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Abstract

In the first part of this article the author defines the n-overlap vector whose coordinates consist of the fraction of the objects (e.g., books, N-grams, etc.) that belong to 1, 2, , n sets (more generally: families) (e.g., libraries, databases, etc.). With the aid of the Lorenz concentration theory, a theory of n-overlap similarity is conceived together with corresponding measures, such as the generalized Jaccard index (generalizing the well-known Jaccard index in case n 5 2). Next, the distributional form of the n-overlap vector is determined assuming certain distributions of the object's and of the set (family) sizes. In this section the decreasing power law and decreasing exponential distribution is explained for the n-overlap vector. Both item (token) n-overlap and source (type) n-overlap are studied. The n-overlap properties of objects indexed by a hierarchical system (e.g., books indexed by numbers from a UDC or Dewey system or by N-grams) are presented in the final section. The author shows how the results given in the previous section can be applied as well as how the Lorenz order of the n-overlap vector is respected by an increase or a decrease of the level of refinement in the hierarchical system (e.g., the value N in N-grams).

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Abstract

Focuses on possible mathematical theories of citation and on the intrinsic problems related to it. Sheds light on aspects of mathematical complexity as encountered in, for example, fractal theory and Mandelbrot's law. Also discusses dynamical aspects of citation theory as reflected in evolutions of journal rankings, centres of gravity or of the set of source journals. Makes some comments in this connection on growth and obsolescence

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Abstract

This article studies concentration aspects of bibliographies. More, in particular, we study the impact of incompleteness of such a bibliography on its concentration values (i.e., its degree of inequality of production of its sources). Incompleteness is modeled by sampling in the complete bibliography. The model is general enough to comprise truncation of a bibliography as well as a systematic sample on sources or items. In all cases we prove that the sampled bibliography (or incomplete one) has a higher concentration value than the complete one. These models, hence, shed some light on the measurement of production inequality in incomplete bibliographies.

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Date

14. 2.2012 12:53:22

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Source

Journal of information science. 22(1996) no.3, S.165-170

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Date

14. 8.2004 19:17:22