Related papers: Citations and the Zipf-Mandelbrot's law
For words, rank-frequency distributions have long been heralded for adherence to a potentially-universal phenomenon known as Zipf's law. The hypothetical form of this empirical phenomenon was refined by Ben\^{i}ot Mandelbrot to that which…
Zipf's law is well known in linguistics: the frequency of a word is inversely proportional to its rank. This is a special case of a more general power law, a common phenomenon in many kinds of real-world statistical data. Here, it is shown…
The binary many-step Markov chain with the step-like memory function is considered as a model for the analysis of rank distributions of words in stochastic symbolic dynamical systems. We prove that the envelope curve for this distribution…
Besides of complexities concerning to football championships, it is identified some regularities in them. These regularities refer to goal distributions by goal-players and by games. In particular, the goal distribution by goal-players it…
The distribution $N(x)$ of citations of scientific papers has recently been illustrated (on ISI and PRE data sets) and analyzed by Redner [Eur. Phys. J. B {\bf 4}, 131 (1998)]. To fit the data, a stretched exponential ($N(x) \propto…
Building on ideas from linguistics, psychology, and social sciences about the possible mechanisms of human decision-making, we propose a novel theoretical framework for the citation analysis. Given the existing trend to investigate citation…
In a language corpus, the probability that a word occurs $n$ times is often proportional to $1/n^2$. Assigning rank, $s$, to words according to their abundance, $\log s$ vs $\log n$ typically has a slope of minus one. That simple Zipf's law…
Gradually Truncated Power law distribution - Citation of scientists Hari M. Gupta, Jose R. Campanha and Bianca A. Ferrari Unesp - Physics Dpto. - Rio Claro Sao Paulo - Brazil Abstract The number of times, a scientist is cited in other…
Zipf's law is the main regularity of quantitative linguistics. Despite of many works devoted to foundations of this law, it is still unclear whether it is only a statistical regularity, or it has deeper relations with information-carrying…
Physics seeks to uncover the laws of Nature and express them through mathematical equations. Despite the vast diversity of natural phenomena, physical equations exhibit structural regularities that set them apart from arbitrary mathematical…
Zipf's law is found when the vocabulary of long written texts is ranked according to the frequency of word occurrences, establishing a power-law decay for the frequency vs rank relation. This law is a robust statistical property observed…
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…
Languages across the world exhibit Zipf's law of abbreviation, namely more frequent words tend to be shorter. The generalized version of the law - an inverse relationship between the frequency of a unit and its magnitude - holds also for…
Power law distributions characterise several natural and social phenomena. The Zipf law for cities is one of those. The study views the question of whether that global regularity is independent of different spatial distributions of cities.…
In his pioneering research, G. K. Zipf observed that more frequent words tend to have more meanings, and showed that the number of meanings of a word grows as the square root of its frequency. He derived this relationship from two…
Although Zipf's law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the…
Zipf's law is a hallmark of several complex systems with a modular structure, such as books composed by words or genomes composed by genes. In these component systems, Zipf's law describes the empirical power law distribution of component…
Zipf's law states that the frequency of an observation with a given value is inversely proportional to the square of that value; Taylor's law, instead, describes the scaling between fluctuations in the size of a population and its mean.…
Scientific cooperation on an international level has been well studied in the literature. However, much less is known about this cooperation on the intercontinental level. In this paper, we address this issue by creating a collection of…
Zipf's law for cities is probably the most famous regularity in social sciences. So much that, a hundred years of publication later, its status is not clear: is it a law of social organisation? Is it an instrument of description of city…