Related papers: Derivation of Relations between Scaling Exponents …
Highly accurate estimates of the urban fractal dimension $D_f$ are obtained by implementing the Detrended Moving Average algorithm (DMA) on WorldView2 satellite high-resolution multi-spectral images covering the largest European cities.…
We report on a quantitative analysis of relationships between the number of homicides, population size and other ten urban metrics. By using data from Brazilian cities, we show that well defined average scaling laws with the population size…
More than a half of world population is now living in cities and this number is expected to be two-thirds by 2050. Fostered by the relevancy of a scientific characterization of cities and for the availability of an unprecedented amount of…
The rank-size regularity known as Zipf's law is one of scaling laws and frequently observed within the natural living world and in social institutions. Many scientists tried to derive the rank-size scaling relation by entropy-maximizing…
The scaling exponent of a hierarchy of cities used to be regarded as a fractal parameter. The Pareto exponent was treated as the fractal dimension of size distribution of cities, while the Zipf exponent was treated as the reciprocal of the…
The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…
Many stochastic complex systems are characterized by the fact that their configuration space doesn't grow exponentially as a function of the degrees of freedom. The use of scaling expansions is a natural way to measure the asymptotic growth…
We discuss the problem of observation of natural similarity in skeletal evolution of terrestrial mammals. Analysis is given by means of testing of the power scaling laws established in long bone allometry, which describe development of…
In machine learning, the scaling law describes how the model performance improves with the model and data size scaling up. From a learning theory perspective, this class of results establishes upper and lower generalization bounds for a…
Cities can be characterised and modelled through different urban measures. Consistency within these observables is crucial in order to advance towards a science of cities. Bettencourt et al have proposed that many of these urban measures…
Scaling laws are powerful summaries of the variations of urban attributes with city size. However, the validity of their universal meaning for cities is hampered by the observation that different scaling regimes can be encountered for the…
One of the most fundamental rules in metabolic ecology is the allometric equation, which is a power-law scaling that describes the connection between body measurements and body size. The biological dynamics of this essentially empirical…
The origin of allometric scaling patterns that are multiples of 1/4 has long fascinated biologists. While not universal, scaling relationships with exponents that are close to multiples of 1/4 are common and have been described in all major…
Previous works have shown the universality of allometric scalings under density and total value at city level, but our understanding about the size effects of regions on them is still poor. Here, we revisit the scaling relations between…
The area-perimeter allometric scaling is a basic and important approach for researching fractal cities and has been studied for a long time. However, the boundary dimension of a city is always numerically overestimated by the traditional…
The emerging field of the Science of Cities has unveiled previously undiscovered facets of urban life. Contrary to the expectation of chaotic behaviour influenced solely by cultural and geographic factors, cities globally exhibit universal…
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…
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…
An ecological flow network is a weighted directed graph in which nodes are species, edges are "who eats whom" relationships and weights are rates of energy or nutrients transfer between species. Allometric scaling is a ubiquitous feature…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…