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When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear…
Zipf's law has been found in many human-related fields, including language, where the frequency of a word is persistently found as a power law function of its frequency rank, known as Zipf's law. However, there is much dispute whether it is…
The joint probability distribution of many degrees of freedom in biological systems, such as firing patterns in neural networks or antibody sequence composition in zebrafish, often follow Zipf's law, where a power law is observed on a…
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…
Background: Zipf's discovery that word frequency distributions obey a power law established parallels between biological and physical processes, and language, laying the groundwork for a complex systems perspective on human communication.…
Many studies in Economics and other disciplines have been reporting distributions following power-law behavior (i.e distributions of incomes (Pareto's law), city sizes (Zipf's law), frequencies of words in long sequences of text etc.)[1, 6,…
A key aim in biology and psychology is to identify fundamental principles underpinning the behavior of animals, including humans. Analyses of human language and the behavior of a range of non-human animal species have provided evidence for…
The frequencies at which individual words occur across languages follow power law distributions, a pattern of findings known as Zipf's law. A vast literature argues over whether this serves to optimize the efficiency of human communication,…
An important body of quantitative linguistics is constituted by a series of statistical laws about language usage. Despite the importance of these linguistic laws, some of them are poorly formulated, and, more importantly, there is no…
In this study, we investigate whether speech symbols, learned through deep learning, follow Zipf's law, akin to natural language symbols. Zipf's law is an empirical law that delineates the frequency distribution of words, forming…
A new model, called "Human Dynamics", has been recently proposed that individuals execute activities based on a perceived priority of tasks, which can be characterized by a power-law distribution of waiting time between consecutive tasks…
Present human languages display slightly asymmetric log-normal (Gauss) distribution for size [1-3], whereas present cities follow power law (Pareto-Zipf law)[4]. Our model considers the competition between languages and that between cities…
A curious observation was made that the rank statistics of scientific citation numbers follows Zipf-Mandelbrot's law. The same pow-like behavior is exhibited by some simple random citation models. The observed regularity indicates not so…
A set of data with positive values follows a Pareto distribution if the log-log plot of value versus rank is approximately a straight line. A Pareto distribution satisfies Zipf's law if the log-log plot has a slope of -1. Since many types…
It is shown that the distribution of low variability periods in the activity of human heart rate typically follows a multi-scaling Zipf's law. The presence or failure of a power law, as well as the values of the scaling exponents, are…
The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been…
We extract the individual names of persons mentioned in news reports from a Philippine-based daily in the English language from 2010-2012. Names are extracted using a learning algorithm that filters adjacent capitalized words and runs it…
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…
Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Based on the idea from general fractals and scaling,…
Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in…