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We show that the laws of Zipf and Benford, obeyed by scores of numerical data generated by many and diverse kinds of natural phenomena and human activity are related to the focal expression of a generalized thermodynamic structure. This…
In the last years, researchers have realized the difficulties of fitting power-law distributions properly. These difficulties are higher in Zipf's systems, due to the discreteness of the variables and to the existence of two representations…
Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…
Many natural or human-made systems encompassing local reactions and diffusion processes exhibit spatially distributed patterns of some relevant dynamical variable. These interactions, through self-organization and critical phenomena, give…
Zipf's law, and power laws in general, have attracted and continue to attract considerable attention in a wide variety of disciplines - from astronomy to demographics to software structure to economics to linguistics to zoology, and even…
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 spatial distribution of people exhibits clustering across a wide range of scales, from household ($\sim 10^{-2}$ km) to continental ($\sim 10^4$ km) scales. Empirical data indicates simple power-law scalings for the size distribution of…
In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…
Statistical properties of the taxonomic classification of human languages are studied. It is shown that, at the highest levels of the taxonomic hierarchy, the frequency of taxon members as a function of the number of languages belonging to…
Recent studies have investigated siamese network architectures for learning invariant speech representations using same-different side information at the word level. Here we investigate systematically an often ignored component of siamese…
Many scientists are interested in but puzzled by the various inverse power laws with a negative exponent 1 such as the rank-size rule. The rank-size rule is a very simple scaling law followed by many observations of the ubiquitous empirical…
Evaluating whether large language models (LLMs) capture the structure of natural language beyond local fluency remains an open challenge. Existing evaluation methods, largely based on task performance or short-context behavior, provide…
Intermittent transitions, associated with critical dynamics and characterized by power-law distributions, are commonly observed during sleep. These critical behaviors are evident at the microscopic level through neuronal avalanches and at…
Power-law distributions are widely recognized in complex systems physics as indicative of underlying complexity in interaction networks and critical macroscopic behavior. Previous studies, notably those of Newman and others, have emphasized…
Zipf-like distributions characterize a wide set of phenomena in physics, biology, economics and social sciences. In human activities, Zipf-laws describe for example the frequency of words appearance in a text or the purchases types in…
We consider a version of D. Price's model for the growth of a bibliographic network, where in each iteration a constant number of citations is randomly allocated according to a weighted combination of accidental (uniformly distributed) and…
A mass of traces of human activities show rich dynamic patterns. In this article, we comprehensively investigate the dynamic patterns of 50 thousands of researchers' activities in Sciencenet, the largest multi-disciplinary academic…
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…
According to Zipf's meaning-frequency law, words that are more frequent tend to have more meanings. Here it is shown that a linear dependency between the frequency of a form and its number of meanings is found in a family of models of…
Zipf's law predicts a power-law relationship between word rank and frequency in language communication systems, and is widely reported in texts yet remains enigmatic as to its origins. Computer simulations have shown that language…