How complexity emerges in urban systems: Theory of urban morphology

Detecting the interaction between urban elements evolution with population dynamics model

Exploring the evolution of urban elements can improve understanding of the developmental process of city and drive such development into a better direction. However, the non-linearity and complexity of changes in urban elements have brought great challenges to understanding this process. In this paper, we propose a cross-diffusion partial differential equation based on ecological dynamics to simulate the evolutionary process of urban elements from the microscopic viewpoint. The interaction between urban elements is simulated by constructing a non-linear and spatiotemporal change equation, and the main influence between elements is evaluated by the key parameters in the discussed equation. Our model is first experimented to time-series data on population density and housing prices to analyzes the interaction of these two elements in the evolution process. We then extend the model to label data, land cover data, to obtain a quantitative expression of the interaction between different land types in the process of urban land cover change.

From cognitive maps to spatial schemas

A schema refers to a structured body of prior knowledge that captures common patterns across related experiences. Schemas have been studied separately in the realms of episodic memory and spatial navigation across different species and have been grounded in theories of memory consolidation, but there has been little attempt to integrate our understanding across domains, particularly in humans. We propose that experiences during navigation with many similarly structured environments give rise to the formation of spatial schemas (for example, the expected layout of modern cities) that share properties with but are distinct from cognitive maps (for example, the memory of a modern city) and event schemas (such as expected events in a modern city) at both cognitive and neural levels. We describe earlier theoretical frameworks and empirical findings relevant to spatial schemas, along with more targeted investigations of spatial schemas in human and non-human animals. Consideration of architecture and urban analytics, including the influence of scale and regionalization, on different properties of spatial schemas may provide a powerful approach to advance our understanding of spatial schemas.

Identification of robust retailing location patterns with complex network approaches

The problem of location is the cornerstone of strategic decisions in retail management. This decision is usually complex and multidimensional. One of the most relevant success factors is an adequate balanced tenancy, i.e., a complementary ecosystem of retail stores in the surroundings, both in planned and unplanned areas. In this paper, we use network theory to analyze the commercial spatial interactions in all the cities of Castile and Leon (an autonomous community in north-western Spain), Madrid, and Barcelona. Our approach encompasses different proposals both for the definition of the interaction networks and for their subsequent analyses. These methodologies can be used as pre-processing tools to capture features that formalize the relational dimension for location recommendation systems. Our results unveil the retail structure of different urban areas and enable a meaningful comparison between cities and methodologies. In addition, by means of consensus techniques, we identify a robust core of commercial relationships, independent of the particularities of each city, and thus help to distinguish transferable knowledge between cities. The results also suggest greater specialization of commercial space with city size.

Spatiotemporal behaviors of the ridership of a public transportation system during an epidemic outbreak: case of MERS in Seoul

During May and June 2015, an outbreak of the Middle East respiratory syndrome (MERS) occurred in Korea, which raised the fear of contagion throughout society and suppressed the use of public transportation systems. Exploring daily ridership data of the Seoul bus transportation system, along with the number of infected patients and search volume in web portals, we observe that ridership decreased abruptly while attention was heavily focused online. Then this temporal reduction recovered exponentially with a characteristic time of 3 weeks when newly confirmed cases began to decrease. We also find with the data of ranked keywords of web portals that areas with severely reduced ridership tended to cluster and spatiotemporal variations of such clusters were highly associated with general hospitals where MERS patients were treated. On the other hand, the spatial reduction in ridership relaxed algebraically with the distance from a general hospital while the outbreak was severe. We further probe the influence of the epidemic outbreak in the framework of linear response theory, which relates the responses to the epidemic outbreak ("perturbation") with correlations in the absence of the perturbation. Indeed, the spatial correlation function of the ridership changes is observed to follow a power law, sharing the same exponent as the spatial relaxation of the response function. This new theoretical approach offers a useful tool for understanding responses of public transportation system to epidemic or accidental disasters.

Characterizing the sectoral development of cities

Previous research has identified a predictive model of how a nation's distribution of gross domestic product (GDP) among agriculture (a), industry (i), and services (s) changes as a country develops. Here we use this national model to analyze the composition of GDP for US Metropolitan Statistical Areas (MSA) over time. To characterize the transfer of GDP shares between the sectors in the course of economic development we explore a simple system of differential equations proposed in the country-level model. Fitting the model to more than 120 MSAs we find that according to the obtained parameters MSAs can be classified into 6 groups (consecutive, high industry, re-industrializing; each of them also with reversed development direction). The consecutive transfer (a → i → s) is common but does not represent all MSAs examined. At the 95% confidence level, 40% of MSAs belong to types exhibiting an increasing share of GDP from agriculture. In California, such MSAs, which we classify as part of an agriculture renaissance, are found in the Central Valley.

Rethinking vulnerability in city-systems: A methodological proposal to assess "urban entropy"

This paper aims at proposing a possible alternative point of view to investigate the vulnerability of urban systems. The basic ideal refers to the possibility of thinking about vulnerability as deriving by the interactions of several risks that can affect the urban system and by the interactions among them. In this sense, it is possible to refer to an "integrated territorial risk". Considering the city as a complex and dynamic system that while evolving produce entropy is the main theoretical reference supporting this study. The loss of energy during the evolution of the system corresponds to some conditions of inefficiency that involve the whole system and, as such, this lost energy can be assumed as a "systemic entropy". Is it possible to measure the levels of this vulnerability of the urban system when it stays in ordinary conditions, namely not during stress states that modify the state of equilibrium of the system itself? It is possible to assess the production of this "internal entropy"? In order to answer to these questions in mind, this study aims at analyzing dyscrasias that can occur within the main components of the urban system in order to individuate possible strategies able both to mitigate the fragility of the urban system and to improve its resilience.

Spatial point pattern and urban morphology: Perspectives from entropy, complexity, and networks

Spatial organization of physical form of an urban system, or city, both manifests and influences the way its social form functions. Mathematical quantification of the spatial pattern of a city is, therefore, important for understanding various aspects of the system. In this work, a framework to characterize the spatial pattern of urban locations based on the idea of entropy maximization is proposed. Three spatial length scales in the system with discerning interpretations in terms of the spatial arrangement of the locations are calculated. Using these length scales, two quantities are introduced to quantify the system's spatial pattern, namely, mass decoherence and space decoherence, whose combination enables the comparison of different cities in the world. The comparison reveals different types of urban morphology that could be attributed to the cities' geographical background and development status.

From the betweenness centrality in street networks to structural invariants in random planar graphs

The betweenness centrality, a path-based global measure of flow, is a static predictor of congestion and load on networks. Here we demonstrate that its statistical distribution is invariant for planar networks, that are used to model many infrastructural and biological systems. Empirical analysis of street networks from 97 cities worldwide, along with simulations of random planar graph models, indicates the observed invariance to be a consequence of a bimodal regime consisting of an underlying tree structure for high betweenness nodes, and a low betweenness regime corresponding to loops providing local path alternatives. Furthermore, the high betweenness nodes display a non-trivial spatial clustering with increasing spatial correlation as a function of the edge-density. Our results suggest that the spatial distribution of betweenness is a more accurate discriminator than its statistics for comparing  static congestion patterns and  its evolution across cities as demonstrated by analyzing 200 years of street data for Paris.

The betweenness centrality is a metric commonly used in network analysis. Here the authors show that the distribution of this metric in urban street networks is invariant in the case of 97 cities. This invariance could affect network flows, dynamics and congestion management in cities.

Universal scaling of the distribution of land in urban areas

In this work, we explore the spatial structure of built zones and green areas in diverse western cities by analyzing the probability distribution of areas and a coefficient that characterize their respective shapes. From the analysis of diverse datasets describing land lots in urban areas, we found that the distribution of built-up areas and natural zones in cities obey inverse power laws with a similar scaling for the cities explored. On the other hand, by studying the distribution of shapes of lots in urban regions, we are able to detect global differences in the spatial structure of the distribution of land. Our findings introduce information about spatial patterns that emerge in the structure of urban settlements; this knowledge is useful for the understanding of urban growth, to improve existing models of cities, in the context of sustainability, in studies about human mobility in urban areas, among other applications.

Morphology of travel routes and the organization of cities

The city is a complex system that evolves through its inherent social and economic interactions. Mediating the movements of people and resources, urban street networks offer a spatial footprint of these activities. Of particular interest is the interplay between street structure and its functional usage. Here, we study the shape of 472,040 spatiotemporally optimized travel routes in the 92 most populated cities in the world, finding that their collective morphology exhibits a directional bias influenced by the attractive (or repulsive) forces resulting from congestion, accessibility, and travel demand. To capture this, we develop a simple geometric measure, inness, that maps this force field. In particular, cities with common inness patterns cluster together in groups that are correlated with their putative stage of urban development as measured by a series of socio-economic and infrastructural indicators, suggesting a strong connection between urban development, increasing physical connectivity, and diversity of road hierarchies.

Complex networks are a useful tool to investigate the structure of cities and their street networks. Here the authors investigate the shape of travel routes in 92 cities and define a metric called inness which reveals connections between common urban features in cities with similar inness profiles.