相关论文: A Paradoxical Property of the Monkey Book
We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a…
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…
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.…
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…
The dependence with text length of the statistical properties of word occurrences has long been considered a severe limitation quantitative linguistics. We propose a simple scaling form for the distribution of absolute word frequencies…
This article is devoted to the verification of the empirical Heaps law in European languages using Google Books Ngram corpus data. The connection between word distribution frequency and expected dependence of individual word number on text…
The text-length-dependence of real word-frequency distributions can be connected to the general properties of a random book. It is pointed out that this finding has strong implications, when deciding between two conceptually different views…
Evidence is given for a systematic text-length dependence of the power-law index gamma of a single book. The estimated gamma values are consistent with a monotonic decrease from 2 to 1 with increasing length of a text. A direct connection…
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
We review recent progress in understanding the meaning of mutual information in natural language. Let us define words in a text as strings that occur sufficiently often. In a few previous papers, we have shown that a power-law distribution…
Heaps' or Herdan's law is a linguistic law describing the relationship between the vocabulary/dictionary size (type) and word counts (token) to be a power-law function. Its existence in genomes with certain definition of DNA words is…
Traditional linguistic theories have largely regard language as a formal system composed of rigid rules. However, their failures in processing real language, the recent successes in statistical natural language processing, and the findings…
Human language, the most powerful communication system in history, is closely associated with cognition. Written text is one of the fundamental manifestations of language, and the study of its universal regularities can give clues about how…
The power law is ubiquitous in natural and social phenomena, and is considered as a universal relationship between the frequency and its rank for diverse social systems. However, a general model is still lacking to interpret why these…
The Zipf's law is the major regularity of statistical linguistics that served as a prototype for rank-frequency relations and scaling laws in natural sciences. Here we show that the Zipf's law -- together with its applicability for a single…
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…
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…
Natural languages are full of rules and exceptions. One of the most famous quantitative rules is Zipf's law which states that the frequency of occurrence of a word is approximately inversely proportional to its rank. Though this `law' of…
Given a discrete distribution, an interesting problem is to determine the minimum size of a random sample drawn from this distribution, in order to observe a given number of different records. This problem is related with many applied…
We study a deliberately simple, fully non-linguistic model of text: a sequence of independent draws from a finite alphabet of letters plus a single space symbol. A word is defined as a maximal block of non-space symbols. Within this…