Related papers: Scaling and Universality in City Space Syntax: bet…
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…
In a language corpus, the probability that a word occurs $n$ times is often proportional to $1/n^2$. Assigning rank, $s$, to words according to their abundance, $\log s$ vs $\log n$ typically has a slope of minus one. That simple Zipf's law…
We study centrality in urban street patterns of different world cities represented as networks in geographical space. The results indicate that a spatial analysis based on a set of four centrality indices allows an extended visualization…
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…
Zipf's law, which states that the probability of an observation is inversely proportional to its rank, has been observed in many domains. While there are models that explain Zipf's law in each of them, those explanations are typically…
In the setting of minimal local grammar-based coding, the input string is represented as a grammar with the minimal output length defined via simple symbol-by-symbol encoding. This paper discusses four contributions to this field. First, we…
In this article, the relationship between two well-accepted empirical propositions regarding the distribution of population in cities, namely, Gibrat's law and Zipf's law, are rigorously examined using the Chinese census data. Our findings…
The time evolution of Earth with her cities, languages and countries is considered in terms of the multiplicative noise and the fragmentation- processes, where the related families, size distributions, lifetimes, bilinguals, etc. are…
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…
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…
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,…
We study a resource utilization scenario characterized by intrinsic fitness. To describe the growth and organization of different cities, we consider a model for resource utilization where many restaurants compete, as in a game, to attract…
We inspect the deductive connection between the neural scaling law and Zipf's law -- two statements discussed in machine learning and quantitative linguistics. The neural scaling law describes how the cross entropy rate of a foundation…
Map generalization is a process of producing maps at different levels of detail by retaining essential properties of the underlying geographic space. In this paper, we explore how the map generalization process can be guided by the…
Cities are typical dynamic complex systems that connect people and facilitate interactions. Revealing universal collective patterns behind spatio-temporal interactions between residents is crucial for various urban studies, of which we are…
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…
Spatial organisation of physical form of an urban system, or city, both manifests and influences the way its social form functions. Mathematical quantification of the spatial pattern of a city is, therefore, important for understanding…
Although power laws of the Zipf type have been used by many workers to fit rank distributions in different fields like in economy, geophysics, genetics, soft-matter, networks etc., these fits usually fail at the tails. Some distributions…
The frequencies at which individual words occur across languages follow power law distributions, a pattern of findings known as Zipf's law. A vast literature argues over whether this serves to optimize the efficiency of human communication,…
Inverse power-law interaction forms, such as the inverse-square law, recur across a wide range of physical, social, and spatial systems. While traditionally derived from specific microscopic mechanisms, the ubiquity of these laws suggests a…