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Zipf's law states that if words of language are ranked in the order of decreasing frequency in texts, the frequency of a word is inversely proportional to its rank. It is very robust as an experimental observation, but to date it escaped…
A major problem for evolutionary theory is understanding the so called {\em open-ended} nature of evolutionary change, from its definition to its origins. Open-ended evolution (OEE) refers to the unbounded increase in complexity that seems…
Long-range correlations are found in symbolic sequences from human language, music and DNA. Determining the span of correlations in dolphin whistle sequences is crucial for shedding light on their communicative complexity. Dolphin whistles…
In this overview, we discuss the connections between the observations of critical dynamics in neuronal networks and the maximum entropy models that are often used as statistical models of neural activity, focusing in particular on the…
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…
Some authors have recently argued that a finite-size scaling law for the text-length dependence of word-frequency distributions cannot be conceptually valid. Here we give solid quantitative evidence for the validity of such scaling law,…
With Zipf's law being originally and most famously observed for word frequency, it is surprisingly limited in its applicability to human language, holding over no more than three to four orders of magnitude before hitting a clear break in…
Research collaborations provide the foundation for scientific advances, but we have only recently begun to understand how they form and grow on a global scale. Here we analyze a model of the growth of research collaboration networks to…
The importance of statistical patterns of language has been debated over decades. Although Zipf's law is perhaps the most popular case, recently, Menzerath's law has begun to be involved. Menzerath's law manifests in language, music and…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the…
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…
We show that statistical criticality, i.e. the occurrence of power law frequency distributions, arises in samples that are maximally informative about the underlying generating process. In order to reach this conclusion, we first identify…
A plethora of natural and socio-economic phenomena share a striking statistical regularity, that is the magnitude of elements decreases with a power law as a function of their position in a ranking of magnitude. Such regularity is known as…
In this article, I conduct a textual and contextual analysis of the empirical literature on Zipf's law for cities. Building on previous meta-analysis material openly available, I collect full texts and bibliographies of 66 scientific…
The study of complex systems is limited by the fact that only few variables are accessible for modeling and sampling, which are not necessarily the most relevant ones to explain the systems behavior. In addition, empirical data typically…
Zipf's power law is a general empirical regularity found in many natural and social systems. A recently developed theory predicts that Zipf's law corresponds to systems that are growing according to a maximally sustainable path in the…
The length of coding sequence series in microbial genomes were regarded as a fluctuating system and characterized by the methods of statistical physics. The distribution and the correlatin properties of 50 genomes including bacteria and…
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…
The Zipf's law establishes that if the words of a (large) text are ordered by decreasing frequency, the frequency versus the rank decreases as a power law with exponent close to $-1$. Previous work has stressed that this pattern arises from…