Related papers: Schelling's Segregation Model: Parameters, Scaling…

Racial segregation is a widespread social and physical phenomenon present in every city across the United States. Although prevalent nationwide, each city has a unique history of racial segregation, resulting in distinct "shapes" of…

Cities are often compared through scaling laws, usually expressed as power-law relations between population size and aggregate urban quantities related to infrastructure, socioeconomic activity, or environmental impacts. These laws are…

Residential segregation in metropolitan areas is a phenomenon that can be observed all over the world. Recently, this was investigated via game-theoretic models. There, selfish agents of two types are equipped with a monotone utility…

We investigate the dependence of steady-state properties of Schelling's segregation model on the agents' activation order. Our basic formalism is the Pollicott-Weiss version of Schelling's segregation model. Our main result modifies this…

Degree distributions of graph representations for compact urban patterns are scale-dependent. Therefore, the degree statistics alone does not give us the enough information to reach a qualified conclusion on the structure of urban spatial…

Challenges due to the rapid urbanization of the world -- especially in emerging countries -- range from an increasing dependence on energy, to air pollution, socio-spatial inequalities, environmental and sustainability issues. Modelling the…

Clustering is the problem of separating a set of objects into groups (called clusters) so that objects within the same cluster are more similar to each other than to those in different clusters. Spectral clustering is a now well-known…

Urban morphology has presented significant intellectual challenges to mathematicians and physicists ever since the eighteenth century, when Euler first explored the famous Konigsberg bridges problem. Many important regularities and scaling…

A long-standing expectation is that large, dense, and cosmopolitan areas support socioeconomic mixing and exposure between diverse individuals. It has been difficult to assess this hypothesis because past approaches to measuring…

We study a random aggregation process involving rectangular clusters. In each aggregation event, two rectangles are chosen at random and if they have a compatible side, either vertical or horizontal, they merge along that side to form a…

Human development has far-reaching impacts on the surface of the globe. The transformation of natural land cover occurs in different forms and urban growth is one of the most eminent transformative processes. We analyze global land cover…

The idealized general model of aggregate growth is considered on the basis of the simple additive rules that correspond to one-step aggregation process. The two idealized cases were analytically investigated and simulated by Monte Carlo…

We explore analytically and numerically agglomeration driven by advection and localized source. The system is inhomogeneous in one dimension, viz. along the direction of advection. We analyze a simplified model with mass-independent…

Segregation is widespread in all realms of human society. Several influential studies have argued that intolerance is not a prerequisite for a segregated society, and that segregation can arise even when people generally prefer diversity.…

In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…

An unsupervised classification method for point events occurring on a network of lines is proposed. The idea relies on the distributional flexibility and practicality of random partition models to discover the clustering structure featuring…

We propose a social network-aware approach to studying socio-economic segregation. The key question that we address is whether patterns of segregation are more pronounced in social networks than the common spatial neighborhood-focused…

Sharing rides could drastically improve the efficiency of car and taxi transportation. Unleashing such potential, however, requires understanding how urban parameters affect the fraction of individual trips that can be shared, a quantity…

Homophily and heterophobia, the tendency for people with similar characteristics to preferentially interact with (or avoid) each other are pervasive in human social networks. Here, we develop an extension of the mathematical theory of urban…

Segregation, defined as the degree of separation between two or more population groups, helps to understand a complex social environment and subsequently provides a basis for public policy intervention. To measure segregation, past works…