1. NASA Workshop on Collectives Ames Lab, 6 August 2002 Complex System Management: Hoping for the Best by Coping with the Worst Hoping for the best... but coping with the worst Neil F. Johnson n.johnson@physics.ox.ac.uk Department of Physics, Oxford University, U.K. Collaborators on several of the projects discussed: P. Jefferies, D. Lamper, M. Hart, R. Kay, P.M. Hui & Damien Challet

2. Outline Collectives & complex systems: design issues  global outcomes: best-case vs. OK-case vs. worst-case  static vs. dynamical Dynamical collectives: multi-agent models  generalized binary games with time-dependent global resources  deterministic vs. stochastic formalism  undesirable outcomes -- system crashes & their control  -- fate, or just bad luck ?  immunization of a complex system/collective Static collectives: optimal collectives of autonomous defects  near-perfect combinations of defective components  defective component + defective component = working device Winning by losing: optimal collectives of autonomous games  successful combinations of unsuccessful games  lose + lose = win, failure + failure = success, unsafe + unsafe = safe Topology of collectives: network-based multi-agent games Risk management in collectives & complex systems

3. Topic Collectives & complex systems: design issues  global outcomes: best-case vs. OK-case vs. worst-case  static vs. dynamical Dynamical collectives: multi-agent models  generalized binary games with time-dependent global resources  deterministic vs. stochastic formalism  undesirable outcomes -- system crashes & their control  -- fate, or just bad luck ?  immunization of a complex system/collective Static collectives: optimal collectives of autonomous defects  near-perfect combinations of defective components  defective component + defective component = working device Winning by losing: optimal collectives of autonomous games  successful combinations of unsuccessful games  lose + lose = win, failure + failure = success, unsafe + unsafe = safe Topology of collectives: network-based multi-agent games Risk management in collectives & complex systems

4. Complex Systems Many degrees of freedom with internal frustration, feedback, history-dependence, adaptation, evolution, non-stationarity, non-equilibrium, memory, single realization, exogenous effects Collectives, multi-agent systems, forward and inverse problems Mix of deterministic and stochastic behavior The Right Stuff System’s evolution can be optimized, controlled, managed. Robust The Wrong Stuff System has a bad day... Heads down wrong path, leading to dangerous values, fluctuations, crashes. Endogenous and exogenous factors. Instabilities. Spontaneous secondary mission. Brittle The Good Stuff System behaves OK, not great but not bad Avoids bad scenarios, e.g. system crash  PLAN B may be ‘best’ e.g. lowest risk

5.  Consider the global performance S(t) of a collective/complex system  Examples [Workshop website, Tumer & Wolpert]:  throughput in a data network  total scientific information gathered by a constellation of deployable instruments  GDP growth in a human economy  percentage of available free energy exploited by an ecosystem The Right Stuff: optimize/maximize global performance S(t)  mission successful The Good Stuff:  S(t) less/more than S critical for all time t, or time-window T  less/more than S critical for all time t, or time-window T  Var[ S(t) ] less/more than  critical for all time t, or time-window T  less/more than X for any n etc….   mission reasonably successful … not a disaster –  mission not a disaster !

6. system’s time evolution S (t) … + 1 … + 3 … + 4 … + 5 … + 2 real-world static system e.g. minimize error by adjusting initial ‘quenched disorder’ time actual response L +  ideal response L(t) = L

7. … + 1 … + 3 … + 4 … + 5 … + 2 global resource level L(t) deterministic vs. stochastic continuous vs. discrete known vs. unknown endogenous vs. exogenous real-world dynamical system system’s time evolution S (t)

8. … + 1 … + 3 … + 4 … + 5 … + 2 e.g. minimize ‘noise’, typical fluctuation size, hence optimize winnings, efficiency, use of global resource L(t) = L system’s time evolution S (t) killer app: ‘designer system’ I

9. time … + 1 … + 3 … + 4 … + 5 … + 2 e.g. avoid ‘dangerous’ large changes system’s time evolution S (t) killer app: ‘designer system’ II

10. Distribution of increments of S (t )  big problem for standard risk analysis Complex Systems: Tails of the Unexpected Typically Levy-like Sits somewhere between Lorentzian and Gaussian, but hard to tell since finite dataset non-stationarity Fat tails etc. are ‘obvious’ from statistics but … temporal correlations (e.g. system crashes) do not show up!

11. Topic Collectives & complex systems: design issues  global outcomes: best-case vs. OK-case vs. worst-case  static vs. dynamical Dynamical collectives: multi-agent models  generalized binary games with time-dependent global resources  deterministic vs. stochastic formalism  undesirable outcomes -- system crashes & their control  -- fate, or just bad luck ?  immunization of a complex system/collective Static collectives: optimal collectives of autonomous defects  near-perfect combinations of defective components  defective component + defective component = working device Winning by losing: optimal collectives of autonomous games  successful combinations of unsuccessful games  lose + lose = win, failure + failure = success, unsafe + unsafe = safe Topology of collectives: network-based multi-agent games Risk management in collectives & complex systems

12. history at time t +1.... 0 1 1 e.g. buy Binary game Challet & Zhang 0 e.g. sell S N history at time t.... 1 0 agent memory m = 2 strategies limited global resource level don’t enter the game at time t histories In general, define w(t) according to the game of interest SO.... WHAT’S THE GAME ?

13. frequency w time t attendance A (t) L(t)=L+L 0 sin w t system ‘confused’ Binary version of El Farol Game with time-dependent resource level (i.e. seating capacity) L(t) correlation between L(t) and A(t) system ‘learns’

14.  Binary games behave as a stochastically perturbed deterministic system  Replace stochastic term from coin-tossing agents by its mean zJefferies, Hart & NFJ Phys. Rev. E 65, 016105 (2002) Stochastic perturbations from coin-tossing agents Periods of entirely deterministic behaviour Global information  (t) for m=2 Deterministic map of binary game evolution

15. [ PRE 65, 016105 (2002) ] 3040052003 0007010700 4706010040 0000803200 1500040004 0407060300 3000100107 0010300230 0203027040 4070430300 strategy R strategy R’ random matrix  initial strategy allocation  quenched disorder s = 2 In general, success & payoff may not be so simple to define  w(t) complicated functional form Deterministic map of binary game evolution  ‘ attendance ’ = ‘ demand ’ A ( t ) = n 1 (t) - n 0 (t) = D ( t ) [not always true!] ‘ volume ’ V ( t ) = n 1 (t) + n 0 (t)  S (t) strategy score vector  r confidence level   (t) global information  {0,1,..P-1} P = 2 m  a  ( t ) response of strategies to  ( t ) ; a R  {-1,1}   symmetrized strategy allocation tensor  Deterministic game defined by mapping equations:  Binary El Farol Game: w(t) = L(t) V(t) - n 1 (t)  MG: L(t)=0.5 w(t) > 0  1 wins w (t) < 0  0 wins

16. coin-toss Crowd - Anticrowd effect crowd - anticrowd pairs execute uncorrelated random walks sum of variances   … also works for generalized games walk step-size # of walks e.g. MG large crowds   >> 0  wastage but   0 for stochastic strategy use mixed-ability populations J. Phys. A: Math. Gen. 32, L427 (1999) Physica A 298, 537 (2001)

17. $G11 m =3 $G11 m =10 $G13 m =3 $G13 m =10 GCMG m =3GCMG m =10 dynamical properties very sensitive to game’s microstructure Jefferies & NFJ cond-mat/0207523 Design of generalized binary games

18. Jefferies & NFJ, cond-mat/0201540 Lamper & NFJ, PRL 017902 (2002)

19.  During persistence demand described by: time during crash Assume: crash length: participating ‘crash’ nodes  Expected demand (and volume) during crash are thus given by: Anatomy of a system crash Jefferies & NFJ, cond-mat/0201540 Lamper & NFJ, PRL 017902 (2002)

20. Convergence of ‘parallel-world’ trajectories prior to crash Hart & NFJ cond-mat/0207588 Physica A (2002) in press system’s evolution : spread of paths indicates role of ‘fate’ vs. ‘bad luck’

21. Protecting the system Can reduce chances of system crash, by forcing earlier down-movements  system gets immunized Immunizing against system crash Hart & NFJ cond-mat/0207588 Physica A (2002) in press

22. Topic Collectives & complex systems: design issues  global outcomes: best-case vs. OK-case vs. worst-case  static vs. dynamical Dynamical collectives: multi-agent models  generalized binary games with time-dependent global resources  deterministic vs. stochastic formalism  undesirable outcomes -- system crashes & their control  -- fate, or just bad luck ?  immunization of a complex system/collective Static collectives: optimal collectives of autonomous defects  near-perfect combinations of defective components  defective component + defective component = working device Winning by losing: optimal collectives of autonomous games  successful combinations of unsuccessful games  lose + lose = win, failure + failure = success, unsafe + unsafe = safe Topology of collectives: network-based multi-agent games Risk management in collectives & complex systems

23. output … + 1 … + 3 … + 4 … + 5 … + 2 Optimal collectives of autonomous defects e.g. nanodevice output, robot action,... Challet & NFJ, PRL 89, 028701 (2002) Tumer and Wolpert (2002) time actual output L +  ideal output L(t) = L N defective devices with a distribution of errors Combine a subset M < N to form high performance (i.e. low-error) collective: unconstrained, analog constrained, analog unconstrained, binary constrained, binary

24. unconstrained, analog N devices constrained, analog N devices Optimal collectives of autonomous defects e.g. nanodevice output, robot action,... Challet & NFJ, PRL 89, 028701 (2002) Tumer and Wolpert (2002) <><> <><>  med random cost approach average error over all components N = 10 N = 20

25. Optimal collectives of autonomous defects e.g. nanodevice output, robot action,... [Challet & NFJ, PRL (2002)] <><> unconstrained, analog N devices MG with agents accounting for their impact 2 strategies per agent <><>

26. N binary components Each component has I input bits Can perform F different logical operations, hence P = F 2 I transformations f = probability that component i systematically gives wrong output  = fraction of component sets with at least one perfect subset Optimal collectives of autonomous defects e.g. nanodevice output, robot action,... [Challet & NFJ, PRL (2002)] f unconstrained, binary N devices 0.2 0.25 0.3 simple enumeration & sorting 

27. Optimal collectives of autonomous defects e.g. nanodevice output, robot action,... [Challet & NFJ, PRL (2002)] unconstrained, binary N devices 0.2 0.25 0.3 f   Optimum: average over 10,000 samples Majority Game: average over 300 samples, 500P iterations 2 components/agent  = fraction of component sets with at least one perfect subset Majority Game constrains the system to M=N/2 Possible improvement with Grand Canonical Majority Game GCMajG ? simple enumeration & sorting

28. Topic Collectives & complex systems: design issues  global outcomes: best-case vs. OK-case vs. worst-case  static vs. dynamical Dynamical collectives: multi-agent models  generalized binary games with time-dependent global resources  deterministic vs. stochastic formalism  undesirable outcomes -- system crashes & their control  -- fate, or just bad luck ?  immunization of a complex system/collective Static collectives: optimal collectives of autonomous defects  near-perfect combinations of defective components  defective component + defective component = working device Winning by losing: optimal collectives of autonomous games  successful combinations of unsuccessful games  lose + lose = win, failure + failure = success, unsafe + unsafe = safe Topology of collectives: network-based multi-agent games Risk management in collectives & complex systems

29. GAME A rotate randomly by win lose GAME B rotate randomly by Randomly playing Games A and B Winning by losing losing game + losing game = winning game unsafe + unsafe = safe

30. Pareto Nash Switching randomly between 2 ‘losing’ games gives ‘winning’ game

31. +1 -1 -1 +1 +1 +1 Generalization to 2 history-dependent games: R. Kay & NFJ cond-mat/0207386 Application to quantum computing: C.F. Lee & NFJ quant-ph/0203043 J. Parrondo et al. PRL (1999)

32. Topic Collectives & complex systems: design issues  global outcomes: best-case vs. OK-case vs. worst-case  static vs. dynamical Dynamical collectives: multi-agent models  generalized binary games with time-dependent global resources  deterministic vs. stochastic formalism  undesirable outcomes -- system crashes & their control  -- fate, or just bad luck ?  immunization of a complex system/collective Static collectives: optimal collectives of autonomous defects  near-perfect combinations of defective components  defective component + defective component = working device Winning by losing: optimal collectives of autonomous games  successful combinations of unsuccessful games  lose + lose = win, failure + failure = success, unsafe + unsafe = safe Topology of collectives: network-based multi-agent games Risk management in collectives & complex systems

33. Network games Eguiluz & Zimmerman, PRL 85, 5659 (2001)  power-law tails Zheng, NFJ et al., Eur. Phys. J. B 27, 213 (2002) Analytics using generating function  tune power-law exponent Herding  like-minded agents form clusters  power-law distribution of cluster sizes & signal S(t)

34. Topic Collectives & complex systems: design issues  global outcomes: best-case vs. OK-case vs. worst-case  static vs. dynamical Dynamical collectives: multi-agent models  generalized binary games with time-dependent global resources  deterministic vs. stochastic formalism  undesirable outcomes -- system crashes & their control  -- fate, or just bad luck ?  immunization of a complex system/collective Static collectives: optimal collectives of autonomous defects  near-perfect combinations of defective components  defective component + defective component = working device Winning by losing: optimal collectives of autonomous games  successful combinations of unsuccessful games  lose + lose = win, failure + failure = success, unsafe + unsafe = safe Topology of collectives: network-based multi-agent games Risk management in collectives & complex systems

35. Risk management in collectives  borrow terminology from finance [c.f. Hogg, Huberman]  avoid standard local-in-time stochastic p.d.e. approach  allow for non-Gaussian, non-stationary distributions, temporal correlations  include friction due to communication/intervention costs  variation of global `wealth’:  apply ‘no free lunch’  minimize the ‘risk’ by choosing a suitable risk-management strategy

36. no risk management change in ‘wealth’ of system probability mission successful mission unsuccessful

37. risk management … but assume no friction i.e. it ‘costs’ nothing to intervene 30 interventions 3 interventions standard deviation of ‘wealth’ distribution change in ‘wealth’ of system time between interventions probability

38. 30 interventions 3 interventions probability risk management … and friction i.e. it ‘costs’ something to intervene change in ‘wealth’ of system standard deviation of ‘wealth’ distribution time between interventions there is an ‘optimal’ time-delay between interventions