Tracking random walks.

In empirical studies, trajectories of animals or individuals are sampled in space and time. Yet, it is unclear how sampling procedures bias the recorded data. Here, we consider the important case of movements that consist of alternating rests and moves of random durations and study how the estimate of their statistical properties is affected by the way we measure them.

Balancing building and maintenance costs in growing transport networks.

The costs associated to the length of links impose unavoidable constraints to the growth of natural and artificial transport networks. When future network developments cannot be predicted, the costs of building and maintaining connections cannot be minimized simultaneously, requiring competing optimization mechanisms. Here, we study a one-parameter nonequilibrium model driven by an optimization functional, defined as the convex combination of building cost and maintenance cost.

Patterns of Residential Segregation.

The spatial distribution of income shapes the structure and organisation of cities and its understanding has broad societal implications. Despite an abundant literature, many issues remain unclear. In particular, all definitions of segregation are implicitely tied to a single indicator, usually rely on an ambiguous definition of income classes, without any consensus on how to define neighbourhoods and to deal with the polycentric organization of large cities.

A typology of street patterns.

We propose a quantitative method to classify cities according to their street pattern. We use the conditional probability distribution of shape factor of blocks with a given area and define what could constitute the 'fingerprint' of a city. Using a simple hierarchical clustering method, these fingerprints can then serve as a basis for a typology of cities.

Scaling in transportation networks.

Subway systems span most large cities, and railway networks most countries in the world. These networks are fundamental in the development of countries and their cities, and it is therefore crucial to understand their formation and evolution. However, if the topological properties of these networks are fairly well understood, how they relate to population and socio-economical properties remains an open question.

How congestion shapes cities: from mobility patterns to scaling.

The recent availability of data for cities has allowed scientists to exhibit scalings which present themselves in the form of a power-law dependence on population of various socio-economical and structural indicators. We propose here a stochastic theory of urban growth which accounts for some of the observed scalings and we confirm these predictions on US and OECD empirical data. In particular, we show that the dependence on population size of the total number of miles driven daily, the total length of the road network, the total traffic delay, the total consumption of gasoline, the quantity of CO2 emitted and the relation between area and population of cities, are all governed by a single parameter which characterizes the sensitivity to congestion.

Universal size effects for populations in group-outcome decision-making problems.

Elections constitute a paradigm of decision-making problems that have puzzled experts of different disciplines for decades. We study two decision-making problems, where groups make decisions that impact only themselves as a group. In both studied cases, participation in local elections and the number of democratic representatives at different scales (from local to national), we observe a universal scaling with the constituency size.

Modeling the polycentric transition of cities.

Empirical evidence suggests that most urban systems experience a transition from a monocentric to a polycentric organization as they grow and expand. We propose here a stochastic, out-of-equilibrium model of the city, which explains the appearance of subcenters as an effect of traffic congestion. We show that congestion triggers the instability of the monocentric regime and that the number of subcenters and the total commuting distance within a city scale sublinearly with its population, predictions that are in agreement with data gathered for around 9000 U.

Emergence of hierarchy in cost-driven growth of spatial networks.

One of the most important features of spatial networks--such as transportation networks, power grids, the Internet, and neural networks--is the existence of a cost associated with the length of links. Such a cost has a profound influence on the global structure of these networks, which usually display a hierarchical spatial organization. The link between local constraints and large-scale structure is not elucidated, however, and we introduce here a generic model for the growth of spatial networks based on the general concept of cost-benefit analysis.