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Arcaute E, Molinero C, Hatna E, Murcio R, Vargas-Ruiz C, Masucci AP, Batty M. Cities and regions in Britain through hierarchical percolation. R Soc Open Sci 2016; 3:150691. [PMID: 27152211 PMCID: PMC4852634 DOI: 10.1098/rsos.150691] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2015] [Accepted: 02/16/2016] [Indexed: 05/19/2023]
Abstract
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.
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Affiliation(s)
- Elsa Arcaute
- Centre for Advanced Spatial Analysis (CASA), University College London, London, UK
- Author for correspondence: Elsa Arcaute e-mail:
| | - Carlos Molinero
- Centre for Advanced Spatial Analysis (CASA), University College London, London, UK
| | - Erez Hatna
- Centre for Advanced Spatial Analysis (CASA), University College London, London, UK
- Center for Advanced Modeling, The Johns Hopkins University, Baltimore, MD, USA
| | - Roberto Murcio
- Centre for Advanced Spatial Analysis (CASA), University College London, London, UK
- Consumer Research Data Centre, Geography, University College London, London, UK
| | - Camilo Vargas-Ruiz
- Centre for Advanced Spatial Analysis (CASA), University College London, London, UK
- Consumer Research Data Centre, Geography, University College London, London, UK
| | - A. Paolo Masucci
- Centre for Advanced Spatial Analysis (CASA), University College London, London, UK
| | - Michael Batty
- Centre for Advanced Spatial Analysis (CASA), University College London, London, UK
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Murcio R, Masucci AP, Arcaute E, Batty M. Multifractal to monofractal evolution of the London street network. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 92:062130. [PMID: 26764655 DOI: 10.1103/physreve.92.062130] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2015] [Indexed: 05/11/2023]
Abstract
We perform a multifractal analysis of the evolution of London's street network from 1786 to 2010. First, we show that a single fractal dimension, commonly associated with the morphological description of cities, does not suffice to capture the dynamics of the system. Instead, for a proper characterization of such a dynamics, the multifractal spectrum needs to be considered. Our analysis reveals that London evolves from an inhomogeneous fractal structure, which can be described in terms of a multifractal, to a homogeneous one, which converges to monofractality. We argue that London's multifractal to monofractal evolution might be a special outcome of the constraint imposed on its growth by a green belt. Through a series of simulations, we show that multifractal objects, constructed through diffusion limited aggregation, evolve toward monofractality if their growth is constrained by a nonpermeable boundary.
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Affiliation(s)
- Roberto Murcio
- Centre for Advanced Spatial Analysis. University College London, First floor, 90 Tottenham Court Road, London, United Kingdom
| | - A Paolo Masucci
- Centre for Advanced Spatial Analysis. University College London, First floor, 90 Tottenham Court Road, London, United Kingdom
| | - Elsa Arcaute
- Centre for Advanced Spatial Analysis. University College London, First floor, 90 Tottenham Court Road, London, United Kingdom
| | - Michael Batty
- Centre for Advanced Spatial Analysis. University College London, First floor, 90 Tottenham Court Road, London, United Kingdom
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Masucci AP, Arcaute E, Hatna E, Stanilov K, Batty M. On the problem of boundaries and scaling for urban street networks. J R Soc Interface 2015; 12:20150763. [PMID: 26468071 PMCID: PMC4614511 DOI: 10.1098/rsif.2015.0763] [Citation(s) in RCA: 41] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2015] [Accepted: 09/21/2015] [Indexed: 12/04/2022] Open
Abstract
Urban morphology has presented significant intellectual challenges to mathematicians and physicists ever since the eighteenth century, when Euler first explored the famous Königsberg bridges problem. Many important regularities and scaling laws have been observed in urban studies, including Zipf's law and Gibrat's law, rendering cities attractive systems for analysis within statistical physics. Nevertheless, a broad consensus on how cities and their boundaries are defined is still lacking. Applying an elementary clustering technique to the street intersection space, we show that growth curves for the maximum cluster size of the largest cities in the UK and in California collapse to a single curve, namely the logistic. Subsequently, by introducing the concept of the condensation threshold, we show that natural boundaries of cities can be well defined in a universal way. This allows us to study and discuss systematically some of the regularities that are present in cities. We show that some scaling laws present consistent behaviour in space and time, thus suggesting the presence of common principles at the basis of the evolution of urban systems.
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Affiliation(s)
- A Paolo Masucci
- Centre for Advanced Spatial Analysis, University College London, 90 Tottenham Court Road, London W1N 6TR, UK
| | - Elsa Arcaute
- Centre for Advanced Spatial Analysis, University College London, 90 Tottenham Court Road, London W1N 6TR, UK
| | - Erez Hatna
- Center for Advanced Modeling, The Johns Hopkins University, Baltimore, MD, USA
| | - Kiril Stanilov
- Centre for Advanced Spatial Analysis, University College London, 90 Tottenham Court Road, London W1N 6TR, UK Centre for Sustainable Infrastructure and Construction, University of Cambridge, Cambridge CB2 1TN, UK
| | - Michael Batty
- Centre for Advanced Spatial Analysis, University College London, 90 Tottenham Court Road, London W1N 6TR, UK
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Masucci AP, Stanilov K, Batty M. Exploring the evolution of London's street network in the information space: a dual approach. Phys Rev E Stat Nonlin Soft Matter Phys 2014; 89:012805. [PMID: 24580279 DOI: 10.1103/physreve.89.012805] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2013] [Indexed: 06/03/2023]
Abstract
We study the growth of London's street network in its dual representation, as the city has evolved over the past 224 years. The dual representation of a planar graph is a content-based network, where each node is a set of edges of the planar graph and represents a transportation unit in the so-called information space, i.e., the space where information is handled in order to navigate through the city. First, we discuss a novel hybrid technique to extract dual graphs from planar graphs, called the hierarchical intersection continuity negotiation principle. Then we show that the growth of the network can be analytically described by logistic laws and that the topological properties of the network are governed by robust log-normal distributions characterizing the network's connectivity and small-world properties that are consistent over time. Moreover, we find that the double-Pareto-like distributions for the connectivity emerge for major roads and can be modeled via a stochastic content-based network model using simple space-filling principles.
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Affiliation(s)
- A Paolo Masucci
- Centre for Advanced Spatial Analysis, University College of London, London, United Kingdom
| | - Kiril Stanilov
- Centre for Advanced Spatial Analysis, University College of London, London, United Kingdom and Martin Centre, University of Cambridge, Cambridge, United Kingdom
| | - Michael Batty
- Centre for Advanced Spatial Analysis, University College of London, London, United Kingdom
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Abstract
We investigate the growth dynamics of Greater London defined by the administrative boundary of the Greater London Authority, based on the evolution of its street network during the last two centuries. This is done by employing a unique dataset, consisting of the planar graph representation of nine time slices of Greater London's road network spanning 224 years, from 1786 to 2010. Within this time-frame, we address the concept of the metropolitan area or city in physical terms, in that urban evolution reveals observable transitions in the distribution of relevant geometrical properties. Given that London has a hard boundary enforced by its long standing green belt, we show that its street network dynamics can be described as a fractal space-filling phenomena up to a capacitated limit, whence its growth can be predicted with a striking level of accuracy. This observation is confirmed by the analytical calculation of key topological properties of the planar graph, such as the topological growth of the network and its average connectivity. This study thus represents an example of a strong violation of Gibrat's law. In particular, we are able to show analytically how London evolves from a more loop-like structure, typical of planned cities, toward a more tree-like structure, typical of self-organized cities. These observations are relevant to the discourse on sustainable urban planning with respect to the control of urban sprawl in many large cities which have developed under the conditions of spatial constraints imposed by green belts and hard urban boundaries.
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Affiliation(s)
- A Paolo Masucci
- Centre for Advanced Spatial Analysis, University College of London, London, UK.
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Masucci AP, Serras J, Johansson A, Batty M. Gravity versus radiation models: on the importance of scale and heterogeneity in commuting flows. Phys Rev E Stat Nonlin Soft Matter Phys 2013; 88:022812. [PMID: 24032888 DOI: 10.1103/physreve.88.022812] [Citation(s) in RCA: 52] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2012] [Revised: 06/18/2013] [Indexed: 05/28/2023]
Abstract
We test the recently introduced radiation model against the gravity model for the system composed of England and Wales, both for commuting patterns and for public transportation flows. The analysis is performed both at macroscopic scales, i.e., at the national scale, and at microscopic scales, i.e., at the city level. It is shown that the thermodynamic limit assumption for the original radiation model significantly underestimates the commuting flows for large cities. We then generalize the radiation model, introducing the correct normalization factor for finite systems. We show that even if the gravity model has a better overall performance the parameter-free radiation model gives competitive results, especially for large scales.
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Affiliation(s)
- A Paolo Masucci
- Centre for Advanced Spatial Analysis, University College London, W1T 4TJ, London, United Kingdom
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Masucci AP, Kalampokis A, Eguíluz VM, Hernández-García E. Extracting directed information flow networks: an application to genetics and semantics. Phys Rev E Stat Nonlin Soft Matter Phys 2011; 83:026103. [PMID: 21405885 DOI: 10.1103/physreve.83.026103] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2010] [Revised: 11/25/2010] [Indexed: 05/30/2023]
Abstract
We introduce a general method to infer the directional information flow between populations whose elements are described by n-dimensional vectors of symbolic attributes. The method is based on the Jensen-Shannon divergence and on the Shannon entropy and has a wide range of application. We show here the results of two applications: first we extract the network of genetic flow between meadows of the seagrass Poseidonia oceanica, where the meadow elements are specified by sets of microsatellite markers, and then we extract the semantic flow network from a set of Wikipedia pages, showing the semantic channels between different areas of knowledge.
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Affiliation(s)
- A P Masucci
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), E-07122 Palma de Mallorca, Spain
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Abstract
We investigate the nature of written human language within the framework of complex network theory. In particular, we analyze the topology of Orwell's "1984" focusing on the local properties of the network, such as the properties of the nearest neighbors and the clustering coefficient. We find a composite power law behavior for both the average nearest neighbor's degree and average clustering coefficient as a function of the vertex degree. This implies the existence of different functional classes of vertices. Furthermore, we find that the second order vertex correlations are an essential component of the network architecture. To model our empirical results we extend a previously introduced model for language due to Dorogovtsev and Mendes. We propose an accelerated growing network model that contains three growth mechanisms: linear preferential attachment, local preferential attachment, and the random growth of a predetermined small finite subset of initial vertices. We find that with these elementary stochastic rules we are able to produce a network showing syntacticlike structures.
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Affiliation(s)
- A P Masucci
- Department of Mathematical Sciences, Brunel University, Uxbridge UB8 3PH, Middlesex, United Kingdom
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