arXiv subjects

Michael Batty

Publications and source records attributed to Michael Batty.

35 records · Page 2Linked to original sources

arXiv2015

Urban transfer entropy across scales

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.

physics.soc-ph↗

arXiv2015

The Fractured Nature of British Politics

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.

physics.soc-ph↗

arXiv2014

Constructing cities, deconstructing scaling laws

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.

physics.soc-ph↗

arXiv2013

Exploring the Evolution of London's Street Network in the Information Space: a Dual Approach

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.

physics.soc-ph↗

arXiv2013

Limited Urban Growth: London's Street Network Dynamics since the 18th Century

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.

physics.data-an↗

arXiv2013

Complexity Aided Design: the FuturICT Technological Innovation Paradigm

"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?"

physics.soc-ph↗

arXiv2012

A long-time limit of world subway networks

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.

physics.soc-ph↗

arXiv2010

Structure of urban movements: polycentric activity and entangled hierarchical flows

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.

physics.soc-ph↗

arXiv2009

Laws of Population Growth

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.

physics.soc-ph↗

arXiv2009

An evolutionary model of long tailed distributions in the social sciences

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.

physics.soc-ph↗

arXiv2008

Scaling and allometry in the building geometries of Greater London

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.

physics.soc-ph↗

arXiv2008

An application of the Deutsch-Josza algorithm to formal languages and the word problem in groups

We adapt the Deutsch-Josza algorithm to the context of formal language theory. Specifically, we use the algorithm to distinguish between trivial and nontrivial words in groups given by finite presentations, under the promise that a word is of a certain type. This is done by extending the original algorithm to functions of arbitrary length binary output, with the introduction of a more general concept of parity. We provide examples in which properties of the algorithm allow to reduce the number of oracle queries with respect to the deterministic classical case. This has some consequences for the word problem in groups with a particular kind of presentation.

quant-ph↗

arXiv2006

The Geography of Scientific Productivity: Scaling in U.S. Computer Science

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.

physics.soc-ph↗

arXiv2005

Extending the Promise of the Deutsch--Jozsa--Hoyer Algorithm for Finite Groups

Hoyer has given a generalisation of the Deutsch--Jozsa algorithm which uses the Fourier transform on a group G which is (in general) non-Abelian. His algorithm distinguishes between functions which are either perfectly balanced (m-to-one) or constant, with certainty, and using a single quantum query. Here, we show that this algorithm (which we call the Deutsch--Jozsa--Hoyer algorithm) can in fact deal with a broader range of promises, which we define in terms of the irreducible representations of G.

quant-ph↗

arXiv2003

A rigorous definition of axial lines: ridges on isovist fields

We suggest that 'axial lines' defined by (Hillier and Hanson, 1984) as lines of uninterrupted movement within urban streetscapes or buildings, appear as ridges in isovist fields (Benedikt, 1979). These are formed from the maximum diametric lengths of the individual isovists, sometimes called viewsheds, that make up these fields (Batty and Rana, 2004). We present an image processing technique for the identification of lines from ridges, discuss current strengths and weaknesses of the method, and show how it can be implemented easily and effectively.

cs.CV↗

arXiv2003

Quantum algorithms in group theory

We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.

quant-ph↗

arXiv1998

Modeling Urban Growth Patterns with Correlated Percolation

We propose and test a model that describes the morphology of cities, the scaling of the urban perimeter of individual cities, and the area distribution of systems of cities. The model is also consistent with observable urban growth dynamics, our results agreeing both qualitatively and quantitatively with urban data. The resulting growth morphology can be understood from interactions among the constituent units forming an urban region, and can be modeled using a correlated percolation model in the presence of a gradient.

cond-mat.dis-nn↗