of intellectual influence in scientific research,
*Sociology of Education*, 43 (1970) No. 4, 377–403; I. V. MARSHAKOVA prospective connection in the system of scientific publications. In:*Systems Research Yearbook — 1976*, Moscow, 1977.Google Scholar - 21.S. C. BRADFORD,
*Documentation*, London, 1948.Google Scholar - 22.An important feature of this case is exactly that the corresponding set of journals should reflect with sufficient completeness the sphere of knowledge under study. “The law of dispersal of papers in the journals is valid only after a certain time interval has elapsed during which the mass of publications pertaining to a given topic will be formed, in other words, on the expiration of time required for the general spread of interest in a given subject”. [A. AVRAMESCU, The modelling of scientific information transfer,
*Mezhdunarodnyi forum po informatsii i dokumentatsii*, 1 (1975) No. 1, 18]. For this reason, by the way, the validity of Bradford's law for a given information data base can serve as an indication of a sufficiently well formed scientific field.Google Scholar - 23.B. C. BROOKES, Bradford's law and the bibliography of science,
*Nature*, 224 (1969) No. 5223, 953–956.Google Scholar - 24.J. S. DONOHUE,
*Understanding Scientific Literatures — a Bibliometric Approach*. The MIT press, Cambridge (Mass.), London, 1973.Google Scholar - 25.The empirical parameter S equals one for very “narrow” scientific fields and grows with the increase of the range of problems treated in a given field. Therefore, its definition can be used in order to estimate quantitatively the degree of broadness of the discipline under study. For example, A.
*Pope*[see: A. Pope, Bradford's law and the periodical literature of information science.*Journal of the American Society for Information Science*, 26 (1975) No. 4] having analyzed the corresponding bibliographical data bases, arrived at a conclusion that information science (S=2.6) occupies an intermediate position between library science (S=1) and computational science (S=3.4), i.c., the set of its subjects is broader than the former but narrower than the latter which agrees, by the way, also with the intuitive concepts about the broadness of the set of subjects in these three disciplines.Google Scholar - 26.
- 27.E. A. Wilkinson, The ambiguity of Bradford's law,
*Journal of Documentation*, 28 (1972) No. 2.Google Scholar - 28.Note that such peculiar feature of representing scientific information as its quantization in the form of papers, books, unification of papers into discrete quantization units (journals), etc. exercise informational structure, its stability, the formation of Bradford's law, etc. For instance, it is noted that a peculiar feature of Bradford's law which consists in the presence of a “nucleus” in a collection with its own dynamics of scientific information can be explained by “such specific form of quantization as periodicals” (A. I. MIKHAILOV, A. I. CHERNYI, R. C. GILYAREVSKY,
*Scientific Communications and Informatics*, Moscow, 1976, p. 184). For this reson the “quantum” approach to the study of regularities of the organizing of the information base is of interest, and not only for informatics but for the science of sciences as well, for instance, in connection with the analysis of scienfitic communication. Recent papers of A.*Hill*et al. [B. HILL, Zipf's law and prior distributions for the composition of a population,*Journal of the American Statistical Association*, 65 (331) (1970) 1220 B. HILL, Rank frequency forms of Zipf's law,*Journal of the American Statistical Association*, 69 (348) (1974) 1017; B. HILL, M. WOODROOFE, Stronger forms of Zipf's law,*Journal of the American Statistical Association*, 70 (349) (1975) 212; M. WOODROOFE, B. HILL, On Zipf's law,*Journal of Applied Probability*, 12 (1975) 425–434], in which Bose-Einstein statistics (see, e.g., W. FELLER,*An Introduction to Probability Theory and its Applications*, Wiley & Sons, Inc., London, Chapman & Hall Ltd., 1957) is used for derivation of Zipf's law, the ranks and analog of Lotka's law (Bradford's law representing the cumulative form of Zipf's law), provide an interesting example of the application of quantum statistics.Google Scholar - 29.See, e.g., D. CRANE,
*op. cit.*, note 11; Even if one considers only the scientific output measured, for instance, not by publications but by the number of new ideas, according to*Crane's*results concerning the spreading of innovations in agriculture (See: D. CRANE,*Invisible Colleges. Diffusion of Knowledge in Scientific Communities*, Chicago, 1972), the distribution of the number of innovations advanced by various scientists is also governed by Lotka's law. The author of the law*A. J. Lotka*who analyzed no only the chemical abstract journal but*F. Auerbach's Geschichtstafeln der Physik*for 1600–1900 and obtained an agreement between the corresponding distributions of scientific output (as judged by publications and discoveries) noted the same. A. I. MIKHAILOW et al.,*op. cit.*, note 28.*Scientific Communications and Informatics*, Moscow, 1976, p. 184).Google Scholar - 30.D. CRANE,
*ibid., Invisible Colleges. Diffusion of Knowledge in Scientific Communities*, Chicago, 1972. A. I. MIKHAILOV et al.,*op. cit. Scientific Communications and Informatics*, Moscow, 1976, p. 213.Google Scholar - 31.The concept of hierarchic structure as a way of ensuring stability of a complex system under development with the presence of external limitations or the existence of contradictory requirements of centralized and decentralized control is quite widely spread in modern system analysis (see, for example, N. N. MOISEEV, The Mathematician Asks Questions ... Moscow, 1974.).Google Scholar
- 32.A. J. MIKHAILOV et al.,
*op. cit.*, note 28,*Scientific Communications and Informatics*, Moscow, 1976, p. 66.Google Scholar - 33.A. J. YABLONSKY,
*op. cit.*, note 9. Statistical models of scientific activity. In:*Systems Research Yearbook — 1975*, Moscow, 1976.Google Scholar - 34.A. J. YABLONSKY,
*ibid.*Statistical models of scientific activity. In:*Systems Research Yearbook — 1975*, Moscow, 1976.Google Scholar - 35.W. FELLER,
*An Introduction to Probability Theory and its Applications*, Vol. 2. J. Wiley & Sons, New York—London—Sydney, 1966; B. V. GNEDENKO, A. N. KOLMOGOROV,*Limiting Distributions for Sums of Independent Random Variables*, Moscow-Leningrad, 1949.Google Scholar - 36.See: A. J. YABLONSKY,
*op. cit.*, note 9, Statistical models of scientific activity. In:*Systems Research Yearbook — 1975*, Moscow, 1976. for the analysis of the scientological aspects of this connection.Google Scholar - 37.M. G. KENDALL, Natural law in the social sciences,
*Journal of the Royal Statistical Society*, 124 (1964) part 1, p. 4.Google Scholar - 38.See. e.g., B. MANDELBROT,.Google Scholar
- 39.A. J. YABLONSKY. The development of science as an open system. In:
*Systems Research Yearbook — 1978*, Moscow, 1978.Google Scholar - 40.M. G. KENDALL, ; G. K. ZIPF,
*Human Behaviour and the Principle of Least Effort*, Cambridge, 1949.Google Scholar - 41.J. VLACHÝ,.Google Scholar
- 42.Yu. K. ORLOV, On the statistical structure of communications optimal for human perception (on the formulation of the question),
*Nauchno-tekhnicheskaya informatsiya*, Ser. 2, 1970, No. 8.Google Scholar - 43.Yu. A. SHREIDER, Complex systems and cosmological principles. In:
*Systems Research Yearbook — 1975*, Moscow, 1976.Google Scholar - 44.N. WIENER,
*I am a Mathematician*. Doubleday Book Co., Inc., Garden-City, New York, 1956; A. A. IGNAT'EV, A. I. YABLONSKY, Analytic structures of scientific communication. In:*Systems Research Yearbook — 1975*, Moscow, 1976: A. J. YABLONSKY,.Google Scholar - 45.T. E. HARRIS,
*The Theory of Branching Processes*, Springer-Verlag, Berlin—Gottingen—Heidelberg, 1963.Google Scholar - 46.A. T. BHARUCHA-REID,
*Elements of the Theory of Markov Processes and their Applications*, McGraw-Hill Book Co., Inc., New York—Toronto—London, 1960.Google Scholar - 47.H. A. SIMON, On a class of skew distribution function,
*Biometrika*, 42 (1955) 425.Google Scholar - 48.G. X. YULE, A mathematical theory of evolution based on conclusions of dr. J. C. Willis,
*Philosophical Transactions of the Royal Society*, London, 213 (1924) Ser. B, 21–87.Google Scholar - 49.
*Price*[See: D. de S. PRICE, A general theory of bibliometric and other cumulative advantage processes,*Journal of the American Society for Informations Science*, 27 (1976) No. 5, 292–306] obtained the same distribution on the basis of somewhat different considerations (depending, as well as*Simon's*approach on finding a stable solution of the finite difference equation for the dynamics of the author) calls it “the cumulative advantage distribution”.Google Scholar - 50.A. J. YABLONSKY,
*op. cit.*, note 9. Statistical models of scientific activity. In:*Systems Research Yearbook — 1975*, Moscow, 1976.Google Scholar - 51.D. de SOLLAPRICE.Google Scholar
- 52.See, e.g., L. BRILLOUIN,
*Science and Information Theory*, Academic Press, Inc., New York, 1956.Google Scholar - 53.See, e.g., A. Avramescu, Contribution to the foundation of bibliometric laws,
*Studii si cercetarii de documentare*, 15 (1973) No. 1.Google Scholar - 54.W. Goffman, K. S. Warren, Dispersion of papers among journals based of a mathematical analysis of two diverse literatures,
*Nature*, 221 (1969) No. 5187.Google Scholar