Buch, Englisch, 432 Seiten, Format (B × H): 168 mm x 246 mm, Gewicht: 975 g
Reihe: Wiley Series in Computational and Quantitative Social Science
New Tools for Complexity Science
Buch, Englisch, 432 Seiten, Format (B × H): 168 mm x 246 mm, Gewicht: 975 g
Reihe: Wiley Series in Computational and Quantitative Social Science
ISBN: 978-1-118-92227-9
Verlag: Wiley
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.
Autoren/Hrsg.
Fachgebiete
- Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
- Sozialwissenschaften Soziologie | Soziale Arbeit Soziologie Allgemein Empirische Sozialforschung, Statistik
- Wirtschaftswissenschaften Volkswirtschaftslehre Regional- und Städtische Wirtschaft
- Mathematik | Informatik Mathematik Mathematik Interdisziplinär Systemtheorie
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
Weitere Infos & Material
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
4.2.1 The Method 34
4.2.2 With All Initial Values Equal 35
4.2.3 Equivalence to Entropy Maximisation 36
4.2.4 Estimation with Some Known Flows 37
4.2.5 Drawbacks to Estimating Services Flows with IPF 37
4.3 Estimating Services Flows Using Commodities Flows 37
4.3.1 The Gravity Model 37
4.3.2 Splitting Up Value Added 40
4.4 A Comparison of The Methods 40
4.4.1 Unbalanced Row and Column Margins 42
4.4.2 Iterative Proportional Fitting 42
4.4.3 Gravity Model 42
4.4.4 Gravity Model Followed by IPF 44
4.5 Results 45
4.5.1 Selecting a Representative Sector 45
4.5.2 Estimated in-Sample Flows 46
4.5.3 Estimated Export Totals 47
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
5.4.1 Concept 54
5.4.2 Estimation Procedure 55
5.4.3 Cross-Validation 57
5.5 In-Sample Assessment of The Estimates 58
5.5.1 Summary Statistics 58
5.5.2 Visual Comparison 61
5.6 Out-of-Sample Discussion of The Estimates 63
5.6.1 Final Demand Closeness 63
5.6.2 Technical Coefficient Clustering 65
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
6.5.1 The Accounts for the Farming Industry 79
6.5.2 A Final Point on The Farming Flows 79
6.6 The Algorithm to Determine The Natural Resources Trade Flows 80
6.6.1 The Accounts for The Natural Resources Sector 80
6.7 The Algorithm to Determine Manufacturing Trade Flows 81
6.7.1 The Accounts for The Manufacturing Industry 82
6.8 The Dynamics 83
6.9 Experimental Results 84
6.9.1 Concluding Comments 88
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
7.2.1 Definitions 92
7.2.2 The Production Account 94
7.2.3 The Commodity Markets Account 94
7.2.4 The Household Account 94
7.2.5 The Capital Markets Account 94
7.2.6 The Rest of the World (RoW) Account 94
7.2.7 The Government Account 95
7.2.8 The Net Worth of an Economy and Revaluations 95
7.2.9 Overview of the National Accounts 95
7.2.10 Closing the Model: Making Final Demand Endogenous 96
7.3 The Dynamical International Model 97
7.3.1 Supply and Demand 97
7.3.2 The National Accounts Revisited 99
7.4 Investment: Modelling Production Capacity: The Capacity Planning Model 100
7.4.1 The Multi-region, Multi-sector Capacity Planning Model 100
7.5 Modelling Production Capacity: The Investment Growth Approach 103
7.5.1 Multi-region, multi-sector Investment Growth Models with Reversibility 103
7.5.2 One-country, One-sector Investment Growth Model with Reversibility 104
7.5.3 Two-country, Two-sector Investment Growth Model with Reversibility 106
7.5.4 A Multi-region, Multi-sector, Investment Growth Model without Reversibility 108
7.5.5 A Multi-region, Multi-sector, Investment Growth Model without Reversibility, with Variable Trade Coefficients 111
7.5.6 Dynamical Final Demand 114
7.5.7 Labour 115
7.5.8 The Price Model 118
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
8.1.1 Clustering 127
8.1.2 Clustering of Urban Crime 129
8.1.3 The Knox Test 130
8.2 Application in Novel Areas 132
8.2.1 Maritime Piracy 132
8.2.2 Space–Time Clustering of Piracy 134
8.2.3 Insurgency and Counterinsurgency in Iraq 136
8.3 Motif Analysis 138
8.3.1 Introduction 138
8.3.2 Event Networks 140
8.3.3 Network Motifs 140
8.3.4 Statistical Analysis 141
8.3.5 Random Network Generation 142
8.3.6 Results 143
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
9.2 Characteristics of Disorder 156
9.3 The Model 158
9.3.1 Outline 158
9.3.2 General Concepts 158
9.3.3 Riot Participation 159
9.3.4 Spatial Assignment 160
9.3.5 Interaction between Police and Rioters 162
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
11.6.1 Two Models of Global Military Expenditure 207
11.6.2 The Alliance Measure C ij 208
11.6.3 A Spatial Richardson Model of Global Military Expenditure 210
11.6.4 Results 211
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
12.3.1 Defining Maritime Piracy Maps 221
12.3.2 Defining Vessel Route Maps 222
12.3.3 Defining Pirates’, Naval Units’ and Vessels’ Behaviours 224
12.3.4 Comparing Risk Maps 227
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
13.2.1 Binary Classification 238
13.2.2 Measures of Classifier Performance 238
13.2.3 Stochastic Processes 240
13.3 The NANIA Predator–prey Model 241
13.3.1 Background 241
13.3.2 An ODD Description of the NANIA Model 241
13.3.3 Behaviour of the NANIA Model 245
13.3.4 Extinctions in the NANIA Model 246
13.4 Computer Simulation 247
13.4.1 Data Generation 247
13.4.2 Categorisation of the Data 249
13.5 Period Detection 249
13.6 A Monte Carlo Approach to Prediction 252
13.6.1 Binned Data 252
13.6.2 Confidence Intervals 257
13.6.3 Predicting Extinctions using Binned Population Data 257
13.6.4 ROC and Precision-recall Curves for Monte Carlo Prediction of Predator Extinctions 260
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
14.3.1 Introduction 272
14.3.2 Case: r 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<
