Related papers: Geographical Analysis: from Distance-based Space t…
Understanding the complex nature of spatial information is crucial for problem solving in social and environmental sciences. This study investigates how the underlying patterns of spatial data can significantly influence the outcomes of…
The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. A textural fractal can be employed to explain the scale-free property of regional boundaries such as border lines,…
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…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…
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…
Irregular boundary lines can be characterized by fractal dimension, which provides important information for spatial analysis of complex geographical phenomena such as cities. However, it is difficult to calculate fractal dimension of…
The spatial distributions of cities fall into two groups: one is the simple distribution with characteristic scale (e.g. exponential distribution), and the other is the complex distribution without characteristic scale (e.g. power-law…
Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities…
The use of geospatially dependent information, which has been stipulated as a law in geography, to model geographic patterns forms the cornerstone of geostatistics, and has been inherited in many data science based techniques as well, such…
Geospatial semantics is a broad field that involves a variety of research areas. The term semantics refers to the meaning of things, and is in contrast with the term syntactics. Accordingly, studies on geospatial semantics usually focus on…
Deep generative models are universal tools for learning data distributions on high dimensional data spaces via a mapping to lower dimensional latent spaces. We provide a study of latent space geometries and extend and build upon previous…
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…
Traditional studies of chaos in conservative and driven dissipative systems have established a correspondence between sensitive dependence on initial conditions and fractal basin boundaries, but much less is known about the relation between…
Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the…
It is shown that fractal dimension can be estimated seeking a solution of functional equation defined for areas of coverages of different scales. The method proposed is compared with widely known way to estimate fractal dimension via linear…
We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several…
This study builds a bridge between two well-studied but distant topics: fractal dimension and Discrete Global Grid System (DGGS). DGGSs are used as covering sets for geospatial vector data to calculate the Minkowski-Bouligand dimension.…
We argue that dimensionality is not absolute, but that it depends on the scale of resolution, from the Planck to the macro scale.
There is a contradiction at the heart of our current understanding of individual and collective mobility patterns. On one hand, a highly influential stream of literature on human mobility driven by analyses of massive empirical datasets…