Related papers: A Topological Representation for Taking Cities as …
Network topology is a fundamental aspect of network science that allows us to gather insights into the complicated relational architectures of the world we inhabit. We provide a first specific study of neighbourhood degree sequences in…
Various topological concepts are often involved in the research of mathematical logic, and almost all of these concepts can be regarded as developing from the Stone representation theorem. In the Stone representation theorem, a Boolean…
This paper presents a model architecture for encoding the representations of part-whole hierarchies in images in form of a graph. The idea is to divide the image into patches of different levels and then treat all of these patches as nodes…
Topological data analysis is an approach to study shape of a data set by means of topology. Its main object of study is the persistence diagram, which represents the topological features of the data set at different spatial resolutions.…
Since the industrial revolution, accelerated urban growth has overflown administrative divisions, merged cities into large built extensions, and blurred the boundaries between urban and rural land-uses. These traits, present in most of…
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…
Cities are complex products of human culture, characterised by a startling diversity of visible traits. Their form is constantly evolving, reflecting changing human needs and local contingencies, manifested in space by many urban patterns.…
Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…
We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…
Transport in crowded, complex environments occurs across many spatial scales. Geometric restrictions can hinder the motion of individuals and, combined with crowding between individuals, can have drastic effects on global transport…
In this short review, we pay attention to some subtleties in the study of projective representations, contrasting local to global properties and their interplay. The analysis is exposed rigorously, showing and demonstrating the main…
This article analyzes the complex geometry of urban transportation networks as a gateway to understanding their encompassing urban systems. Using a proposed ring-buffer approach and applying it to 50 urban areas in the United States, we…
Almost all representations considered in computable analysis are partial. We provide arguments in favor of total representations (by elements of the Baire space). Total representations make the well known analogy between numberings and…
Hierarchies permeate the structure of real networks, whose nodes can be ranked according to different features. However, networks are far from tree-like structures and the detection of hierarchical ordering remains a challenge, hindered by…
While representation learning has yielded a great success on many graph learning tasks, there is little understanding behind the structures that are being captured by these embeddings. For example, we wonder if the topological features,…
In this paper, we propose a topology optimization (TO) framework where the design is parameterized by a set of convex polygons. Extending feature mapping methods in TO, the representation allows for direct extraction of the geometry. In…
In this paper we analyse the profile of land use and population density with respect to the distance to the city centre for the European city. In addition to providing the radial population density and soil-sealing profiles for a large set…
This paper examines the former location-based social medium Brightkite, over its three-year life span, based on the concept of natural cities. The term 'natural cities' refers to spatially clustered geographic events, such as the…
We describe those complete linearly ordered topological spaces $X$ which are homogeneous (=CHLOTS). That is, $X$ is order isomorphic with any nonempty open interval in $X$. Using countable tail-like ordinals as indices, we build towers of…
Locales have been studied as "topologies without points", mainly by tools of category theory. While traditional topology presents a space as a set of points with specified neighborhoods, localic topology presents a space as a lattice of…