Related papers: Exploring the Level of Urbanization Based on Zipf'…
Ecosystems and other naturally resilient systems exhibit allometric scaling in the distribution of sizes of their elements. In this paper we define an allometry inspired scaling indicator for cities that is a first step towards quantifying…
There is strong expectation that cities, across time, culture and level of development, share much in common in terms of their form and function. Recently, attempts to formalize mathematically these expectations have led to the hypothesis…
This work studies the Zipf Law for cities in Brazil. Data from censuses of 1970, 1980, 1991 and 2000 were used to select a sample containing only cities with 30,000 inhabitants or more. The results show that the population distribution in…
A good understanding of cities is crucial to implement urban planning policies leading to social and economic sustainability and an efficient use of resources. While urban concentration has been associated with both positive and negative…
For the first time the systems of cities in seven countries or regions among the largest in the world (China, India, Brazil, Europe, the Former Soviet Union (FSU), the United States and South Africa) are made comparable through the building…
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…
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…
The dependence with text length of the statistical properties of word occurrences has long been considered a severe limitation quantitative linguistics. We propose a simple scaling form for the distribution of absolute word frequencies…
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…
In this paper we analyse the profile of land use and population density with respect to the distance to the city centre for the European city. In addition to providing the radial population density and soil-sealing profiles for a large set…
We investigated the socioeconomic scaling behavior of all cities with more than 50,000 inhabitants in the Netherlands and found significant superlinear scaling of gross urban product with population size. Of these cities, 22 major cities…
Zipf's law on word frequency is observed in English, French, Spanish, Italian, and so on, yet it does not hold for Chinese, Japanese or Korean characters. A model for writing process is proposed to explain the above difference, which takes…
We present a general approach to explain the Zipf's law of city distribution. If the simplest interaction (pairwise) is assumed, individuals tend to form cities in agreement with the well-known statistics
Cities are some of the most intricate and advanced creations of humanity. Most objects in cities are perfectly synchronised to coordinate activities such as jobs, education, transportation, entertainment, and waste management. Although each…
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…
Zipf's law states that the frequency of an observation with a given value is inversely proportional to the square of that value; Taylor's law, instead, describes the scaling between fluctuations in the size of a population and its mean.…
Understanding quantitative relationships between urban elements is crucial for a wide range of applications. The observation at the macroscopic level demonstrates that the aggregated urban quantities (e.g., gross domestic product) scale…
We study a few dynamical systems composed of many components whose sizes evolve according to multiplicative stochastic rules. We compare them with respect to the emergence of power laws in the size distribution of their components. We show…
A longstanding puzzle in urban science is whether there's an intrinsic match between human populations and the mass of their built environments. Previous findings have revealed various urban properties scaling nonlinearly with population,…
Two classical hypotheses are examined about the population growth in a system of cities: Hypothesis 1 pertains to Gibrat's and Zipf's theory which states that the city growth-decay process is size independent; Hypothesis 2 pertains to the…