相关论文: Geography as a Science of the Earth's Surface Foun…

Scaling of geographic space refers to the fact that for a large geographic area its small constituents or units are much more common than the large ones. This paper develops a novel perspective to the scaling of geographic space using large…

The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…

Many models for spatial and spatio-temporal data assume that "near things are more related than distant things," which is known as the first law of geography. While geography may be important, it may not be all-important, for at least two…

According to Christopher Alexander's theory of centers, a whole comprises numerous, recursively defined centers for things or spaces surrounding us. Wholeness is a type of global structure or life-giving order emerging from the whole as a…

A city is not a tree but a semi-lattice. To use a perhaps more familiar term, a city is a complex network. The complex network constitutes a unique topological perspective on cities and enables us to better understand the kind of problem a…

This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension. 2. It defines…

A geometric conception is a method of a geometry construction. The Riemannian geometric conception and a new T-geometric one are considered. T-geometry is built only on the basis of information included in the metric (distance between two…

3D scene modeling techniques serve as the bedrocks in the geospatial engineering and computer science, which drives many applications ranging from automated driving, terrain mapping, navigation, virtual, augmented, mixed, and extended…

This paper explores the idea that information is an essential and distinctive feature of living systems. Unlike non-living systems, living systems actively acquire, process, and use information about their environments to respond to…

The space-like hypersurface of the Universe at the present cosmological time is a three-dimensional manifold. A non-trivial global topology of this space-like hypersurface would imply that the apparently observable universe (the sphere of…

Geometry is essentially a global language, which is fully understood in different times, countries and cultures. The proof of a geometric theorem (e.g. the Pythagorean Theorem) or a geometric construction (e.g. the construction of an…

Scale invariance property in the global geometry of Earth may lead to a coupled interactive behaviour between various components of the climate system. One of the most interesting correlations exists between spatial statistics of the global…

The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data…

Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual…

Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function $ d$, or by the world function $\sigma =d^{2}/2$. One suggests a new general method of the…

In this essay the ontological structure of reality is explored. The question of reducibility of biology to physics is considered in the context of their ultimate principles. It is shown that biology is an ontologically autonomous science…

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…

This letter establishes a procedure which can determine an algebra of exotic particles obeying fractional statistics and living in two-dimensional space using a non-commuting coordinates.

Historically, there have been many attempts to produce an appropriate mathematical formalism for modeling the nature of physical space, such as Euclid's geometry, Descartes' system of Cartesian coordinates, the Argand plane, Hamilton's…

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…