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

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

ISBN: 978-1-118-92227-9 September 2016 432 Pages

**Hardcover**

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$125.00

## Description

**Geo-mathematical modelling: models from complexity science**

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*Sir Alan Wilson, Centre for Advanced Spatial Analysis, University College London*

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**Mathematical and computer models for a complexity science tool kit**

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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

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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.

## Related Resources

### Student

Notes on Contributors xv

Acknowledgements xxi

About the Companion Website xxiii

**Part I APPROACHES**

1 The Toolkit 3*Alan 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 9***Adam 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 26***Simone 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 33***Robert 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 51***Thomas 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 71***Hannah 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 91***Anthony 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 127***Toby 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 153***Toby 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 170***Peter 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 195***Peter 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 217***Elio 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 237***Thomas 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 269***Minette 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 283***Peter 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 293***Janina 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 306***Thomas 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 343***Francesca 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 363***Sean 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 378***Robert 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 399***Alan G. Wilson*

Index 403