From Politics and Finance to Power Grids and Products: Addressing Complexity in the Interconnected World

Transcription

1 From Politics and Finance to Power Grids and Products: Addressing Complexity in the Interconnected World Dan Braha

2 You are Currently Using Complex Systems routers connected by physical connections generators connected by transmission lines Number of links The number of links grows faster than the number of nodes Number of nodes

3 You are Currently Using Complex Systems Before Robustness Against Attacks After Fraction of Largest Component Random Failure Targeted Failure Fraction of Nodes Removed

4 Giant Component Appearance of Connectivity Thin-tailed Contagion and Viral Spreading Wild Variability Fat-tailed Fat-tailed extremely large Skewness or coefficient of variation Thin-tailed % Open Problems Global Corporate Control Large-Scale Vehicle Design Interior Sedan Exterior Sedan Time Fan In- In-In Fan Out Loans among Financial Institutions Common Themes Universality patterns found to be the same in a wide variety of systems Internet Protein Food Web Universality Wild Variability very uneven distribution of connections. Some nodes are very highly connected ( hubs ), while most have small degrees Number of links Coupling and correlations extent of dependencies and range of correlation between subsystems Degree- Degree Fan In- Fan Out Number of links In-In In-Out Out-In Out-Out

5 Common Themes linear linear size of police force size of police force nonlinear, nonlinear, gradual decay threshold, size of police force size of police force Product Development Stock Market Ecosystem coupling panic/news harvest rate project time/budget crime rate crime rate systemic risk crime rate crime rate biomass Out-of-Equilibrium Dynamics Firm and Industry Dynamics 2005 Civil Unrest in France Phase transitions changes in qualitative behavior between different states of organization System State Conditions Out-of-Equilibrium dynamics behavior driven by internal ordering and external perturbations

6 Why large scale engineering systems fail? Mars Climate Orbiter Gulf of Mexico Disaster damage to thermal protection tiles multiple lightning strikes mixture of pounds and kilograms sea-floor oil gusher Why technology projects fail? Advanced Automation System Taurus Paperless Stock Trading System Started: 1990 Scrapped: 1993 Spent: $600M Started: 1982 Scrapped: 1994 Spent: $6B connectivity and coupling

7 Complex Engineering Networks engineering nodes ( people, tasks, subroutines, logic gates ) connected by information flows ( engineering change orders, parameters, specifications, signals )

8 Complex Engineering Networks Sparseness Small World

9 Complex Engineering Networks Product Development Nodes: 582 Links: 4123 Nodes: 889 Links: 8178 Sending information to Sending information to Fat-tailed in-degree and out-degree distributions Receiving information from Number of links Linux Kernel Receiving information from Number of links Electronic Circuit Nodes: 5420 Links: Nodes: Links: Information Bottlenecks (Receivers & Generators) Asymmetric Information Flows Sending information to Sending information to Receiving information from Receiving information from Number of links Number of links

10 Error/Change Propagation on Complex Engineering Networks Coupling Coefficient Recovery Coefficient Coupling Dynamics Information flow dynamics is controlled by the extent of coupling and correlations % Open Problems Exterior Sedan Interior Sedan Time

11 Error/Change Propagation in Complex Engineering Networks (Random Network) Stability Recovery Coefficient r average connectivity Instability Coupling Coefficient,

12 Error/Change Propagation in Complex Engineering Networks (Random Network) Recovery Coefficient r average connectivity Coupling Coefficient,

13 Error/Change Propagation in Complex Engineering Networks (Correlated Network) Error Recovery r Stability Instability Error Diffusion,

14 Java-based development projects at the Apache Software Foundation Negative binomial regression models Expected number = of defects e ( 1 correlations + 2 skewness + other factors ) per product (Sosa et al, JMD 2011) Harnessing Complex Engineering Networks Focusing engineering efforts of central nodes Civil Engineering Software High leverage Fraction of controlled nodes High leverage Financial Networks and Systemic Risk setting higher regulatory requirements on highly connected banks (e.g., capital/liquidity ratios)

15 Robustness and Fragility of Complex Engineering Networks Civil Engineering High vulnerability Software High vulnerability random random High error tolerance Fraction of weakened nodes High error tolerance Financial Networks and Systemic Risk Connectivity between financial institutions could lead to diversification and reduction of individual risk; but at the same time increase systemic risk.

16 How complex socio-economic systems evolve in the first place? out-of-equilibrium dynamics and universal mechanisms in space and time

17 Modeling Spatial Socio-Economic Networks Competition Financial R&D Formal Joint ventures

18 Modeling Spatial Socio-Economic Networks Distance (km) Link length (km) Firms embedded in physical space In/out degree distributions Probability Competition with others Competition from others Competition probability and geographic distance Competition probability Probability # competitors Link length distribution

19 The Evolution of Spatial Socio-Economic Networks Geographical location of firms 2000 Population density Firm and Industry Dynamics 1) Latitude and longitude of a new firm determined by population density 2) Connect new firm i to established firm j with probability: p k i j j d ij

20 The Evolution of Spatial Socio-Economic Networks Degree as a Signaling Mechanism Firm size 1) Latitude and longitude of a new firm determined by the population density # Competitors Firm and Industry Dynamics 2) New firms assigned a size of "one arbitrary unit. 3) Connect new firm i to established firm j with probability: p s i j j d ij 4) Evolve firms size according to Gibrat's Law

21 Comparing Models with Empirical Observations Link length distributions Degree distributions Probability Model 1 Real Model 1 Model Model 2 2 Probability Real Model 1 Model 2 Link length # Competitors All effects occur simultaneously Geographic Distance Cumulative Advantage Population Density

22 Why financial systems crash? Contagion and herding, phase transitions, and out-of equilibrium dynamics

23 Social and Economic Contagion Fads and fashion trends Ideas and innovations Conventions, norms and standards Rumors Teen smoking Ebb and flow of crime waves Financial bubbles Social unrest Obesity

24 Tulip Mania (Holland, ) Status symbol Semper Augustus Supply squeeze Mosaic virus and "broken flowers Speculators and future contracts traded in Dutch taverns ( ) Rare bulb sold for 5,200 guilders (A skilled craftsman could expect to get 150 guilders a year) Early collapse: buyers refused to show up at a routine bulb auction Panic had spread across the country

25 South Sea Bubble December 1718 December 1721 I can calculate the movement of the stars, but not the madness of men Newton re-enters with a lot Newton s friends get rich Newton exits happy Newton exits broke Newton invests a bit Wall Street Crash of 1929 Dotcom Crash Bear market of S&P 500 S&P 500 S&P

26 Modeling Financial Contagion good news bad news stock market......

27 number of up stocks good news Modeling Financial Contagion p( k N ) U k 1 N D k k N k N D U 1 N 1 Co-Movement of Stocks total number of stocks bad news U=D=5.79 U=D=3.66 U=D=2.21 Comparing Model with Empirical Observations (Russell 3000) Probability % up stocks % up stocks % up stocks U=D=2.32 U=D=1.77 U=D=1.24 Probability % up stocks % up stocks % up stocks

28 Early Warning Signals of Crises Model parameter and the Dow Jones Industrial Average for the period mimicry parameter Collective mimicry leads to a self-organized crash U Dow U=1 The edge of panic Financial Crisis

29 Financial Contagion: The Fragility of Interdependency US$ trillions Value of Outstanding Derivative Contracts Year

30 Early Warning Signals of Crises mimicry parameter U Early Warning Signal increased mimicry presages self-induced panics and large single day drops in the Dow Relative change

31 what causes the magnitude of civil unrest spreading? Contagion and herding, social networks, and out-of-equilibrium dynamics

32 Social Unrest Contagion civil disorder spread between geographic regions connected through social and communication networks

33 2005 Civil Unrest in France Departments with more car burnings than usual Departments with more car burnings than usual the day before

34 Social Unrest Contagion

35 Observed Social Unrest Event Count Asia Distributions Africa Probability Europe America Total number of civil unrest incidents per year

36 Effect of Mass/Social Media on Civil Unrest Media per Capita Data after 1950 Data before 1950 All Data Probability Year Internet traffic to and from Egypt Total number of civil unrest events Egypt Twitter Influence Network

37 Social Unrest Spatial Contagion Model Small-World Connections Unrest Susceptibility Spontaneous Outburst Infectiousness

38 Comparing Model with Empirical Observations Western Asia South-Eastern Asia Eastern Asia Southern Central Asia Probability Western Africa Southern Africa Middle Africa Eastern Africa Total number of civil unrest incidents per year

39 Comparing Model with Empirical Observations Western Europe Southern Europe Northern Europe Eastern Europe Probability Total number of civil unrest incidents per year Caribbean, Central, and South America North America Probability Total number of civil unrest incidents per year

40 Effect of Network Structure on Civil Unrest Western Asia South-Eastern Asia Cumulative distribution Eastern Asia Southern Central Asia

41 I can calculate the movement of the stars, but not the madness of men