A multidimensional analysis of scientific dynamics. Part I. Case studies of mathematical logic in the 20th century

Berg, Jan; Wagner-Döbler, Roland

doi:10.1007/bf02016904

Cited by 16 publications

(7 citation statements)

References 8 publications

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“…Further discrete calculations on Lotka's law in the connection of Price's law can be found in Egghe (1987). Practical investigations on the validity of Price's law can be found in Berg and Wagner‐Döbler (1996), Nicholls (1988), and Gupta, Sharma, and Kumar (1998).…”

Section: A Characterization Of Price's Law Of Concentrationmentioning

confidence: 99%

Zipfian and Lotkaian continuous concentration theory

Egghe

2005

J. Am. Soc. Inf. Sci.

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In this article concentration (i.e., inequality) aspects of the functions of Zipf and of Lotka are studied. Since both functions are power laws (i.e., they are mathematically the same) it suffices to develop one concentration theory for power laws and apply it twice for the different interpretations of the laws of Zipf and Lotka. After a brief repetition of the functional relationships between Zipf's law and Lotka's law, we prove that Price's law of concentration is equivalent with Zipf's law. A major part of this article is devoted to the development of continuous concentration theory, based on Lorenz curves. The Lorenz curve for power functions is calculated and, based on this, some important concentration measures such as the ones of Gini, Theil, and the variation coefficient. Using Lorenz curves, it is shown that the concentration of a power law increases with its exponent and this result is interpreted in terms of the functions of Zipf and Lotka. IntroductionThe historical law of Lotka (1926) is the basis of modern informetrics and is expressed as follows: the number of authors with n (n ϭ 1,2,3, . . .) publications is proportional to where a Ͼ 0. In other words, there is a constant C Ͼ 0 such that (1) where f(n) denotes the number of authors with n publications. More generally, f(n) can denote the number of sources (authors, journals, word types...) with n items (publications, articles, word occurrences, respectively); henceforth, this dual source/item terminology will be used (see also Egghe, 1989Egghe, , 1990Egghe and Rousseau, 1990a).A totally different informetric formulation, originating from linguistics (in terms of word types and word occurrences) is given by the Zipf law: If we rank the sourcesaccording to their number of items (starting with the source with the highest number of items, hence giving to this source the rank r ϭ 1) then the number of items in the source on rank r (r ϭ 1, 2, 3, . . .) is proportional to where b Ͼ 0. In other words, denoting by g(r) this number of items in the source on rank r, there exists a constant D Ͼ 0 such thatAlthough their informetric definitions are different (they are dual in the sense that, in f and g, the roles of sources and items are interchanged), the functions 1 and 2 are mathematically the same, namely decreasing power laws. A power law is the most occurring regularity in informetrics and far beyond (e.g., also found in economics and sociology, including the description of social networks, see e.g., Egghe and Rousseau, 2003 and references therein) and has the characterizing property (see Roberts, 1979) that, if the argument (x) is multiplied by a constant, k, we obtain the same power law with the same exponent: for we have (ϳ denotes is proportional to). This self-similar property explains its widespread occurrence in real-life examples and also its use in the description of power type informetrics in terms of self-similar fractals (see Feder, 1988). Intuitively, the self-similarity expresses that, independent of the scale at which we examine an "object...

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Section: A Characterization Of Price's Law Of Concentrationmentioning

confidence: 99%

Zipfian and Lotkaian continuous concentration theory

Egghe

2005

J. Am. Soc. Inf. Sci.

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“…It may be worth mentioning that the Lotka distribution of that period has analogous attributes. 19 The interpretation of the Groos droop and the circumstances of the area under consideration are in harmony with similar observations and interpretations of Eto 22 in technological topics of applied science. It is noteworthy that also the mathematical theory of differential equations seemed to show the "epidemic" droop in the decade 1831-1840 (cf.…”

Section: Further Examples Of the Phase-dependence Of The Bradford Dismentioning

confidence: 66%

Time dependencies of Bradford distributions: Structures of journal output in 20th-century logic and 19th-century mathematics

Wagner-Döbler

1997

Scientometrics

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Time dependencies of Bradford distributions are investigated for 19th-century mathematics and for 20th-century logic. To facilitate comparisons, for the representation of empirical Bradford distributions "Pareto's law" and Lorenz diagrams are used. It is shown that the character of a Bradford distribution (including the "core zone" and the "Groos droop") depends on the stage in the development of a scientific field and that it varies with the time-span considered.

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“…To interpret the larger scientific surroundings, we need to apply or even develop additional tools. At the social level, Berg and Wagner-Döbler (1996) hold that the structure of a research area can be seen as a combination of a “middle class” of authors around an established “prolific elite”. The elite have an important say in which themes are considered important and subsequently provide opportunity to gain status or impact for members of the “middle class”, as well as outsiders.…”

Section: Resultsmentioning

confidence: 99%

“…Converging research has not been the topic of many scientometric publications, although there are a lot of descriptions and analyses of emerging research, like for example Mathematical Logic (Berg and Wagner-Döbler 1996), Bioelectronics (Hinze 1994) or Nanoscience and Nanotechnology (Schummer 2004). Additionally, investigations of interdisciplinary developments have been described in for example Davidse and Van Raan (1997), Rinia et al (2002), and Morillo et al (2003).…”

Section: Introductionmentioning

confidence: 99%

Searching for converging research using field to field citations

2010

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We define converging research as the emergence of an interdisciplinary research area from fields that did not show interdisciplinary connections before. This paper presents a process to search for converging research using journal subject categories as a proxy for fields and citations to measure interdisciplinary connections, as well as an application of this search. The search consists of two phases: a quantitative phase in which pairs of citing and cited fields are located that show a significant change in number of citations, followed by a qualitative phase in which thematic focus is sought in publications associated with located pairs. Applying this search on publications from the Web of Science published between 1995 and 2005, 38 candidate converging pairs were located, 27 of which showed thematic focus, and 20 also showed a similar focus in the other, reciprocal pair.

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A multidimensional analysis of scientific dynamics. Part I. Case studies of mathematical logic in the 20th century

Cited by 16 publications

References 8 publications

Zipfian and Lotkaian continuous concentration theory

Zipfian and Lotkaian continuous concentration theory

Time dependencies of Bradford distributions: Structures of journal output in 20th-century logic and 19th-century mathematics

Searching for converging research using field to field citations

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