Related papers: A Topological Representation for Taking Cities as …
We described the average traffic congestion in several populous cities around the world from a new concept, namely landscape percolation. The ratio of the residential area size to road width is a fundamental parameter that controls the…
Complex systems are difficult to study not only because they are nonlinear, multiscale, and often nonstationary, but because their scientifically relevant organization is often invisible at the level of individual components, pairwise…
Understanding the morphology of an urban system is an important step toward unveiling the dynamical processes of its growth and development. At the foundation of every urban system, transportation system is undeniably a crucial component in…
Hierarchies can be modeled by a set of exponential functions, from which we can derive a set of power laws indicative of scaling. The solution to a scaling relation equation is always a power law. The scaling laws are followed by many…
Dimensionality is one of the most important properties of complex physical systems. However, only recently this concept has been considered in the context of complex networks. In this paper we further develop the previously introduced…
According to Aristotle, a philosopher in Ancient Greece, "the whole is greater than the sum of its parts". This observation was adopted to explain human perception by the Gestalt psychology school of thought in the twentieth century. Here,…
Cities are some of the most intricate and advanced creations of humanity. Most objects in cities are perfectly synchronised to coordinate activities such as jobs, education, transportation, entertainment, and waste management. Although each…
We study the influence that population density and the road network have on each others' growth and evolution. We use a simple model of formation and evolution of city roads which reproduces the most important empirical features of street…
We study centrality in urban street patterns of different world cities represented as networks in geographical space. The results indicate that a spatial analysis based on a set of four centrality indices allows an extended visualization…
Urban scaling laws relate socio-economic, behavioral, and physical variables to the population size of cities and allow for a new paradigm of city planning, and an understanding of urban resilience and economies. Independently of culture…
At large scales, typologies of urban form and corresponding generating processes remain an open question with important implications regarding urban planning policies and sustainability. We propose in this paper to generate urban…
We attempt to take a comprehensive look at the challenges of representing the spatio-temporal structures and dynamic processes defining a city's overall characteristics. For the task of urban planning and urban operation, we take the stance…
Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we…
The topological information of a network can be retrieved equivalently from its complement consisting of the same nodes but complementary edges. Hence the partition of a network into certain substructures based on given criteria should be…
Localization is a topological technique that allows us to make global equivariant computations in terms of local data at the fixed points. For example, we may compute a global integral by summing integrals at each of the fixed points. Or,…
The value of graph-based big data can be unlocked by exploring the topology and metrics of the networks they represent, and the computational approaches to this exploration take on many forms. The use-case of performing global computations…
The understanding of the immense and intricate topological structure of the World Wide Web (WWW) is a major scientific and technological challenge. This has been tackled recently by characterizing the properties of its representative graphs…
Graph vertex ordering is widely employed in spatial data analysis, especially in urban analytics, where street graphs serve as spatial discretization for modeling and simulation. It is also crucial for visualization, as many methods require…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…
With a model of a geometric theory in an arbitrary topos, we associate a site obtained by endowing a category of generalized elements of the model with a Grothendieck topology, which we call the antecedent topology. Then we show that the…