Related papers: Citations and the Zipf-Mandelbrot's law
We present an extensive analysis of long-term statistics of the queries to websites using logs collected on several web caches in Russian academic networks and on US IRCache caches. We check the sensitivity of the statistics to several…
The study of citations in the scientific literature crosses the boundaries between the traditional branches of science and stands on its own as a most profitable research field dubbed the `science of science'. Although the understanding of…
Bayesian modelling and statistical text analysis rely on informed probability priors to encourage good solutions. This paper empirically analyses whether text in medical discharge reports follow Zipf's law, a commonly assumed statistical…
Usually, the study of city population distribution has been reduced to power laws. In such analysis, a common practice is to consider cities with more than one hundred thousand inhabitants. Here, we argue that the distribution of cities for…
In this paper, we will see that the proportion of d as leading digit, d $\in$ 1, 9, in data (obtained thanks to the hereunder developed model) is more likely to follow a law whose probability distribution is determined by a specific upper…
Causal processes can give rise to distinctive distributions in the linguistic variables that they affect. Consequently, a secure understanding of a variable's distribution can hold a key to understanding the forces that have causally shaped…
Many human knowledge systems, such as science, law, and invention, are built on documents and the citations that link them. Citations, while serving multiple purposes, primarily function as a way to explicitly document the use of prior work…
The citation network constituted by the SPIRES data base is investigated empirically. The probability that a given paper in the SPIRES data base has $k$ citations is well described by simple power laws, $P(k) \propto k^{-\alpha}$, with…
A random variable (r.v.) X is said to follow Benford's law if log(X) is uniform mod 1. Many experimental data sets prove to follow an approximate version of it, and so do many mathematical series and continuous random variables. This…
We show that the laws of Zipf and Benford, obeyed by scores of numerical data generated by many and diverse kinds of natural phenomena and human activity are related to the focal expression of a generalized thermodynamic structure. This…
Memes are the cultural equivalent of genes that spread across human culture by means of imitation. What makes a meme and what distinguishes it from other forms of information, however, is still poorly understood. Our analysis of memes in…
Zipf's law states that the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat's rule of proportional growth but require additional constraints. We show that Gibrat's rule, at all…
This is a report about the use and misuse of citation data in the assessment of scientific research. The idea that research assessment must be done using ``simple and objective'' methods is increasingly prevalent today. The ``simple and…
Mathematical models of the scientific citation process predict a strong "first-mover" effect under which the first papers in a field will, essentially regardless of content, receive citations at a rate enormously higher than papers…
A new indicator, a real valued $s$-index, is suggested to characterize a quality and impact of the scientific research output. It is expected to be at least as useful as the notorious $h$-index, at the same time avoiding some its obvious…
The occurrence of the nonzero leftmost digit, i.e., 1, 2, ..., 9, of numbers from many real world sources is not uniformly distributed as one might naively expect, but instead, the nature favors smaller ones according to a logarithmic…
The frequency distributions of DNA k-mers are shaped by fundamental biological processes and offer a window into genome structure and evolution. Inspired by analogies to natural language, prior studies have attempted to model genomic k-mer…
The word-frequency distribution provides the fundamental building blocks that generate discourse in language. It is well known, from empirical evidence, that the word-frequency distribution of almost any text is described by Zipf's law, at…
We propose a new citation model which builds on the existing models that explicitly or implicitly include "direct" and "indirect" (learning about a cited paper's existence from references in another paper) citation mechanisms. Our model…
This paper revisits Menzerath's Law, also known as the Menzerath-Altmann Law, which models a relationship between the length of a linguistic construct and the average length of its constituents. Recent findings indicate that simple…