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  • Author or Editor: R. Bailón-Moreno x
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Abstract  

Here, the quantitative theory of translation is shown to be of great utility in describing scientific networks. In fact, we deduce a new Zipf's Law for the descriptors of a set of documents, based on the concepts of centres of interest and of irreversible parallel translations. This new law can be generalized to other phenomena, such as the distribution of the sizes of cocitation clusters. Finally, we have established the model, for descriptor presence in a network, which closely fits the values recorded.

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Abstract  

The fundamentals have been developed for a quantitative theory on the structure and dynamics of scientific networks. These fundamentals were conceived through a new vision of translation, defined mathematically as the derivative or gradient of the quality of the actors as a function of the coordinates for the space in which they perform. If we begin with the existence of a translation barrier, or an obstacle that must be overcome by the actors in order to translate, and if we accept the Maxwell-Boltzmann distribution as representative of the translating capacity of the actors, it becomes possible to demonstrate the known principle of “success breeds success.” We also propose two types of elemental translation: those which are irreverisble and those which are in equilibrium. In addition, we introduce the principle of composition, which enables, from elemental translations, the quantification of more complex ones.

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Scientometrics
Authors: R. Bailón-Moreno, E. Jurado-Alameda, R. Ruiz-Baños, and J. P. Courtial

Summary A unified scientometric model has been developed on the basis of seven principles: the actor-network principle, the translation principle, the spatial principle, the quantativity principle, the composition principle, the centre-periphery or nucleation principle, and the unified principle of cumulative advantages. The paradigm of the fractal model has been expanded by introducing the concept of fractality index and transfractality. In this work, as the first demonstration of the power of the model proposed, all the bibliometric laws known and all their mathematical expressions are deduced, both the structural distributions (Zipf, Bradford and Lotka) as well as the Price's Law of the exponential growth of science and Brookes' and Avramescu's Laws of ageing.

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Scientometrics
Authors: R. Bailón-Moreno, E. Jurado-Alameda, R. Ruiz-Baños, and J. P. Courtial

Summary The bibliometric laws of Zipf, Bradford, and Lotka, in their various mathematical expressions, frequently present difficulties in the fitting of empirical values. The empirical flaws of fit take place in the frequency of the words, in the productivity of the authors and the journals, as well as in econometric and demographic aspects. This indicates that the underlying fractal model should be revised, since, as shown, the inverse power equations (of the Zipf-Mandelbrot type) are not adequate, as they need to include exponential terms. These modifications not only affect Bibliometrics and Scientometrics, but also, for the generality of the fractal model, apply to Economy, Demography, and even Natural Sciences in general.

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Summary By the information system of CoPalRed© and with the treatment of 63,543 bibliographical references of scientific articles, the field of surfactants has been analysed in the light of the Unified Scientometric Model. It was found that the distributions of actors (countries, centres, and research laboratories, journals, researchers, key words of documents) fit Zif's Unified Law better than the Zipf-Mandelbrot Law. The model showed an especially good fit for relational indicators such as density and centrality. Using the Unified Bradford Law, the three zones fit were: core, straight fraction, and Groos droop. The fractality index was used to verify that Science can present fractal as well as transfractal structures. In conclusion, the Unified Scientometric Model is, for its flexibility and its integrating capacity, an appropriate model for representing Science, joining non-relational with relational Scientometrics under the same paradigm.

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