Book description
Geomathematical 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 accountbased models and biproportional fitting, structural dynamics, spacetime statistical analysis, realtime response models, LotkaVolterra models representing ‘war’, agentbased models, epidemiology and reactiondiffusion approaches, game theory, network models and finally, integrated models.
Geomathematical 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
 Cover
 Title Page
 Notes on Contributors
 Acknowledgements
 About the Companion Website
 Part One: Approaches

Part Two: Estimating Missing Data: Biproportional Fitting and Principal Components Analysis
 Chapter 2: The Effects of Economic and Labour Market Inequalities on Interregional Migration in Europe
 Chapter 3: Test of BiProportional Fitting Procedure Applied to International Trade
 Chapter 4: Estimating Services Flows
 Chapter 5: A Method for Estimating Unknown National Input–Output Tables Using Limited Data

Part Three: Dynamics in Accountbased Models

Chapter 6: A Dynamic Global Trade Model With Four Sectors: Food, Natural Resources, Manufactured Goods and Labour
 6.1 Introduction
 6.2 Definition of Variables for System Description
 6.3 The Pricing and Trade Flows Algorithm
 6.4 Initial Setup
 6.5 The Algorithm to Determine Farming Trade Flows
 6.6 The Algorithm to Determine The Natural Resources Trade Flows
 6.7 The Algorithm to Determine Manufacturing Trade Flows
 6.8 The Dynamics
 6.9 Experimental Results
 References

Chapter 7: Global Dynamical Input–Output Modelling
 7.1 Towards a Fully Dynamic Intercountry Input–Output Model
 7.2 National Accounts
 7.3 The Dynamical International Model
 7.4 Investment: Modelling Production Capacity: The Capacity Planning Model
 7.5 Modelling Production Capacity: The Investment Growth Approach
 7.6 Conclusions
 References
 Appendix
 A.1 Proof of Linearity of the Static Model and the Equivalence of Two Modelling Approaches

Chapter 6: A Dynamic Global Trade Model With Four Sectors: Food, Natural Resources, Manufactured Goods and Labour
 Part Four: SpaceTime Statistical Analysis
 Part Five: RealTime Response Models
 Part Six: The Mathematics of War
 Part Seven: AgentBased Models
 Part Eight: Diffusion Models

Part Nine: Game Theory
 Chapter 15: From Colonel Blotto to Field Marshall Blotto

Chapter 16: Modelling Strategic Interactions in a Global Context
 16.1 Introduction
 16.2 The Theoretical Model
 16.3 Strategic Estimation
 16.4 International Sources of Uncertainty in the Context of Repression and Rebellion
 16.5 International Sources of Uncertainty Related to Outcomes
 16.6 Empirical Analysis
 16.7 Results
 16.8 Additional Considerations Related to International Uncertainty
 16.9 Conclusion
 References
 Chapter 17: A General Framework for Static, Spatially Explicit Games of Search and Concealment
 Part Ten: Networks
 Part Eleven: Integration
 End User License Agreement
Product information
 Title: Approaches to Geomathematical Modelling
 Author(s):
 Release date: September 2016
 Publisher(s): Wiley
 ISBN: 9781118922279
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