Urban segregation on multilayered transport networks: a random walk approach.

We present a novel method for analysing socio-spatial segregation in cities by considering constraints imposed by transportation networks. Using a multilayered network approach, we model the interaction probabilities of socio-economic groups with random walks and Lévy flights. This method allows for evaluation of new transport infrastructure's impact on segregation while quantifying each network's contribution to interaction opportunities. The proposed random walk segregation index measures the probability of individuals encountering diverse social groups based on their available means of transit via random walks. The index incorporates temporal constraints in urban mobility with a parameter, α ∈ [ 0 , 1 ) , of the probability of the random walk continuing at each time step. By applying this to a toy model and conducting a sensitivity analysis, we explore how the index changes dependent on this temporal constraint. When the parameter equals zero, the measure simplifies to an isolation index. When the parameter approaches one it represents the city's overall socio-economic distribution by mirroring the steady-state of the random walk process. Using Cuenca, Ecuador as a case study, we illustrate the method's applicability in transportation planning as a valuable tool for policymakers, addressing spatial distribution of socio-economic groups and the connectivity of existing transport networks, thus promoting equitable interactions throughout the city.

The wild cost of invasive feral animals worldwide.

Invasive non-native species are a growing burden to economies worldwide. While domesticated animals (i.e. livestock, beasts of burden or pets) have enabled our ways of life and provide sustenance for countless individuals, they may cause substantial impacts when they escape or are released (i.e. become feral) and then become invasive with impacts. We used the InvaCost database to evaluate monetary impacts from species in the Domestic Animal Diversity Information System database. We found a total cost of $141.95 billion from only 18 invasive feral species. Invasive feral livestock incurred the highest costs at $90.03 billion, with pets contributing $50.93 billion and beasts of burden having much lower costs at $0.98 billion. Agriculture was the most affected sector at $80.79 billion, followed by the Environment ($43.44 billion), and Authorities-Stakeholders sectors ($5.52 billion). Damage costs comprised the majority ($124.94 billion), with management and mixed damage-management costs making up the rest ($9.62 and $7.38 billion, respectively). These economic impacts were observed globally, where Oceania, North America and Europe were the most impacted regions. Islands recorded a higher economic burden than continental areas, with livestock species dominating costs more on islands than mainlands compared to other feral species. The costs of invasive feral animals were on average twice higher than those of wild species. The management of invasive feral populations requires higher investment, updated regulations, and comprehensive risk assessments. These are especially complex when considering the potential conflicts arising from interventions with species that have close ties to humans. Effective communication to raise public awareness of the impacts of feral populations and appropriate legislation to prevent or control such invasive feral populations will substantially contribute to minimizing their socioeconomic and environmental impacts.

Uncovering structural diversity in commuting networks: global and local entropy.

In this paper we revisit the concept of mobility entropy. Over time, the structure of spatial interactions among urban centres tends to become more complex and evolves from centralised models to more scattered origin and destination patterns. Entropy measures can be used to explore this complexity, and to quantify the degree of structural diversity of in- and out-flows at different scales and across the system. We use toy models of commuting networks to examine global and local measures, allowing the comparison to occur between different parts of the system. We show that entropy at the link and node level give different insights on the characteristics of the systems, enabling us to identify employment hubs and interdependencies between and within different parts of the system. We compute the measures in the commuting networks of the Northern Powerhouse and Greater South East regions in the UK to examine their relevance when studying real systems of cities. Finally we discuss how these can be used to inform planning and policy decisions oriented towards decentralisation and resilience.

How the geometry of cities determines urban scaling laws.

Urban scaling laws relate socio-economic, behavioural and physical variables to the population size of cities. They allow for a new paradigm of city planning and for an understanding of urban resilience and economics. The emergence of these power-law relations is still unclear. Improving our understanding of their origin will help us to better apply them in practical applications and further research their properties. In this work, we derive the basic exponents for spatially distributed variables from fundamental fractal geometric relations in cities. Sub-linear scaling arises as the ratio of the fractal dimension of the road network and of the distribution of the population embedded in three dimensions. Super-linear scaling emerges from human interactions that are constrained by the geometry of a city. We demonstrate the validity of the framework with data from 4750 European cities. We make several testable predictions, including the relation of average height of cities and population size, and the existence of a critical density above which growth changes from horizontal densification to three-dimensional growth.

Urban retail location: Insights from percolation theory and spatial interaction modeling.

Characterising road networks has been the focus of a large body of research due to it being the main driver of activities in an urban ecosystem and the structuring factor in the dynamics of the city. One of these activities, and one with the largest economical impact in a city, is retail dynamics and its evolution. Therefore, the mathematical modeling of the location of retail activities and of the emergence of clustering in retail centers has as well generated a large number of works. Despite these two interwoven components strongly depending on one another and their fundamental importance in understanding cities, little work has been done in order to compare their local and global properties. Here we compare the road network's hierarchical structure, unveiled through a percolation analysis of the network, with the retail location distribution defined by exploiting a gravity-based retail model. We interpret the great agreement in the city's organizations as it emerges from both methodologies as new evidence of the interdependence of these two crucial dimensions of a city's life.

The angular nature of road networks.

Road networks are characterised by several structural and geometrical properties. The topological structure determines partially the hierarchical arrangement of roads, but since these are networks that are spatially constrained, geometrical properties play a fundamental role in determining the network's behaviour, characterising the influence of each of the street segments on the system. In this work, we apply percolation theory to the UK's road network using the relative angle between street segments as the occupation probability. The appearance of the spanning cluster is marked by a phase transition, indicating that the system behaves in a critical way. Computing Shannon's entropy of the cluster sizes, different stages of the percolation process can be discerned, and these indicate that roads integrate to the giant cluster in a hierarchical manner. This is used to construct a hierarchical index that serves to classify roads in terms of their importance. The obtained classification is in very good correspondence with the official designations of roads. This methodology hence provides a framework to consistently extract the main skeleton of an urban system and to further classify each road in terms of its hierarchical importance within the system.

Cities and regions in Britain through hierarchical percolation.

Urban systems present hierarchical structures at many different scales. These are observed as administrative regional delimitations which are the outcome of complex geographical, political and historical processes which leave almost indelible footprints on infrastructure such as the street network. In this work, we uncover a set of hierarchies in Britain at different scales using percolation theory on the street network and on its intersections which are the primary points of interaction and urban agglomeration. At the larger scales, the observed hierarchical structures can be interpreted as regional fractures of Britain, observed in various forms, from natural boundaries, such as National Parks, to regional divisions based on social class and wealth such as the well-known North-South divide. At smaller scales, cities are generated through recursive percolations on each of the emerging regional clusters. We examine the evolution of the morphology of the system as a whole, by measuring the fractal dimension of the clusters at each distance threshold in the percolation. We observe that this reaches a maximum plateau at a specific distance. The clusters defined at this distance threshold are in excellent correspondence with the boundaries of cities recovered from satellite images, and from previous methods using population density.