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Register a new userThe inconsistency of h-index: a mathematical analysis
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Added by
Ricardo Brito
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Citation distributions are lognormal. We use 30 lognormally distributed synthetic series of numbers that simulate real series of citations to investigate the consistency of the h index. Using the lognormal cumulative distribution function, the equation that defines the h index can be formulated; this equation shows that h has a complex dependence on the number of papers (N). We also investigate the correlation between h and the number of papers exceeding various citation thresholds, from 5 to 500 citations. The best correlation is for the 100 threshold but numerous data points deviate from the general trend. The size-independent indicator h/N shows no correlation with the probability of publishing a paper exceeding any of the citation thresholds. In contrast with the h index, the total number of citations shows a high correlation with the number of papers exceeding the thresholds of 10 and 50 citations; the mean number of citations correlates with the probability of publishing a paper that exceeds any level of citations. Thus, in synthetic series, the number of citations and the mean number of citations are much better indicators of research performance than h and h/N. We discuss that in real citation distributions there are other difficulties.
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The characteristics of the $h$-index in the field of condensed matter physics are studied using high-quality data from ResearcherID. The results are examined in terms of theoretical descriptions of the $h$-index overall dependence on a researchers total number of published papers, and total number of citations. In particular, the models by Hirsch, Egghe and Rousseau, as well as by Glanzel and Schubert are examined. Special emphasis is placed on the deviations from such statistical descriptions, and it is argued that the deviation of a particular researchers $h$ value from the Egghe-Rouseau models prediction can be used as a supplementary measure of impact. A corresponding analysis with similar results is performed using the multi-author $h_m$-index.
We revisit our recent study [Predicting results of the Research Excellence Framework using departmental h-index, Scientometrics, 2014, 1-16; arXiv:1411.1996] in which we attempted to predict outcomes of the UKs Research Excellence Framework (REF~2014) using the so-called departmental $h$-index. Here we report that our predictions failed to anticipate with any accuracy either overall REF outcomes or movements of individual institutions in the rankings relative to their positions in the previous Research Assessment Exercise (RAE~2008).
We use the data of tenured and tenure-track faculty at ten public and private math departments of various tiered rankings in the United States, as a case study to demonstrate the statistical and mathematical relationships among several variables, e.g., the number of publications and citations, the rank of professorship and AMS fellow status. At first we do an exploratory data analysis of the math departments. Then various statistical tools, including regression, artificial neural network, and unsupervised learning, are applied and the results obtained from different methods are compared. We conclude that with more advanced models, it may be possible to design an automatic promotion algorithm that has the potential to be fairer, more efficient and more consistent than human approach.
Academic leadership is essential for research innovation and impact. Until now, there has been no dedicated measure of leadership by bibliometrics. Popular bibliometric indices are mainly based on academic output, such as the journal impact factor and the number of citations. Here we develop an academic leadership index based on readily available bibliometric data that is sensitive to not only academic output but also research efficiency. Our leadership index was tested in two studies on peer-reviewed journal papers by extramurally-funded principal investigators in the field of life sciences from China and the USA, respectively. The leadership performance of these principal investigators was quantified and compared relative to university rank and other factors. As a validation measure, we show that the highest average leadership index was achieved by principal investigators at top national universities in both countries. More interestingly, our results also indicate that on an individual basis, strong leadership and high efficiency are not necessarily associated with those at top-tier universities nor with the most funding. This leadership index may become the basis of a comprehensive merit system, facilitating academic evaluation and resource management.
Negative index materials are artificial structures whose refractive index has a negative value over some frequency range. These materials were postulated and investigated theoretically by Veselago in 1964 and were confirmed experimentally by Shelby, Smith, and Schultz in 2001. New fabrication techniques now allow for the construction of negative index materials at scales that are interesting for applications, which has made them a very active topic of investigation. In this paper, we report various mathematical results on the properties of negative index materials and their applications. The topics discussed herein include superlensing using complementary media, cloaking using complementary media, cloaking an object via anomalous localized resonance, and the well-posedness and the finite speed propagation in media consisting of dispersive metamaterials. Some of the results have been refined and have simpler proofs than the original ones.
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