Tipping the balances of a small world

Recent progress in the large scale mapping of social networks is opening new quantitative windows into the structure of human societies. These networks are largely the result of how we access and utilize information. Here I show that a universal decision mechanism, where we base our choices upon the actions of others, can explain much of their structure. Such collective social arrangements emerge from successful strategies to handle information flow at the individual level. They include the formation of closely-knit communities and the emergence of well-connected individuals. The latter can command the following of others while only exercising ordinary judgement.Comment: 10 pages, 4 figures, uses RevTe

Urban Scaling in Europe

Over the last decades, in disciplines as diverse as economics, geography, and complex systems, a perspective has arisen proposing that many properties of cities are quantitatively predictable due to agglomeration or scaling effects. Using new harmonized definitions for functional urban areas, we examine to what extent these ideas apply to European cities. We show that while most large urban systems in Western Europe (France, Germany, Italy, Spain, UK) approximately agree with theoretical expectations, the small number of cities in each nation and their natural variability preclude drawing strong conclusions. We demonstrate how this problem can be overcome so that cities from different urban systems can be pooled together to construct larger datasets. This leads to a simple statistical procedure to identify urban scaling relations, which then clearly emerge as a property of European cities. We compare the predictions of urban scaling to Zipf's law for the size distribution of cities and show that while the former holds well the latter is a poor descriptor of European cities. We conclude with scenarios for the size and properties of future pan-European megacities and their implications for the economic productivity, technological sophistication and regional inequalities of an integrated European urban system.Comment: 35 pages, 7 Figures, 1 Tabl

Urban Geography and Scaling of Contemporary Indian Cities

This paper attempts to create a first comprehensive analysis of the integrated characteristics of contemporary Indian cities, using scaling and geographic analysis over a set of diverse indicators. We use data at the level of Urban Agglomerations in India from the Census 2011 and from a few other sources to characterize patterns of urban population density, infrastructure, urban services, economic performance, crime and innovation. Many of the results are in line with expectations from urban theory and with the behaviour of analogous quantities in other urban systems in both high and middle-income nations. India is a continental scale, fast developing urban system, and consequently there are also a number of interesting exceptions and surprises related to both specific quantities and strong regional patterns of variation. We characterize these patterns in detail for crime and innovation and connect them to the existing literature on their determinants in a specifically Indian context. The paucity of data at the urban level and the absence of official definitions for functional cities in India create a number of limitations and caveats to any present analysis. We discuss these shortcomings and spell out the challenge for a systematic statistical data collection relevant to cities and urban development in India.Comment: 20 pages, 11 figure

Multiple-Scale Analysis of Quantum Systems

Conventional weak-coupling Rayleigh-Schr\"odinger perturbation theory suffers from problems that arise from resonant coupling of successive orders in the perturbation series. Multiple-scale analysis, a powerful and sophisticated perturbative method that quantitatively analyzes characteristic physical behaviors occurring on various length or time scales, avoids such problems by implicitly performing an infinite resummation of the conventional perturbation series. Multiple-scale perturbation theory provides a good description of the classical anharmonic oscillator. Here, it is extended to study (1) the Heisenberg operator equations of motion and (2) the Schr\"odinger equation for the quantum anharmonic oscillator. In the former case, it leads to a system of coupled operator differential equations, which is solved exactly. The solution provides an operator mass renormalization of the theory. In the latter case, multiple-scale analysis elucidates the connection between weak-coupling perturbative and semiclassical nonperturbative aspects of the wave function.Comment: 30 pages, LaTeX/RevTeX, no figures. Available through anonymous ftp from ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at http://euclid.tp.ph.ic.ac.uk/Papers

Formation of Scientific Fields as a Universal Topological Transition

Scientific fields differ in terms of their subject matter, research techniques, collaboration sizes, rates of growth, and so on. We investigate whether common dynamics might lurk beneath these differences, affecting how scientific fields form and evolve over time. Particularly important in any field's history is the moment at which shared concepts and techniques allow widespread exchange of ideas and collaboration. At that moment, co-authorship networks show the analog of a percolation phenomenon, developing a giant connected component containing most authors. We develop a general theoretical framework for analyzing finite, evolving networks in which each scientific field is an instantiation of the same large-scale topological critical phenomenon. We estimate critical exponents associated with the transition and find evidence for universality near criticality implying that, as various fields approach the topological transition, they do so with the same set of critical exponents consistent with an effective dimensionality $d \simeq 1$. These results indicate that a common dynamics is at play in all scientific fields, which in turn may hold policy implications for ways to encourage and accelerate the creation of scientific and technological knowledge.Comment: 8 pages, including 5 figure

When is social computation better than the sum of its parts?

Social computation, whether in the form of searches performed by swarms of agents or collective predictions of markets, often supplies remarkably good solutions to complex problems. In many examples, individuals trying to solve a problem locally can aggregate their information and work together to arrive at a superior global solution. This suggests that there may be general principles of information aggregation and coordination that can transcend particular applications. Here we show that the general structure of this problem can be cast in terms of information theory and derive mathematical conditions that lead to optimal multi-agent searches. Specifically, we illustrate the problem in terms of local search algorithms for autonomous agents looking for the spatial location of a stochastic source. We explore the types of search problems, defined in terms of the statistical properties of the source and the nature of measurements at each agent, for which coordination among multiple searchers yields an advantage beyond that gained by having the same number of independent searchers. We show that effective coordination corresponds to synergy and that ineffective coordination corresponds to independence as defined using information theory. We classify explicit types of sources in terms of their potential for synergy. We show that sources that emit uncorrelated signals provide no opportunity for synergetic coordination while sources that emit signals that are correlated in some way, do allow for strong synergy between searchers. These general considerations are crucial for designing optimal algorithms for particular search problems in real world settings.Comment: 5 pages, 1 figure; In H. Liu, J. J. Salerno, and M. J. Young, editors, Social Computing, Behavior Modeling, and Prediction, 200

Urban Skylines: building heights and shapes as measures of city size

The shape of buildings plays a critical role in the energy efficiency, lifestyles, land use and infrastructure systems of cities. Thus, as most of the world's cities continue to grow and develop, understanding the interplay between the characteristics of urban environments and the built form of cities is essential to achieve local and global sustainability goals. Here, we compile and analyze the most extensive data set of building shapes to date, covering more than 4.8 million individual buildings across several major cities in North America. We show that average building height increases systematically with city size and follows theoretical predictions derived from urban scaling theory. We also study the allometric relationship between surface area and volume of buildings in terms of characteristic shape parameters. This allows us to demonstrate that the reported trend towards higher (and more voluminous) buildings effectively decreases the average surface-to-volume ratio, suggesting potentially significant energy savings with growing city size. At the same time, however, the surface-to-volume ratio increases in the downtown cores of large cities, due to shape effects and specifically to the proliferation of tall, needlelike buildings. Thus, the issue of changes in building shapes with city size and associated energy management problem is highly heterogeneous. It requires a systematic approach that includes the factors that drive the form of built environments, entangling physical, infrastructural and socioeconomic aspects of cities

The hypothesis of urban scaling: formalization, implications and challenges

There is strong expectation that cities, across time, culture and level of development, share much in common in terms of their form and function. Recently, attempts to formalize mathematically these expectations have led to the hypothesis of urban scaling, namely that certain properties of all cities change, on average, with their size in predictable scale-invariant ways. The emergence of these scaling relations depends on a few general properties of cities as social networks, co-located in space and time, that conceivably apply to a wide range of human settlements. Here, we discuss the present evidence for the hypothesis of urban scaling, some of the methodological issues dealing with proxy measurements and units of analysis and place these findings in the context of other theories of cities and urban systems. We show that a large body of evidence about the scaling properties of cities indicates, in analogy to other complex systems, that they cannot be treated as extensive systems and discuss the consequences of these results for an emerging statistical theory of cities.Comment: 37 pages, 6 figure

Thermal vortex dynamics in a two-dimensional condensate

We carry out an analytical and numerical study of the motion of an isolated vortex in thermal equilibrium, the vortex being defined as the point singularity of a complex scalar field $\psi(\r,t)$ obeying a nonlinear stochastic Schr\"odinger equation. Because hydrodynamic fluctuations are included in this description, the dynamical picture of the vortex emerges as that of both a massive particle in contact with a heat bath, and as a passive scalar advected to a background random flow. We show that the vortex does not execute a simple random walk and that the probability distribution of vortex flights has non-Gaussian (exponential) tails.Comment: RevTex, 9 pages, 3 figures, To appear in Phys. Rev.

Professional diversity and the productivity of cities

The relationships between diversity, productivity and scale determine much of the structure and robustness of complex biological and social systems. While arguments for the link between specialization and productivity are common, diversity has often been invoked as a hedging strategy, allowing systems to evolve in response to environmental change. Despite their general appeal, these arguments have not typically produced quantitative predictions for optimal levels of functional diversity consistent with observations. One important reason why these relationships have resisted formalization is the idiosyncratic nature of diversity measures, which depend on given classification schemes. Here, we address these issues by analyzing the statistics of professions in cities and show how their probability distribution takes a universal scale-invariant form, common to all cities, obtained in the limit of infinite resolution of given taxonomies. We propose a model that generates the form and parameters of this distribution via the introduction of new occupations at a rate leading to individual specialization subject to the preservation of access to overall function via their ego social networks. This perspective unifies ideas about the importance of network structure in ecology and of innovation as a recombinatory process with economic concepts of productivity gains obtained through the division and coordination of labor, stimulated by scale.Comment: Press embargo in place until publicatio