Related papers: Characteristic Scales, Scaling, and Geospatial Ana…
The traditional concept of space in geography is based on the notion of distance. Where there is a spatial analysis, there is a distance measurement. However, the precondition for effective distance-based space is that the geographical…
Geographical research was successfully quantified through the quantitative revolution of geography. However, the succeeding theorization of geography encountered insurmountable difficulties. The largest obstacle of geography's theorization…
Characteristic scale is a notion that pervades the geophysical sciences, but it has no widely accepted precise definition. The wavelet transform decomposes a time series into coefficients that are associated with different scales. The…
The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools…
Scale is a fundamental concept that has attracted persistent attention in geography literature over the past several decades. However, it creates enormous confusion and frustration, particularly in the context of geographic information…
Geospatial analysis is very much dominated by a Gaussian way of thinking, which assumes that things in the world can be characterized by a well-defined mean, i.e., things are more or less similar in size. However, this assumption is not…
A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…
Although the ``scale-free'' literature is large and growing, it gives neither a precise definition of scale-free graphs nor rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many…
Complex networks are characterized by several topological properties: degree distribution, clustering coefficient, average shortest path length, etc. Using a simple model to generate scale-free networks embedded on geographical space, we…
Hierarchical networks actually have many applications in the real world. Firstly, we propose a new class of hierarchical networks with scale-free and fractal structure, which are the networks with triangles compared to traditional…
The conventional concept of geographical space is mainly referred to actual space based on landscape, maps, and remote sensing images. However, this notion of space is not enough to interpret different types of fractal dimension of cities.…
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…
Analyses of urban scaling laws assume that observations in different cities are independent of the existence of nearby cities. Here we introduce generative models and data-analysis methods that overcome this limitation by modelling…
The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a measure of scale dependence, which indicates the scale-free distribution of urban…
Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information…
Human mobility is known to be distributed across several orders of magnitude of physical distances , which makes it generally difficult to endogenously find or define typical and meaningful scales. Relevant analyses, from movements to…
We study the statistical properties of the sampled scale-free networks, deeply related to the proper identification of various real-world networks. We exploit three methods of sampling and investigate the topological properties such as…
Ecology studies biodiversity in its variety and complexity. It describes how species distribute and perform in response to environmental changes. Ecological processes and structures are highly complex and adaptive. In order to quantify…
Although geographic features, such as mountains and coastlines, are fractal, some studies have claimed that the fractal property is not universal. This claim, which is false, is mainly attributed to the strict definition of fractal…
To remove the confusion of concepts about different sorts of geographical space and dimension, a new framework of space theory is proposed in this paper. Based on three sets of fractal dimensions, the geographical space is divided into…