Econophysics and Sociophysics: Trends and Perspectives Book

Preface     XIX
List of Contributors     XXIII
A Thermodynamic Formulation of Economics   Juergen Mimkes     1
Introduction     1
Differential Forms     2
Exact Differential Forms     2
Not Exact Differential Forms     3
The Integrating Factor     4
The First and Second Law of Differential Forms     5
Not Exact Differential Forms in Thermodynamics and Economics     5
The First Law of Economics     6
The First Law: Capital Balance of Production     6
Work (W)     7
Surplus ([Delta]Q)     7
Capital (E)     8
The Second Law of Economics     8
The Second Law: Existence of a System Function (S)     8
The Integrating Factor (T)     8
Entropy and Production Function (S)     9
Pressure and Personal Freedom     9
The Exact Differential (dS(T,V))     9
The Maxwell Relation     10
Lagrange Function     10
Statistics     11
Combinations     11
Normal Distribution     11
Polynomial Distribution     11
Lagrange Function in StochasticSystems     12
Boltzmann Distribution     13
Entropy in Economics     16
Entropy as a Production Function     16
Entropy of Commodity Distribution     17
Entropy of Capital Distribution     19
Entropy of Production     20
Summary of Entropy     21
Mechanism of Production and Trade     21
The Carnot Process     21
The Origin of Growth and Wealth     23
World Trade Mechanism     25
Returns     26
Dynamics of Production: Economic Growth     27
Two Interdependent Systems; Industry and Households     27
Linear and Exponential Growth (0 < p < 0.5)     28
Trailing Economies: USA and Japan (0.5 < p < 1)     29
Converging Economies, West and East Germany (p > 1)     29
Conclusion     29
References     53
Zero-intelligence Models of Limit-order Markets   Robin Stinchcombe     35
Introduction     35
Possible Zero-intelligence Models     39
Data Analysis and Empirical Facts Regarding Statics     41
Dynamics: Processes, Rates, and Relationships     45
Resulting Model     49
Results from the Model     50
Analytic Studies: Introduction and Mean-field Approach     51
Random-walk Analyses     54
Independent Interval Approximation     59
Concluding Discussion     60
References     62
Understanding and Managing the Future Evolution of a Competitive Multi-agent Population   David M.D. Smith   Neil F. Johnson     65
Introduction     65
A Game of Two Dice     67
Formal Description of the System's Evolution     77
Binary Agent Resource System     81
Natural Evolution: No System Management     83
Evolution Management via Perturbations to Population's Composition     87
Reducing the Future-Cast Formalism     91
Concluding Remarks and Discussion     95
References     97
Growth of Firms and Networks   Yoshi Fujiwara   Hideaki Aoyama   Wataru Souma     99
Introduction     99
Growth of Firms     101
Dataset of European Firms     101
Pareto-Zipf's Law for Distribution     103
Gibrat's Law for Growth     103
Detailed Balance     105
Pareto-Zipf and Gibrat under Detailed Balance      107
Kinematics     108
Growth of Firms and Universality of Zipf's Law     109
Small and Mid-sized Firms     113
Data for Small and Mid-sized Firms     113
Growth and Fluctuations     114
Network of Firms     117
Shareholding Networks     117
Degree Distribution     117
Correlation Between Degree and a Firm's Growth     119
Simple Model of Shareholding Network     120
Business Networks     122
Bankruptcy of Firms     122
Distribution of Debt     123
Lifetime of Bankrupted Firms     124
Chain of Bankruptcy and Business Network     125
Conclusion     127
References     128
A Review of Empirical Studies and Models of Income Distributions in Society   Peter Richmond   Stefan Hutzler   Ricardo Coelho   Przemek Repetowicz     131
Introduction     131
Pareto and Early Models of Wealth Distribution     132
Pareto's Law     132
Pareto's View of Society     135
Gibrat and Rules of Proportionate Growth     137
The Stochastic Model of Champernowne     138
Mandelbrot's Weighted Mixtures and Maximum Choice     139
Current Studies     140
Generalized Lotka-Volterra Model     141
Family Network Model     143
Collision Models     145
A Case Study of UK Income Data     148
Conclusions     157
References     158
Models of Wealth Distributions - A Perspective   Abhijit Kar Gupta     161
Introduction     161
Pure Gambling     164
Uniform Saving Propensity     166
Distributed Saving Propensity     169
Power Law from Mean-field Analysis     171
Power Law from Reduced Situation     172
Understanding by Means of the Transition Matrix     173
Distributions from the Generic Situation     177
Role of Selective Interaction     180
Measure of Inequality     183
Distribution by Maximizing Inequality     185
Confusions and Conclusions     187
References     189
The Contribution of Money-transfer Models to Economics   Yougui Wang   Ning Xi   Ning Ding     191
Introduction     191
Understanding Monetary Circulation     194
Velocity of Money Circulation and its Determinants     194
Holding Time versus Velocity of Money     196
From Holding Time to Velocity of Money     196
Calculation of Average Holding Time     198
Keynesian Multiplier versus Velocity of Money     199
Inspecting Money Creation and its Impacts     201
Money Creation and Monetary Aggregate     202
A Simplified Multiplier Model     202
A Modified Money-transfer Model     203
Money Creation and Velocity of Money     205
Velocity of Narrow Money     205
Velocity of Broad Money     208
Refining Economic Mobility     210
Concept and Index of Measurement     211
Mobility in a Money-transfer Model     212
Modification in the Measurement Index     214
Summary     216
References     216
Fluctuations in Foreign Exchange markets   Yukihiro Aiba   Naomichi Hatano     219
Introduction     219
Modeling Financial Fluctuations with Concepts of Statistical Physics     220
Sznajd Model     220
Sato and Takayasu's Dealer Model     222
Triangular Arbitrage as an Interaction among Foreign Exchange Rates      225
A Macroscopic Model of a Triangular Arbitrage Transaction     228
Basic Time Evolution     230
Estimation of Parameters     231
A Microscopic Model of Triangular Arbitrage Transaction     236
Microscopic Model of Triangular Arbitrage: Two Interacting ST Models     237
The Microscopic Parameters and the Macroscopic Spring Constant     240
Summary     246
References     246
Econophysics of Stock and Foreign Currency Exchange Markets   Marcel Ausloos     249
A Few Robust Techniques     251
Detrended Fluctuation Analysis Technique     251
Zipf Analysis Technique     254
Other Techniques for Searching for Correlations in Financial Indices     255
Statistical, Phenomenological and "Microscopic" Models     258
ARCH, GARCH, EGARCH, IGARCH, FIGARCH Models     259
Distribution of Returns     260
Crashes     265
Crash Models     267
The Maslov Model     268
The Sandpile Model     268
Percolation Models     269
The Cont-Bouchaud model     270
Crash Precursor Patterns     272
The Lux-Marchesi Model     274
The Spin Models     275
References     276
A Thermodynamic Formulation of Social Science   Juergen Mimkes     279
Introduction     279
Probability     280
Normal Distribution     280
Constraints     281
Probability with Constraints (Lagrange Principle)     282
Elements of Societies     283
Agents     284
Groups     284
Interactions     286
Classes     287
States: Collective vs Individual     289
Homogenious Societies     291
The Three States of Homogeneous Societies     291
Atomic Systems: H2O     291
Social Systems: Guided Tours     292
Economic Systems: Companies     292
Political Systems: Countries     293
Change of State, Crisis, Revolution     294
Hierarchy, Democracy and Fertility     294
Heterogeneous Societies     296
The Six States of Binary Societies     296
Partnership     298
Integration     299
Segregation     300
Dynamics of Societies     301
Hierarchy and Opinion Formation      301
Simulation of Segregation     304
Phase Diagrams     304
Intermarriage     305
Simulation of Aggression     307
Conclusion     308
References     309
Computer Simulation of Language Competition by Physicists   Christian Schulze   Dietrich Stauffer     311
Introduction     311
Differential Equations     312
Microscopic Models     320
Few Languages     320
Many Languages     321
Colonization     321
Bit-string Model     323
Conclusion     329
Appendix     331
Viviane Colonization Model     331
Our Bit-string Model     331
References     337
Social Opinion Dynamics   Gerard Weisbuch     339
Introduction     339
Binary Opinions     341
Full Mixing     342
Lattices as Surrogate Social Nets     343
Cellular Automata     344
Growth     344
INCA     346
Probabilistic Dynamics     348
Group Processes     349
Continuous Opinion Dynamics      349
The Basic Case: Complete Mixing and one Fixed Threshold     350
Social Networks     352
Extremism     354
Diffusion of Culture     357
Binary Traits     357
Results     358
Axelrod Model of Cultural Diffusion     359
Conclusions     360
Range and Limits of Opinion Dynamics Models     360
How to Convince     360
How to Make Business     361
Final Conclusions     364
References     364
Opinion Dynamics, Minority Spreading and Heterogeneous Beliefs   Serge Galam     367
The Interplay of Rational Choices and Beliefs     367
Rumors and Collective Opinions in a Perfect World     370
Arguing by Groups of Size Three     372
Arguing by Groups of Size Four     372
Contradictory Public Opinions in Similar Areas     375
Segregation, Democratic Extremism and Coexistence     378
Arguing in Groups of Various Sizes     381
The Model is Capable of Predictions     388
Sociophysics is a Promising Field     390
References     391
Global Terrorism versus Social Permeability to Underground Activities   Serge Galam      393
Terrorism and Social Permeability     394
A Short Introduction to Percolation     395
Modeling a Complex Problem as Physicists do     396
The World Social Grid     398
Passive Supporters and Open Spaces to Terrorists     400
The Geometry of Terrorism is Volatile     404
From the Model to Some Real Facts of Terrorism     406
When Regional Terrorism Turns Global     409
The Situation Seems Hopeless     412
Reversing the Strategy from Military to Political     413
Conclusion and Some Hints for the Future     415
References     416
How a "Hit" is Born: The Emergence of Popularity from the Dynamics of Collective Choice   Sitabhra Sinha   Raj Kumar Pan     417
Introduction     417
Empirical Popularity Distributions     419
Examples     421
City Size     421
Company Size     422
Scientists and Scientific Papers     422
Newspaper and Magazines     424
Movies     424
Websites and Blogs     428
File Downloads     430
Groups     431
Elections     431
Books      434
Language     435
Time-evolution of Popularity     436
Discussion     437
Models of Popularity Distribution     438
A Model for Bimodal Distribution of Collective Choice     440
Conclusions     444
References     446
Crowd Dynamics   Anders Johansson   Dirk Helbing     449
Pedestrian Modeling: A Survey     449
State-of-the-art of Pedestrian Modeling     450
Social-force Model     450
Cellular Automata Models     451
Fluid-dynamic Models     451
Queueing Models     451
Calibration and Validation     451
Self-organization     452
Lane Formation     453
Strip Formation     454
Turbulent and Stop-and-go Waves     455
Other Collective Crowd Phenomena     456
Herding     456
Synchronization     456
Traffic Organization in Ants     457
Pedestrian Trail Formation     457
Bottlenecks     458
Uni-directional Bottleneck Flows     458
Analytical Treatment of Evacuation Through an Exit     459
Intermittent Flows and Faster-is-slower Effect     461
Quantifying the Obstruction Effect     461
Bi-directional Bottleneck Flows     463
Optimization     463
Pedestrian Flow Optimization with a Genetic Algorithm     463
Boolean Grid Representation     464
Results     466
Optimization of Parameter Values     467
Summary and Selected Applications     470
References     471
Complexities of Social Networks: A Physicist's Perspective   Parongama Sen     473
Introduction     473
The Beginning: Milgram's Experiments     474
Topological Properties of Networks     474
Some Prototypes of Small-world Networks     477
Watts and Strogatz (WS) Network     478
Networks with Small-world and Scale-free Properties     478
Euclidean and Time-dependent Networks     479
Social Networks: Classification and Examples     479
Distinctive Features of Social Networks     481
Community Structure in Social Networks     482
Detecting Communities: Basic Methods     483
Agglomerative and Divisive Methods     483
A Measure of the Community Structure Identification      483
Some Novel Community Detection Algorithms     485
Optimization Methods     486
Spectral Methods     487
Methods Based on Dissimilarity     488
Another Local Method     489
Community-detection Methods Based on Physics     489
Network as an Electric Circuit     489
Application of Potts and Ising Models     490
Overlap of Communities and a Network at a Higher Level     491
Preferential Attachment of Communities     493
Models of Social Networks     493
Static Models     493
Dynamical Models     496
Is it Really a Small World? Searching: Post Milgram     498
Searching in Small-world Networks     498
Searching in Scale-free Graphs     499
Search in a Social Network     499
Experimental Studies of Searching     500
Endnote     501
Appendix: The Indian Railways Network     502
References     502
Emergence of Memory in Networks of Nonlinear Units: From Neurons to Plant Cells   Jun-ichi Inoue     507
Introduction     507
Neural Networks     508
The Model System     509
Equations of States      510
p = 1 Case     510
Entropy of the System     512
Internal Energy Density     513
Compressibility     513
Overlap at the Ground State for [mu] = 0     514
Replica Symmetric Calculations for the Case of Extensive Patterns     514
Evaluation of the Saddle Point     517
Phase Diagrams     518
Para-spin-glass Phase Boundary     519
Critical Chemical Potential [mu subscript c] at T = 0     520
Saddle-point Equations for [mu] < [mu subscript c] at T = 0     520
Entropy of the System     521
High-temperature Limit     522
At the Ground State     522
Internal Energy     523
The Compressibility     524
Summary: Neural Networks     525
Plant Intelligence: Brief Introduction     525
The I-V Characteristics of Cell Membranes     526
A Solvable Plant-intelligence Model and its Replica Analysis     527
Replica Symmetric Solution     527
Phase Diagrams     528
Saddle-point Equations     529
T = 0 Noiseless Limit     529
Spin-glass Para-phase Boundary     529
Phase Diagrams for T [NotEqual] 0      530
Negative [lambda] case     530
Summary and Discussion     531
References     533
Self-organization Principles in Supply Networks and Production Systems   Dirk Helbing   Thomas Seidel   Stefan Lammer   Karsten Peters     535
Introduction     535
Complex Dynamics and Chaos     537
The Slower-is-faster Effect     539
Observations in Traffic Systems     541
Panicking Pedestrians     541
Freeway Traffic     541
Intersecting Vehicle and Pedestrian Streams     543
Relevance to Production and Logistics     545
Semi-conductor Chip Manufacturing     545
Container Terminals     545
Packaging and Other Industries     547
Adaptive Control     550
Traffic Equations for Production Systems     550
Re-routing Strategies and Machine Utilization     552
Self-organized Scheduling     554
Summary and Outlook     557
References     558
Can we Recognize an Innovation?: Perspective from an Evolving Network Model   Sanjay Jain   Sandeep Krishna     561
Introduction     561
A Framework for Modeling Innovation: Graph Theory and Dynamical Systems     563
Definition of the Model System     564
Time Evolution of the System     566
Innovation     567
Six Categories of Innovation     572
A Short-lived Innovation: Uncaring and Unviable Winners&n