List of Figures

1. 1.1 Social media terminology.

2. 1.2 Common expressions of social media information.

3. 1.3 Overview of the organization of this book.

4. 2.1 Topology of major social media sites.

5. 2.2 Example of an internet meme.

6. 3.1 Historical evolution of information spread research.

7. 3.2 Overview of the scientific method.

8. 4.1 Individuals 1 and 2 in a simple symmetric relationship.

9. 4.2 A three-node relationship mapping of individuals 1,2, and 3.

10. 4.3 Individual 2 acts as an intermediary.

11. 4.4 A simplified complex social network.

12. 4.5 U.S. trust in mass media trends.

13. 4.6 Example of a simple triad relationship.

14. 4.7 Randomly generated fifty-node network.

15. 4.8 User interface for the Social Network Visualizer tool.

16. 4.9 Social Network Visualizer: centrality and clustering.

17. 5.1 Comparison of sparse and dense networks.

18. 5.2 Illustration of a structural hole.

19. 5.3 Strong and weak ties.

20. 5.4 A random network demonstrating centrality and distance.

21. 5.5 Sample small world network group.

22. 5.6 Polarization of the U.S. Political Blogosphere

23. 5.7 Revisiting the three-node relationship map.

24. 5.8 Sociogram of a fencing club.

25. 6.1 Microscopic and macroscopic modeling of vehicular traffic.

26. 6.2 Summary of model development steps.

27. 6.3 A spring-mass system.

28. 6.4 A predator-prey system.

29. 6.5 An RLC circuit.

30. 6.6 Sample evolution of an epidemic model.

31. 6.7 Freeway system and ramp metering.

32. 6.8 Experimental findings: flow-occupancy relationship.

33. 6.9 Experimental findings: speed-occupancy relationship.

34. 6.10 Fundamental diagram using Greenshields’ model.

35. 6.11 ODE model for traffic flow on a network arc.

36. 7.1 A state transition for an epidemic model.

37. 7.2 State transitions for an SIR epidemic model.

38. 7.3 Sample system evolution of an SIR epidemic model.

39. 7.4 State transitions for an SEIR epidemic model.

40. 7.5 Herd immunity in SIR-based epidemic models.

41. 7.6 Comparing no intervention and intervention strategies.

42. 7.7 Flow diagram for the Ignorant-Spreader model.

43. 7.8 Time Evolution of an Ignorant-Spreader model

44. 7.9 Flow diagram for the Ignorant-Spreader-Ignorant model.

45. 7.10 Sample evolution of the Ignorant-Spreader-Ignorant model.

46. 7.11 Flow diagram for the Ignorant-Spreader-Recovered model.

47. 7.12 Sample time evolution of an ISR model.

48. 7.13 Sample time evolution of an ISR model.

49. 7.14 R₀ Comparison: low R₀ value.

50. 7.15 R₀ Comparison: high R₀ value.

51. 7.16 Sample time evolution of the ISR model for social media.

52. 7.17 ISR model for social media with decay.

53. 7.18 Flow diagram for ISCR model class interactions.

54. 7.19 ISCR: No counter-spreaders.

55. 7.20 ISCR: Spreaders dominate.

56. 7.21 ISCR: Counter-spreaders dominate.

57. 7.22 ISCR: Even mix of spreaders and counter-spreaders.

58. 7.23 Spreader twice receptive to outside influence.

59. 7.24 Heavily-dominant spreader is much more receptive.

60. 7.25 Spreader is stifled twice as strongly as a counter-spreader.

61. 7.26 Counter-spreader is spreading strongly.

62. 7.27 Flow diagram for ISCR two-community interactions.

63. 7.28 Hybrid ISCR groups: dominant spreader & counter-spreader.

64. 7.29 Hybrid ISCR groups: equal bidirectional diffusion.

65. 7.30 Hybrid ISCR groups: skewed receptivity.

66. 7.31 Hybrid ISCR groups: receptivity tipping point.

67. 7.32 Hybrid ISCR groups: skewed receptivity between the groups.

68. 7.33 Class interactions for the ISSRR model.

69. 7.34 ISSRR scenario: strong Group 1 spreading.

70. 7.35 ISSRR scenario: minor influence of Group 2 over Group 1.

71. 8.1 Brownian motion of large particles.

72. 8.2 Simulation of Brownian motion for two particles.

73. 8.3 Stochastic realization of a sinusoidal signal.

74. 8.4 Stochastic realizations of an ISI network.

75. 9.1 Social networks and external influences.

76. 9.2 Flow diagram for an event-triggered social chatter model.

77. 9.3 Event-triggered social media chatter model without control.

78. 9.4 Event-triggered social media chatter with control.

79. 9.5 Intermittent control over time

80. 10.1 Google Trends search: “iPhone”.

81. 10.2 Google Trends search: “iPhone11”.

82. 10.3 Google Trends search: “iPhone7”.

83. 10.4 Normalized daily tweet volume of event triggered hashtags.

84. 10.5 Daily Tweet volume of shooting-related hashtags.

85. 10.6 Simulation results: event-triggered chatter on #Shooting.

86. 10.7 Normalized daily tweet volume of social campaign hashtags.

87. 10.8 Daily tweet volume of MeToo-related hashtags.

88. 10.9 Simulation results: social chatter on #MeToo.

89. 10.10 Tweet volume of #WhyWeWearBlack.

90. 10.11 Reconstructed ISR groups for #WhyWeWearBlack.

91. 10.12 Simulation of ISR groups without decay.

92. 10.13 Simulation of ISR groups with decay.

93. 10.14 The original The Dress picture.

94. 10.15 Tweet volume of #BlueandBlack and #WhiteandGold.

95. 10.16 Reconstructed ISCR groups.

96. 10.17 Simulation of ISCR groups.

97. 11.1 Control input and output.

98. 11.2 Open-loop control system.

99. 11.3 Bread toaster: open-loop feedback control system.

100. 11.4 Closed-loop control system.

101. 11.5 Cruise control: closed loop control system.

102. 11.6 Multi-Input Multi-Output: three mass swinger.

103. 11.7 Steps for control system design.

104. 12.1 A block diagram of a PID controller.

105. 12.2 Brachystochrone problem.

106. 12.3 Optimal time car problem.

107. 12.4 Sample trajectories.

108. 12.5 Optimal trajectories.

109. 13.1 Social and technical subsystems as socio-technical systems.

110. 13.2 Interaction of social and technical domains.

111. 13.3 Flow diagram for event-triggered social media chatter.

112. 14.1 Comparing intermittent and optimal control

113. 14.2 Control trajectories for intermittent and optimal control.

114. 15.1 Comparing random initial control and optimal control.

115. 15.2 Control trajectories for random and optimal control.