Related papers: Re-evaluating phoneme frequencies
The spatial distribution of people exhibits clustering across a wide range of scales, from household ($\sim 10^{-2}$ km) to continental ($\sim 10^4$ km) scales. Empirical data indicates simple power-law scalings for the size distribution of…
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…
Power laws arise in a variety of phenomena ranging from matter undergoing phase transition to the distribution of word frequencies in the English language. Usually, their presence is only apparent when data is abundant, and accurately…
Many man-made and natural phenomena, including the intensity of earthquakes, population of cities and size of international wars, are believed to follow power-law distributions. The accurate identification of power-law patterns has…
Zipf's law is shown to arise as the variational solution of a problem formulated in Fisher's terms. An appropriate minimization process involving Fisher information and scale-invariance yields this universal rank distribution. As an example…
The time evolution of Earth with her cities, languages and countries is considered in terms of the multiplicative noise and the fragmentation- processes, where the related families, size distributions, lifetimes, bilinguals, etc. are…
When following a sequence - such as reading a text or tracking a user's activity - one can measure how the "dictionary" of distinct elements (types) grows with the number of observations (tokens). When this growth follows a power law, it is…
In prefix coding over an infinite alphabet, methods that consider specific distributions generally consider those that decline more quickly than a power law (e.g., Golomb coding). Particular power-law distributions, however, model many…
Zipf's law is the most common statistical distribution displaying scaling behavior. Cities, populations or firms are just examples of this seemingly universal law. Although many different models have been proposed, no general theoretical…
In the setting of minimal local grammar-based coding, the input string is represented as a grammar with the minimal output length defined via simple symbol-by-symbol encoding. This paper discusses four contributions to this field. First, we…
In the principles-and-parameters framework, the structural features of languages depend on parameters that may be toggled on or off, with a single parameter often dictating the status of multiple features. The implied covariance between…
The historical and geographical spread from older to more modern languages has long been studied by examining textual changes and in terms of changes in phonetic transcriptions. However, it is more difficult to analyze language change from…
It is traditionally assumed that Zipf's law implies the power-law growth of the number of different elements with the total number of elements in a system - the so-called Heaps' law. We show that a careful definition of Zipf's law leads to…
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.…
Exploiting the fact that natural languages are complex systems, the present exploratory article proposes a direct method based on frequency distributions that may be useful when making a decision on the status of problematic phonemes, an…
In this article, I conduct a textual and contextual analysis of the empirical literature on Zipf's law for cities. Building on previous meta-analysis material openly available, I collect full texts and bibliographies of 66 scientific…
In Phys. Rev. Letters (73:2, 5 Dec. 94), Mantegna et al. conclude on the basis of Zipf rank frequency data that noncoding DNA sequence regions are more like natural languages than coding regions. We argue on the contrary that an empirical…
Natural language data follows a power-law distribution, with most knowledge and skills appearing at very low frequency. While a common intuition suggests that reweighting or curating data towards a uniform distribution may help models…
We present an overview of possible reasons for the appearance of heavy-tailed distributions in applications to the natural sciences. These distributions include the laws of Pareto, Lotka, and some new ones. The reasons are illustrated using…
Languages vary considerably in syntactic structure. About 40% of the world's languages have subject-verb-object order, and about 40% have subject-object-verb order. Extensive work has sought to explain this word order variation across…