Approaches to Geo-mathematical Modelling: New Tools for Complexity Science

Geo–mathematical modelling: models from complexity science   Sir Alan Wilson, Centre for Advanced Spatial Analysis, University College London   Mathematical and computer models for a complexity science tool kit   Geographical systems are characterised by locations, activities at locations, interactions between them and the infrastructures that carry these activities and flows. They can be described at a great variety of scales, from individuals and organisations to countries. Our understanding, often partial, of these entities, and in many cases this understanding is represented in theories and associated mathematical models.   In this book, the main examples are models that represent elements of the global system covering such topics as trade, migration, security and development aid together with examples at finer scales. This provides an effective toolkit that can not only be applied to global systems, but more widely in the modelling of complex systems. All complex systems involve nonlinearities involving path dependence and the possibility of phase changes and this makes the mathematical aspects particularly interesting. It is through these mechanisms that new structures can be seen to emerge , and hence the current notion of emergent behaviour . The range of models demonstrated include account–based models and biproportional fitting, structural dynamics, space–time statistical analysis, real–time response models, Lotka–Volterra models representing war , agent–based models, epidemiology and reaction–diffusion approaches, game theory, network models and finally, integrated models.   Geo–mathematical modelling: Presents mathematical models with spatial dimensions. Provides representations of path dependence and phase changes. Illustrates complexity science using models of trade, migration, security and development aid. Demonstrates how generic models from the complexity science tool kit can each be applied in a variety of situations   This book is for practitioners and researchers in applied mathematics, geography, economics, and interdisciplinary fields such as regional science and complexity science. It can also be used as the basis of a modelling course for postgraduate students. INDICE: Notes on Contributors xv .Acknowledgements xxi .About the Companion Website xxiii .Part I APPROACHES .1 The Toolkit 3Alan G. Wilson .Part II ESTIMATING MISSING DATA: BI–PROPORTIONAL FITTING AND PRINCIPAL COMPONENTS ANALYSIS .2 The Effects of Economic and Labour Market Inequalities on Interregional Migration in Europe 9Adam Dennett .2.1 Introduction 9 .2.2 The Approach 12 .2.3 Data 12 .2.4 Preliminary Analysis 13 .2.5 Multinomial Logit Regression Analysis 15 .2.6 Discussion 22 .2.7 Conclusions 24 .References 25 .3 Test of Bi–Proportional Fitting Procedure Applied to International Trade 26Simone Caschili and Alan G. Wilson .3.1 Introduction 26 .3.2 Model 27 .3.3 Notes of Implementation 28 .3.4 Results 30 .References 32 .4 Estimating Services Flows 33Robert G. Levy .4.1 Introduction 33 .4.2 Estimation Via Iterative Proportional Fitting 34 .4.3 Estimating Services Flows Using Commodities Flows 37 .4.4 A Comparison of The Methods 40 .4.5 Results 45 .4.6 Conclusion 49 .References 50 .5 A Method for Estimating Unknown National Input Output Tables Using Limited Data 51Thomas P. Oléron Evans and Robert G. Levy .5.1 Motivation and Aims 51 .5.2 Obstacles to The Estimation of National Input Output Tables 52 .5.3 Vector Representation of Input Output Tables 53 .5.4 Method 54 .5.5 In–Sample Assessment of The Estimates 58 .5.6 Out–of–Sample Discussion of The Estimates 63 .5.7 Conclusion 67 .References 68 .Part III DYNAMICS IN ACCOUNT–BASED MODELS .6 A Dynamic Global Trade Model With Four Sectors: Food, Natural Resources, Manufactured Goods and Labour 71Hannah M. Fry, Alan G. Wilson and Frank T. Smith .6.1 Introduction 71 .6.2 Definition of Variables for System Description 73 .6.3 The Pricing and Trade Flows Algorithm 73 .6.4 Initial Setup 75 .6.5 The Algorithm to Determine Farming Trade Flows 77 .6.6 The Algorithm to Determine The Natural Resources Trade Flows 80 .6.7 The Algorithm to Determine Manufacturing Trade Flows 81 .6.8 The Dynamics 83 .6.9 Experimental Results 84 .References 90 .7 Global Dynamical Input Output Modelling 91Anthony P. Korte and Alan G. Wilson .7.1 Towards a Fully Dynamic Inter–country Input Output Model 91 .7.2 National Accounts 92 .7.3 The Dynamical International Model 97 .7.4 Investment: Modelling Production Capacity: The Capacity Planning Model 100 .7.5 Modelling Production Capacity: The Investment Growth Approach 103 .7.6 Conclusions 121 .References 122 .Appendix 123 .A.1 Proof of Linearity of the Static Model and the Equivalence of Two Modelling Approaches 123 .Part IV SPACE TIME STATISTICAL ANALYSIS .8 Space Time Analysis of Point Patterns in Crime and Security Events 127Toby P. Davies, Shane D. Johnson, Alex Braithwaite and Elio Marchione .8.1 Introduction 127 .8.2 Application in Novel Areas 132 .8.3 Motif Analysis 138 .8.4 Discussion 147 .References 148 .Part V REAL–TIME RESPONSE MODELS .9 The London Riots 1: Epidemiology, Spatial Interaction and Probability of Arrest 153Toby P. Davies, Hannah M. Fry, Alan G. Wilson and Steven R. Bishop .9.1 Introduction 153 .Contents ix .9.2 Characteristics of Disorder 156 .9.3 The Model 158 .9.4 Demonstration Case 162 .9.5 Concluding Comments 166 .References 166 .Appendix 168 .A.1 Note on Methods: Data 168 .A.2 Numerical Simulations 169 .10 The London Riots 2: A Discrete Choice Model 170Peter Baudains, Alex Braithwaite and Shane D. Johnson .10.1 Introduction 170 .10.2 Model Setup 170 .10.3 Modelling the Observed Utility 172 .10.4 Results 176 .10.5 Simulating the 2011 London Riots: Towards a Policy Tool 181 .10.6 Modelling Optimal Police Deployment 187 .References 190 .Part VI THE MATHEMATICS OF WAR .11 Richardson Models with Space 195Peter Baudains .11.1 Introduction 195 .11.2 The Richardson Model 196 .11.3 Empirical Applications of Richardson s Model 202 .11.4 A Global Arms Race Model 204 .11.5 Relationship to a Spatial Conflict Model 206 .11.6 An Empirical Application 207 .11.7 Conclusion 212 .References 213 .Part VII AGENT–BASED MODELS .12 Agent–based Models of Piracy 217Elio Marchione, Shane D. Johnson and Alan G. Wilson .12.1 Introduction 217 .12.2 Data 219 .12.3 An Agent–based Model 221 .12.4 Model Calibration 232 .12.5 Discussion 232 .References 235 .13 A Simple Approach for the Prediction of Extinction Events in Multi–agent Models 237Thomas P. Oléron Evans, Steven R. Bishop and Frank T. Smith .13.1 Introduction 237 .13.2 Key Concepts 238 .13.3 The NANIA Predator prey Model 241 .13.4 Computer Simulation 247 .13.5 Period Detection 249 .13.6 A Monte Carlo Approach to Prediction 252 .13.7 Conclusions 263 .References 264 .Part VIII DIFFUSION MODELS .14 Urban Agglomeration Through the Diffusion of Investment Impacts 269Minette D Lima, Francesca R. Medda and Alan G. Wilson .14.1 Introduction 269 .14.2 The Model 270 .14.3 Mathematical Analysis for Agglomeration Conditions 272 .14.4 Simulation Results 275 .14.5 Conclusions 279 .References 279 .Part IX GAME THEORY .15 From Colonel Blotto to Field Marshall Blotto 283Peter Baudains, Toby P. Davies, Hannah M. Fry and Alan G. Wilson .15.1 Introduction 283 .15.2 The Colonel Blotto Game and its Extensions 285 .15.3 Incorporating a Spatial Interaction Model of Threat 286 .15.4 Two–front Battles 288 .15.5 Comparing Even and Uneven Allocations in a Scenario with Five Fronts 289 .15.6 Conclusion 292 .References 292 .16 Modelling Strategic Interactions in a Global Context 293Janina Beiser .16.1 Introduction 293 .16.2 The Theoretical Model 294 .16.3 Strategic Estimation 295 .16.4 International Sources of Uncertainty in the Context of Repression and Rebellion 297 .16.5 International Sources of Uncertainty Related to Outcomes 299 .16.6 Empirical Analysis 301 .16.7 Results 303 .16.8 Additional Considerations Related to International Uncertainty 304 .16.9 Conclusion 304 .References 305 .17 A General Framework for Static, Spatially Explicit Games of Search and Concealment 306Thomas P. Oléron Evans, Steven R. Bishop and Frank T. Smith .17.1 Introduction 306 .17.2 Game Theoretic Concepts 307 .17.3 Games of Search and Security: A Review 310 .17.4 The Static Spatial Search Game (SSSG) 314 .17.5 The Graph Search Game (GSG) 324 .17.6 Summary and Conclusions 335 .References 336 .Part X NETWORKS .18 Network Evolution: A Transport Example 343Francesca Pagliara, Alan G. Wilson and Valerio de Martinis .18.1 Introduction 343 .18.2 A Hierarchical Retail Structure Model as a Building Block 344 .18.3 Extensions to Transport Networks 345 .18.4 An Application in Transport Planning 347 .18.5 A Case Study: Bagnoli in Naples 350 .18.6 Conclusion 360 .References 361 .19 The Structure of Global Transportation Networks 363Sean Hanna, Joan Serras and Tasos Varoudis .19.1 Introduction 363 .19.2 Method 364 .19.3 Analysis of the European Map 366 .19.4 Towards a Global Spatial Economic Map: Economic Analysis by Country 368 .19.5 An East–west Divide and Natural Economic Behaviour 373 .19.6 Conclusion 376 .References 377 .20 Trade Networks and Optimal Consumption 378Robert J. Downes and Robert G. Levy .20.1 Introduction 378 .20.2 The Global Economic Model 379 .20.3 Perturbing Final Demand Vectors 380 .20.4 Analysis 384 .20.5 Conclusions 393 .Acknowledgements 394 .References 394 .Appendix 396 .Part XI INTEGRATION .21 Research Priorities 399Alan G. Wilson .Index 403

• ISBN: 978-1-118-92227-9
• Editorial: Wiley–Blackwell
• Encuadernacion: Cartoné
• Páginas: 432
• Fecha Publicación: 30/09/2016
• Nº Volúmenes: 1
• Idioma: Inglés