Related papers: Zipf's law, Hierarchical Structure, and Shuffling-…
Fundamental laws of human mobility have been extensively studied, yet we are still lacking a comprehensive understanding of the mobility patterns of sharing conveyances. Since travellers would highly probably no longer possess their own…
It has been shown recently that a specific class of path-dependent stochastic processes, which reduce their sample space as they unfold, lead to exact scaling laws in frequency and rank distributions. Such Sample Space Reducing processes…
Understanding cities is central to addressing major global challenges from climate and health to economic resilience. Although increasingly perceived as fundamental socio-economic units, the detailed fabric of urban economic activities is…
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…
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…
The things surrounding us vary dramatically, which implies that there are far more small things than large ones, e.g., far more small cities than large ones in the world. This dramatic variation is often referred to as fractal or scaling.…
Background: Zipf's discovery that word frequency distributions obey a power law established parallels between biological and physical processes, and language, laying the groundwork for a complex systems perspective on human communication.…
Zipf's law states that sequential frequencies of words in a text correspond to a power function. Its probabilistic model is an infinite urn scheme with asymptotically power distribution. The exponent of this distribution must be estimated.…
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…
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 propose a bare-bones stochastic model that takes into account both the geographical distribution of people within a country and their complex network of connections. The model, which is designed to give rise to a scale-free network of…
Urban morphology has presented significant intellectual challenges to mathematicians and physicists ever since the eighteenth century, when Euler first explored the famous Konigsberg bridges problem. Many important regularities and scaling…
Human language, the most powerful communication system in history, is closely associated with cognition. Written text is one of the fundamental manifestations of language, and the study of its universal regularities can give clues about how…
Formation of a layered structure is studied in a globally coupled map of chaotic units with a plastic coupling strength that changes depending on the states of units globally and an external input. In the parameter region characterized by…
Scaling properties of language are a useful tool for understanding generative processes in texts. We investigate the scaling relations in citywise Twitter corpora coming from the Metropolitan and Micropolitan Statistical Areas of the United…
The growth dynamics of complex systems often exhibit statistical regularities involving power-law relationships. For real finite complex systems formed by countable tokens (animals, words) as instances of distinct types (species, dictionary…
An important body of quantitative linguistics is constituted by a series of statistical laws about language usage. Despite the importance of these linguistic laws, some of them are poorly formulated, and, more importantly, there is no…
From genomes and ecosystems to bureaucracies and cities, the growth of complex systems occurs by adding new types of functions and expanding existing ones. We present a simple generative model that generalizes the Yule-Simon process by…
The spatial arrangement of urban hubs and centers and how individuals interact with these centers is a crucial problem with many applications ranging from urban planning to epidemiology. We utilize here in an unprecedented manner the large…
Economy is demanding new models, able to understand and predict the evolution of markets. To this respect, Econophysics offers models of markets as complex systems, that try to comprehend macro-, system-wide states of the economy from the…