Dynamical fluctuations in a simple housing market model

We consider a simple stochastic model of a urban rental housing market, in which the interaction of tenants and landlords induces rent fluctuations. We simulate the model numerically and measure the equilibrium rent distribution, which is found to be close to a lognormal law. We also study the influence of the density of agents (or equivalently, the vacancy rate) on the rent distribution. A simplified version of the model, amenable to analytical treatment, is studied and leads to a lognormal distribution of rents. The predicted equilibrium value agrees quantitatively with numerical simulations, while a qualitative agreement is obtained for the standard deviation. The connection with non-equilibrium statistical physics models like ratchets is also emphasized.Comment: 12 pages, 5 figures, to appear in J. Stat. Mec

Transfer matrix analysis of one-dimensional majority cellular automata with thermal noise

Thermal noise in a cellular automaton refers to a random perturbation to its function which eventually leads this automaton to an equilibrium state controlled by a temperature parameter. We study the 1-dimensional majority-3 cellular automaton under this model of noise. Without noise, each cell in this automaton decides its next state by majority voting among itself and its left and right neighbour cells. Transfer matrix analysis shows that the automaton always reaches a state in which every cell is in one of its two states with probability 1/2 and thus cannot remember even one bit of information. Numerical experiments, however, support the possibility of reliable computation for a long but finite time.Comment: 12 pages, 4 figure

Financial interaction networks inferred from traded volumes

In order to use the advanced inference techniques available for Ising models, we transform complex data (real vectors) into binary strings, by local averaging and thresholding. This transformation introduces parameters, which must be varied to characterize the behaviour of the system. The approach is illustrated on financial data, using three inference methods -- equilibrium, synchronous and asynchronous inference -- to construct functional connections between stocks. We show that the traded volume information is enough to obtain well known results about financial markets, which use however the presumably richer price information: collective behaviour ("market mode") and strong interactions within industry sectors. Synchronous and asynchronous Ising inference methods give results which are coherent with equilibrium ones, and more detailed since the obtained interaction networks are directed.Comment: 14 pages, 6 figure

Road network distances and detours in Europe: Radial profiles and city size effects

peer reviewedThe form and the size of cities influence their social, economic and environmental outcomes. The form of a city is itself influenced by the shape of its road network, but this relationship and how it is affected by city size are unclear. We analyse how road distances to the main centre vary across 300 European cities and how radial physical detours (i.e. the distance on the road network compared to the Euclidean distance) are affected by city size and extent. We use landuse and population data to sample potential residences and compute the fastest routes to the main centre. We find a linear relationship between road and Euclidean distances, and for the first time document an average radial physical detour of 1.343 across Europe. We then rescale distance bands so to make cities of different population size comparable and show the effect of different urban delineations. We find that physical detour ratios increase when core cities only are considered without suburbs. At the urban region scale, radial physical detours increase with city size, especially when other significant geographical factors (latitude, longitude, elevation change and proximity to coast) are controlled for. When the central part of cities only is considered, larger cities have smaller radial physical detours

Gibrat’s law and the change in artificial land use within and between European cities

editorial reviewedSeen from a satellite, observing land use in the daytime or at night, most cities have circular shapes, organised around a city centre. A radial analysis of artificial land use growth is conducted in order to understand what the recent changes in urbanisation are across Europe and how it relates to city size. We focus on the most fundamental differentiation regarding urban land use: has it been artificialised for human uses (residence or roads for instance) or is it natural, or at least undeveloped? Using spatially detailed data from the EU Copernicus Urban Atlas, profiles of artificial land use (ALU) are calculated and compared between two years, 2006 and 2012. Based on the homothety of urban forms found by Lemoy and Caruso (2018), a simple scaling law is used to compare the internal structure of cities after controlling for population size. We firstly show that when using the functional urban area (FUA) definition of cities, a kind of Gibrat’s law for land use appears to hold. However, when we examine cities internally, this is no longer clear as there are differences on average between city size categories. We also look at further city groupings using regions and topography to show that artificial land use growth across European cities is not homogeneous. Our findings have important implications relative to the sustainability of cities as this evidence is pointing towards increasing urban sprawl and stagnant growth in urban centres across cities of all sizes. It also has theoretical implications on the nature of sprawl and its scaling with city size

MAS Simulation of a “Bush Taxi” Transportation Service : Summary of a project carried out during the MAPS training course

International audienceThe human and social sciences have always sought to improve their tools and resources in order to spread their knowledge. The most recent of these tools, Multi-Agent Systems (MAS), also known as Agent-Based Models (ABM), is a remarkable means of formalization and visualization of spatial processes. Multi-Agent Systems have already proved to be extremely useful modeling tools in various disciplines such as epidemiology, biology, and ecology, but also economics and geography (Amblard F. 2006). Today's research and methods aiming to deal with spatial problems are more and more treated within the paradigm and theories of complex systems. Indeed, one of the advantages of multi-agent systems, in the domain of human and social sciences, is their ability to accurately represent the underlying systems in the simplest way possible, while at the same time successfully integrating complexity in each of the scales considered (Daudé E. 2003). The main problem, when using this approach, is to design, in accordance with Occam's Razor, simple operating rules and strategies for the agents, which are carefully chosen to respond to a clearly identified problem. Given the components and parameters of the system, this tool allows us to observe and understand the comprehensive self-organized behavior, including the effects of structuring, transition, emergence, etc. (M. Vidal J. 2007). Today's society is increasingly mobile and people's daily mobility is determined by processes linked to their behavior, the infrastructure, and their environment (roads, etc.), but also by the services available to them (busses, taxis, etc.) (Marilleau N. et al. 2005). Therefore, their movements are strongly influenced by the environment which surrounds them. Working on a variety of themes which are all relevant to the same problem, mobility, our group has brought together several young researchers for whom the MAPS training course fulfills the need for training in the domain of the science of complexity, in the realms of both methodological skills and practical multi-agent modeling.Les sciences humaines et sociales ont toujours cherché à améliorer leurs outils afin de diffuser leurs connaissances. Le dernier d'entre eux, les Systèmes Multi-Agents (S.M.A.) est un vecteur remarquable de la formalisation et de la visualisation des processus spatiaux. Les SMA ont déjà fait leurs preuves en tant qu'outil puissant de modélisation, dans différentes disciplines comme l'épidémiologie, la biologie, l'écologie, mais aussi l'économie et la géographie (Amblard F. 2006). La multiplication des recherches et des méthodes visant à répondre à des problématiques spatiales s'inscrivent, aujourd'hui, dans le paradigme et les théories des systèmes complexes. En effet, l'un des atouts des systèmes multi-agents, dans les domaines relevant des sciences humaines et sociales, réside dans leur pertinence à représenter les systèmes sous-jacents le plus simplement possible, tout en intégrant au mieux la complexité aux différentes échelles considérées (Daudé E. 2003). Tout l'enjeu de cette approche est de concevoir, selon le principe de parcimonie, des règles de fonctionnement et des stratégies simples des agents, mais précisément choisies pour répondre à une problématique clairement identifiée. Connaissant les composantes et les paramètres du système, l'outil permet alors d'observer et de comprendre un comportement global auto-organisé, avec des effets de structuration, de transition, d'émergence, etc. (M. Vidal J. 2007). Vivant dans une société chaque jour plus mobile, les personnes se déplacent quotidiennement selon des dynamiques dictées par leurs comportements, par les infrastructures, leur milieu (routes, etc.), mais aussi par les services qui leurs sont proposés (bus, taxis, etc.) (Marilleau N. et al. 2005). Les déplacements sont ainsi fortement conditionnés par l'environnement qui nous entoure. Travaillant sur des thématiques différentes, mais relevant toutes d'une problématique commune : celle de la mobilité, notre groupe réunit de jeunes chercheurs, pour lesquel la formation MAPS est une réponse à nos besoins d'aprentissage dans le domaine des sciences de la complexité, tant sur le plan des compétences méthodologiques que sur le plan pratique de modélisation multi-agents

Socio-economic utility and chemical potential

In statistical physics, the conservation of particle number results in the equalization of the chemical potential throughout a system at equilibrium. In contrast, the homogeneity of utility in socio-economic models is usually thought to rely on the competition between individuals, leading to Nash equilibrium. We show that both views can be reconciled by introducing a notion of chemical potential in a wide class of socio-economic models, and by relating it in a direct way to the equilibrium value of the utility. This approach also allows the dependence of utility across the system to be determined when agents take decisions in a probabilistic way. Numerical simulations of a urban economic model also suggest that our result is valid beyond the initially considered class of solvable models.Comment: 6 pages, 3 figures, final versio

: Recueil de fiches pédagogiques du réseau MAPS

DoctoralLe réseau thématique MAPS «Modélisation multi-Agent appliquée aux Phénomènes Spatialisés » propose depuis 2009 des évènements scientifiques ayant pour but de diffuser les pratiques de modélisations multi-agents au sein des Sciences de l’Homme et de la Société (SHS). Ce collectif pluridisciplinaire de chercheurs, d’enseignants-chercheurs et de doctorants est labellisé en tant que ≪ réseau thématique » par le Réseau National des Systèmes Complexes (GIS RNSC) et bénéficie du soutien du CNRS au titre de la Formation Permanente. Depuis 2009, plusieurs modèles ont été développés au cours d'événements MAPS. Ces modèles ont fait l'objet de fiches pédagogiques détaillées destinées aux communautés éducatives et universitaires et en particulier aux enseignants qui souhaiteraient faire découvrir la modélisation à leurs étudiants, mais aussi à ceux qui envisagent d’approfondir certains aspects avec un public plus averti. Elles sont également destinées à tous les curieux qui souhaiteraient découvrir ce que la modélisation apporte aux SHS, du point de vue heuristique et du point de vue opérationnel. Enfin, elles sont aussi des supports pour toutes les personnes qui souhaiteraient diffuser les réflexions scientifiques sur la modélisation et la simulation qui ont présidé à la rédaction de ces fiches

La Ville comme Système Complexe. Physique Statistique et Simulations Multi-Agents sur des Modèles Urbains

Social and natural sciences share an interest for collective phenomena, which constitute an important part of the domain of complex systems. This thesis focuses on the study of urban systems, using analytical tools inspired by statistical physics, and also simulations, in particular agent-based models. A first analytical resolution of a Schelling spatial segregation model is presented, using a statistical physics framework linking individual and collective dynamics. This framework shows that utility or welfare in socio-economic models corresponds to a chemical potential in physics, a correspondence which is applied to a urban housing model. The housing market is further studied with a parsimonious price formation model. The implementation of an agent-based model, which reproduces the results of the standard urban economics (AMM) model, provides a second point of view on urban systems and the interaction between transport and land use. The simulations give results also when analytical resolution is lacking. The model is used to study the economic, environmental and social outcomes of having an amenity in the urban area and of polycentric cities. With two income groups, this work provides insights on the different urban social structures in North American and European cities for instance.Les sciences "dures" et les sciences humaines ont un intérêt commun pour les phénomènes collectifs, qui sont également un sujet de recherche important dans le domaine des systèmes complexes. Cette thèse se focalise sur l'étude des systèmes urbains, en utilisant des outils analytiques venant de la physique statistique, et des simulations, en particulier la modélisation multi-agents. Une première résolution analytique d'un modèle de ségrégation spatiale de Schelling est obtenue à l'aide d'un formalisme de physique statistique qui relie la dynamique individuelle et collective. Ce formalisme montre que l'utilité ou le bien être des modèles socio-économiques correspond à un potentiel chimique en physique, ce qu'illustre un modèle de logement urbain. Le marché du logement est étudié plus en détail grâce à un modèle parcimonieux de formation du prix. La mise en oeuvre d'un modèle multi-agents, qui reproduit les résultats du modèle standard de l'économie urbaine (AMM), donne un deuxième point de vue sur les systèmes urbains et l'interaction entre transport et localisation résidentielle. Les simulations fournissent des résultats là où la résolution analytique fait défaut. Ce modèle est utilisé pour étudier les impacts économique, environnemental et social de l'introduction d'une aménité dans l'espace urbain et de la ville polycentrique. Avec deux catégories de revenu, ce travail fournit des hypothèses quant aux différentes structures sociales urbaines dans les villes nord-américaines et européennes par exemple