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The spatial heterogeneity of cities -- the uneven distribution of population and activities -- is fundamental to urban dynamics and related to critical issues such as infrastructure overload, housing affordability, and social inequality.…

As the African continent continues to urbanise, cities are becoming increasingly central to the transformations of societies and economies. Many studies highlight the limits of urban planning in these cities, emphasising the high share of…

The emerging field of the Science of Cities has unveiled previously undiscovered facets of urban life. Contrary to the expectation of chaotic behaviour influenced solely by cultural and geographic factors, cities globally exhibit universal…

This chapter investigates the concept of living structure - which is defined as a structural hierarchy that has a recurring pattern of an abundance of small substructures compared to larger ones - and the application of such structures in…

Cities can be characterised and modelled through different urban measures. Consistency within these observables is crucial in order to advance towards a science of cities. Bettencourt et al have proposed that many of these urban measures…

The spatial structure of modern cities exhibits highly diverse patterns and keeps evolving under numerous constraints. Two key dimensions have recently achieved prominence in characterizing this diversity: heterogeneity and spreading.…

In this paper, we present a modelling experiment developed to study systems of cities and processes of urbanisation in large territories over long time spans. Building on geographical theories of urban evolution, we rely on agent-based…

The spatial arrangement of urban hubs and centers and how individuals interact with these centers is a crucial problem with many applications ranging from urban planning to epidemiology. We utilize here in an unprecedented manner the large…

We call for a theory of the particle-scale structure of materials that is based on the general notion of information rather than its special case of symmetry. An inherent limitation to the symmetry-based understanding of structure is…

We show that the way in which the Shannon entropy of sequences produced by an information source converges to the source's entropy rate can be used to monitor how an intelligent agent builds and effectively uses a predictive model of its…

Collective organization in matter plays a significant role in its expressed physical properties. Typically, it is detected via an order parameter, appropriately defined for each given system's observed emergent patterns. Recent developments…

Urban population density always follows the exponential distribution and can be described with Clark's model. Because of this, the spatial distribution of urban population used to be regarded as non-fractal pattern. However, Clark's model…

Different models of random walks on the dual graphs of compact urban structures are considered. Analysis of access times between streets helps to detect the city modularity. The statistical mechanics approach to the ensembles of lazy random…

Urban density, in the form of residents' and visitors' concentration, is long considered to foster diverse exchanges of interpersonal knowledge and skills, which are intrinsic to sustainable human settlements. However, with current urban…

Analyses of urban scaling laws assume that observations in different cities are independent of the existence of nearby cities. Here we introduce generative models and data-analysis methods that overcome this limitation by modelling…

We present a novel, model-independent framework for studying the architecture of an exoplanetary system at the system level. This framework allows us to characterise, quantify, and classify the architecture of an individual planetary…

We propose and test a model that describes the morphology of cities, the scaling of the urban perimeter of individual cities, and the area distribution of systems of cities. The model is also consistent with observable urban growth…

The encoding of cities into non-planar dual graphs reveals their complex structure. We investigate the statistics of the typical space syntax measures for the five different compact urban patterns. Universal statistical behavior of space…

Urban cultures and architectural styles vary significantly across cities due to geographical, chronological, historical, and socio-political factors. Understanding these differences is essential for anticipating how cities may evolve in the…

Entanglement measures based on a logarithmic functional form naturally emerge in any attempt to quantify the degree of entanglement in the state of a multipartite quantum system. These measures can be regarded as generalizations of the…