Related papers: Web Maps and Their Algebra
Knowledge graphs represent concepts (e.g., people, places, events) and their semantic relationships. As a data structure, they underpin a digital information system, support users in resource discovery and retrieval, and are useful for…
For a representation of a Lie algebra, one can construct a diagram of the representation, i. e. a directed graph with edges labeled by matrix elements of the representation. This article explains how to use these diagrams to describe normal…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
The multi-layered nature of societal developments poses a challenge in the teaching and learning of history of mathematics. As an attempt to tackle this challenge we experimented with the use of Knowledge-Maps. The focus of our interest…
The problem of mathematical modeling in geography is one of the most important strategies in order to establish the evolution and the prevision of geographical phenomena. Models must have a simplified structure, to reflect essential…
Google's PageRank method was developed to evaluate the importance of web-pages via their link structure. The mathematics of PageRank, however, are entirely general and apply to any graph or network in any domain. Thus, PageRank is now…
Mapping is an important part of many robotic applications. In order to measure the performance of the mapping process we have to measure the quality of its result: the map. The map is essential for robotic algorithms like localization and…
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
This is a survey article on real algebra and geometry, and in particular on its recent applications in optimization and convexity. We first introduce basic notions and results from the classical theory. We then explain how these relate to…
On a geometrical view, the conception of map geometries are introduced, which is a nice model of the Smarandache geometries, also new kind of and more general intrinsic geometry of surface. Results convinced one that map geometries are…
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…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
Aiming at a generalization of a classical theorem of Moebius, we study maps that take line intervals to plane curves, and also maps that take line intervals to conics from certain linear systems.
Human knowledge provides a formal understanding of the world. Knowledge graphs that represent structural relations between entities have become an increasingly popular research direction towards cognition and human-level intelligence. In…
A regular map is a surface together with an embedded graph, having properties similar to those of the surface and graph of a platonic solid. We analyze regular maps with reflection symmetry and a graph of density strictly exceeding 1/2, and…
Geographic data plays an essential role in various Web, Semantic Web and machine learning applications. OpenStreetMap and knowledge graphs are critical complementary sources of geographic data on the Web. However, data veracity, the lack of…
The notion of quadratic maps between arbitrary groups appeared at several places in the literature on quadratic algebra. Here a unified extensive treatment of their properties is given; the relation with a relative version of Passi's…
Computational topology is an area that revisits topological problems from an algorithmic point of view, and develops topological tools for improved algorithms. We survey results in computational topology that are concerned with graphs drawn…
Projective geometry provides the preferred framework for most implementations of Euclidean space in graphics applications. Translations and rotations are both linear transformations in projective geometry, which helps when it comes to…
This text is a survey of derived algebraic geometry. It covers a variety of general notions and results from the subject with a view on the recent developments at the interface with deformation quantization.