Search (58 results, page 2 of 3)

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Abstract

Fractional frequency distributions of, for example, authors with a certain (fractional) number of papers are very irregular and, therefore, not easy to model or to explain. This article gives a first attempt to this by assuming two simple Lotka laws (with exponent 2): one for the number of authors with n papers (total count here) and one for the number of papers with n authors, n E N. Based an an earlier made convolution model of Egghe, interpreted and reworked now for discrete scores, we are able to produce theoretical fractional frequency distributions with only one parameter, which are in very close agreement with the practical ones as found in a large dataset produced earlier by Rao. The article also shows that (irregular) fractional frequency distributions are a consequence of Lotka's law, and are not examples of breakdowns of this famous historical law.

Source

Journal of the American Society for Information Science and technology. 53(2002) no.10, S.789-801

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Abstract

This article studies the h-index (Hirsch index) and the g-index of authors, in case one counts authorship of the cited articles in a fractional way. There are two ways to do this: One counts the citations to these papers in a fractional way or one counts the ranks of the papers in a fractional way as credit for an author. In both cases, we define the fractional h- and g-indexes, and we present inequalities (both upper and lower bounds) between these fractional h- and g-indexes and their corresponding unweighted values (also involving, of course, the coauthorship distribution). Wherever applicable, examples and counterexamples are provided. In a concrete example (the publication citation list of the present author), we make explicit calculations of these fractional h- and g-indexes and show that they are not very different from the unweighted ones.

Source

Journal of the American Society for Information Science and Technology. 59(2008) no.10, S.1608-1616

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Abstract

Observed aging curves are influenced by publication delays. In this article, we show how the 'undisturbed' aging function and the publication delay combine to give the observed aging function. This combination is performed by a mathematical operation known as convolution. Examples are given, such as the convolution of 2 Poisson distributions, 2 exponential distributions, a 2 lognormal distributions. A paradox is observed between theory and real data

Source

Journal of the American Society for Information Science. 51(2000) no.2, S.158-165

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Abstract

In a previous article, we introduced a general transformation on sources and one on items in an arbitrary information production process (IPP). In this article, we investigate the influence of these transformations on the h-index and on the g-index. General formulae that describe this influence are presented. These are applied to the case that the size-frequency function is Lotkaian (i.e., is a decreasing power function). We further show that the h-index of the transformed IPP belongs to the interval bounded by the two transformations of the h-index of the original IPP, and we also show that this property is not true for the g-index.

Source

Journal of the American Society for Information Science and Technology. 59(2008) no.8, S.1304-1312

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Abstract

Fundamental mathematical properties of rhythm sequences are studied. In particular, a set of three axioms for valid rhythm indicators is proposed, and it is shown that the R-indicator satisfies only two out of three but that the R-indicator satisfies all three. This fills a critical, logical gap in the study of these indicator sequences. Matrices leading to a constant R-sequence are called baseline matrices. They are characterized as matrices with constant w-year diachronous impact factors. The relation with classical impact factors is clarified. Using regression analysis matrices with a rhythm sequence that is on average equal to 1 (smaller than 1, larger than 1) are characterized.

Source

Journal of the American Society for Information Science and Technology. 59(2008) no.9, S.1469-1478

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Abstract

Naranan's important theorem, published in Nature in 1970, states that if the number of journals grows exponentially and if the number of articles in each journal grows exponentially (at the same rate for each journal), then the system satisfies Lotka's law and a formula for the Lotka's exponent is given in function of the growth rates of the journals and the articles. This brief communication re-proves this result by showing that the system satisfies Zipf's law, which is equivalent with Lotka's law. The proof is short and algebraic and does not use infinitesimal arguments.

Source

Journal of the American Society for Information Science and Technology. 61(2010) no.12, S.2581-2583

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Abstract

The author presents a different view on properties of impact measures than given in the paper of De Visscher (2011). He argues that a good impact measure works better when citations are concentrated rather than spread out over articles. The author also presents theoretical evidence that the g-index and the R-index can be close to the square root of the total number of citations, whereas this is not the case for the A-index. Here the author confirms an assertion of De Visscher.

Source

Journal of the American Society for Information Science and Technology. 63(2012) no.10, S.2118-2121

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Abstract

One aim of science evaluation studies is to determine quantitatively the contribution of different players (authors, departments, countries) to the whole system. This information is then used to study the evolution of the system, for instance to gauge the results of special national or international programs. Taking articles as our basic data, we want to determine the exact relative contribution of each coauthor or each country. These numbers are brought together to obtain country scores, or department scores, etc. It turns out, as we will show in this article, that different scoring methods can yield totally different rankings. Conseqeuntly, a ranking between countries, universities, research groups or authors, based on one particular accrediting methods does not contain an absolute truth about their relative importance

Source

Journal of the American Society for Information Science. 51(2000) no.2, S.145-157

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Abstract

Measurement of the degree of interconnectedness in graph like networks of hyperlinks or citations can indicate the existence of research fields and assist in comparative evaluation of research efforts. In this issue we begin with Egghe and Rousseau who review compactness measures and investigate the compactness of a network as a weighted graph with dissimilarity values characterizing the arcs between nodes. They make use of a generalization of the Botofogo, Rivlin, Shneiderman, (BRS) compaction measure which treats the distance between unreachable nodes not as infinity but rather as the number of nodes in the network. The dissimilarity values are determined by summing the reciprocals of the weights of the arcs in the shortest chain between two nodes where no weight is smaller than one. The BRS measure is then the maximum value for the sum of the dissimilarity measures less the actual sum divided by the difference between the maximum and minimum. The Wiener index, the sum of all elements in the dissimilarity matrix divided by two, is then computed for Small's particle physics co-citation data as well as the BRS measure, the dissimilarity values and shortest paths. The compactness measure for the weighted network is smaller than for the un-weighted. When the bibliographic coupling network is utilized it is shown to be less compact than the co-citation network which indicates that the new measure produces results that confirm to an obvious case.

Source

Journal of the American Society for Information Science and technology. 54(2003) no.3, S.193-202

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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).

Source

Journal of the American Society for Information Science and Technology. 57(2006) no.9, S.1165-1177

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Abstract

Let (DS, DQ, sim) be a retrieval system consisting of a document space DS, a query space QS, and a function sim, expressing the similarity between a document and a query. Following D.M. Everett and S.C. Cater (1992), we introduce topologies on the document space. These topologies are generated by the similarity function sim and the query space QS. 3 topologies will be studied: the retrieval topology, the similarity topology and the (pseudo-)metric one. It is shown that the retrieval topology is the coarsest of the three, while the (pseudo-)metric is the strongest. These 3 topologies are generally different, reflecting distinct topological aspects of information retrieval. We present necessary and sufficient conditions for these topological aspects to be equal

Source

Journal of the American Society for Information Science. 49(1998) no.13, S.1144-1160

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Abstract

We present a rationale for the Hirsch-index rank-order distribution and prove that it is a power law (hence a straight line in the log-log scale). This is confirmed by experimental data of Pyykkö and by data produced in this article on 206 mathematics journals. This distribution is of a completely different nature than the impact factor (IF) rank-order distribution which (as proved in a previous article) is S-shaped. This is also confirmed by our example. Only in the log-log scale of the h-index distribution do we notice a concave deviation of the straight line for higher ranks. This phenomenon is discussed.

Source

Journal of the American Society for Information Science and Technology. 60(2009) no.10, S.2142-2144

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Abstract

Based on earlier results about the shifted Lotka function, we prove an implicit functional relation between the Hirsch index (h-index) and the total number of sources (T). It is shown that the corresponding function, h(T), is concavely increasing. Next, we construct an implicit relation between the h-index and the impact factor IF (an average number of items per source). The corresponding function h(IF) is increasing and we show that if the parameter C in the numerator of the shifted Lotka function is high, then the relation between the h-index and the impact factor is almost linear.

Source

Journal of the American Society for Information Science and Technology. 63(2012) no.5, S.1048-1053

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Abstract

The discrete Lotka power function describes the number of sources (e.g., authors) with n = 1, 2, 3, ... items (e.g., publications). As in econometrics, informetrics theory requires functions of a continuous variable j, replacing the discrete variable n. Now j represents item densities instead of number of items. The continuous Lotka power function describes the density of sources with item density j. The discrete Lotka function one obtains from data, obtained empirically; the continuous Lotka function is the one needed when one wants to apply Lotkaian informetrics, i.e., to determine properties that can be derived from the (continuous) model. It is, hence, important to know the relations between the two models. We show that the exponents of the discrete Lotka function (if not too high, i.e., within limits encountered in practice) and of the continuous Lotka function are approximately the same. This is important to know in applying theoretical results (from the continuous model), derived from practical data.

Source

Journal of the American Society for Information Science and Technology. 56(2005) no.7, S.664-668

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Abstract

The relation between Pearson's correlation coefficient and Salton's cosine measure is revealed based on the different possible values of the division of the L1-norm and the L2-norm of a vector. These different values yield a sheaf of increasingly straight lines which together form a cloud of points, being the investigated relation. The theoretical results are tested against the author co-citation relations among 24 informetricians for whom two matrices can be constructed, based on co-citations: the asymmetric occurrence matrix and the symmetric co-citation matrix. Both examples completely confirm the theoretical results. The results enable us to specify an algorithm that provides a threshold value for the cosine above which none of the corresponding Pearson correlations would be negative. Using this threshold value can be expected to optimize the visualization of the vector space.

Source

Journal of the American Society for Information Science and Technology. 60(2009) no.5, S.1027-1036

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Abstract

A problem, raised by Wallace (JASIS, 37,136-145,1986), on the relation between the journal's median citation age and its number of articles is studied. Leaving open the problem as such, we give a statistical explanation of this relationship, when replacing "median" by "mean" in Wallace's problem. The cloud of points, found by Wallace, is explained in this sense that the points are scattered over the area in first quadrant, limited by a curve of the form y=1 + E/x**2 where E is a constant. This curve is obtained by using the Central Limit Theorem in statistics and, hence, has no intrinsic informetric foundation. The article closes with some reflections on explanations of regularities in informetrics, based on statistical, probabilistic or informetric results, or on a combination thereof

Source

Journal of the American Society for Information Science and technology. 52(2001) no.5, S.371-377

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Abstract

Adding or deleting items such as self-citations has an influence on the h-index of an author. This influence will be proved mathematically in this article. We hereby prove the experimental finding in E. Gianoli and M.A. Molina-Montenegro ([2009]) that the influence of adding or deleting self-citations on the h-index is greater for low values of the h-index. Why this is logical also is shown by a simple theoretical example. Adding or deleting sources such as adding or deleting minor contributions of an author also has an influence on the h-index of this author; this influence is modeled in this article. This model explains some practical examples found in X. Hu, R. Rousseau, and J. Chen (in press).

Source

Journal of the American Society for Information Science and Technology. 61(2010) no.2, S.370-373

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Abstract

Type/Token-Taken informetrics is a new part of informetrics that studies the use of items rather than the items itself. Here, items are the objects that are produced by the sources (e.g., journals producing articles, authors producing papers, etc.). In linguistics a source is also called a type (e.g., a word), and an item a token (e.g., the use of words in texts). In informetrics, types that occur often, for example, in a database will also be requested often, for example, in information retrieval. The relative use of these occurrences will be higher than their relative occurrences itself; hence, the name Type/ Token-Taken informetrics. This article studies the frequency distribution of Type/Token-Taken informetrics, starting from the one of Type/Token informetrics (i.e., source-item relationships). We are also studying the average number my* of item uses in Type/Token-Taken informetrics and compare this with the classical average number my in Type/Token informetrics. We show that my* >= my always, and that my* is an increasing function of my. A method is presented to actually calculate my* from my, and a given a, which is the exponent in Lotka's frequency distribution of Type/Token informetrics. We leave open the problem of developing non-Lotkaian Type/TokenTaken informetrics.

Source

Journal of the American Society for Information Science and technology. 54(2003) no.7, S.603-610

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Abstract

Power laws as defined in 1926 by A. Lotka are increasing in importance because they have been found valid in varied social networks including the Internet. In this article some unique properties of power laws are proven. They are shown to characterize functions with the scalefree property (also called seif-similarity property) as weIl as functions with the product property. Power laws have other desirable properties that are not shared by exponential laws, as we indicate in this paper. Specifically, Naranan (1970) proves the validity of Lotka's law based on the exponential growth of articles in journals and of the number of journals. His argument is reproduced here and a discrete-time argument is also given, yielding the same law as that of Lotka. This argument makes it possible to interpret the information production process as a seif-similar fractal and show the relation between Lotka's exponent and the (seif-similar) fractal dimension of the system. Lotkaian informetric systems are seif-similar fractals, a fact revealed by Mandelbrot (1977) in relation to nature, but is also true for random texts, which exemplify a very special type of informetric system.

Source

Journal of the American Society for Information Science and Technology. 56(2005) no.7, S.669-675

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Abstract

The notions aging, obsolescence, impact, growth, utilization, and their relations are studied. It is shown how to correct an observed citation distribution for growth, once the growth distribution is known. The relation of this correction procedure with the calculation of impact measures is explained. More interestingly, we have shown how the influence of growth on aging can be studied over a complete period as a whole. Here, the difference between the so-called average and global aging distributions is the main factor. Our main result is that growth can influence aging but that it does not cause aging. A short overview of some classical articles on this topic is given. Results of these earlier works are placed in the framework set up in this article

Source

Journal of the American Society for Information Science. 51(2000) no.11, S.1004-1017