Trends

1. Trends • Information technology allows us to create systems with bewildering complexity. • Networking which is: • Ubiquitous, pervasive • Convergent, heterogeneous • Hierarchical, multiscale • Biology is shifting from an exclusive focus on the molecular basis of life to systems questions. • Modeling, analysis, and simulation of complex systems.

2. Trends • “Anything we can imagine, we can build.” • Robustness and reliability become the dominant design challenges. • Theoretical foundation is fragmented into fairly isolated technical disciplines: computational complexity, information theory, control theory, dynamical systems. • “New science of complexity” lacks rigor and relevance. • But the need for a new science remains.

3. New science of complexity? • Much attention has been given to “complex adaptive systems” in the last decade. • Popularization of not just information and entropy, but phase transitions, criticality, fractals, self-similarity, power laws, chaos, emergence, self-organization, etc. • Aim is to find universal characteristics of complexity. • From Physics: an emphasis on emergent complexity via self-organization of a homogeneous substrate near a critical or bifurcation point (SOC/EOC).

5. New science of complexity? • The Web/Internet, perhaps more than any other complex system, can be described readily and convincingly in these terms. • Provides a convenient starting place for a critical evaluation of the status of complex systems theory. • Reveals interesting features of the Web/Internet. • Introduce a view (HOT) of complex systems which is radically different from complex-adaptive-systems-edge-of-chaos-self-organized-criticality (CAS/EOC/SOC). • See also next week’s theory seminar by Jean Carlson, Physics, UCSB (Friday, 2pm)

6. Highly Optimized Tolerance (HOT) • Complex systems in biology, ecology, technology, sociology, economics, … • are driven by design or evolution to high-performance states which are also tolerant to uncertainty in the environment and components. • This leads to specialized, modular, hierarchical structures, often with enormous “hidden” complexity, • with new sensitivities to unknown or neglected perturbations and design flaws. • “Robust, yet fragile!”

7. Motivating examples • Web/Internet and convergent, ubiquitous networking • Power and transportation systems • Simulation-based design of complex systems • Biological regulatory networks and evolution • Turbulence in shear flows • Ecosystems and global change • Financial and economic systems • Natural and man-made disasters

8. Uncertainty and Robustness Complexity Interconnection/ Feedback Dynamics Hierarchical/ Multiscale Heterogeneous Nonlinearity

9. Uncertainty and Robustness Complexity Interconnection/ Feedback Dynamics Hierarchical/ Multiscale Heterogeneous Nonlinearity

10. Tight Loose coupling Organisms Turbulent Shear flows Power grid Ecosystems Telephone system Internet Post office Socio-economic systems Ideal gas Homogeneous Heterogeneous

11. Tight Loose coupling Organisms Turbulent Shear flows Power grid HOT Ecosystems Telephone system Internet Post office Socio- economic systems Ideal gas Homogeneous Heterogeneous

12. Uncertainty and Robustness Complexity Interconnection/ Feedback Dynamics Hierarchical/ Multiscale Heterogeneous Nonlinearity

13. Uncertainty and Robustness Complexity Interconnection/ Feedback Dynamics Hierarchical/ Multiscale Heterogeneous Nonlinearity

14. Robustness Complexity Interconnection Aim: simplest possible story

15. All None design Control Theory Information Theory Computational Theory of Complex systems? Complexity Statistical Physics Dynamical Systems 1 dimension 

16. All None design Control Theory Information Theory Computational Internet Complexity Statistical Physics Dynamical Systems 1 dimension 

17. Assumptions Hopefully, you are familiar with: • Internet protocols, HTTP/TCP/IP • Source coding for data compression or • Statistical self-similarity and renormalization, -stable distributions, power laws, fractal noise, etc,

18. High-level functionality How are complex systems structured? Physical implementation

19. Building complexity High-level functionality Layers of rules and protocols Physical implementation

20. Building complexity High-level functionality • Transparent to the user • mostly for robustness • easy to ignore from outside Physical implementation

21. Early computing. Machine code High-level functionality Layers of rules and protocols Logic Transistors Physical implementation

22. Modern computation. User interface Applications High-level functionality Applications Layers of rules and protocols OS Computer Board VLSI Physical implementation

23. VLSI design User interface Instructions Applications Logic Applications Topology OS Geometry Computer Timing Board Fabrication VLSI Silicon

24. Designed versusgeneric Instructions Climate Logic Weather Topology Navier-Stokes Geometry Boltzmann dist Keep only sets of measure zero. Throw away sets of measure zero. Timing particle dynamics Fabrication Quantum mech. Silicon ???

25. Network protocols. HTTP TCP IP

26. Network protocols. HTTP TCP IP Routers

27. Network protocols. HTTP Transparent to the user

28. Network protocols.

29. Network protocols.

30. Network protocols. Transparent to the user Danger: It is easy to weave intriguing but impossible notions about how this works. It often requires great internal complexity to create a robust, simple interface.

31. web traffic Is streamed out on the net. Web client Web servers Creating internet traffic

32. Network protocols. HTTP TCP IP Routers

33. Network protocols. Files HTTP TCP IP packets packets packets packets packets packets Routers

34. web traffic Let’s look at some internet traffic Is streamed out on the net. Web client Web servers Creating internet traffic

35. Notices of the AMS, September 1998

36. Measured Poisson “bursty” on all time scales Internet traffic Standard Poisson models don’t capture long-range correlations.

37. web traffic Let’s look at some web traffic Is streamed out on the net. Web client Web servers Creating internet traffic

38. 6 10 -1 -1/2 4 10 2 10 0 10 -6 -4 -2 0 2 10 10 10 10 10 Data compression (Huffman) WWW files Mbytes (Crovella) Cumulative Frequency Forest fires 1000 km2 (Malamud) Size of events (codewords, files, fires)

39. 3 10 2 10 Frequency of outages > N 1 10 US Power outages 1984-1997 0 10 4 5 6 7 10 10 10 10 N= # of customers affected by outage

40. 3 10 2 10 1 10 2 0 1 10 4 5 6 7 10 10 10 10 Raw data (li,Pi = i) Frequency of outages > N N= # of customers affected by outage

41. 3 10 2 10 1 10 August 10, 1996 0 10 4 5 6 7 10 10 10 10 Frequency of outages > N N= # of customers affected by outage

42. log(probability) p  s--1 Size of events vs. frequency log(Prob > size) log(size)

43. 6 10 4 10 2 10 0 10 -6 -4 -2 0 2 10 10 10 10 10 Raw data DC (li,Pi ) Cumulative WWW Frequency FF Size of events

44. 18 Sep 1998 Forest Fires: An Example of Self-Organized Critical Behavior Bruce D. Malamud, Gleb Morein, Donald L. Turcotte

45. Examples of fat tail distributions • Power outages, forest fires, web files • UNIX files, CPU utilization • Meteor impacts, earthquakes • Deaths and dollars lost due to man-made disasters • Deaths and dollars lost due to natural disasters • Word rank in English (Zipf’s law) • Income and wealth of individuals and companies • Variations in stock prices and federal budgets • Masses or sizes of objects in this room • Ecosystem and specie extinction events? • All of these involve frequencies of “events”

47. Large scale phenomena is extremely non-Gaussian • The microscopic world is largely exponential • The laboratory world is largely Gaussian because of the central limit theorem • The large scale phenomena has heavy tails (fat tails) and power laws

48. Gaussian, Exponential Robust Robust, yet fragile Good (small events) Log(freq.) cumulative Bad (large events) yet fragile Log(event sizes)

49. Power laws and fat tail distributions • We need a clear picture of the origin and nature of power laws and fat tails. • And how various notions of self-similarity are connected.

50. Stable laws Consider a sequence of i.i.d. random variables (white noise) (We’ll assume zero mean, symmetric distributions.) Fix  > 0. For each n  1, define transformations