A model of urban scaling laws based on distance dependent interactions

Abstract

Socio-economic related properties of a city grow faster than a linear relationship with the population, in a log–log plot, the so-called superlinear scaling. Conversely, the larger a city, the more efficient it is in the use of its infrastructure, leading to a sublinear scaling on these variables. In this work, we addressed a simple explanation for those scaling laws in cities based on the interaction range between the citizens and on the fractal properties of the cities. To this purpose, we introduced a measure of social potential which captured the influence of social interaction on the economic performance and the benefits of amenities in the case of infrastructure offered by the city. We assumed that the population density depends on the fractal dimension and on the distance-dependent interactions between individuals. The model suggests that when the city interacts as a whole, and not just as a set of isolated parts, there is improvement of the socio-economic indicators. Moreover, the bigger the interaction range between citizens and amenities, the bigger the improvement of the socio-economic indicators and the lower the infrastructure costs of the city. We addressed how public policies could take advantage of these properties to improve cities development, minimizing negative effects. Furthermore, the model predicts that the sum of the scaling exponents of social-economic and infrastructure variables are 2, as observed in the literature. Simulations with an agent-based model are confronted with the theoretical approach and they are compatible with the empirical evidences.

Negative Outcomes of Individual Spatial Distance Reductions in Urban Environments: A Theoretical Analysis of Entropic Organizational Citizenship Behavior and Toxic Organizations in Urban Deconstruction

“…Theil [3], conceptualizes entropy as a measure of dividedness and dispersion in the development of his "evenness of spread" entropy concept. Theil's [3], notion of entropy is regarded as providing the conceptual base for the development of a formal model of organizational citizenship entropy outlined in the current paper in relation the delineation of a toxic organizational heuristic built from specific negative OCE processes arising from spatial reductions in individual interactions afforded by urban environments [4] which can infect other organizations and lead to more general urban entropic deconstruction [6.]. Landsberg [13], proposes a simple order/disorder entropy theory based on thermodynamics and information theory which defines entropy (total disorder) in a system that arises when a system's capacity for disorder is 'overwhelmed' by its capacity for absorbing further information.…”

“…In a similar individual interaction level micro, bottom-up analysis Ribeiro et al [4], indicate that, "When humanity built the first cities, they brought individuals previously separated by space, increasing social and economic interactions, through the shared infrastructure of the cities, in a more constant and efficient way. Since then, the city as a social organization of humanity has become an important place to create interactions in space and time between individuals".…”

“…Although, Ribeiro et al [4] point out that: "We are not modelling the mechanisms behind how an individual may influence others. We are just considering that the influence strength decays over the social network through distance in a pairwise interaction at the micro level", they clearly state in their model that the influence of reductions in space between individuals afforded by city living increases interactions that generate specific overall benefits.…”

Cities, from information to interaction

“…The linear form of this city allows continuous movement across a sequence of locations, eliminating centrality factors while taking into account periodic boundary conditions in order to reduce border effects, eliminating the role of topology while isolating the problem of physical distance [89]. Our hypothesis is that as (a) physical proximity latent in environmental information 1 tends to increase interactions between agents [90][91][92], its association with (b) environmental information 2 created by diversity in locational patterns increases the potential for interactions and the coordination of actions, leading to reductions in the entropy of action in enacted information 3.…”

Social Interaction and the City: The Effect of Space on the Reduction of Entropy

“…If they could, and given the fact that they are formed by space and that space is not fully malleable, is it reasonable to suppose that certain spatial formations could ease such momentary connections? We know that proximity increases the intensity of interaction [52,53]. But what form should urbanized space take in order to meet such systemic expectations?…”