相关论文: Citations to articles citing Benford's law: a Benf…
The minimization of Fisher's information (MFI) approach of Frieden et al. [Phys. Rev. E {\bf 60} 48 (1999)] is applied to the study of size distributions in social groups on the basis of a recently established analogy between scale…
We derive a necessary and sufficient condition for the sum of M independent continuous random variables modulo 1 to converge to the uniform distribution in L^1([0,1]), and discuss generalizations to discrete random variables. A consequence…
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…
The law of large numbers (LLN) and central limit theorem (CLT) are long and widely been known as two fundamental results in probability theory. Recently problems of model uncertainties in statistics, measures of risk and superhedging in…
In an article written five years ago [arXiv:0809.0522], we described a method for predicting which scientific papers will be highly cited in the future, even if they are currently not highly cited. Applying the method to real citation data…
For decades the number of scientific publications has been rapidly increasing, effectively out-dating knowledge at a tremendous rate. Only few scientific milestones remain relevant and continuously attract citations. Here we quantify how…
We prove a general ergodic-theoretic result concerning the return time statistic, which, properly understood, sheds some new light on the common sense phenomenon known as {\it the law of series}. Let \proc be an ergodic process on finitely…
The purpose of this paper is to propose the use of models, theories and laws in bibliometrics and scientometrics to enhance information retrieval processes, especially ranking. A common pattern in many man-made data sets is Lotka's Law…
Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with…
It is a matter of debate whether a shrinking proportion of scholarly literature is getting most of the references over time. It is also less well understood how a narrowing literature usage would affect the circulation of ideas in the…
Large language models (LLMs) frequently make errors when handling even simple numerical problems, such as comparing two small numbers. A natural hypothesis is that these errors stem from how LLMs represent numbers, and specifically, whether…
In this Digest we review a recent study released by the Google Scholar team on the apparently increasing fraction of citations to old articles from studies published in the last 24 years (1990-2013). First, we describe the main findings of…
We analyze time evolution of statistical distributions of citations to scientific papers published in one year. While these distributions can be fitted by a power-law dependence we find that they are nonstationary and the exponent of the…
Nadarajah and Gupta (2004) introduced the beta Fr\'echet (BF) distribution, which is a generalization of the exponentiated Fr\'echet (EF) and Fr\'echet distributions, and obtained the probability density and cumulative distribution…
In this paper, we examine the evolution of the impact of older scholarly articles. We attempt to answer four questions. First, how often are older articles cited and how has this changed over time. Second, how does the impact of older…
In the past two decades, a series of important results have been established in the empirical and theoretical modeling of complex networks, although considered are mainly pairwise networks. However, with the development of science and…
This short note records an unusual situation with some Google Scholar's profiles that imply the existence of "supernovae" articles, i.e., articles whose impact -- in terms of number of citations -- in a single year gets (almost) an order of…
Citation distributions are crucial for the analysis and modeling of the activity of scientists. We investigated bibliometric data of papers published in journals of the American Physical Society, searching for the type of function which…
References, the mechanism scientists rely on to signal previous knowledge, lately have turned into widely used and misused measures of scientific impact. Yet, when a discovery becomes common knowledge, citations suffer from obliteration by…
The prevailing maximum likelihood estimators for inferring power law models from rank-frequency data are biased. The source of this bias is an inappropriate likelihood function. The correct likelihood function is derived and shown to be…