Related papers: Zipf and Heaps laws from dependency structures in …
A new angle of view is proposed to find the simple rules dominating complex systems and regular patterns behind random phenomena such as cities. Hierarchy of cities reflects the ubiquitous structure frequently observed in the natural world…
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…
Zipf's law is just one out of many universal laws proposed to describe statistical regularities in language. Here we review and critically discuss how these laws can be statistically interpreted, fitted, and tested (falsified). The modern…
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…
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…
The formation of sentences is a highly structured and history-dependent process. The probability of using a specific word in a sentence strongly depends on the 'history' of word-usage earlier in that sentence. We study a simple…
The rank-size plots of a large number of different physical and socio-economic systems are usually said to follow Zipf's law, but a unique framework for the comprehension of this ubiquitous scaling law is still lacking. Here we show that a…
Why does Zipf's law give a good description of data from seemingly completely unrelated phenomena? Here it is argued that the reason is that they can all be described as outcomes of a ubiquitous random group division: the elements can be…
The performance of deep learning in natural language processing has been spectacular, but the reasons for this success remain unclear because of the inherent complexity of deep learning. This paper provides empirical evidence of its…
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…
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…
Component systems - ensembles of realizations built from a shared repertoire of modular parts - are ubiquitous in biological, ecological, technological, and socio-cultural domains. From genomes to texts, cities, and software, these systems…
Zipf's law is a fundamental paradigm in the statistics of written and spoken natural language as well as in other communication systems. We raise the question of the elementary units for which Zipf's law should hold in the most natural way,…
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…
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…
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…
Languages across the world exhibit Zipf's law of abbreviation, namely more frequent words tend to be shorter. The generalized version of the law - an inverse relationship between the frequency of a unit and its magnitude - holds also for…
The availability of large datasets requires an improved view on statistical laws in complex systems, such as Zipf's law of word frequencies, the Gutenberg-Richter law of earthquake magnitudes, or scale-free degree distribution in networks.…
Fractals, 1/f noise, Zipf's law, and the occurrence of large catastrophic events are typical ubiquitous general empirical observations across the individual sciences which cannot be understood within the set of references developed within…
A family of information theoretic models of communication was introduced more than a decade ago to explain the origins of Zipf's law for word frequencies. The family is a based on a combination of two information theoretic principles:…