Table of Contents. Preface... xiii. Introduction... xv

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1 Preface... xiii Introduction... xv Chapter 1. Modeling Concepts Used in Spatial Analysis... 1 François DURAND-DASTÈS 1.1. Introduction Modeling universals Logical frames for modeling The language of models Material or physical model languages The language of images: iconic models Modeling in mathematical language A few specific features of spatial models Spatial models: a study grid Sequencing and explanation The group and the individual The random and the determined Movement and balance Conclusion Bibliography Chapter 2. Geographical Scales and Multidimensional Statistical Methods Hélène MATHIAN and Marie PIRON 2.1. Introduction Scaling issues... 31

2 vi Models in Spatial Analysis The consideration of different geographical levels: two possible approaches Formalization of relations between two levels Nested relations and partition graph Neighborhood relations and proximity graphs Processing of multilevel information Multilevel structure and attributes Multidimensional statistical methods Change of levels, change of structures Scale and variability Exploratory analysis of the scale system Analysis of aggregated levels or interclass analysis Transition analysis between two levels or intraclass analysis Application of outlying Ouagadougou space to the social and spatial organization Integration of the different levels The scale: a set of territorial and spatial references The analysis of local differences Other local analysis methods Multilevel models Contextual effects and regression models Multilevel modeling Conclusion Bibliography Chapter 3. Location of Public Services: From Theory to Application Dominique PEETERS and Isabelle THOMAS 3.1. Introduction The modeling approach A typology of public services: an attempt Estimating demand Analyzing supply Adjusting supply to demand Evaluating the solutions Methodological perspectives A prototype location model: the k-median An example: recycling centers The problem: the optimal location of recycling centers Results of the model Conclusion Bibliography... 92

3 vii Chapter 4. Time-geography: Individuals in Time and Space Sonia CHARDONNEL 4.1. Introduction: why integrate time when we analyze space? The study of spatio-temporal processes For a time-integrated geography The foundations of time-geography The premises A certain vision of the world The conceptual framework of time-geography The creation of a notation system Tools to decrypt daily life Trajectory, station, project: basic concepts Different types of constraints A transversal analysis of the three worlds Time-geography in practice Simulation of individual activity programs: public transport possibilities in the city of Karlstad an application by Bo Lenntorp General features of the simulation model The application of Karlstad New implementations and operational methods in time-geographic research Partial conclusion Daily lives of women: adaptation strategies in time and space the Tora Friberg method From Højrup s life forms to Friberg s three women life forms Relation with time-geography Conclusion Bibliography Chapter 5. The Process of Spatial Diffusion and Modeling Change Thérèse SAINT-JULIEN 5.1. Introduction The manifestations of diffusion in space Elements and levels of approach of a spatial diffusion process Distances and propagation channels Spatial diffusion in time Simulating a spatial diffusion process: Hägerstrand s pioneer approach A probabilistic model The rules of the basic model Diffusion in a homogenous space

4 viii Models in Spatial Analysis Diffusion in a heterogeneous space Simulation procedure Analysis models, interpretative models References Models of form Explanatory models Conclusion Bibliography Chapter 6. Spatial Microsimulation Models Einar HOLM and Lena SANDERS 6.1. Introduction Choosing the aggregation level for modeling Micro-objects and spatial analysis Arguments for choosing a modeling level Individuals as the favored micro-objects in spatial microsimulation Theoretical point of view: interactions and emergence phenomena Thematic point of view: the driving role of the inter-individual diversity Technical point of view: management of information tables The elements of a dynamic microsimulation model The different sources of microdata: comprehensive information, samplings, artificial worlds Statistical procedures or agent type autonomy: the different ways to formalize individual change National forecasts and simulation of individual biographies with the SVERIGE model Classical aggregate outputs The biography of Kristina A simulation of population spatial dynamics with MICDYN Operation of the MICDYN model Determining workplaces and places of residence of migrants Simulating the population evolutions Perspectives Conclusion Bibliography

5 ix Chapter 7. Multi-agent Simulations of Spatial Dynamics Jean-Pierre TREUIL, Christian MULLON, Edith PERRIER and Marie PIRON 7.1. Introduction The multi-agent approach Multi-agent systems Multi-agent simulation of natural and social phenomena Modeling of spatial dynamics Computer models and simulation of spatial dynamics An example: modeling of the ecosystem of the interior delta of the river Niger The concepts of a computer model of spatial dynamics Mathematical models of spatial dynamics Eulerian and Lagrangian approaches An example on water runoff modeling Computer and mathematical models of spatial dynamics toward convergence A common duality: Eulerian point of view and Lagrangian point of view Source and necessity of the comparison: simulation and its limits The multi-agent approach in spatial dynamics modeling: a point of view The methodology Hierarchy of choices and the place of agents: an example Conclusion Bibliography Chapter 8. From Image to Model: Remote Sensing and Urban Modeling Françoise DUREAU and Christiane WEBER 8.1. Introduction A modeling of urban reality Objectives of the chapter The satellite image in the demographic information production The different phases of information production from satellite imagery Area sampling method on satellite image: general principles Application in Bogota in The use of imagery in urban modeling The potential model and satellite data Application of the model to satellite imagery Application in Bogota

6 x Models in Spatial Analysis 8.4. Spatial information and dynamic modeling Towards a dynamic multilevel model Application in Bogota: a preliminary simulation Conclusion Bibliography Chapter 9. Mathematical Formalization for Spatial Interactions Alain FRANC 9.1. Introduction Formalizations Notion of perfect aggregation of variables Mean field Example of the Ising model Use of mean field notion in ecology Reaction-diffusion models Conclusion Bibliography Chapter 10. Fractals and Geography Pierre FRANKHAUSER and Denise PUMAIN Introduction Fractality and structuring of the geographical space Density: a traditional but unsuitable measure The fractals: references adapted to the space of human societies Fractal models of spatial structures Surface models Line models Multifractal models Stochastic models Measuring fractality Notion of fractal dimension Global analysis methods The grid analysis The correlation analysis Local methods of analysis Radial analysis The curve of scaling behavior The morphology of contours The morphology of land occupation Form of occupied surfaces Intensity of land occupation

7 xi The morphology of hierarchies: population and systems Urban hierarchies Measuring the morphology of networks Towards dynamic models Conclusion Bibliography List of Authors Index