Related papers: Snooker Statistics and Zipf's Law
Zipf's law establishes a scaling behavior for word-frequencies in large text corpora. The appearance of Zipfian properties in human language has been previously explained as an optimization problem for the interests of speakers and hearers.…
Time evolution of the cities and of the languages is considered in terms of multiplicative noise and fragmentation processes; where power law (Pareto-Zipf law) and slightly asymmetric log-normal (Gauss) distribution result for the size…
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 many competitive settings, from education to politics, rules do not reward effort evenly, and thresholds (e.g., grade cutoffs or electoral majorities) make some moments disproportionately important. Success thus depends on efficiently…
The Chapter starts with introductory information about quantitative linguistics notions, like rank--frequency dependence, Zipf's law, frequency spectra, etc. Similarities in distributions of words in texts with level occupation in quantum…
We study behavioral action sequences of players in a massive multiplayer online game. In their virtual life players use eight basic actions which allow them to interact with each other. These actions are communication, trade, establishing…
We observe the statistical properties of blogs that are expected to reflect social human interaction. Firstly, we introduce a basic normalization preprocess that enables us to evaluate the genuine word frequency in blogs that are…
The analysis of thousands of time series in different languages reveals that word usage presents oscillations with a prevalence of 16-year cycles, mounted on slowly varying trends. These components carry different information: while similar…
We study a resource utilization scenario characterized by intrinsic fitness. To describe the growth and organization of different cities, we consider a model for resource utilization where many restaurants compete, as in a game, to attract…
Power law or generalized polynomial regressions with unknown real-valued exponents and coefficients, and weakly dependent errors, are considered for observations over time, space or space--time. Consistency and asymptotic normality of…
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,…
In this paper, a statistical analysis of the structure of one blog community, a kind of social networks, is presented. The quantities such as degree distribution, clustering coefficient, average shortest path length are calculated to…
Many complex phenomena, from the selection of traits in biological systems to hierarchy formation in social and economic entities, show signs of competition and heterogeneous performance in the temporal evolution of their components, which…
Kauffman net is a dynamical system of logical variables receiving two random inputs and each randomly assigned a boolean function. We show that the attractor and transient lengths exhibit scaleless behavior with power-law distributions over…
As is the case of many signals produced by complex systems, language presents a statistical structure that is balanced between order and disorder. Here we review and extend recent results from quantitative characterisations of the degree of…
In this paper we quantify the consistency of word usage in written texts represented by complex networks, where words were taken as nodes, by measuring the degree of preservation of the node neighborhood.} Words were considered highly…
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,…
We propose a stochastic model for the number of different words in a given database which incorporates the dependence on the database size and historical changes. The main feature of our model is the existence of two different classes of…
Patterns of wins and losses in pairwise contests, such as occur in sports and games, consumer research and paired comparison studies, and human and animal social hierarchies, are commonly analyzed using probabilistic models that allow one…
The different between the inverse power function and the negative exponential function is significant. The former suggests a complex distribution, while the latter indicates a simple distribution. However, the association of the power-law…