Related papers: Explaining Zipf's Law via Mental Lexicon
Zipf's law of abbreviation, the tendency of more frequent words to be shorter, is one of the most solid candidates for a linguistic universal, in the sense that it has the potential for being exceptionless or with a number of exceptions…
We inspect the deductive connection between the neural scaling law and Zipf's law -- two statements discussed in machine learning and quantitative linguistics. The neural scaling law describes how the cross entropy rate of a foundation…
In this paper we combine statistical analysis of large text databases and simple stochastic models to explain the appearance of scaling laws in the statistics of word frequencies. Besides the sublinear scaling of the vocabulary size with…
The task of text segmentation may be undertaken at many levels in text analysis---paragraphs, sentences, words, or even letters. Here, we focus on a relatively fine scale of segmentation, hypothesizing it to be in accord with a stochastic…
The pioneering research of G. K. Zipf on the relationship between word frequency and other word features led to the formulation of various linguistic laws. The most popular is Zipf's law for word frequencies. Here we focus on two laws that…
Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes, or texts as sets of words. On one hand, the joint occurrence of…
The distribution of word probabilities in the monkey model of Zipf's law is associated with two universality properties: (1) the power law exponent converges strongly to $-1$ as the alphabet size increases and the letter probabilities are…
Zipf's law seems to be ubiquitous in human languages and appears to be a universal property of complex communicating systems. Following the early proposal made by Zipf concerning the presence of a tension between the efforts of speaker and…
We present a simple structure based model of how words are formed from morphemes. The model explains two major empirical facts: the typical distribution of word lengths and the appearance of Zipf like rank frequency curves. In contrast to…
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…
Here we present a new class of optimality for coding systems. Members of that class are displaced linearly from optimal coding and thus exhibit Zipf's law, namely a power-law distribution of frequency ranks. Within that class, Zipf's law,…
Human language, as a typical complex system, its organization and evolution is an attractive topic for both physical and cultural researchers. In this paper, we present the first exhaustive analysis of the text organization of human speech.…
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…
In his pioneering research, G. K. Zipf formulated a couple of statistical laws on the relationship between the frequency of a word with its number of meanings: the law of meaning distribution, relating the frequency of a word and its…
We use the formulation of equilibrium statistical mechanics in order to study some important characteristics of language. Using a simple expression for the Hamiltonian of a language system, which is directly implied by the Zipf law, we are…
We show that the Zipf's law for Chinese characters perfectly holds for sufficiently short texts (few thousand different characters). The scenario of its validity is similar to the Zipf's law for words in short English texts. For long…
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…
The mapping of lexical meanings to wordforms is a major feature of natural languages. While usage pressures might assign short words to frequent meanings (Zipf's law of abbreviation), the need for a productive and open-ended vocabulary,…
We explore a probabilistic model of an artistic text: words of the text are chosen independently of each other in accordance with a discrete probability distribution on an infinite dictionary. The words are enumerated 1, 2, $\ldots$, and…
Zipf's law is a paradigm describing the importance of different elements in communication systems, especially in linguistics. Despite the complexity of the hierarchical structure of language, music has in some sense an even more complex…