The dynamics of urban systems can be understood from an evolutionary perspective, in some sense extending biological and cultural evolution. Models for systems of cities implementing elementary evolutionary processes remain however to be investigated. We propose here such a model for urban dynamics at the macroscopic scale, in which the diffusion of innovations between cities captures transformation processes (mutations) and transmission processes (diffusion), using two coupled spatial interaction models. Explorations of the model on synthetic systems of cities show the role of spatial interaction and innovation diffusion ranges on measures of diversity and utility, and the existence of intermediate ranges yielding an optimal utility. Multi-objective optimization shows how the model produces a compromise between utility and diversity. This model paves the way towards more elaborated formalizations of urban evolution.
While great emphasis has been placed on the role of social interactions as driver of innovation growth, very few empirical studies have explicitly investigated the impact of social network structures on the innovation performance of cities. Past research has mostly explored scaling laws of socio-economic outputs of cities as determined by, for example, the single predictor of population. Here, by drawing on a publicly available dataset of the startup ecosystem, we build the first Workforce Mobility Network among US metropolitan areas. We found that node centrality computed on this network acco…
Successful innovations achieve large geographical coverage by spreading across settlements and distances. For decades, spatial diffusion has been argued to take place along the urban hierarchy such that the innovation first spreads from large to medium cities then later from medium to small cities. Yet, the role of geographical distance, the other major factor of spatial diffusion, was difficult to identify in hierarchical diffusion due to missing data on spreading events. In this paper, we exploit spatial patterns of individual invitations on a social media platform sent from registered users…
Over the years, the growing availability of extensive datasets about registered patents allowed researchers to better understand technological innovation drivers. In this work, we investigate how the technological contents of patents characterise the development of metropolitan areas and how innovation is related to GDP per capita. Exploiting worldwide data from 1980 to 2014, and through network-based techniques that only use information about patents, we identify coherent distinguished groups of metropolitan areas, either clustered in the same geographical area or similar from an economic poi…
Only a fast and global transformation towards decarbonization and sustainability can keep the Earth in a civilization-friendly state. As hotspots for (green) innovation and experimentation, cities could play an important role in this transition. They are also known to profit from each other's ideas, with policy and technology innovations spreading to other cities. In this way, cities can be conceptualized as nodes in a globe-spanning learning network. The dynamics of this process are important for society's response to climate change and other challenges, but remain poorly understood on a macr…
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-in…
We study a stochastic model of urban growth generating spatial distributions of population densities at an intermediate mesoscopic scale. The model is based on the antagonist interplay between the two opposite abstract processes of aggregation (preferential attachment) and diffusion (urban sprawl). Introducing indicators to quantify precisely urban form, the model is first statistically validated and intensively explored to understand its complex behavior across the parameter space. We then compute real morphological measures on local areas of size 50km covering all European Union, and show th…
Superlinear scaling in cities, which appears in sociological quantities such as economic productivity and creative output relative to urban population size, has been observed but not been given a satisfactory theoretical explanation. Here we provide a network model for the superlinear relationship between population size and innovation found in cities, with a reasonable range for the exponent.
The access to an ever increasing amount of information in the modern world gave rise to the development of many quantitative indicators about urban regions in the globe. Therefore, there is a growing need for a precise definition of how to delimit urban regions, so as to allow proper respective characterization and modeling. Here we present a straightforward methodology to automatically detect urban region borders around a single seed point. The method is based on a diffusion process having street crossings and terminations as source points. We exemplify the potential of the methodology by cha…
The ways in which an innovation (e.g., new behaviour, idea, technology, product) diffuses among people can determine its success or failure. In this paper, we address the problem of diffusion of innovations over multiplex social networks where the neighbours of a person belong to one or multiple networks (or layers) such as friends, families, or colleagues. To this end, we generalise one of the basic game-theoretic diffusion models, called networked coordination game, for multiplex networks. We present analytical results for this extended model and validate them through a simulation study, fin…
Innovation diffusion has been studied extensively in a variety of disciplines, including sociology, economics, marketing, ecology, and computer science. Traditional literature on innovation diffusion has been dominated by models of aggregate behavior and trends. However, the agent-based modeling (ABM) paradigm is gaining popularity as it captures agent heterogeneity and enables fine-grained modeling of interactions mediated by social and geographic networks. While most ABM work on innovation diffusion is theoretical, empirically grounded models are increasingly important, particularly in guidi…
The spatial distribution of population and activities within urban areas, or urban form at the mesoscopic scale, is the outcome of multiple antagonist processes. We propose in this paper to benchmark different models of urban morphogenesis, to systematically compare the urban forms they can produce. Different types of approaches are included, such as a reaction-diffusion model, a gravity-based model, and correlated percolation. Applying a diversity search algorithm, we estimate the feasible space of each model within a space of urban form indicators, in comparison of empirical values for world…
Sustainable Development Goals are intrinsically competing, but their embedding into urban systems furthermore emphasises such compromises, due to spatial complexity, the non-optimal nature of such systems, and multi-objective aspects of their agents, among other reasons. We propose in this paper to use a stylised simulation model for systems of cities, focused on innovation diffusion and population dynamics, to show how trade-offs may operate at such a scale. We proceed in particular to a bi-objective optimisation of emissions and innovation utilities, and show that no single urban optimum exi…
Innovation diffusion in the networked population is an essential process that drives the progress of human society. Despite the recent advances in network science, a fundamental understanding of network properties that regulate such processes is still lacking. Focusing on an innovation diffusion model with pairwise transmission and macro-level social influence, i.e., more adopters in the networked population lead to a higher adoption tendency among the remaining individuals, we observe discontinuous phase transitions when the influence is sufficiently strong. Through extensive analyses of a la…
The current science of cities can provide a useful foundation for future urban policies, provided that these proposals have been validated by correct observations of the diversity of situations in the world. However, international comparisons of the evolution of cities often produce uncertain results because national territorial frameworks are not always in strict correspondence with the dynamics of urban systems. We propose to provide various compositions of systems of cities to better take into account the dynamic networking of cities that go beyond regional and national territorial boundari…
The municipal actors of the Catalan capital wish to obtain a reversal of the negative representations concerning the lack of attractiveness of the district of Poblenou considered as one of the poorest and most marginalized districts of the city while having as identity the expression of "Manchester southern Europe", recalling its role as a factory for Spain and an emblem of the Industrial Revolution for the Iberian Peninsula. Conceptualization, programming and construction of a new image of the city through this large urban wasteland are made concrete thanks to an urban marketing operation. Th…
Based on a recent model of paradigm shifts by Bornholdt et al., we studied mean-field opinion dynamics in an infinite population where an infinite number of ideas compete simultaneously with their values publicly known. We found that a highly innovative society is not characterized by heavy concentration in highly valued ideas: Rather, ideas are more broadly distributed in a more innovative society with faster progress, provided that the rate of adoption is constant, which suggests a positive correlation between innovation and technological disparity. Furthermore, the distribution is generally…
We introduce a heterogeneous network structure into the Bass diffusion model, in order to study the diffusion times of innovation or information in networks with a scale-free structure, typical of regions where diffusion is sensitive to geographic and logistic influences (like for instance Alpine regions). We consider both the diffusion peak times of the total population and of the link classes. In the familiar trickle-down processes the adoption curve of the hubs is found to anticipate the total adoption in a predictable way. In a major departure from the standard model, we model a trickle-up…
The interaction between cities and their respective green regions corresponds to an interesting issue that has received growing attention over the last decades. These relationships have multiple natures, ranging from providing habitat for animal life to temperature and humidity dynamics. Several methods based on area, size, shape, and distance have been considered in the literature. Given that several important contributions of green regions to urban areas involve temperature, humidity and gases (e.g.~oxygen) exchanges, which are intrinsically related to physical diffusion, it becomes particul…
Axelrod model describes the dissemination of a set of cultural traits in a society constituted by individual agents. In a social context, nevertheless, individual choices toward a specific attitude are also at the basis of the formation of communities, groups, parties. The membership in a group changes completely the behavior of single agents who start acting according to a social identity. Groups act and interact among them as single entities, but still conserve an internal dynamics. We show that, under certain conditions on social dynamics, the introduction of group dynamics in a cultural di…
When multiple innovations compete for adoption, historical chance leading to early advantage can generate lock-in effects that allow suboptimal innovations to succeed at the expense of superior alternatives. Research on the diffusion of innovafacetion has identified many possible sources of early advantage, but these mechanisms can benefit both optimal and suboptimal innovations. This paper moves beyond chance-as-explanation to identify structural principles that systematically impact the likelihood that the optimal strategy will spread. A formal model of innovation diffusion shows that the ne…
In this work, the aim is to study the diffusion of innovation of two competing products. The main focus has been to understand the effects of the competitive dynamic market on the diffusion of innovation. The global smartphone operating system sales are chosen as an example. The availability of the sales and the number of users data, as well as the predictions for the future number of users, make the smartphone diffusion a new laboratory to test the innovation of diffusion models for the competitive markets. In this work, the Bass model and its extensions which incorporate the competition betw…
It is shown that under certain conditions it is possible to model a complex system in a way that leads to results that do not depend on system size. As an example of complex system an innovation diffusion model is considered. In that model a set of individuals (the agents), which are interconnected, must decide if adopt or not an innovation. The agents are connected in a member of the networks family known as small worlds networks (SWN). It is found that for a subfamily of the SWN the saturation time and the form of the adoption curve are invariants respect to the change in the size of the sys…
A fundamental question related to innovation diffusion is how the social network structure influences the process. Empirical evidence regarding real-world influence networks is very limited. On the other hand, agent-based modeling literature reports different and at times seemingly contradictory results. In this paper we study innovation diffusion processes for a range of Watts-Strogatz networks in an attempt to shed more light on this problem. Using the so-called Sznajd model as the backbone of opinion dynamics, we find that the published results are in fact consistent and allow to predict th…
We present a new model for the diffusion of innovation. Here, the population is segmented into distinct groups. Adoption by a particular group of some cultural product may be inhibited both by large numbers of its own members already having adopted but also, in particular, by members of another group having adopted. Intergroup migration is also permitted. We determine the equilibrium points and carry out stability analysis for the model for a two-group population. We also simulate a discrete time version of the model. Lastly, we present data on tablet use in eight countries from 2012-2016 and …
Adoption of cultural innovation (e.g., music, beliefs, language) is often geographically correlated, with adopters largely residing within the boundaries of relatively few well-studied, socially significant areas. These cultural regions are often hypothesized to be the result of either (i) identity performance driving the adoption of cultural innovation, or (ii) homophily in the networks underlying diffusion. In this study, we show that demographic identity and network topology are both required to model the diffusion of innovation, as they play complementary roles in producing its spatial pro…
We generalize the classical Bass model of innovation diffusion to include a new class of agents --- Luddites --- that oppose the spread of innovation. Our model also incorporates ignorants, susceptibles, and adopters. When an ignorant and a susceptible meet, the former is converted to a susceptible at a given rate, while a susceptible spontaneously adopts the innovation at a constant rate. In response to the \emph{rate} of adoption, an ignorant may become a Luddite and permanently reject the innovation. Instead of reaching complete adoption, the final state generally consists of a population o…
The urban-rural divide is increasing in modern societies calling for geographical extensions of social influence modelling. Improved understanding of innovation diffusion across locations and through social connections can provide us with new insights into the spread of information, technological progress and economic development. In this work, we analyze the spatial adoption dynamics of iWiW, an Online Social Network (OSN) in Hungary and uncover empirical features about the spatial adoption in social networks. During its entire life cycle from 2002 to 2012, iWiW reached up to 300 million frie…
A model, applicable to a range of innovation diffusion applications with a strong peer to peer component, is developed and studied, along with methods for its investigation and analysis. A particular application is to individual households deciding whether to install an energy efficiency measure in their home. The model represents these individuals as nodes on a network, each with a variable representing their current state of adoption of the innovation. The motivation to adopt is composed of three terms, representing personal preference, an average of each individual's network neighbours' sta…
Urban morphogenesis is the process of formation of its elements and the specialization of its suburbs. Street networks are the structural part of the system. Understand their formation reveals crucial information about urban transformation and dynamics behind its functioning. In this work we focus on the morphogenesis of street networks and we study it through a spatial network generator model. This latter is composed by three layers (a reaction-diffusion layer, a dynamic vector field and a spatial network) surrounded by an environment. The emerging network feeds back to its morphogenetic elem…
We study the dynamics of the adoption of new products by agents with continuous opinions and discrete actions (CODA). The model is such that the refusal in adopting a new idea or product is increasingly weighted by neighbor agents as evidence against the product. Under these rules, we study the distribution of adoption times and the final proportion of adopters in the population. We compare the cases where initial adopters are clustered to the case where they are randomly scattered around the social network and investigate small world effects on the final proportion of adopters. The model pred…
Haynes et al. (1977) derived a nonlinear differential equation to determine the spread of innovations within a social network across space and time. This model depends upon the imitators and the innovators within the social system, where the imitators respond to internal influences, whilst the innovators react to external factors. Here, this differential equation is applied to simulate the uptake of a low-carbon technology (LCT) within a local electricity network situated in the UK. This network comprises of many households that are assigned to certain feeders. Firstly, travelling wave solutio…
The contagion threshold for diffusion of innovations is defined and calculated in finite graphs (two-dimensional regular lattices, regular random networks (RRNs), and two kinds of scale-free networks (SFNs)) with and without the bilingual option. Without the bilingual option, degree inhomogeneity and clustering enhance the contagion threshold in non-regular networks except for those with an unrealistically small average degree. It is explained by the friendship paradox and detour effect. We found the general boundary of the cost that makes the bilingual option effective. With a low-cost biling…
A micro-level agent-based model of innovation diffusion was developed that explicitly combines (a) an individual's perception of the advantages or relative utility derived from adoption, and (b) social influence from members of the individual's social network. The micro-model was used to simulate macro-level diffusion patterns emerging from different configurations of micro-model parameters. Micro-level simulation results matched very closely the adoption patterns predicted by the widely-used Bass macro-level model (Bass, 1969). For a portion of the domain, results from micro-simulations were …
Social identities are among the key factors driving behavior in complex societies. Signals of social identity are known to influence individual behaviors in the adoption of innovations. Yet the population-level consequences of identity signaling on the diffusion of innovations are largely unknown. Here we use both analytical and agent-based modeling to consider the spread of a beneficial innovation in a structured population in which there exist two groups who are averse to being mistaken for each other. We investigate the dynamics of adoption and consider the role of structural factors such a…
Axelrod's model for the dissemination of culture contains two key factors required to model the process of diffusion of innovations, namely, social influence (i.e., individuals become more similar when they interact) and homophily (i.e., individuals interact preferentially with similar others). The strength of these social influences are controlled by two parameters: $F$, the number of features that characterizes the cultures and $q$, the common number of states each feature can assume. Here we assume that the innovation is a new state of a cultural feature of a single individual -- the innova…
We propose a model for the diffusion of several products competing in a common market based on the generalization of the Ising model of statiscal mechanics (Potts model). Using an agent based implementation, we analyze two problems: (i) a three options case, i.e. to adopt a product A, a product B, or non-adoption and (ii) a four options case, i.e. the adoption of product A, product B, both, or none. In the first case we analyze a launching strategy for one of the two products, which delays its launching with the objective of competing with improvements. Market shares reached by each product ar…
The Triple Helix model of university-industry-government relations can be generalized from a neo-institutional model of networks to a neo-evolutionary model of how three selection environments operate upon one another. The neo-evolutionary model enables us to appreciate both organizational integration in university-industry-government relations and differentiation among functions like the generation of intellectual capital, creation of wealth, and their attending legislation. The specification of innovation systems in terms of nations, sectors, cities, and regions can then be formulated as emp…
The prevalence of many urban phenomena changes systematically with population size. We propose a theory that unifies models of economic complexity and cultural evolution to derive urban scaling. The theory accounts for the difference in scaling exponents and average prevalence across phenomena, as well as the difference in the variance within phenomena across cities of similar size. The central ideas are that a number of necessary complementary factors must be simultaneously present for a phenomenon to occur, and that the diversity of factors is logarithmically related to population size. The …
Why do some economic activities agglomerate more than others? And, why does the agglomeration of some economic activities continue to increase despite recent developments in communication and transportation technologies? In this paper, we present evidence that complex economic activities concentrate more in large cities. We find this to be true for technologies, scientific publications, industries, and occupations. Using historical patent data, we show that the urban concentration of complex economic activities has been continuously increasing since 1850. These findings suggest that the increa…
Cities are the drivers of socio-economic innovation, and are also forced to address the accelerating risk of failure in providing essential services such as water supply today and in the future. Here, we investigate the resilience of urban water supply security, which is defined in terms of the services that citizens receive. The resilience of services is determined by the availability and robustness of critical system elements, or 'capitals' (water resources, infrastructure, finances, management efficacy and community adaptation). We translate quantitative information about this portfolio of …
In the last decades, the notion that cities are in a state of equilibrium with a centralised organisation has given place to the viewpoint of cities in disequilibrium and organised from bottom to up. In this perspective, cities are evolving systems that exhibit emergent phenomena built from local decisions. While urban evolution promotes the emergence of positive social phenomena such as the formation of innovation hubs and the increase in cultural diversity, it also yields negative phenomena such as increases in criminal activity. Yet, we are still far from understanding the driving mechanism…
Diffusion of innovation can be interpreted as a social spreading phenomena governed by the impact of media and social interactions. Although these mechanisms have been identified by quantitative theories, their role and relative importance are not entirely understood, since empirical verification has so far been hindered by the lack of appropriate data. Here we analyse a dataset recording the spreading dynamics of the world's largest Voice over Internet Protocol service to empirically support the assumptions behind models of social contagion. We show that the rate of spontaneous service adopti…
Cities are inherently dynamic. Interesting patterns of behavior typically manifest at several key areas of a city over multiple temporal resolutions. Studying these patterns can greatly help a variety of experts ranging from city planners and architects to human behavioral experts. Recent technological innovations have enabled the collection of enormous amounts of data that can help in these studies. However, techniques using these data sets typically focus on understanding the data in the context of the city, thus failing to capture the dynamic aspects of the city. The goal of this work is to…
