Related papers: The growth equation of cities
Understanding the morphology of an urban system is an important step toward unveiling the dynamical processes of its growth and development. At the foundation of every urban system, transportation system is undeniably a crucial component in…
The advent of geographic online social networks such as Foursquare, where users voluntarily signal their current location, opens the door to powerful studies on human movement. In particular the fine granularity of the location data, with…
The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…
We consider the scaling laws, second-order statistics and entropy of the consumed energy of metropolis cities which are hybrid complex systems comprising social networks, engineering systems, agricultural output, economic activity and…
Urban-induced microclimate variations, such as urban heat islands and air pollution, scale with city size, producing distinctive relations between average climate variables and city-scale quantities (e.g., total population). However, these…
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…
In the present paper, our goal is to establish a framework for the mathematical modelling and the analysis of the spread of an epidemic in a large population commuting regularly, typically along a time-periodic pattern, as is roughly…
Spatial distribution of the human population is distinctly heterogeneous, e.g. showing significant difference in the population density between urban and rural areas. In the historical perspective, i.e. on the timescale of centuries, the…
Natural languages are full of rules and exceptions. One of the most famous quantitative rules is Zipf's law which states that the frequency of occurrence of a word is approximately inversely proportional to its rank. Though this `law' of…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
Urban space is highly heterogeneous, with population and human activities concentrating in localized centers. However, the global organization of such intra-urban centers remains poorly understood due to the lack of consistent, comparable…
Understanding if and how mutants reach fixation in populations is an important question in evolutionary biology. We study the impact of population growth has on the success of mutants. To systematically understand the effects of growth we…
The coupling between population growth and transport accessibility has been an elusive problem for more than 60 years now. Due to the lack of theoretical foundations, most of the studies that considered how the evolution of transportation…
Urban systems present hierarchical structures at many different scales. These are observed as administrative regional delimitations which are the outcome of complex geographical, political and historical processes which leave almost…
Recent studies of urban scaling show that important socioeconomic city characteristics such as wealth and innovation capacity exhibit a nonlinear, particularly a power law scaling with population size. These nonlinear effects are common to…
The question as to why most higher organisms reproduce sexually has remained open despite extensive research, and has been called "the queen of problems in evolutionary biology". Theories dating back to Weismann have suggested that the key…
Chaos associated with bifurcation makes a new science, but the origin and essence of chaos are not yet clear. Based on the well-known logistic map, chaos used to be regarded as intrinsic randomicity of determinate dynamics systems. However,…
We study the influence that population density and the road network have on each others' growth and evolution. We use a simple model of formation and evolution of city roads which reproduces the most important empirical features of street…
Cities are physical manifestations of our competitive and cooperative behaviours. The tension between these two forces generates dynamic equilibriums whose material expressions are cities and their evolutions. In a Darwinian cooperative…
We study a mathematical model to describe the evolution of a city, which is determined by the interaction of two large populations of agents, workers and firms. The map of the city is described by a network with the edges representing at…