1. netlogo demo

2. Complexity and Networks Melanie Mitchell Portland State University and Santa Fe Institute

3. What are Complex Systems? Large networks of simple interacting elements, which, following simple rules, produce emergent, collective, complex behavior.

4. Brains

7. Insect Colonies

8. Immune Systems

9. Financial Markets

10. Central question for the sciences of complexity

11. How do large networks with

12. Central question for the sciences of complexity How do large networks with — simple components

13. Central question for the sciences of complexity How do large networks with — simple components — limited communication among components

14. Central question for the sciences of complexity How do large networks with — simple components — limited communication among components — no central control

15. Central question for the sciences of complexity How do large networks with — simple components — limited communication among components — no central control give rise to complex (“adaptive”, “living”, “intelligent”) behavior, involving

16. Central question for the sciences of complexity How do large networks with — simple components — limited communication among components — no central control give rise to complex (“adaptive”, “living”, “intelligent”) behavior, involving — information processing and computation

17. Central question for the sciences of complexity How do large networks with — simple components — limited communication among components — no central control give rise to complex (“adaptive”, “living”, “intelligent”) behavior, involving — information processing and computation — complex dynamics

18. Central question for the sciences of complexity How do large networks with — simple components — limited communication among components — no central control give rise to complex (“adaptive”, “living”, “intelligent”) behavior, involving — information processing and computation — complex dynamics — evolution and learning?

19. Core disciplines of the science of complexity

20. Dynamics: The study of continually changing structure and behavior of systems

21. Core disciplines of the science of complexity Dynamics: The study of continually changing structure and behavior of systems Information: The study of representation, symbols, and communication

22. Core disciplines of the science of complexity Dynamics: The study of continually changing structure and behavior of systems Information: The study of representation, symbols, and communication Computation: The study of how systems process information and act on the results

23. Core disciplines of the science of complexity Dynamics: The study of continually changing structure and behavior of systems Information: The study of representation, symbols, and communication Computation: The study of how systems process information and act on the results Evolution and learning: The study of how systems adapt to constantly changing environments

24. Methodologies

28. Goals of the Science of Complexity

29. Cross-disciplinary insights into complex systems

30. Goals of the Science of Complexity Cross-disciplinary insights into complex systems “General” theory?

31. Network Thinking

32. Neural Network (C. Elegans) http://gephi.org/wp-content/uploads/2008/12/screenshot-celegans.png

33. Food Web http://1.bp.blogspot.com/_vIFBm3t8boU/SBhzqbchIeI/AAAAAAAAAXk/RsC- Pj45Avc/s400/food%2Bweb.bmp

34. Metabolic Network http://www.funpecrp.com.br/gmr/year2005/vol3-4/wob01_full_text.htm

35. Genetic Regulatory Network http://expertvoices.nsdl.org/cornell-info204/files/2009/03/figure-3.jpeg

36. Bank Network From Schweitzer et al., Science, 325, 422-425, 2009 http://www.sciencemag.org/cgi/content/full/325/5939/422

37. Airline Routes http://virtualskies.arc.nasa.gov/research/tutorial/images/12routemap.gif

38. US Power Grid http://images.encarta.msn.com/xrefmedia/aencmed/targets/maps/map/000a5302.gif

39. Internet http://www.visualcomplexity.com/vc/images/270_big01.jpg

40. World Wide Web (small part) From M. E. J. Newman and M. Girvin, Physical Review Letters E, 69, 026113, 2004.

41. Social Network http://ucsdnews.ucsd.edu/graphics/images/2007/07-07socialnetworkmapLG.jpg

42. The Science of Networks

43. Are there properties common to all complex networks? The Science of Networks

44. Are there properties common to all complex networks? If so, why? The Science of Networks

45. Are there properties common to all complex networks? If so, why? Can we formulate a general theory of the structure, evolution, and dynamics of networks? The Science of Networks

46. Observed common properties: Small world property Scale-free degree distribution Clustering and community structure Robustness to random node failure Vulnerability to targeted hub attacks Vulnerability to cascading failures

47. Small-World Property (Watts and Strogatz, 1998)

49. me

50. Small-World Property (Watts and Strogatz, 1998) me Barack Obama

51. Small-World Property (Watts and Strogatz, 1998) me Barack Obama my mother

52. Small-World Property (Watts and Strogatz, 1998) me Barack Obama my mother Nancy Bekavac

53. Small-World Property (Watts and Strogatz, 1998) me Barack Obama my mother Nancy Bekavac Hillary Clinton

54. Small-World Property (Watts and Strogatz, 1998) me Barack Obama my mother Nancy Bekavac Hillary Clinton

55. Small-World Property (Watts and Strogatz, 1998) me Barack Obama

56. Small-World Property (Watts and Strogatz, 1998) memy cousin Matt Dunne Barack Obama

57. Small-World Property (Watts and Strogatz, 1998) me Barack Obama Patrick Leahy my cousin Matt Dunne

58. Small-World Property (Watts and Strogatz, 1998) me Barack Obama Patrick Leahy my cousin Matt Dunne

59. Stanley Milgram

60. Nebraska farmer Boston stockbroker

61. Stanley Milgram Nebraska farmer Boston stockbroker

62. Stanley Milgram Nebraska farmer Boston stockbroker

63. Stanley Milgram On average: “six degrees of separation” Nebraska farmer Boston stockbroker

64. The Small-World Property The network has relatively few “long- distance” links but there are short paths between most pairs of nodes, usually created by “hubs”.

65. Most real-world complex networks seem to have the small-world property! The Small-World Property

66. The network has relatively few “long- distance” links but there are short paths between most pairs of nodes, usually created by “hubs”. Most real-world complex networks seem to have the small-world property! But why? The Small-World Property

67. And how can the shortest paths actually be found? The Small-World Property

68. Scale-Free Structure (Albert and Barabási, 1998)

69. Typical structure of World Wide Web (nodes = web pages, links = links between pages) Typical structure of a randomly connected network http://www.dichotomistic.com/images/random %20network.gif part of WWW

70. Concept of “Degree Distribution” A node with degree 3

71. Concept of “Degree Distribution” A node with degree 3

72. Concept of “Degree Distribution” 1 2 3 4 5 6 7 8 9 10 Degree Number of Nodes 65432106543210 A node with degree 3

73. part of WWW Degree Number of nodes Degree Number of nodes

74. part of WWW Degree Number of nodes Degree Number of nodes

75. The Web’s approximate Degree Distribution Number of nodes Degree

76. Number of nodes Degree The Web’s approximate Degree Distribution

77. Number of nodes The Web’s approximate Degree Distribution Number of nodes Degree

78. Number of nodes The Web’s approximate Degree Distribution Number of nodes Degree

79. The Web’s approximate Degree Distribution Number of nodes

80. Degree “Scale-free” distribution The Web’s approximate Degree Distribution Number of nodes

81. Degree “Scale-free” distribution The Web’s approximate Degree Distribution Number of nodes

82. Degree “Scale-free” distribution The Web’s approximate Degree Distribution Number of nodes “power law”

83. Degree “Scale-free” distribution The Web’s approximate Degree Distribution Number of nodes “power law” “Scale-free” distribution = “power law” distribution

84. http://scienceblogs.com/builtonfacts/2009/02/the_central_limit_theorem_made.php Example: Human height follows a normal distribution Height Frequency

85. Example: Population of cities follows a power-law (“scale- free) distribution http://upload.wikimedia.org/wikipedia/commons/4/49/Powercitiesrp.png http://www.streetsblog.org/wp-content/uploads 2006/09/350px_US_Metro_popultion_graph.png http://cheapukferries.files.wordpress.com/2010/06/hollandcit ypopulation1.png

86. part of WWW The scale-free structure of the Web helps to explain why Google works so well

87. It also explains some of the success of other scale-free networks in nature! part of WWW

88. Scale-Free Networks are “fractal-like” http://en.wikipedia.org/wiki/File:WorldWideWebAroundGoogle.png

91. Scale-Free Networks have high clustering part of WWW High Clustering: Low Clustering:

92. High-Clustering Helps in Discovering Community Structure in Networks

94. How are Scale-Free Networks Created?

95. Web pages

98. Preferential attachment demo (Netlogo)

99. Robustness of Scale-Free Networks

100. Vulnerable to targeted “hub” failure

101. Robustness of Scale-Free Networks Vulnerable to targeted “hub” failure Robust to random node failure

102. Robustness of Scale-Free Networks Vulnerable to targeted “hub” failure Robust to random node failure unless.... nodes can cause other nodes to fail Can result in cascading failure

103. August, 2003 electrical blackout in northeast US and Canada 9:29pm 1 day before 9:14pm Day of blackout http://earthobservatory.nasa.gov/ images/imagerecords/3000/3719/ NE_US_OLS2003227.jpg

104. http://www.geocities.com/WallStreet/Exchange/9807/Charts/SP500/fdicfail_0907.jpg

105. We see similar patterns of cascading failure in biological systems, ecological systems, computer and communication networks, wars, etc.

106. Normal (“bell-curve) distribution http://resources.esri.com/help/9.3/arcgisdesktop/com/gp_toolref/process_simulations_sensitivity_analysis_and_error_analysi s_modeling/Random_Normal_Distribution.gif

107. Normal (“bell-curve) distribution http://resources.esri.com/help/9.3/arcgisdesktop/com/gp_toolref/process_simulations_sensitivity_analysis_and_error_analysi s_modeling/Random_Normal_Distribution.gif “Events in ‘tail’ are highly unlikely”

108. Power law (“scale free”) distribution http://www.marketoracle.co.uk/images/mauldin_16_10_07image003.gif

109. Power law (“scale free”) distribution http://www.marketoracle.co.uk/images/mauldin_16_10_07image003.gif Notion of “heavy tail”: Events in tail are more likely than in normal distribution

110. Power law (“scale free”) distribution “More normal than ‘normal’ ” http://www.marketoracle.co.uk/images/mauldin_16_10_07image003.gif

115. Duncan Watts: “Next to the mysteries of dynamics on a network ― whether it be epidemics of disease, cascading failures in power systems, or the outbreak of revolutions ― the problems of networks that we have encountered up to now are just pebbles on the seashore.”