Related papers: Zipf's and Taylor's Laws
We investigate the origin of Zipf's law for words in written texts by means of a stochastic dynamical model for text generation. The model incorporates both features related to the general structure of languages and memory effects inherent…
Phenomena as diverse as breeding bird populations, the size of U.S. firms, money invested in mutual funds, the GDP of individual countries and the scientific output of universities all show unusual but remarkably similar growth…
We present empirical data on frequency and pattern of misprints in citations to twelve high-profile papers. We find that the distribution of misprints, ranked by frequency of their repetition, follows Zipf's law. We propose a stochastic…
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…
Statistical regularities in human language have fascinated researchers for decades, suggesting deep underlying principles governing its evolution and information structuring for efficient communication. While Zipf's Law describes the…
We show that Zipf's Law for the largest clusters is not valid in an exact sense at the critical point of the fragmentation phase transition, contrary to previous claims. Instead, the extracted distributions of the largest clusters reflects…
Quantifying the similarity between symbolic sequences is a traditional problem in Information Theory which requires comparing the frequencies of symbols in different sequences. In numerous modern applications, ranging from DNA over music to…
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…
The interaction of all mobile species with their environment hinges on their movement patterns: the places they visit and how frequently they go there. In human society, where the prevalent form of cohabitation is in cities, the highly…
Zipf's law is found when the vocabulary of long written texts is ranked according to the frequency of word occurrences, establishing a power-law decay for the frequency vs rank relation. This law is a robust statistical property observed…
Data of proportional elections show a striking feature: If the parties are ranked according to the number of their voters, the number of votes grows exponentially with the rank of the party. This so-called Zipf's law has been reported…
Power law distributions characterise several natural and social phenomena. The Zipf law for cities is one of those. The study views the question of whether that global regularity is independent of different spatial distributions of cities.…
Analyzing and modeling the mobility process with tour behavior is fundamental to understanding a wide range of complex systems, including animal foraging, human mobility and freight transportation. However, despite their importance, the…
By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto-Zipf law), and that in this region the growth rate of each firm is…
Using data from gene expression databases on various organisms and tissues, including yeast, nematodes, human normal and cancer tissues, and embryonic stem cells, we found that the abundances of expressed genes exhibit a power-law…
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…
Identifying statistical patterns characterizing human trajectories is crucial for public health, traffic engineering, city planning, and epidemic modeling. Recent developments in global positioning systems and mobile phone networks have…
We address the role of multiplicative stochastic processes in modeling the occurrence of power-law city size distributions. As an explanation of the result of Zipf's rank analysis, Simon's model is presented in a mathematically elementary…
Zipf's law for cities is probably the most famous regularity in social sciences. So much that, a hundred years of publication later, its status is not clear: is it a law of social organisation? Is it an instrument of description of city…
We propose hypotheses describing the empirical finding of an association between the exponents of urban GDP scaling and Zipf's law for cities. These hypotheses represent various combinations of directional or reciprocal causal links between…