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Approaches to Geo-mathematical Modelling

Book Description

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.

Table of Contents

  1. Cover
  2. Title Page
    1. Copyright
  3. Notes on Contributors
  4. Acknowledgements
  5. About the Companion Website
  6. Part One: Approaches
    1. Chapter 1: The Toolkit
  7. Part Two: Estimating Missing Data: Bi-proportional Fitting and Principal Components Analysis
    1. Chapter 2: The Effects of Economic and Labour Market Inequalities on Interregional Migration in Europe
      1. 2.1 Introduction
      2. 2.2 The Approach
      3. 2.3 Data
      4. 2.4 Preliminary Analysis
      5. 2.5 Multinomial Logit Regression Analysis
      6. 2.6 Discussion
      7. 2.7 Conclusions
      8. References
    2. Chapter 3: Test of Bi-Proportional Fitting Procedure Applied to International Trade
      1. 3.1 Introduction
      2. 3.2 Model
      3. 3.3 Notes of Implementation
      4. 3.4 Results
      5. References
    3. Chapter 4: Estimating Services Flows
      1. 4.1 Introduction
      2. 4.2 Estimation Via Iterative Proportional Fitting
      3. 4.3 Estimating Services Flows Using Commodities Flows
      4. 4.4 A Comparison of The Methods
      5. 4.5 Results
      6. 4.6 Conclusion
      7. References
    4. Chapter 5: A Method for Estimating Unknown National Input–Output Tables Using Limited Data
      1. 5.1 Motivation and Aims
      2. 5.2 Obstacles to The Estimation of National Input–Output Tables
      3. 5.3 Vector Representation of Input–Output Tables
      4. 5.4 Method
      5. 5.5 In-Sample Assessment of The Estimates
      6. 5.6 Out-of-Sample Discussion of The Estimates
      7. 5.7 Conclusion
      8. References
  8. Part Three: Dynamics in Account-based Models
    1. Chapter 6: A Dynamic Global Trade Model With Four Sectors: Food, Natural Resources, Manufactured Goods and Labour
      1. 6.1 Introduction
      2. 6.2 Definition of Variables for System Description
      3. 6.3 The Pricing and Trade Flows Algorithm
      4. 6.4 Initial Setup
      5. 6.5 The Algorithm to Determine Farming Trade Flows
      6. 6.6 The Algorithm to Determine The Natural Resources Trade Flows
      7. 6.7 The Algorithm to Determine Manufacturing Trade Flows
      8. 6.8 The Dynamics
      9. 6.9 Experimental Results
      10. References
    2. Chapter 7: Global Dynamical Input–Output Modelling
      1. 7.1 Towards a Fully Dynamic Inter-country Input–Output Model
      2. 7.2 National Accounts
      3. 7.3 The Dynamical International Model
      4. 7.4 Investment: Modelling Production Capacity: The Capacity Planning Model
      5. 7.5 Modelling Production Capacity: The Investment Growth Approach
      6. 7.6 Conclusions
      7. References
      8. Appendix
      9. A.1 Proof of Linearity of the Static Model and the Equivalence of Two Modelling Approaches
  9. Part Four: Space-Time Statistical Analysis
    1. Chapter 8: Space–Time Analysis of Point Patterns in Crime and Security Events
      1. 8.1 Introduction
      2. 8.2 Application in Novel Areas
      3. 8.3 Motif Analysis
      4. 8.4 Discussion
      5. References
  10. Part Five: Real-Time Response Models
    1. Chapter 9: The London Riots – 1: Epidemiology, Spatial Interaction and Probability of Arrest
      1. 9.1 Introduction
      2. 9.2 Characteristics of Disorder
      3. 9.3 The Model
      4. 9.4 Demonstration Case
      5. 9.5 Concluding Comments
      6. References
      7. Appendix
      8. A.1 Note on Methods: Data
      9. A.2 Numerical Simulations
    2. Chapter 10: The London Riots – 2: A Discrete Choice Model
      1. 10.1 Introduction
      2. 10.2 Model Setup
      3. 10.3 Modelling the Observed Utility
      4. 10.4 Results
      5. 10.5 Simulating the 2011 London Riots: Towards a Policy Tool
      6. 10.6 Modelling Optimal Police Deployment
      7. References
  11. Part Six: The Mathematics of War
    1. Chapter 11: Richardson Models with Space
      1. 11.1 Introduction
      2. 11.2 The Richardson Model
      3. 11.3 Empirical Applications of Richardson's Model
      4. 11.4 A Global Arms Race Model
      5. 11.5 Relationship to a Spatial Conflict Model
      6. 11.6 An Empirical Application
      7. 11.7 Conclusion
      8. References
  12. Part Seven: Agent-Based Models
    1. Chapter 12: Agent-based Models of Piracy
      1. 12.1 Introduction
      2. 12.2 Data
      3. 12.3 An Agent-based Model
      4. 12.4 Model Calibration
      5. 12.5 Discussion
      6. References
    2. Chapter 13: A Simple Approach for the Prediction of Extinction Events in Multi-agent Models
      1. 13.1 Introduction
      2. 13.2 Key Concepts
      3. 13.3 The NANIA Predator–prey Model
      4. 13.4 Computer Simulation
      5. 13.5 Period Detection
      6. 13.6 A Monte Carlo Approach to Prediction
      7. 13.7 Conclusions
      8. References
  13. Part Eight: Diffusion Models
    1. Chapter 14: Urban Agglomeration Through the Diffusion of Investment Impacts
      1. 14.1 Introduction
      2. 14.2 The Model
      3. 14.3 Mathematical Analysis for Agglomeration Conditions
      4. 14.4 Simulation Results
      5. 14.5 Conclusions
      6. References
  14. Part Nine: Game Theory
    1. Chapter 15: From Colonel Blotto to Field Marshall Blotto
      1. 15.1 Introduction
      2. 15.2 The Colonel Blotto Game and its Extensions
      3. 15.3 Incorporating a Spatial Interaction Model of Threat
      4. 15.4 Two-front Battles
      5. 15.5 Comparing Even and Uneven Allocations in a Scenario with Five Fronts
      6. 15.6 Conclusion
      7. References
    2. Chapter 16: Modelling Strategic Interactions in a Global Context
      1. 16.1 Introduction
      2. 16.2 The Theoretical Model
      3. 16.3 Strategic Estimation
      4. 16.4 International Sources of Uncertainty in the Context of Repression and Rebellion
      5. 16.5 International Sources of Uncertainty Related to Outcomes
      6. 16.6 Empirical Analysis
      7. 16.7 Results
      8. 16.8 Additional Considerations Related to International Uncertainty
      9. 16.9 Conclusion
      10. References
    3. Chapter 17: A General Framework for Static, Spatially Explicit Games of Search and Concealment
      1. 17.1 Introduction
      2. 17.2 Game Theoretic Concepts
      3. 17.3 Games of Search and Security: A Review
      4. 17.4 The Static Spatial Search Game (SSSG)
      5. 17.5 The Graph Search Game (GSG)
      6. 17.6 Summary and Conclusions
      7. References
  15. Part Ten: Networks
    1. Chapter 18: Network Evolution: A Transport Example
      1. 18.1 Introduction
      2. 18.2 A Hierarchical Retail Structure Model as a Building Block
      3. 18.3 Extensions to Transport Networks
      4. 18.4 An Application in Transport Planning
      5. 18.5 A Case Study: Bagnoli in Naples
      6. 18.6 Conclusion
      7. References
    2. Chapter 19: The Structure of Global Transportation Networks
      1. 19.1 Introduction
      2. 19.2 Method
      3. 19.3 Analysis of the European Map
      4. 19.4 Towards a Global Spatial Economic Map: Economic Analysis by Country
      5. 19.5 An East-west Divide and Natural Economic Behaviour
      6. 19.6 Conclusion
      7. References
    3. Chapter 20: Trade Networks and Optimal Consumption
      1. 20.1 Introduction
      2. 20.2 The Global Economic Model
      3. 20.3 Perturbing Final Demand Vectors
      4. 20.4 Analysis
      5. 20.5 Conclusions
      6. Acknowledgements
      7. References
      8. Appendix
  16. Part Eleven: Integration
    1. Chapter 21: Research Priorities
    2. Index
  17. End User License Agreement