Related papers: Citation indices and dimensional homogeneity
The metric (resp. edge metric or mixed metric) dimension of a graph $G$, is the cardinality of the smallest ordered set of vertices that uniquely recognizes all the pairs of distinct vertices (resp. edges, or vertices and edges) of $G$ by…
M. Goresky and R. MacPherson intersection homology is also defined from the singular chain complex of a filtered space by H. King, with a key formula to make selections among singular simplexes. This formula needs a notion of dimension for…
This paper analyzes publication efficiency in terms of Hirsch-index or h-index and total citations, with an analogy to the Carnot efficiency used in thermodynamics. Such publication efficiency, with typical value of 30%, can be utilized to…
In our chapter we address the statistical analysis of percentiles: How should the citation impact of institutions be compared? In educational and psychological testing, percentiles are already used widely as a standard to evaluate an…
We propose a simple new index, named the $CI$-index, based on the Choquet integral to characterize the scientific output of researchers. This index is an improvement of the $A$-index and $R$-index and has a notable feature that highly cited…
The h-index provides us with nine natural classes which can be written as a matrix of three vectors. The three vectors are: X=(X1, X2, X3) indicate publication distribution in the h-core, the h-tail, and the uncited ones, respectively;…
In the final analysis citation-based indicators are inferior to effective peer review and even peer review is flawed. It is impossible to accurately measure the value or impact of scientific research and a key task of scientometricians…
Despite all its well-known flaws and calls for its dismissal, the notorious $h$-index is still used in many instances when awarding grants, or promoting and hiring scientists. To address this, I set out to devise a better index, with the…
We propose a definition of magnitude for a length space with a Borel measure, which involves integrals over the set of geodesics. This quantity agrees with the magnitude of finite metric spaces, up to re-scaling the metric to ensure the…
The metric dimension has been introduced independently by Harary, Melter and Slater in 1975 to identify vertices of a graph G using its distances to a subset of vertices of G. A resolving set X of a graph G is a subset of vertices such…
The h-index (Hirsch, 2005) is robust, remaining relatively unaffected by errors in the long tails of the citations-rank distribution, such as typographic errors that short-change frequently-cited papers and create bogus additional records.…
Recent works on Hierarchical Clustering (HC), a well-studied problem in exploratory data analysis, have focused on optimizing various objective functions for this problem under arbitrary similarity measures. In this paper we take the first…
Modern large-scale datasets are frequently said to be high-dimensional. However, their data point clouds frequently possess structures, significantly decreasing their intrinsic dimensionality (ID) due to the presence of clusters, points…
Bibliometric indicators can be determined by comparing specific citation records with the percentiles of a reference set. However, there exists an ambiguity in the computation of percentiles because usually a significant number of papers…
Universality or near-universality of citation distributions was found empirically a decade ago but its theoretical justification has been lacking so far. Here, we systematically study citation distributions for different disciplines in…
I propose the P-Index that genuinely constitutes a well-defined, compact author citation metric.
Scientific behavior is often characterized by a tension between building upon established knowledge and introducing novel ideas. Here, we investigate whether this tension is reflected in the relationship between the similarity of a…
The $\alpha$ person is the dominant person in a group. We define the $\alpha$-author of a paper as the author of the paper with the highest $h$-index among all the coauthors, and an $\alpha$-paper of a scientist as a paper authored or…
An important aspect in the theory of algebras with polynomial identities is the study of the asymptotic behavior of the codimension sequence $c_n(A),\, n\geq 1,$ which measures the growth of polynomial identities of a given algebra $A$. In…
The unit Euclidean distance degree and the generic Euclidean distance degree are two well-studied invariants of projective varieties. These quantities measure the algebraic complexity of nearest-point problems on a variety, and in many…