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Sustainable development is an imperative worldwide but metrics and data on poverty and quality of life have remained too coarse and abstract to characterize challenges adequately and guide practical progress. Nowhere is this challenge greater than in Africa where we still know relatively little about the systematic spatial details and scope of development. Here, we leverage a complete, high-precision dataset of building footprints to identify infrastructure deficits and infer informal settlements down to the street level everywhere in sub-Saharan Africa. We identify a general pattern of informality with urbanized areas showing, on average, greater access to infrastructure and services than rural and periurban areas, each characterized by a statistically consistent spectrum of uneven local development. We show that our physical measures of informality are systematically associated with many indicators of low human development, and that these form a single principal component predicted by specific functional changes of the built environment. These results demonstrate that the localization of sustainable development is possible down to the street level at a continental scale and provide a general distributed strategy for accelerating progress in infrastructure and service expansion that taps local innovations in a way that is equitable and context appropriate., Comment: 20 pages, 4 Figures (plus 6 supplementary)

Homophily and heterophobia, the tendency for people with similar characteristics to preferentially interact with (or avoid) each other are pervasive in human social networks. Here, we develop an extension of the mathematical theory of urban scaling which describes the effects of homophily and heterophobia on social interactions and resulting economic outputs of cities. Empirical tests of our model show that increased residential racial heterophobia and segregation in U.S. cities are associated with reduced economic outputs and that the strength of this relationship increased throughout the 2010s. Our findings provide the means for the formal incorporation of general homophilic and heterophobic effects into theories of modern urban science and suggest that racial segregation is increasingly and adversely impacting the economic performance and connectivity of urban societies in the U.S.

Stochastic multiplicative dynamics characterize many complex natural phenomena such as selection and mutation in evolving populations, and the generation and distribution of wealth within social systems. Population heterogeneity in stochastic growth rates has been shown to be the critical driver of diversity dynamics and of the emergence of wealth inequality over long time scales. However, we still lack a general statistical framework that systematically explains the origins of these heterogeneities from the adaptation of agents to their environment. In this paper, we derive population growth parameters resulting from the interaction between agents and their knowable environment, conditional on subjective signals each agent receives. We show that average growth rates converge, under specific conditions, to their maximal value as the mutual information between the agent's signal and the environment, and that sequential Bayesian learning is the optimal strategy for reaching this maximum. It follows that when all agents access the same environment using the same inference model, the learning process dynamically attenuates growth rate disparities, reversing the long-term effects of heterogeneity on inequality. Our approach lays the foundation for a unified general quantitative modeling of social and biological phenomena such as the dynamical effects of cooperation, and the effects of education on life history choices., Comment: 12 pages, 4 figures

Understanding the statistical dynamics of growth and inequality is a fundamental challenge to ecology and society. Recent analyses of wealth and income dynamics in contemporary societies show that economic inequality is very dynamic and that individuals experience substantially different growth rates over time. However, despite a fast growing body of evidence for the importance of fluctuations, we still lack a general statistical theory for understanding the dynamical effects of heterogeneneous growth across a population. Here we derive the statistical dynamics of correlated growth rates in heterogeneous populations. We show that correlations between growth rate fluctuations at the individual level influence aggregate population growth, while only driving inequality on short time scales. We also find that growth rate fluctuations are a much stronger driver of long-term inequality than earnings volatility. Our findings show that the dynamical effects of statistical fluctuations in growth rates are critical for understanding the emergence of inequality over time and motivate a greater focus on the properties and endogenous origins of growth rates in stochastic environments., Comment: 7 pages, 4 figures

We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number $\mathcal{R}(t)$. We discuss the estimation of the underlying SIR parameters with a generalized least squares (GLS) estimation technique. We do this in the context of appropriate statistical models for the measurement process. We use asymptotic statistical theories to derive the mean and variance of the limiting (Gaussian) sampling distribution and to perform post statistical analysis of the inverse problems. We illustrate the ideas and pitfalls (e.g., large condition numbers on the corresponding Fisher information matrix) with both synthetic and influenza incidence data sets.

The current outbreak of novel coronavirus disease 2019 (COVID-19) poses an unprecedented global health and economic threat to interconnected human societies. Until a vaccine is developed, strategies for controlling the outbreak rely on aggressive social distancing. These measures largely disconnect the social network fabric of human societies, especially in urban areas. Here, we estimate the growth rates and reproductive numbers of COVID-19 in US cities from March 14th through March 19th to reveal a power-law scaling relationship to city population size. This means that COVID-19 is spreading faster on average in larger cities with the additional implication that, in an uncontrolled outbreak, larger fractions of the population are expected to become infected in more populous urban areas. We discuss the implications of these observations for controlling the COVID-19 outbreak, emphasizing the need to implement more aggressive distancing policies in larger cities while also preserving socioeconomic activity.

The emergence of India as an urbanized nation is one of the most significant socioeconomic and political processes of the 21st century. An essential feature of India's urbanization has been the growth and persistence of informal settlements (slums) in its fast-developing cities. Whether living conditions in Indian urban slums constitute a path to human development or a poverty trap is therefore an issue of vital importance. Here, we characterize census data using the framework of urban scaling to systematically characterize the relative properties of Indian urban slums, focusing on attributes of neighborhoods such as access to basic services like water, sanitation, and electrical power. We find that slums in larger cities offer systematically higher levels of service access than those in smaller cities. Perhaps as expected, we also find consistent underperformance in service access in slums in comparison with non-slum neighborhoods in the same cities. However, urban slums, on average, offer greater access to services than neighborhoods in rural areas. This situation, which we quantify systematically, may help explain why Indian larger cities have remained attractive to rural populations in terms of living standards, beyond the need for an economic income premium., Comment: 12 pages, 4 figures

We undertake an exploration of the economic income (Gross Domestic Product, GDP) of Indian districts and cities based on scaling analyses of the dependence of these quantities on associated population size. Scaling analysis provides a straightforward method for the identification of network effects in socioeconomic organization, which are the tell-tale of cities and urbanization. For districts, a sub-state regional administrative division in India, we find almost linear scaling of GDP with population, a result quite different from urban functional units in other national contexts. Using deviations from scaling, we explore the behavior of these regional units to find strong distinct geographic patterns of economic behavior. We characterize these patterns in detail and connect them to the literature on regional economic development for a diverse subcontinental nation such as India. Given the paucity of economic data for Urban Agglomerations in India, we use a set of assumptions to create a new dataset of GDP based on districts, for large cities. This reveals superlinear scaling of income with city size, as expected from theory, while displaying similar underlying patterns of economic geography observed for district economic performance. This analysis of the economic performance of Indian cities is severely limited by the absence of higher-fidelity, direct city level economic data. We discuss the need for standardized and consistent estimates of the size and change in urban economies in India, and point to a number of proxies that can be explored to develop such indicators., Comment: 16 pages, 9 figures

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 figures

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.

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 Table

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 figures

Invention has been commonly conceptualized as a search over a space of combinatorial possibilities. Despite the existence of a rich literature, spanning a variety of disciplines, elaborating on the recombinant nature of invention, we lack a formal and quantitative characterization of the combinatorial process underpinning inventive activity. Here we utilize U.S. patent records dating from 1790 to 2010 to formally characterize the invention as a combinatorial process. To do this we treat patented inventions as carriers of technologies and avail ourselves of the elaborate system of technology codes used by the U.S. Patent Office to classify the technologies responsible for an invention's novelty. We find that the combinatorial inventive process exhibits an invariant rate of "exploitation" (refinements of existing combinations of technologies) and "exploration" (the development of new technological combinations). This combinatorial dynamic contrasts sharply with the creation of new technological capabilities -- the building blocks to be combined -- which has significantly slowed down. We also find that notwithstanding the very reduced rate at which new technologies are introduced, the generation of novel technological combinations engenders a practically infinite space of technological configurations., Comment: Press embargo in place until publication

Understanding cities is central to addressing major global challenges from climate and health to economic resilience. Although increasingly perceived as fundamental socio-economic units, the detailed fabric of urban economic activities is only now accessible to comprehensive analyses with the availability of large datasets. Here, we study abundances of business categories across U.S. metropolitan statistical areas to investigate how diversity of economic activities depends on city size. A universal structure common to all cities is revealed, manifesting self-similarity in internal economic structure as well as aggregated metrics (GDP, patents, crime). A derivation is presented that explains universality and the observed empirical distribution. The model incorporates a generalized preferential attachment process with ceaseless introduction of new business types. Combined with scaling analyses for individual categories, the theory quantitatively predicts how individual business types systematically change rank with city size, thereby providing a quantitative means for estimating their expected abundances as a function of city size. These results shed light on processes of economic differentiation with scale, suggesting a general structure for the growth of national economies as integrated urban systems., Comment: Press embargo in place until publication

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 figures

Understanding the factors driving innovation in energy technologies is of critical importance to mitigating climate change and addressing other energy-related global challenges. Low levels of innovation, measured in terms of energy patent filings, were noted in the 1980s and 90s as an issue of concern and were attributed to low investment in public and private research and development (R&D). Here we build a comprehensive global database of energy patents covering the period 1970-2009 which is unique in its temporal and geographical scope. Analysis of the data reveals a recent, marked departure from historical trends. A sharp increase in rates of patenting has occurred over the last decade, particularly in renewable technologies, despite continued low levels of R&D funding. To solve the puzzle of fast innovation despite modest R&D increases we develop a model that explains the nonlinear response observed in the empirical data of technological innovation to various types of investment. The model reveals a regular relationship between patents, R&D funding, and growing markets across technologies, and accurately predicts patenting rates at different stages of technological maturity and market development. We show quantitatively how growing markets have formed a vital complement to public R&D in driving innovative activity; these two forms of investment have each leveraged the effect of the other in driving patenting trends over long periods of time.

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 publication

The size of cities is known to play a fundamental role in social and economic life. Yet, its relation to the structure of the underlying network of human interactions has not been investigated empirically in detail. In this paper, we map society-wide communication networks to the urban areas of two European countries. We show that both the total number of contacts and the total communication activity grow superlinearly with city population size, according to well-defined scaling relations and resulting from a multiplicative increase that affects most citizens. Perhaps surprisingly, however, the probability that an individual's contacts are also connected with each other remains largely unaffected. These empirical results predict a systematic and scale-invariant acceleration of interaction-based spreading phenomena as cities get bigger, which is numerically confirmed by applying epidemiological models to the studied networks. Our findings should provide a microscopic basis towards understanding the superlinear increase of different socioeconomic quantities with city size, that applies to almost all urban systems and includes, for instance, the creation of new inventions or the prevalence of certain contagious diseases.

Spatial search problems abound in the real world, from locating hidden nuclear or chemical sources to finding skiers after an avalanche. We exemplify the formalism and solution for spatial searches involving two agents that may or may not choose to share information during a search. For certain classes of tasks, sharing information between multiple searchers makes cooperative searching advantageous. In some examples, agents are able to realize synergy by aggregating information and moving based on local judgments about maximal information gathering expectations. We also explore one- and two-dimensional simplified situations analytically and numerically to provide a framework for analyzing more complex problems. These general considerations provide a guide for designing optimal algorithms for real-world search problems., Comment: Journal of Intelligence Community Research and Development, permanently available on Intelink, October 2010

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, 2009

Can lateral connectivity in the primary visual cortex account for the time dependence and intrinsic task difficulty of human contour detection? To answer this question, we created a synthetic image set that prevents sole reliance on either low-level visual features or high-level context for the detection of target objects. Rendered images consist of smoothly varying, globally aligned contour fragments (amoebas) distributed among groups of randomly rotated fragments (clutter). The time course and accuracy of amoeba detection by humans was measured using a two-alternative forced choice protocol with self-reported confidence and variable image presentation time (20-200 ms), followed by an image mask optimized so as to interrupt visual processing. Measured psychometric functions were well fit by sigmoidal functions with exponential time constants of 30-91 ms, depending on amoeba complexity. Key aspects of the psychophysical experiments were accounted for by a computational network model, in which simulated responses across retinotopic arrays of orientation-selective elements were modulated by cortical association fields, represented as multiplicative kernels computed from the differences in pairwise edge statistics between target and distractor images. Comparing the experimental and the computational results suggests that each iteration of the lateral interactions takes at least 37.5 ms of cortical processing time. Our results provide evidence that cortical association fields between orientation selective elements in early visual areas can account for important temporal and task-dependent aspects of the psychometric curves characterizing human contour perception, with the remaining discrepancies postulated to arise from the influence of higher cortical areas., Comment: 18 pages, 8 figures

During development, the mammalian brain differentiates into specialized regions with distinct functional abilities. While many factors contribute to functional specialization, we explore the effect of neuronal density on the development of neuronal interactions in vitro. Two types of cortical networks, dense and sparse, with 50,000 and 12,000 total cells respectively, are studied. Activation graphs that represent pairwise neuronal interactions are constructed using a competitive first response model. These graphs reveal that, during development in vitro, dense networks form activation connections earlier than sparse networks. Link entropy analysis of dense net- work activation graphs suggests that the majority of connections between electrodes are reciprocal in nature. Information theoretic measures reveal that early functional information interactions (among 3 cells) are synergetic in both dense and sparse networks. However, during later stages of development, previously synergetic relationships become primarily redundant in dense, but not in sparse networks. Large link entropy values in the activation graph are related to the domination of redundant ensembles in late stages of development in dense networks. Results demonstrate differences between dense and sparse networks in terms of informational groups, pairwise relationships, and activation graphs. These differences suggest that variations in cell density may result in different functional specialization of nervous system tissue in vivo., Comment: 10 pages, 7 figures

We present a general information theoretic approach for identifying functional subgraphs in complex networks where the dynamics of each node are observable. We show that the uncertainty in the state of each node can be expressed as a sum of information quantities involving a growing number of correlated variables at other nodes. We demonstrate that each term in this sum is generated by successively conditioning mutual informations on new measured variables, in a way analogous to a discrete differential calculus. The analogy to a Taylor series suggests efficient search algorithms for determining the state of a target variable in terms of functional groups of other degrees of freedom. We apply this methodology to electrophysiological recordings of networks of cortical neurons grown it in vitro. Despite strong stochasticity, we show that each cell's patterns of firing are generally explained by the activity of a small number of other neurons. We identify these neuronal subgraphs in terms of their mutually redundant or synergetic character and reconstruct neuronal circuits that account for the state of each target cell., Comment: 4 pages, 4 figures

We apply an information theoretic treatment of action potential time series measured with microelectrode arrays to estimate the connectivity of mammalian neuronal cell assemblies grown {\it in vitro}. We infer connectivity between two neurons via the measurement of the mutual information between their spike trains. In addition we measure higher point multi-informations between any two spike trains conditional on the activity of a third cell, as a means to identify and distinguish classes of functional connectivity among three neurons. The use of a conditional three-cell measure removes some interpretational shortcomings of the pairwise mutual information and sheds light into the functional connectivity arrangements of any three cells. We analyze the resultant connectivity graphs in light of other complex networks and demonstrate that, despite their {\it ex vivo} development, the connectivity maps derived from cultured neural assemblies are similar to other biological networks and display nontrivial structure in clustering coefficient, network diameter and assortative mixing. Specifically we show that these networks are weakly disassortative small world graphs, which differ significantly in their structure from randomized graphs with the same degree. We expect our analysis to be useful in identifying the computational motifs of a wide variety of complex networks, derived from time series data., Comment: 12 pages, 5 figures

Email graphs have been used to illustrate general properties of social networks of communication and collaboration. However, increasingly, the majority of email traffic reflects opportunistic, rather than symbiotic social relations. Here we use e-mail data drawn from a large university to construct directed graphs of email exchange that quantify the differences between social and antisocial behaviors in networks of communication. We show that while structural characteristics typical of other social networks are shared to a large extent by the legitimate component they are not characteristic of antisocial traffic. Interestingly, opportunistic patterns of behavior do create nontrivial graphs with certain general characteristics that we identify. To complement the graph analysis, which suffers from incomplete knowledge of users external to the domain, we study temporal patterns of communication to show that the dynamical properties of email traffic can, in principle, distinguish different types of social relations., Comment: 8 pages and 10 figures

We propose a new detection algorithm that uses structural relationships between senders and recipients of email as the basis for the identification of spam messages. Users and receivers are represented as vectors in their reciprocal spaces. A measure of similarity between vectors is constructed and used to group users into clusters. Knowledge of their classification as past senders/receivers of spam or legitimate mail, comming from an auxiliary detection algorithm, is then used to label these clusters probabilistically. This knowledge comes from an auxiliary algorithm. The measure of similarity between the sender and receiver sets of a new message to the center vector of clusters is then used to asses the possibility of that message being legitimate or spam. We show that the proposed algorithm is able to correct part of the false positives (legitimate messages classified as spam) using a testbed of one week smtp log.

Email is an increasingly important and ubiquitous means of communication, both facilitating contact between private individuals and enabling rises in the productivity of organizations. However the relentless rise of automatic unauthorized emails, a.k.a. spam is eroding away much of the attractiveness of email communication. Most of the attention dedicated to date to spam detection has focused on the content of the emails or on the addresses or domains associated with spam senders. Although methods based on these - easily changeable - identifiers work reasonably well they miss on the fundamental nature of spam as an opportunistic relationship, very different from the normal mutual relations between senders and recipients of legitimate email. Here we present a comprehensive graph theoretical analysis of email traffic that captures these properties quantitatively. We identify several simple metrics that serve both to distinguish between spam and legitimate email and to provide a statistical basis for models of spam traffic., Comment: 9 pages, 21 figures

The population dynamics underlying the diffusion of ideas hold many qualitative similarities to those involved in the spread of infections. In spite of much suggestive evidence this analogy is hardly ever quantified in useful ways. The standard benefit of modeling epidemics is the ability to estimate quantitatively population average parameters, such as interpersonal contact rates, incubation times, duration of infectious periods, etc. In most cases such quantities generalize naturally to the spread of ideas and provide a simple means of quantifying sociological and behavioral patterns. Here we apply several paradigmatic models of epidemics to empirical data on the advent and spread of Feynman diagrams through the theoretical physics communities of the USA, Japan, and the USSR in the period immediately after World War II. This test case has the advantage of having been studied historically in great detail, which allows validation of our results. We estimate the effectiveness of adoption of the idea in the three communities and find values for parameters reflecting both intentional social organization and long lifetimes for the idea. These features are probably general characteristics of the spread of ideas, but not of common epidemics., Comment: 31 pages, 8 figures, update in section 2

We generalize the standard computation of homogeneous nucleation theory at zero temperature to a scenario in which the bubble shape is determined self-consistently with its quantum fluctuations. Studying two scalar models in 1+1 dimensions, we find the self-consistent bounce by employing a two-particle irreducible (2PI) effective action in imaginary time at the level of the Hartree approximation. We thus obtain an effective single bounce action which determines the rate exponent. We use collective coordinates to account for the translational invariance and the growth instability of the bubble and finally present a new nucleation rate prefactor. We compare the results with those obtained using the standard 1-loop approximation and show that the self-consistent rate can differ by several orders of magnitude., Comment: 28 pages, revtex, 7 eps figures

Many quantum field theoretical models possess non-trivial solutions which are stable for topological reasons. We construct a self-consistent example for a self-interacting scalar field--the quantum (or dressed) kink--using a two particle irreducible effective action in the Hartree approximation. This new solution includes quantum fluctuations determined self-consistently and nonperturbatively at the 1-loop resummed level and allowed to backreact on the classical mean-field profile. This dressed kink is static under the familiar Hartree equations for the time evolution of quantum fields. Because the quantum fluctuation spectrum is lower lying in the presence of the defect, the quantum kink has a lower rest energy than its classical counterpart. However its energy is higher than well-known strict 1-loop results, where backreaction and fluctuation self-interactions are omitted. We also show that the quantum kink exists at finite temperature and that its profile broadens as temperature is increased until it eventually disappears., Comment: 13 pages, latex, 3 eps figures; revised with yet additional references, minor rewording

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 RevTex

Social trends or fashions are spontaneous collective decisions made by large portions of a community, often without an apparent good reason. The spontaneous formation of trends provides a well documented mechanism for the spread of information across a population, the creation of culture and the self-regulation of social behavior. Here I introduce an agent based dynamical model that captures the essence of trend formation and collapse. The resulting population dynamics alternates states of great diversity (large configurational entropy) with the dominance by a few trends. This behavior displays a kind of self-organized criticality, measurable through cumulants analogous to those used to study percolation. I also analyze the robustness of trend dynamics subject to external influences, such as population growth or contraction and in the presence of explicit information biases. The resulting population response gives insights about the fragility of public opinion in specific circumstances and suggests how it may be driven to produce social consensus or dissonance., Comment: 23 pages, 15 figures, uses RevTex

I present a summary of recent work \cite{BRS} where we describe the time-evolution of a region of disoriented chiral condensate via Langevin field equations for the linear $\sigma$ model. We analyze the model in equilibrium, paying attention to subtracting ultraviolet divergent classical terms and replacing them by their finite quantum counterparts. We use results from lattice gauge theory and chiral perturbation theory to fix nonuniversal constants. The result is a ultraviolet cutoff independent theory that reproduces quantitatively the expected equilibrium behavior of pion and $\sigma$ quantum fields. We also estimate the viscosity $\eta(T)$, which controls the dynamical timescale in the Langevin equation, so that the near equilibrium dynamical response agrees with theoretical expectations., Comment: 3 pages, 3 figures, contribution to the proceedings of Lattice02

We study the dynamical evolution of a phase interface or bubble in the context of a \lambda \phi^4 + g \phi^6 scalar quantum field theory. We use a self-consistent mean-field approximation derived from a 2PI effective action to construct an initial value problem for the expectation value of the quantum field and two-point function. We solve the equations of motion numerically in (1+1)-dimensions and compare the results to the purely classical evolution. We find that the quantum fluctuations dress the classical profile, affecting both the early time expansion of the bubble and the behavior upon collision with a neighboring interface., Comment: 12 pages, multiple figures

We determine the detailed thermodynamic behavior of vortices in the O(2) scalar model in 2D and of global monopoles in the O(3) model in 3D. We construct new numerical techniques, based on cluster decomposition algorithms, to analyze the point defect configurations. We find that these criteria produce results for the Kosterlitz-Thouless temperature in agreement with a topological transition between a polarizable insulator and a conductor, at which free topological charges appear in the system. For global monopoles we find no pair unbinding transition. Instead a transition to a dense state where pairs are no longer distinguishable occurs at T3 are drawn, based on the observed behavior., Comment: 14 pages, REVTEX, 13 eps figures

Hydrodynamic behavior is a general feature of interacting systems with many degrees of freedom constrained by conservation laws. To date hydrodynamic scaling in relativistic quantum systems has been observed in many high energy settings, from cosmic ray detections to accelerators, with large particle multiplicity final states. Here we show first evidence for the emergence of hydrodynamic scaling in the dynamics of a relativistic quantum field theory. We consider a simple scalar $\lambda \phi^4$ model in 1+1 dimensions in the Hartree approximation and study the dynamics of two colliding kinks at relativistic speeds as well as the decay of a localized high energy density region. The evolution of the energy-momentum tensor determines the dynamical local equation of state and allows the measurement of the speed of sound. Hydrodynamic scaling emerges at high local energy densities., Comment: 4 pages, 4 color eps figures, uses RevTex, v2 some typos corrected and references added

We examine the formation of vortices during the nonequilibrium relaxation of a high-temperature initial state of an Abelian-Higgs system. We equilibrate the scalar and gauge fields using gauge-invariant Langevin equations and relax the system by instantaneously removing thermal fluctuations. For couplings near critical we observe the formation of large clusters of like-sign magnetic vortices. Their appearance has implications for the dynamics of the phase transition, for the observed distribution of topological defects and for late-time phase ordering kinetics. We offer explanations for both the observed vortex densities and vortex configurations., Comment: 4 pages, 6 figures, RevTex. Moderate rewriting with added references. Main conclusions unchanged

Using both analytical arguments and detailed numerical evidence we show that the first order transition in the type-I 2D Abelian Higgs model can be understood in terms of the statistical mechanics of vortices, which behave in this regime as an ensemble of attractive particles. The well-known instabilities of such ensembles are shown to be connected to the process of phase nucleation. By characterizing the equation of state for the vortex ensemble we show that the temperature for the onset of a clustering instability is in qualitative agreement with the critical temperature. Below this point the vortex ensemble collapses to a single cluster, which is a non-extensive phase, and disappears in the absence of net topological charge. The vortex description provides a detailed mechanism for the first order transition, which applies at arbitrarily weak type-I and is gauge invariant unlike the usual field-theoretic considerations, which rely on asymptotically large gauge coupling., Comment: 4 pages, 6 figures, uses RevTex. Additional references added, some small corrections to the text

As the matter produced in a relativistic heavy ion collision cools through the QCD phase transition, the dynamical evolution of the chiral condensate will be driven out of thermal equilibrium. As a prelude to analyzing this evolution, and in particular as a prelude to learning how rapid the cooling must be in order for significant deviations from equilibrium to develop, we present a detailed analysis of the time-evolution of an idealized region of disoriented chiral condensate. We set up a Langevin field equation which can describe the evolution of these (or more realistic) linear sigma model configurations in contact with a heat bath representing the presence of other shorter wavelength degrees of freedom. We first analyze the model in equilibrium, paying particular attention to subtracting ultraviolet divergent classical terms and replacing them by their finite quantum counterparts. We use known results from lattice gauge theory and chiral perturbation theory to fix nonuniversal constants. The result is a theory which is ultraviolet cutoff independent and that reproduces quantitatively the expected equilibrium behavior of the quantum field theory of pions and sigma fields over a wide range of temperatures. Finally, we estimate the viscosity $\eta(T)$, which controls the dynamical timescale in the Langevin equation, by requiring that the timescale for DCC decay agrees with previous calculations. The resulting $\eta(T)$ is larger than that found perturbatively. We also determine the temperature below which the classical field Langevin equation ceases to be a good model for the quantum field dynamics., Comment: 19 pages, 7 figures, uses RevTex; v2 very small change to the caption of Fig.7. Version to appear in Nucl. phys. A

We study the dynamics of a spatially inhomogeneous quantum $\lambda \phi^4$ field theory in 1+1 dimensions in the Hartree approximation. In particular, we investigate the long-time behavior of this approximation in a variety of controlled situations, both at zero and finite temperature. The observed behavior is much richer than that in the spatially homogeneous case. Nevertheless, we show that the fields fail to thermalize in a canonical sense, as expected from analogous results in closely related (mean field) transport theory. We argue that this dynamical approximation is best suited as a means to study the short-time decay of spatially inhomogeneous fields and in the dynamics of coherent quasi-classical inhomogeneous configurations (e.g. solitons) in a background of dynamical self-consistent quantum fluctuations., Comment: 22 pages, 8 figures, uses Revtex

I consider several Langevin and Fokker-Planck classes of dynamics for scalar field theories in contact with a thermal bath at temperature T. These models have been applied recently in the numerical description of the dynamics of second order phase transitions and associated topological defect formation as well as in other studies of these critical phenomena. Closed form solutions of the Fokker-Planck equation are given for the harmonic potential and a dynamical mean-field approximation is developed. These methods allow for an analytical discussion of the behavior of the theories in several circumstances of interest such as critical slowing down at a second order transition and the development of spinodal instabilities. These insights allow for a more detailed understanding of several numerical studies in the literature., Comment: 10 pages, no figures, uses RevTex

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. B