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Ever faster computers are enabling us to extend our standard land use transportation interaction (LUTI) models to systems of cities within which individual cities compete for resources within the wider environment in which they interact.As we scale up in this way, we are able to simulate and measure the impacts of large-scale infrastructures at different spatial levels.Here we build a platform, which is essentially a digital twin, for over 8000 urban places in Great Britain where we can rapidly model all flows between these locations using multi-modal spatial interaction models.We first present the structure of the model and then apply it to population, employment and trip flow data for three modes of travel (road, bus and rail) between small spatial units defining the three countries, England, Scotland and Wales.We then tune and train the model to reproduce a baseline, and follow this with a demonstration of the web-based interface used to run and interact with the model and its predictions.Once we have developed the platform, we are able to explore variants of the twin, partitioning the country in different ways, showing how different forms of spatial representation change the performance of the model.We are developing the model at a much finer scale making comparisons of performance while adding an active travel layer that elaborates the twin.We finally illustrate how the model can be used to measure the impacts of new scenarios for rail, simulating the Integrated Rail Plan and the High Speed 2 proposal, Comment: 26 pages, 8 figures, 4 tables

Walking and cycling, commonly referred to as active travel, have become integral components of modern transport planning. Recently, there has been growing recognition of the substantial role that active travel can play in making cities more liveable, sustainable and healthy, as opposed to traditional vehicle-centred approaches. This shift in perspective has spurred interest in developing new data sets of varying resolution levels to represent, for instance, walking and cycling street networks. This has also led to the development of tailored computational tools and quantitative methods to model and analyse active travel flows. In response to this surge in active travel-related data and methods, our study develops a methodological framework primarily focused on walking and cycling as modes of commuting. We explore commonly used data sources and tools for constructing and analysing walking and cycling networks, with a particular emphasis on distance as a key factor that influences, describes, and predicts commuting behaviour. Our ultimate aim is to investigate the role of different network distances in predicting active commuting flows. To achieve this, we analyse the flows in the constructed networks by looking at the detour index of shortest paths. We then use the Greater London Area as a case study, and construct a spatial interaction model to investigate the observed commuting patterns through the different networks. Our results highlight the differences between chosen data sets, the uneven spatial distribution of their performance throughout the city and its consequent effect on the spatial interaction model and prediction of walking and cycling commuting flows.

The polycentric city model has gained popularity in spatial planning policy, since it is believed to overcome some of the problems often present in monocentric metropolises, ranging from congestion to difficult accessibility to jobs and services. However, the concept 'polycentric city' has a fuzzy definition and as a result, the extent to which a city is polycentric cannot be easily determined. Here, we leverage the fine spatio-temporal resolution of smart travel card data to infer urban polycentricity by examining how a city departs from a well-defined monocentric model. In particular, we analyse the human movements that arise as a result of sophisticated forms of urban structure by introducing a novel probabilistic approach which captures the complexity of these human movements. We focus on London (UK) and Seoul (South Korea) as our two case studies, and we specifically find evidence that London displays a higher degree of monocentricity than Seoul, suggesting that Seoul is likely to be more polycentric than London., Comment: 15 pages, 5 figures

Urban analytics combines spatial analysis, statistics, computer science, and urban planning to understand and shape city futures. While it promises better policymaking insights, concerns exist around its epistemological scope and impacts on privacy, ethics, and social control. This chapter reflects on the history and trajectory of urban analytics as a scholarly and professional discipline. In particular, it considers the direction in which this field is going and whether it improves our collective and individual welfare. It first introduces early theories, models, and deductive methods from which the field originated before shifting toward induction. It then explores urban network analytics that enrich traditional representations of spatial interaction and structure. Next it discusses urban applications of spatiotemporal big data and machine learning. Finally, it argues that privacy and ethical concerns are too often ignored as ubiquitous monitoring and analytics can empower social repression. It concludes with a call for a more critical urban analytics that recognizes its epistemological limits, emphasizes human dignity, and learns from and supports marginalized communities.

Operational urban transport models require to gather heterogeneous sets of data and often integrate different sub-models. Their systematic validation and reproducible application therefore remains problematic. We propose in this contribution to build transport models from the bottom-up using scientific workflow systems with open-source components and data. These open models are aimed in particular at estimating congestion of public transport in all UK urban areas. This allows us building health indicators related to public transport density in the context of the COVID-19 crisis, and testing related policies., Comment: in Proceedings of 29th Annual GIS Research UK Conference (GISRUK), Cardiff, Wales, UK (Online), 14-16 April 2021

This chapter looks at the spatial distribution and mobility patterns of essential and non-essential workers before and during the COVID-19 pandemic in London and compares them to the rest of the UK. In the 3-month lockdown that started on 23 March 2020, 20% of the workforce was deemed to be pursuing essential jobs. The other 80%% were either furloughed, which meant being supported by the government to not work, or working from home. Based on travel journey data between zones (trips were decomposed into essential and non-essential trips. Despite some big regional differences within the UK, we find that essential workers have much the same spatial patterning as non-essential for all occupational groups containing essential and non-essential workers. Also, the amount of travel time saved by working from home during the Pandemic is roughly the same proportion -80%-as the separation between essential and non-essential workers. Further, the loss of travel, reduction in workers, reductions in retail spending as well as increases in use of parks are examined in different London boroughs using Google Mobility Reports which give us a clear picture of what has happened over the last 6 months since the first Lockdown. These reports also now imply that a second wave of infection is beginning., Comment: 19 pages, 9 figures

Urbanization plays a crucial role in the economic development of every country. The mutual relationship between the urbanization of any country and its economic productive structure is far from being understood. We analyzed the historical evolution of product exports for all countries using the World Trade Web (WTW) with respect to patterns of urbanization from 1995-2010. Using the evolving framework of economic complexity, we reveal that a country's economic development in terms of its production and export of goods, is interwoven with the urbanization process during the early stages of its economic development and growth. Meanwhile in urbanized countries, the reciprocal relation between economic growth and urbanization fades away with respect to its later stages, becoming negligible for countries highly dependent on the export of resources where urbanization is not linked to any structural economic transformation., Comment: 11 Pages, 5 Figures

We study the scaling of (i) numbers of workers and aggregate incomes by occupational categories against city size, and (ii) total incomes against numbers of workers in different occupations, across the functional metropolitan areas of Australia and the US. The number of workers and aggregate incomes in specific high income knowledge economy related occupations and industries show increasing returns to scale by city size, showing that localization economies within particular industries account for superlinear effects. However, when total urban area incomes and/or Gross Domestic Products are regressed using a generalised Cobb-Douglas function against the number of workers in different occupations as labour inputs, constant returns to scale in productivity against city size are observed. This implies that the urbanization economies at the whole city level show linear scaling or constant returns to scale. Furthermore, industrial and occupational organisations, not population size, largely explain the observed productivity variable. The results show that some very specific industries and occupations contribute to the observed overall superlinearity. The findings suggest that it is not just size but also that it is the diversity of specific intra-city organization of economic and social activity and physical infrastructure that should be used to understand urban scaling behaviors., Comment: 17 pages, 3 tables

This paper explores Airbnb, a peer-to-peer platform for short-term rental of housing accommodation, examining the geographical pattern of those establishments using data from London. Our purpose is to analyse whether or not the diversity of dwelling types correlate with the distribution of listings. We use a measure of spread based on entropy to indicate the diversity of dwelling types and look at its relationship with the distribution of Airbnb establishments, as well as the type of home ownership using correlation analysis. It is important to note that our study only considers domestic building types, and excludes any information on the diversity of land uses. Two important findings emerge from our analysis. Firstly, the spatial location of Airbnb rentals is negatively correlated with the diversity of dwelling types, and positively correlated with a single dwelling type, which corresponds in general to purpose built flats, conversions and flats in commercial buildings. Secondly, Airbnb is associated with areas that have a high proportion of privately rented properties, detracting more than 1.4% of the housing supply into short-term rentals. Such a phenomenon can reach up to 20% in some neighbourhoods, further exacerbating the process of gentrification. Finally, we discuss the implications of these findings as instruments to inform policies associated with the 'sharing' economy in relation to the disruption of the housing structure.

Since the presentation of the Radiation Model, much work has been done to compare its findings with those obtained from Gravitational Models. These comparisons always aim at measuring the accuracy with which the models reproduce the mobility described by origin-destination matrices. This has been done at different spatial scales using different datasets, and several versions of the models have been proposed to adjust to various spatial systems. However the models, to our knowledge, have never been compared with respect to policy testing scenarios. For this reason, here we use the models to analyze the impact of the introduction of a new transportation network, a Bus Rapid Transport system, in the city of Teresina in Brazil. We do this by measuring the estimated variation in the trip distribution, and formulate an accessibility to employment indicator for the different zones of the city. By comparing the results obtained with the two approaches, we are able, not only to better assess the goodness of fit and the impact of this intervention, but also to understand reasons for the systematic similarities and differences in their predictions., Comment: 12 Pages, 4 Figures

Newly available data on the spatial distribution of retail activities in cities makes it possible to build models formalized at the level of the single retailer. Current models tackle consumer location choices at an aggregate level and the opportunity new data offers for modeling at the retail unit level lacks a theoretical framework. The model we present here helps to address these issues. It is a particular case of the Cross-Nested Logit model, based on random utility theory built with the idea of quantifying the role of floor space and agglomeration in retail location choice. We test this model on the city of London: the results are consistent with a super linear scaling of a retailer's attractiveness with its floor space, and with an agglomeration effect approximated as the total retail floorspace within a $325m$ radius from each shop.

Agglomeration economies are a persistent subject of debate among economists and urban planners. Their definition turns on whether or not larger cities and regions are more efficient and more productive than smaller ones. We complement existing discussion on agglomeration economies and the urban wage premium here by providing a sensitivity analysis of estimated coefficients to different delineations of urban agglomeration as well as to different definitions of the economic measure that summarises the urban premium. This quantity can consist of total wages measured at the place of work, or of income registered at the place of residence. The chosen option influences the scaling behaviour of city size as well as the spatial distribution of the phenomenon at the city level. Spatial discrepancies between the distribution of jobs and the distribution of households at different economic levels makes city definitions crucial to the estimation of economic relations which vary with city size. We argue this point by regressing measures of income and wage over about five thousands different definitions of cities in France, based on our algorithmic aggregation of administrative spatial units at regular cutoffs which reflect density, population thresholds and commuting flows. We also go beyond aggregated observations of wages and income by searching for evidence of larger inequalities and economic segregation in the largest cities. This paper therefore considers the spatial and economic complexity of cities with respect to discussion about how we measure agglomeration economies. It provides a basis for reflection on alternative ways to model the processes which lead to observed variations, and this can provide insights for more comprehensive regional planning., Comment: 21 pages, 13 figures, working paper

Scaling laws are powerful summaries of the variations of urban attributes with city size. However, the validity of their universal meaning for cities is hampered by the observation that different scaling regimes can be encountered for the same territory, time and attribute, depending on the criteria used to delineate cities. The aim of this paper is to present new insights concerning this variation, coupled with a sensitivity analysis of urban scaling in France, for several socio-economic and infrastructural attributes from data collected exhaustively at the local level. The sensitivity analysis considers different aggregations of local units for which data are given by the Population Census. We produce a large variety of definitions of cities (approximatively 5000) by aggregating local Census units corresponding to the systematic combination of three definitional criteria: density, commuting flows and population cutoffs. We then measure the magnitude of scaling estimations and their sensitivity to city definitions for several urban indicators, showing for example that simple population cutoffs impact dramatically on the results obtained for a given system and attribute. Variations are interpreted with respect to the meaning of the attributes (socio-economic descriptors as well as infrastructure) and the urban definitions used (understood as the combination of the three criteria). Because of the Modifiable Areal Unit Problem and of the heterogeneous morphologies and social landscapes in the cities internal space, scaling estimations are subject to large variations, distorting many of the conclusions on which generative models are based. We conclude that examining scaling variations might be an opportunity to understand better the inner composition of cities with regard to their size, i.e. to link the scales of the city-system with the system of cities.

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 su ce 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, that can be described in terms of a multifractal, to a homogeneous one, that converges to monofractality. We argue that London's multifractal to monofracal 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 di usion limited aggregation, evolve towards monofractality if their growth is constrained by a non-permeable boundary., Comment: 13 pages, 6 figures

The morphology of urban agglomeration is studied here in the context of information exchange between different spatio-temporal scales. Cities are multidimensional non-linear phenomena, so understanding the relationships and connectivity between scales is important in determining how the interplay of local/regional urban policies may affect the distribution of urban settlements. In order to quantify these relationships, we follow an information theoretic approach using the concept of Transfer Entropy. Our analysis is based on a stochastic urban fractal model, which mimics urban growing settlements and migration waves. The results indicate how different policies could affect urban morphology in terms of the information generated across geographical scales., Comment: 19 pages, 4 figures

The outcome of the British General Election to be held in just over one week's time is widely regarded as the most difficult in living memory to predict. Current polls suggest that the two main parties are neck and neck but that there will be a landslide to the Scottish Nationalist Party with that party taking most of the constituencies in Scotland. The Liberal Democrats are forecast to loose more than half their seats and the fringe parties of whom the UK Independence Party is the biggest are simply unknown quantities. Much of this volatility relates to long-standing and deeply rooted cultural and nationalist attitudes that relate to geographical fault lines that have been present for 500 years or more but occasionally reveal themselves, at times like this. In this paper our purpose is to raise the notion that these fault lines are critical to thinking about regionalism, nationalism and the hierarchy of cities in Great Britain (excluding Northern Ireland). We use a percolation method (Arcaute et al. 2015) to reveal them that treats Britain as a giant cluster of related places each defined from the intersections of the road network at a very fine spatial scale. We break this giant cluster into a detailed hierarchy of sub-clusters by successively reducing a distance threshold which first breaks off some of the Scottish Islands and then reveals the very distinct nations and regions that make up Britain, all the way down to the definition of the largest cities that appear when the threshold reaches 300m. We use these percolation clusters to apportion the 2010 voting pattern to a new hierarchy of constituencies based on these clusters, and this gives us a picture of how Britain might vote on purely geographical lines. We then examine this voting pattern which provides us with some sense of how important the new configuration of political parties might be to the election next week., Comment: 13 pages, 7 figures, 1 table

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., Comment: 20 pages, 14 figures

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 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.

We study the growth of London's street-network in its dual representation, as the city has evolved over the last 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 lognormal distributions characterising 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 modelled via a stochastic content-based network model using simple space filling principles., Comment: accepted in Phys Rev E

"In the next century, planet earth will don an electronic skin. It will use the Internet as a scaffold to support and transmit its sensations. This skin is already being stitched together. It consists of millions of embedded electronic measuring devices: thermostats, pressure gauges, pollution detectors, cameras, microphones, glucose sensors, EKGs, electroencephalographs. These will probe and monitor cities and endangered species, the atmosphere, our ships, highways and fleets of trucks, our conversations, our bodies--even our dreams ....What will the earth's new skin permit us to feel? How will we use its surges of sensation? For several years--maybe for a decade--there will be no central nervous system to manage this vast signaling network. Certainly there will be no central intelligence...some qualities of self-awareness will emerge once the Net is sensually enhanced. Sensuality is only one force pushing the Net toward intelligence". These statements are quoted by an interview by Cherry Murray, Dean of the Harvard School of Engineering and Applied Sciences and Professor of Physics. It is interesting to outline the timeliness and highly predicting power of these statements. In particular, we would like to point to the relevance of the question "What will the earth's new skin permit us to feel?" to the work we are going to discuss in this paper. There are many additional compelling questions, as for example: "How can the electronic earth's skin be made more resilient?"; "How can the earth's electronic skin be improved to better satisfy the need of our society?";"What can the science of complex systems contribute to this endeavour?"

Cities can be characterised and modelled through different urban measures. Consistency within these observables is crucial in order to advance towards a science of cities. Bettencourt et al have proposed that many of these urban measures can be predicted through universal scaling laws. We develop a framework to consistently define cities, using commuting to work and population density thresholds, and construct thousands of realisations of systems of cities with different boundaries for England and Wales. These serve as a laboratory for the scaling analysis of a large set of urban indicators. The analysis shows that population size alone does not provide enough information to describe or predict the state of a city as previously proposed, indicating that the expected scaling laws are not corroborated. We found that most urban indicators scale linearly with city size regardless of the definition of the urban boundaries. However, when non-linear correlations are present, the exponent fluctuates considerably., Comment: Accepted for publication, Journal of the Royal Society Interface

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 normalisation 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., Comment: in press Phys. Rev. E, 2013

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., Comment: PlosOne, in publication

We study the temporal evolution of the structure of the world's largest subway networks in an exploratory manner. We show that, remarkably, all these networks converge to {a shape which shares similar generic features} despite their geographic and economic differences. This limiting shape is made of a core with branches radiating from it. For most of these networks, the average degree of a node (station) within the core has a value of order 2.5 and the proportion of k=2 nodes in the core is larger than 60%. The number of branches scales roughly as the square root of the number of stations, the current proportion of branches represents about half of the total number of stations, and the average diameter of branches is about twice the average radial extension of the core. Spatial measures such as the number of stations at a given distance to the barycenter display a first regime which grows as r^2 followed by another regime with different exponents, and eventually saturates. These results -- difficult to interpret in the framework of fractal geometry -- confirm and yield a natural explanation in the geometric picture of this core and their branches: the first regime corresponds to a uniform core, while the second regime is controlled by the interstation spacing on branches. The apparent convergence towards a unique network shape in the temporal limit suggests the existence of dominant, universal mechanisms governing the evolution of these structures., Comment: 11 pages, 13 figures, revised version, accepted for publication in Royal Society Interface

The spatial arrangement of urban hubs and centers and how individuals interact with these centers is a crucial problem with many applications ranging from urban planning to epidemiology. We utilize here in an unprecedented manner the large scale, real-time 'Oyster' card database of individual person movements in the London subway to reveal the structure and organization of the city. We show that patterns of intraurban movement are strongly heterogeneous in terms of volume, but not in terms of distance travelled, and that there is a polycentric structure composed of large flows organized around a limited number of activity centers. For smaller flows, the pattern of connections becomes richer and more complex and is not strictly hierarchical since it mixes different levels consisting of different orders of magnitude. This new understanding can shed light on the impact of new urban projects on the evolution of the polycentric configuration of a city and the dense structure of its centers and it provides an initial approach to modeling flows in an urban system., Comment: Revised version, 9 pages, 9 figures

In this paper we analyse the street network of London both in its primary and dual representation. To understand its properties, we consider three idealised models based on a grid, a static random planar graph and a growing random planar graph. Comparing the models and the street network, we find that the streets of London form a self-organising system whose growth is characterised by a strict interaction between the metrical and informational space. In particular, a principle of least effort appears to create a balance between the physical and the mental effort required to navigate the city.

Studies of collective human behavior in the social sciences, often grounded in details of actions by individuals, have much to offer `social' models from the physical sciences concerning elegant statistical regularities. Drawing on behavioral studies of social influence, we present a parsimonious, stochastic model, which generates an entire family of real-world right-skew socio-economic distributions, including exponential, winner-take-all, power law tails of varying exponents and power laws across the whole data. The widely used Albert-Barabasi model of preferential attachment is simply a special case of this much more general model. In addition, the model produces the continuous turnover observed empirically within those distributions. Previous preferential attachment models have generated specific distributions with turnover using arbitrary add-on rules, but turnover is an inherent feature of our model. The model also replicates an intriguing new relationship, observed across a range of empirical studies, between the power law exponent and the proportion of data represented., Comment: 8 pages, 4 figures, 1 table

An important issue in the study of cities is defining a metropolitan area, as different definitions affect the statistical distribution of urban activity. A commonly employed method of defining a metropolitan area is the Metropolitan Statistical Areas (MSA), based on rules attempting to capture the notion of city as a functional economic region, and is constructed using experience. The MSA is time-consuming and is typically constructed only for a subset (few hundreds) of the most highly populated cities. Here, we introduce a new method to designate metropolitan areas, denoted the "City Clustering Algorithm" (CCA). The CCA is based on spatial distributions of the population at a fine geographic scale, defining a city beyond the scope of its administrative boundaries. We use the CCA to examine Gibrat's law of proportional growth, postulating that the mean and standard deviation of the growth rate of cities are constant, independent of city size. We find that the mean growth rate of a cluster utilizing the CCA exhibits deviations from Gibrat's law, and that the standard deviation decreases as a power-law with respect to the city size. The CCA allows for the study of the underlying process leading to these deviations, shown to arise from the existence of long-range spatial correlations in the population growth. These results have socio-political implications, such as those pertaining to the location of new economic development in cities of varied size., Comment: 30 pages, 8 figures

Many aggregate distributions of urban activities such as city sizes reveal scaling but hardly any work exists on the properties of spatial distributions within individual cities, notwithstanding considerable knowledge about their fractal structure. We redress this here by examining scaling relationships in a world city using data on the geometric properties of individual buildings. We first summarise how power laws can be used to approximate the size distributions of buildings, in analogy to city-size distributions which have been widely studied as rank-size and lognormal distributions following Zipf and Gibrat. We then extend this analysis to allometric relationships between buildings in terms of their different geometric size properties. We present some preliminary analysis of building heights from the Emporis database which suggests very strong scaling in world cities. The data base for Greater London is then introduced from which we extract 3.6 million buildings whose scaling properties we explore. We examine key allometric relationships between these different properties illustrating how building shape changes according to size, and we extend this analysis to the classification of buildings according to land use types. We conclude with an analysis of two-point correlation functions of building geometries which supports our non-spatial analysis of scaling., Comment: 28 pages, 8 figures

Here we extract the geographical addresses of authors in the Citeseer database of computer science papers. We show that the productivity of research centres in the United States follows a power-law regime, apart from the most productive centres for which we do not have enough data to reach definite conclusions. To investigate the spatial distribution of computer science research centres in the United States, we compute the two-point correlation function of the spatial point process and show that the observed power-laws do not disappear even when we change the physical representation from geographical space to cartogram space. Our work suggests that the effect of physical location poses a challenge to ongoing efforts to develop realistic models of scientific productivity. We propose that the introduction of a fine scale geography may lead to more sophisticated indicators of scientific output., Comment: 6 pages, 3 figures; minor changes