Juan A. Crespo

The skewness of science in 219 sub-fields and a number of aggregates

This paper studies evidence from Thomson Scientific (TS) about the citation process of 3.7 million articles published in the period 1998–2002 in 219 Web of Science (WoS) categories, or sub-fields. Reference and citation distributions have very different characteristics across sub-fields. However, when analyzed with the Characteristic Scores and Scales (CSS) technique, which is replication and scale invariant, the shape of these distributions over three broad categories of articles appears strikingly similar. Reference distributions are mildly skewed, but citation distributions with a 5-year citation window are highly skewed: the mean is 20 points above the median, while 9–10% of all articles in the upper tail account for about 44% of all citations. The aggregation of sub-fields into disciplines and fields according to several aggregation schemes preserve this feature of citation distributions. It should be noted that when we look into subsets of articles within the lower and upper tails of citation distributions the universality partially breaks down. On the other hand, for 140 of the 219 sub-fields the existence of a power law cannot be rejected. However, contrary to what is generally believed, at the sub-field level the scaling parameter is above 3.5 most of the time, and power laws are relatively small: on average, they represent 2% of all articles and account for 13.5% of all citations. The results of the aggregation into disciplines and fields reveal that power law algebra is a subtle phenomenon.

The measurement of the effect on citation inequality of differences in citation practices across scientific fields.

This paper has two aims: (i) to introduce a novel method for measuring which part of overall citation inequality can be attributed to differences in citation practices across scientific fields, and (ii) to implement an empirical strategy for making meaningful comparisons between the number of citations received by articles in 22 broad fields. The number of citations received by any article is seen as a function of the article’s scientific influence, and the field to which it belongs. A key assumption is that articles in the same quantile of any field citation distribution have the same degree of citation impact in their respective field. Using a dataset of 4.4 million articles published in 1998–2003 with a five-year citation window, we estimate that differences in citation practices between the 22 fields account for 14% of overall citation inequality. Our empirical strategy is based on the strong similarities found in the behavior of citation distributions. We obtain three main results. Firstly, we estimate a set of average-based indicators, called exchange rates, to express the citations received by any article in a large interval in terms of the citations received in a reference situation. Secondly, using our exchange rates as normalization factors of the raw citation data reduces the effect of differences in citation practices to, approximately, 2% of overall citation inequality in the normalized citation distributions. Thirdly, we provide an empirical explanation of why the usual normalization procedure based on the fields’ mean citation rates is found to be equally successful.

The effect on citation inequality of differences in citation practices at the web of science subject category level

This article studies the impact of differences in citation practices at the subfield, or Web of Science subject category level, using the model introduced in Crespo, Li, and Ruiz‐Castillo (2013a), according to which the number of citations received by an article depends on its underlying scientific influence and the field to which it belongs. We use the same Thomson Reuters data set of about 4.4 million articles used in Crespo et al. (2013a) to analyze 22 broad fields. The main results are the following: First, when the classification system goes from 22 fields to 219 subfields the effect on citation inequality of differences in citation practices increases from ∼14% at the field level to 18% at the subfield level. Second, we estimate a set of exchange rates (ERs) over a wide [660, 978] citation quantile interval to express the citation counts of articles into the equivalent counts in the all‐sciences case. In the fractional case, for example, we find that in 187 of 219 subfields the ERs are reliable in the sense that the coefficient of variation is smaller than or equal to 0.10. Third, in the fractional case the normalization of the raw data using the ERs (or subfield mean citations) as normalization factors reduces the importance of the differences in citation practices from 18% to 3.8% (3.4%) of overall citation inequality. Fourth, the results in the fractional case are essentially replicated when we adopt a multiplicative approach.

The Citation Merit of Scientific Publications

We propose a new method to assess the merit of any set of scientific papers in a given field based on the citations they receive. Given a field and a citation impact indicator, such as the mean citation or the -index, the merit of a given set of articles is identified with the probability that a randomly drawn set of articles from a given pool of articles in that field has a lower citation impact according to the indicator in question. The method allows for comparisons between sets of articles of different sizes and fields. Using a dataset acquired from Thomson Scientific that contains the articles published in the periodical literature in the period 1998–2007, we show that the novel approach yields rankings of research units different from those obtained by a direct application of the mean citation or the -index.

Postnikov pieces and BZ/p-homotopy theory

We present a constructive method to compute the cellularization with respect to B m Z/p for any integer m > 1 of a large class of H-spaces, namely all those which have a finite number of non-trivial B m Z/p-homotopy groups (the pointed mapping space map * (B m Z/p, X) is a Postnikov piece). We prove in particular that the B m Z/p-cellularization of an H-space having a finite number of B m Z /p-homotopy groups is ap-torsion Postnikov piece. Along the way, we characterize the BZ/p r -cellular classifying spaces of nilpotent groups.

Relating Postnikov pieces with the Krull filtration: a spin-off of Serre's theorem

Abstract We characterize H-spaces which are p-torsion Postnikov pieces of finite type by a cohomological property together with a necessary acyclicity condition. When the mod p cohomology of an H-space is finitely generated as an algebra over the Steenrod algebra we prove that its homotopy groups behave like those of a finite complex. In particular, a p-complete infinite loop space has a finite number of non-trivial homotopy groups if and only if its mod p cohomology satisfies this finiteness condition.

Noetherian loop spaces

The class of loop spaces of which the mod p cohomology is Noetherian is much larger than the class of p-compact groups (for which the mod p cohomology is required to be finite). It contains Eilenberg-Mac Lane spaces such as CP? and 3-connected covers of compact Lie groups. We study the cohomology of the classifying space BX of such an object and prove it is as small as expected, that is, comparable to that of BCP?. We also show that BX differs basically from the classifying space of a p-compact group in a single homotopy group. This applies in particular to 4-connected covers of classifying spaces of compact Lie groups and sheds new light on how the cohomology of such an object looks like.

Simple rules govern finite-size effects in scale-free networks

We give an intuitive though general explanation of the finite-size effect in scale-free networks in terms of the degree distribution of the starting network. This result clarifies the relevance of the starting network in the final degree distribution. We use two different approaches: the deterministic mean-field approximation used by Barabasi and Albert (but taking into account the nodes of the starting network), and the probability distribution of the degree of each node, which considers the stochastic process. Numerical simulations show that the accuracy of the predictions of the mean-field approximation depend on the contribution of the dispersion in the final distribution. The results in terms of the probability distribution of the degree of each node are very accurate when compared to numerical simulations. The analysis of the standard deviation of the degree distribution allows us to assess the influence of the starting core when fitting the model to real data.