Centre d'Analyse et de Mathématique Sociales

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 scale, real-time 'Oyster' card database of individual person movements in the London subway to reveal the structure and organization of the city. We show that patterns of intraurban movement are strongly heterogeneous in terms of volume, but not in terms of distance travelled, and that there is a polycentric structure composed of large flows organized around a limited number of activity centers. For smaller flows, the pattern of connections becomes richer and more complex and is not strictly hierarchical since it mixes different levels consisting of different orders of magnitude. This new understanding can shed light on the impact of new urban projects on the evolution of the polycentric configuration of a city and the dense structure of its centers and it provides an initial approach to modeling flows in an urban system.

Pervasive infrastructures, such as cell phone networks, enable to capture large amounts of human behavioral data but also provide information about the structure of cities and their dynamical properties. In this article, we focus on these last aspects by studying phone data recorded during 55 days in 31 Spanish cities. We first define an urban dilatation index which measures how the average distance between individuals evolves during the day, allowing us to highlight different types of city structure. We then focus on hotspots, the most crowded places in the city. We propose a parameter free method to detect them and to test the robustness of our results. The number of these hotspots scales sublinearly with the population size, a result in agreement with previous theoretical arguments and measures on employment datasets. We study the lifetime of these hotspots and show in particular that the hierarchy of permanent ones, which constitute the 'heart' of the city, is very stable whatever the size of the city. The spatial structure of these hotspots is also of interest and allows us to distinguish different categories of cities, from monocentric and "segregated" where the spatial distribution is very dependent on land use, to polycentric where the spatial mixing between land uses is much more important. These results point towards the possibility of a new, quantitative classification of cities using high resolution spatio-temporal data.

Abstract. Efficiently reducing natural hazard risks requires a thorough understanding of the costs of natural hazards. Current methods to assess these costs employ a variety of terminologies and approaches for different types of natural hazards and different impacted sectors. This may impede efforts to ascertain comprehensive and comparable cost figures. In order to strengthen the role of cost assessments in the development of integrated natural hazard management, a review of existing cost assessment approaches was undertaken. This review considers droughts, floods, coastal and Alpine hazards, and examines different cost types, namely direct tangible damages, losses due to business interruption, indirect damages, intangible effects, and the costs of risk mitigation. This paper provides an overview of the state-of-the-art cost assessment approaches and discusses key knowledge gaps. It shows that the application of cost assessments in practice is often incomplete and biased, as direct costs receive a relatively large amount of attention, while intangible and indirect effects are rarely considered. Furthermore, all parts of cost assessment entail considerable uncertainties due to insufficient or highly aggregated data sources, along with a lack of knowledge about the processes leading to damage and thus the appropriate models required. Recommendations are provided on how to reduce or handle these uncertainties by improving data sources and cost assessment methods. Further recommendations address how risk dynamics due to climate and socio-economic change can be better considered, how costs are distributed and risks transferred, and in what ways cost assessment can function as part of decision support.

IMPORTANCE: The use and misuse of P values has generated extensive debates. OBJECTIVE: To evaluate in large scale the P values reported in the abstracts and full text of biomedical research articles over the past 25 years and determine how frequently statistical information is presented in ways other than P values. DESIGN: Automated text-mining analysis was performed to extract data on P values reported in 12,821,790 MEDLINE abstracts and in 843,884 abstracts and full-text articles in PubMed Central (PMC) from 1990 to 2015. Reporting of P values in 151 English-language core clinical journals and specific article types as classified by PubMed also was evaluated. A random sample of 1000 MEDLINE abstracts was manually assessed for reporting of P values and other types of statistical information; of those abstracts reporting empirical data, 100 articles were also assessed in full text. MAIN OUTCOMES AND MEASURES: P values reported. RESULTS: Text mining identified 4,572,043 P values in 1,608,736 MEDLINE abstracts and 3,438,299 P values in 385,393 PMC full-text articles. Reporting of P values in abstracts increased from 7.3% in 1990 to 15.6% in 2014. In 2014, P values were reported in 33.0% of abstracts from the 151 core clinical journals (n = 29,725 abstracts), 35.7% of meta-analyses (n = 5620), 38.9% of clinical trials (n = 4624), 54.8% of randomized controlled trials (n = 13,544), and 2.4% of reviews (n = 71,529). The distribution of reported P values in abstracts and in full text showed strong clustering at P values of .05 and of .001 or smaller. Over time, the "best" (most statistically significant) reported P values were modestly smaller and the "worst" (least statistically significant) reported P values became modestly less significant. Among the MEDLINE abstracts and PMC full-text articles with P values, 96% reported at least 1 P value of .05 or lower, with the proportion remaining steady over time in PMC full-text articles. In 1000 abstracts that were manually reviewed, 796 were from articles reporting empirical data; P values were reported in 15.7% (125/796 [95% CI, 13.2%-18.4%]) of abstracts, confidence intervals in 2.3% (18/796 [95% CI, 1.3%-3.6%]), Bayes factors in 0% (0/796 [95% CI, 0%-0.5%]), effect sizes in 13.9% (111/796 [95% CI, 11.6%-16.5%]), other information that could lead to estimation of P values in 12.4% (99/796 [95% CI, 10.2%-14.9%]), and qualitative statements about significance in 18.1% (181/1000 [95% CI, 15.8%-20.6%]); only 1.8% (14/796 [95% CI, 1.0%-2.9%]) of abstracts reported at least 1 effect size and at least 1 confidence interval. Among 99 manually extracted full-text articles with data, 55 reported P values, 4 presented confidence intervals for all reported effect sizes, none used Bayesian methods, 1 used false-discovery rates, 3 used sample size/power calculations, and 5 specified the primary outcome. CONCLUSIONS AND RELEVANCE: In this analysis of P values reported in MEDLINE abstracts and in PMC articles from 1990-2015, more MEDLINE abstracts and articles reported P values over time, almost all abstracts and articles with P values reported statistically significant results, and, in a subgroup analysis, few articles included confidence intervals, Bayes factors, or effect sizes. Rather than reporting isolated P values, articles should include effect sizes and uncertainty metrics.

Urbanisation is a fundamental phenomenon whose quantitative characterisation is still inadequate. We report here the empirical analysis of a unique data set regarding almost 200 years of evolution of the road network in a large area located north of Milan (Italy). We find that urbanisation is characterised by the homogenisation of cell shapes, and by the stability throughout time of high-centrality roads which constitute the backbone of the urban structure, confirming the importance of historical paths. We show quantitatively that the growth of the network is governed by two elementary processes: (i) 'densification', corresponding to an increase in the local density of roads around existing urban centres and (ii) 'exploration', whereby new roads trigger the spatial evolution of the urbanisation front. The empirical identification of such simple elementary mechanisms suggests the existence of general, simple properties of urbanisation and opens new directions for its modelling and quantitative description.

Urban street patterns form planar networks whose empirical properties cannot be accounted for by simple models such as regular grids or Voronoi tesselations. Striking statistical regularities across different cities have been recently empirically found, suggesting that a general and detail-independent mechanism may be in action. We propose a simple model based on a local optimization process combined with ideas previously proposed in studies of leaf pattern formation. The statistical properties of this model are in good agreement with the observed empirical patterns. Our results thus suggest that in the absence of a global design strategy, the evolution of many different transportation networks indeed follows a simple universal mechanism.

Interventions of central, top-down planning are serious limitations to the possibility of modelling the dynamics of cities. An example is the city of Paris (France), which during the 19th century experienced large modifications supervised by a central authority, the 'Haussmann period'. In this article, we report an empirical analysis of more than 200 years (1789-2010) of the evolution of the street network of Paris. We show that the usual network measures display a smooth behavior and that the most important quantitative signatures of central planning is the spatial reorganization of centrality and the modification of the block shape distribution. Such effects can only be obtained by structural modifications at a large-scale level, with the creation of new roads not constrained by the existing geometry. The evolution of a city thus seems to result from the superimposition of continuous, local growth processes and punctual changes operating at large spatial scales.

This paper is devoted to nonlinear propagation phenomena in general unbounded domains of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R Superscript upper N"> <mml:semantics> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">R</mml:mi> </mml:mrow> <mml:mi>N</mml:mi> </mml:msup> <mml:annotation encoding="application/x-tex">\mathbb {R}^N</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , for reaction-diffusion equations with Kolmogorov-Petrovsky-Piskunov (KPP) type nonlinearities. This article is the second in a series of two and it is the follow-up of the paper <italic>The speed of propagation for KPP type problems. I - Periodic framework</italic> , by the authors, which dealt which the case of periodic domains. This paper is concerned with general domains, and we give various definitions of the spreading speeds at large times for solutions with compactly supported initial data. We study the relationships between these new notions and analyze their dependence on the geometry of the domain and on the initial condition. Some a priori bounds are proved for large classes of domains. The case of exterior domains is also discussed in detail. Lastly, some domains which are very thin at infinity and for which the spreading speeds are infinite are exhibited; the construction is based on some new heat kernel estimates in such domains.

The extraction of a clear and simple footprint of the structure of large, weighted and directed networks is a general problem that has relevance for many applications. An important example is seen in origin-destination matrices, which contain the complete information on commuting flows, but are difficult to analyze and compare. We propose here a versatile method, which extracts a coarse-grained signature of mobility networks, under the form of a 2 × 2 matrix that separates the flows into four categories. We apply this method to origin-destination matrices extracted from mobile phone data recorded in 31 Spanish cities. We show that these cities essentially differ by their proportion of two types of flows: integrated (between residential and employment hotspots) and random flows, whose importance increases with city size. Finally, the method allows the determination of categories of networks, and in the mobility case, the classification of cities according to their commuting structure. The availability of pervasive data has opened up possibilities for quantitative approaches to many phenomena, but extracting useful information from huge datasets is difficult. Here, Louail et al. propose a method to extract a coarse-grained signature of large weighted networks and apply it to mobility networks.

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. We apply this method to a set of 131 cities in the world, and at an intermediate level of the dendrogram, we observe four large families of cities characterized by different abundances of blocks of a certain area and shape. At a lower level of the classification, we find that most European cities and American cities in our sample fall in their own sub-category, highlighting quantitatively the differences between the typical layouts of cities in both regions. We also show with the example of New York and its different boroughs, that the fingerprint of a city can be seen as the sum of the ones characterizing the different neighbourhoods inside a city. This method provides a quantitative comparison of urban street patterns, which could be helpful for a better understanding of the causes and mechanisms behind their distinct shapes.

The betweenness centrality, a path-based global measure of flow, is a static predictor of congestion and load on networks. Here we demonstrate that its statistical distribution is invariant for planar networks, that are used to model many infrastructural and biological systems. Empirical analysis of street networks from 97 cities worldwide, along with simulations of random planar graph models, indicates the observed invariance to be a consequence of a bimodal regime consisting of an underlying tree structure for high betweenness nodes, and a low betweenness regime corresponding to loops providing local path alternatives. Furthermore, the high betweenness nodes display a non-trivial spatial clustering with increasing spatial correlation as a function of the edge-density. Our results suggest that the spatial distribution of betweenness is a more accurate discriminator than its statistics for comparing static congestion patterns and its evolution across cities as demonstrated by analyzing 200 years of street data for Paris.

Abstract We consider traveling waves for a nonlinear diffusion equation with a bistable or multistable nonlinearity. The goal is to study how a planar traveling front interacts with a compact obstacle that is placed in the middle of the space ℝ N . As a first step, we prove the existence and uniqueness of an entire solution that behaves like a planar wave front approaching from infinity and eventually reaching the obstacle. This causes disturbance on the shape of the front, but we show that the solution will gradually recover its planar wave profile and continue to propagate in the same direction, leaving the obstacle behind. Whether the recovery is uniform in space is shown to depend on the shape of the obstacle. © 2008 Wiley Periodicals, Inc.

The pervasive use of new mobile devices has allowed a better characterization in space and time of human concentrations and mobility in general. Besides its theoretical interest, describing mobility is of great importance for a number of practical applications ranging from the forecast of disease spreading to the design of new spaces in urban environments. While classical data sources, such as surveys or census, have a limited level of geographical resolution (e.g., districts, municipalities, counties are typically used) or are restricted to generic workdays or weekends, the data coming from mobile devices can be precisely located both in time and space. Most previous works have used a single data source to study human mobility patterns. Here we perform instead a cross-check analysis by comparing results obtained with data collected from three different sources: Twitter, census, and cell phones. The analysis is focused on the urban areas of Barcelona and Madrid, for which data of the three types is available. We assess the correlation between the datasets on different aspects: the spatial distribution of people concentration, the temporal evolution of people density, and the mobility patterns of individuals. Our results show that the three data sources are providing comparable information. Even though the representativeness of Twitter geolocated data is lower than that of mobile phone and census data, the correlations between the population density profiles and mobility patterns detected by the three datasets are close to one in a grid with cells of 2×2 and 1×1 square kilometers. This level of correlation supports the feasibility of interchanging the three data sources at the spatio-temporal scales considered.

Ce texte part de la multiplicité des manières de définir les enjeux de justice auxquels l’école fait face. Un premier modèle est celui de l’égalité des chances méritocratique. Un second invite à rompre avec la stricte égalité pour compenser les inégalités sociales en donnant plus à ceux qui ont moins. Un troisième modèle met en avant la notion d’un minimum de savoirs et de compétences garantis. Enfin, un quatrième insiste sur l’indépendance des «sphères de justice», une école juste étant celle dont les hiérarchies ont relativement peu de conséquences au sortir de l’école, celle qui est d’abord soucieuse de l’intégration sociale de tous et celle dont les classements n’affectent pas l’égale dignité des individus. De fait, chacune de ces conceptions de la justice s’avère contradictoire avec les autres, sinon dans l’ordre des principes, du moins dans celui des pratiques et des politiques scolaires. Pour éclairer les limites de chacun des modèles, le texte s’appuie sur les résultats établis par la sociologie de l’éducation. La conclusion est que l’école juste ne peut être le fruit d’un seul principe de justice, mais plutôt le produit plus ou moins stabilisé d’une combinaison de principes croisés et atténuant réciproquement leurs effets.

Many complex systems, including networks, are not static but can display strong fluctuations at various time scales. Characterizing the dynamics in complex networks is thus of the utmost importance in the understanding of these networks and of the dynamical processes taking place on them. In this article, we study the example of the US airport network in the time period 1990-2000. We show that even if the statistical distributions of most indicators are stationary, an intense activity takes place at the local ("microscopic") level, with many disappearing/appearing connections (links) between airports. We find that connections have a very broad distribution of lifetimes, and we introduce a set of metrics to characterize the links' dynamics. We observe in particular that the links that disappear have essentially the same properties as the ones that appear, and that links that connect airports with very different traffic are very volatile. Motivated by this empirical study, we propose a model of dynamical networks, inspired from previous studies on firm growth, which reproduces most of the empirical observations both for the stationary statistical distributions and for the dynamical properties.

We show that a recently proposed model generates accurate commuting networks on 80 case studies from different regions of the world (Europe and United-States) at different scales (e.g. municipalities, counties, regions). The model takes as input the number of commuters coming in and out of each geographic unit and generates the matrix of commuting flows between the units. The single parameter of the model follows a universal law that depends only on the scale of the geographic units. We show that our model significantly outperforms two other approaches proposing a universal commuting model [1], [2], particularly when the geographic units are small (e.g. municipalities).

This work presents some variational models for the cortical algorithms processing Kanizsa modal subjective contours . These models are based on the geometric concepts of fibration and contact structure. The retinoptic structure of the orientation hypercolumns in the visual area V1 is a functionnal architecture which can be mathematically idealized by the fibration having the retinian plane M as base and the projective line P1 as fiber F. The total space E of Pi p is isomorphic to the direct product M x F. The cortico-cortical horizontal connections implement what is called the local triviality of this fibration, and also a Cartan connection defining a parallel transport between neighboring fibers. Then the paper focuses on the geometrical interpretation of the results of Field, Hayes and Hess concerning the association field. It shows that the latter implements what is called the contact structure of the fibration. The association field expresses an integrability condition for the skew curves in E : they have to be a lifting of their projection on the retinian plane M. This model of fibration endowed with a contact structure is then applied to the modal subjective contours and provides a variant of the elastica model developped by B.K.P. Horn and D. Mumford. The key idea is that the lifting of subjective contours satisfy a "geodesic" condition in the cortical fibration E : they have to be of minimal lenght (for an appropriate metrics) among the class of curves satisfying the integrability condition. These "geodesic" models are then reformulated, according to R. Bryant and P. Griffiths, in the more fondamental geometric framework of Lie groups and Cartan's "repère mobile" (Vielbein). Finally, some experimental possibilities are suggested.

Scaling has been proposed as a powerful tool to analyze the properties of complex systems and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of urban datasets displays apparent nonlinear behaviors whose statistical validity and meaning were recently the focus of many debates. We discuss here another aspect, which is the implication of such scaling forms on individual cities and how they can be used for predicting the behavior of a city when its population changes. We illustrate this discussion in the case of delay due to traffic congestion with a dataset of 101 US cities in the years 1982-2014. We show that the scaling form obtained by agglomerating all of the available data for different cities and for different years does display a nonlinear behavior, but which appears to be unrelated to the dynamics of individual cities when their population grows. In other words, the congestion-induced delay in a given city does not depend on its population only, but also on its previous history. This strong path dependency prohibits the existence of a simple scaling form valid for all cities and shows that we cannot always agglomerate the data for many different systems. More generally, these results also challenge the use of transversal data for understanding longitudinal series for cities.

Human mobility has been traditionally studied using surveys that deliver snapshots of population displacement patterns. The growing accessibility to ICT information from portable digital media has recently opened the possibility of exploring human behavior at high spatio-temporal resolutions. Mobile phone records, geolocated tweets, check-ins from Foursquare or geotagged photos, have contributed to this purpose at different scales, from cities to countries, in different world areas. Many previous works lacked, however, details on the individuals' attributes such as age or gender. In this work, we analyze credit-card records from Barcelona and Madrid and by examining the geolocated credit-card transactions of individuals living in the two provinces, we find that the mobility patterns vary according to gender, age and occupation. Differences in distance traveled and travel purpose are observed between younger and older people, but, curiously, either between males and females of similar age. While mobility displays some generic features, here we show that sociodemographic characteristics play a relevant role and must be taken into account for mobility and epidemiological modelization.

In this commentary we discuss the validity of scaling laws and their relevance for understanding urban systems and helping policy makers. We show how the recent controversy about the scaling of CO2 transport-related emissions with population size, where different authors reach contradictory conclusions, is symptomatic of the lack of understanding of the underlying mechanisms. In particular, we highlight different sources of errors, ranging from incorrect estimate of CO2 to problems related with the definition of cities. We argue here that while data are necessary to build of a new science of cities, they are not enough: they have to go hand in hand with a theoretical understanding of the main processes. This effort of building models whose predictions agree with data is the prerequisite for a science of cities. In the meantime, policy advice are, at best, a shot in the dark.