Related papers: Zipf's Law for All the Natural Cities around the W…
Textual geographic information is indispensable and heavily relied upon in practical applications. The absence of clear distribution poses challenges in effectively harnessing geographic information, thereby driving our quest for…
Disparity in spatial accessibility is strongly associated with growing inequalities among urban communities. Since improving levels of accessibility for certain communities can provide them with upward social mobility and address social…
We consider a simple model of firm/city/etc. growth based on a multi-item criterion: whenever entity B fares better that entity A on a subset of $M$ items out of $K$, the agent originally in A moves to B. We solve the model analytically in…
Zipf's law is shown to arise as the variational solution of a problem formulated in Fisher's terms. An appropriate minimization process involving Fisher information and scale-invariance yields this universal rank distribution. As an example…
We suggest an analytical approach for Pareto-Zipf law, where we assume random multiplicative noise and fragmentation processes for the growth of the number of citizens of each city and the number of the cities, respectively.
The Zipf's law is the major regularity of statistical linguistics that served as a prototype for rank-frequency relations and scaling laws in natural sciences. Here we show that the Zipf's law -- together with its applicability for a single…
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.…
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…
Understanding scaling relations of social and environmental attributes of urban systems is necessary for effectively managing cities. Urban scaling theory (UST) has assumed that population density scales positively with city size. We…
Two fundamental issues surrounding research on the image of the city respectively focus on the city's external and internal representations. The external representation in the context of this paper refers to the city itself, external to…
City-size distributions follow an approximate power law in various countries despite high volatility in relative city sizes over time. Our empirical evidence for the United States and Japan indicates that the scaling law stems from a…
Quantitative linguistics has provided us with a number of empirical laws that characterise the evolution of languages and competition amongst them. In terms of language usage, one of the most influential results is Zipf's law of word…
The law of allometric scaling based on Zipf distributions can be employed to research hierarchies of cities in a geographical region. However, the allometric patterns are easily influenced by random disturbance from the noises in…
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…
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…
Here we present a new class of optimality for coding systems. Members of that class are displaced linearly from optimal coding and thus exhibit Zipf's law, namely a power-law distribution of frequency ranks. Within that class, Zipf's law,…
This paper examines the former location-based social medium Brightkite, over its three-year life span, based on the concept of natural cities. The term 'natural cities' refers to spatially clustered geographic events, such as the…
We perform a quantitative analysis of extensive chess databases and show that the frequencies of opening moves are distributed according to a power-law with an exponent that increases linearly with the game depth, whereas the pooled…
Zipf's law is a paradigm describing the importance of different elements in communication systems, especially in linguistics. Despite the complexity of the hierarchical structure of language, music has in some sense an even more complex…
Zipf's law of abbreviation, the tendency of more frequent words to be shorter, is one of the most solid candidates for a linguistic universal, in the sense that it has the potential for being exceptionless or with a number of exceptions…