1. Hypernetworks for systems of systems of systems Jeffrey Johnson, The Open University, UK Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

2. 3 binary relations  one 3-ary relation Binary relations are not rich enough Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

3. Relational Structure Binary relation 3-ary relation 4-ary relation Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

4. Relational Structure Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

5. From networks to simplicial complexes An abstract p-simplex is an ordered set of vertices,  p =  v 0, v 1, v 2, …, v p . v1v1 v0v0 v2v2 v3v3  3 =  v 0, v 1, v 2, v 3 . Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

6. From networks to simplicial complexes An abstract p-simplex is an ordered set of vertices,  p =  v 0, v 1, v 2, …, v p . e.g. the tetrahedron A face is a sub-simplex. e.g. a triangle v1v1 v0v0 v2v2 v3v3  3 =  v 0, v 1, v 2, v 3 .  3 =  v 0, v 1, v 3 . Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

7. From networks to simplicial complexes An abstract p-simplex is an ordered set of vertices,  p =  v 0, v 1, v 2, …, v p . e.g. the tetrahedron A face is a sub-simplex. e.g. a triangle A simplicial complex is a set of simplices with all their faces v1v1 v0v0 v2v2 v3v3  3 =  v 0, v 1, v 2, v 3 . Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

8. From networks to simplicial complexes Every network is a simplicial complex whose simplices have dimension q = 0 or q = 1.  Simplicial complexes are a multidimensional generalisation of networks. Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

9. Gestalt Psychologist Katz: V anilla I ce C ream  c old + y ellow + soft + s weet + v anilla it is a Gestalt – experienced as a whole From Networks to Hypernetworks Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

10. From Networks to Hypernetworks Set of vertices  relational simplex  clique relational simplex Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

11. Gestalt Psychologist Katz: V anilla I ce C ream  c old + y ellow + soft + s weet + v anilla it is a Gestalt. It is a relational simplex From Networks to Hypernetworks  cold, yellow, soft, sweet, vanilla; R Vanilla_Ice_Cream  Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11 the relation is explicit

12. Gin & Tonic is a Gestalt ! Relational Simplex  gin, tonic, ice, lemon; R mixed  Another example of a relational simplex gin ice tonic lemon Hypernetworks of Relational Simplices 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

13. Example: Road Accidents upset rain speed tired The accident is a whole 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

14. Example: Road Accidents upset rain speed tired The accident is a whole the individual parts may not cause an accident 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

15. Heterogeneous Vertices R: A x B  {T rue, F alse }, A  B Relational Structure & Networks b 1 b 3 b 4 b 3 b 4 b 3 b 7 b 8 b 2 b 2 b 6 b 6 a 1 a 2 a 3 a 4 b5b5 EPSRC Taught Courses Networks in Complex Social Systems LSE 18 Dec 2007

16. Heterogeneous Vertices R: A x B  {T rue, F alse }, A  B Relational Structure & Networks b 1 b 3 b 4 b 3 b 4 b 3 b 7 b 8 b 2 b 2 b 6 b 6 a 1 a 2 a 3 a 4 b5b5 a1a2a3a4a1a2a3a4 b1b2b3b4b5b6b7b8b1b2b3b4b5b6b7b8 EPSRC Taught Courses Networks in Complex Social Systems LSE 18 Dec 2007

17. Heterogeneous Vertices R: A x B  {T rue, F alse }, A  B Relational Structure & Networks b 1 b 3 b 4 b 3 b 4 b 3 b 7 b 8 b 2 b 2 b 6 b 6 a 1 a 2 a 3 a 4 b5b5 a1a2a3a4a1a2a3a4 b1b2b3b4b5b6b7b8b1b2b3b4b5b6b7b8 EPSRC Taught Courses Networks in Complex Social Systems LSE 18 Dec 2007

18. Heterogeneous Vertices R: A x B  {T rue, F alse }, A  B Relational Structure & Networks b 1 b 3 b 4 b 3 b 4 b 3 b 7 b 8 b 2 b 2 b 6 b 6 a 1 a 2 a 3 a 4 b5b5 a1a2a3a4a1a2a3a4 b1b2b3b4b5b6b7b8b1b2b3b4b5b6b7b8 EPSRC Taught Courses Networks in Complex Social Systems LSE 18 Dec 2007

19. Heterogeneous Vertices R: A x B  {T rue, F alse }, A  B Relational Structure & Networks b 1 b 3 b 4 b 3 b 4 b 3 b 7 b 8 b 2 b 2 b 6 b 6 a 1 a 2 a 3 a 4 b5b5 a1a2a3a4a1a2a3a4 b1b2b3b4b5b6b7b8b1b2b3b4b5b6b7b8 EPSRC Taught Courses Networks in Complex Social Systems LSE 18 Dec 2007

20. Heterogeneous Vertices R: A x B  {T rue, F alse }, A  B Relational Structure & Networks b 1 b 3 b 4 b 3 b 4 b 3 b 7 b 8 b 2 b 2 b 6 b 6 a 1 a 2 a 3 a 4 b5b5 a1a2a3a4a1a2a3a4 b1b2b3b4b5b6b7b8b1b2b3b4b5b6b7b8 EPSRC Taught Courses Networks in Complex Social Systems LSE 18 Dec 2007

21. Heterogeneous Vertices R: A x B  {T rue, F alse }, A  B Relational Structure & Networks a1a1 a3a3 a4a4 a2a2 b2b2 b3b3 b1b1 b8b8 b7b7 b6b6 b4b4 b5b5 A hypergraph is a generalization of a graph, where edges connect a number of vertices. EPSRC Taught Courses Networks in Complex Social Systems LSE 18 Dec 2007 a1a2a3a4a1a2a3a4

22. Heterogeneous Vertices R: A x B  {T rue, F alse }, A  B Relational Structure & Networks a1a2a3a4a1a2a3a4 b1b2b3b4b5b6b7b8b1b2b3b4b5b6b7b8 a1a1 a3a3 a4a4 a2a2 b2b2 b3b3 b1b1 b8b8 b7b7 b6b6 b4b4 b5b5 A hypergraph is a generalization of a graph, where edges connect a number of vertices. The Galois hypergraph has all intersections. EPSRC Taught Courses Networks in Complex Social Systems LSE 18 Dec 2007

23. Proposition: H A (B,R) has a lattice structure Relational Structure & Networks a1a2a3a4a1a2a3a4 b1b2b3b4b5b6b7b8b1b2b3b4b5b6b7b8 a1a1 a3a3 a4a4 a2a2 b2b2 b3b3 b1b1 b8b8 b7b7 b6b6 b4b4 b5b5 b3b3 {b 2, b 3 } {b 3, b 4 } { b 6 } {b 1, b 2,b 3 } { b 2, b 3, b 4 } {b 3, b 4, b 5, b 6 } {b 6, b7, b8 }  The lattice is defined by the set inclusion partial order on H A (B,R) EPSRC Taught Courses Networks in Complex Social Systems LSE 18 Dec 2007

24. Proposition. There is dual hypergraph with subsets of A. The hyperedges in the dual A-B hypergraphs are paired and form a lattice (the Galois lattice) Relational Structure & Networks EPSRC Taught Courses Networks in Complex Social Systems LSE 18 Dec 2007

25. From networks to simplicial complexes Graphical representations of multidimensional simplices 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece polyhedron representation Euler Polygon Representation

26. From networks to simplicial complexes 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece q-near Interesting structures

27. Polyhedral Connectivity 0- near polyhedra The intersection of two simplices is called their shared face. They are q-near if their shared face has dimension  q 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

28. Polyhedral Connectivity 1- near polyhedra 0- near polyhedra The intersection of two simplices is called their shared face. They are q-near if their shared face has dimension  q 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

29. Polyhedral Connectivity 0- near polyhedra The intersection of two simplices is called their shared face. They are q-near if their shared face has dimension  q 1- near polyhedra (and also 0-near) 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

30. Polyhedral Connectivity 1- near polyhedra 2- near polyhedra 0- near polyhedra

31. Polyhedral Connectivity Polyhedra can be q-connected through shared faces 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

32. Polyhedral Connectivity Polyhedra can be q-connected through shared faces 1-connected components 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

33. Polyhedral Connectivity Polyhedra can be q-connected through shared faces 1-connected components Q-analysis: listing q-components 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

34. Polyhedral Connectivity & q-transmission Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008 The Bull The Dog The Ship The Royal Oak

35. Polyhedral Connectivity & q-transmission My dog’s got No nose How does he smell ? The Bull The Dog The Ship The Royal Oak Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008

36. Polyhedral Connectivity & q-transmission My dog’s got No nose How does he smell ? The Bull The Dog The Ship The Royal Oak Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008

37. Polyhedral Connectivity & q-transmission My dog’s got No nose How does he smell ? The Bull The Dog The Ship The Royal Oak Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008

38. Polyhedral Connectivity & q-transmission My dog’s got No nose How does he smell ? The Bull The Dog The Ship The Royal Oak Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008

39. Polyhedral Connectivity & q-transmission Terrible! How does he smell ? The joke is q-transmitted through the backcloth The Bull The Dog The Ship The Royal Oak Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008

40. A C E B D F Polyhedral Connectivity & q-transmission

41. Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008 A C B D Polyhedral Connectivity & q-transmission E F

42. Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008 A C B D Polyhedral Connectivity & q-transmission E F

43. Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008 A C B D Polyhedral Connectivity & q-transmission E F

44. Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008 A C B D Polyhedral Connectivity & q-transmission E F

45. Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008 A C B D Polyhedral Connectivity & q-transmission E F

46. Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008 A C B D Polyhedral Connectivity & q-transmission E F

47. Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008 A C B D Polyhedral Connectivity & q-transmission E F

48. Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008 A C B D Polyhedral Connectivity & q-transmission E F

49. Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008 A C B D Polyhedral Connectivity & q-transmission E F

50. Hypernetworks for the dynamics of complex multilevel systems ISCTE Lisbon 12-Jan-2008 A C B D Polyhedral Connectivity & q-transmission E F shared face intra-level: interactions through shared faces

51. From Networks to Hypernetworks Simplices by themselves are not rich enough to discriminate things Here – same parts, different relation, different structure & emergence We must have relational simplices

52. Definition A hypernetwork is a set of relational simplices From Networks to Hypernetworks  cold + yellow + soft + sweet + vanilla; R Vanilla_Ice_Cream  e.g. Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

53. Relational Simplices and Multilevel Systems Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

54. Multilevel Systems Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

55. Multilevel Systems Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

56. Multilevel Systems Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

57. e.g. take a set of 3 blocks Formation of simplices  hierarchical structure {} Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

58. {} R R Formation of simplices  hierarchical structure e.g. take a set of 3 blocks assembled by a 3-ary relation Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

59. {} R Formation of simplices  hierarchical structure e.g. take a set of 3 blocks assembled by a 3-ary relation R The structure has an emergent property Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

60. {} R Formation of simplices  hierarchical structure Level N+1 Level N n-ary relation assembles elements into named structures at a higher level Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

61. {} R Formation of simplices  hierarchical structure Arch n-ary relation assembles elements into named structures at a higher level R Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

62. AND and OR aggregations in multilevel systems Sets, classes Structures Sets of parts Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11 Conventional classification trees don’t have alpha aggregations

63. Example: Recognising cells in noisy images

66. Q: Does the virtual contour exist? At what level?

67. Q: Does the virtual contour exist? A: Yes. Our brains make kinds of virtual stuff out of everything. Computers can (and must!) also make these virtual structures for representing multilevel systems.

68. Observing multilevel systems of systems of systems Hypothesis 1 When we look at systems we see the whole & the parts Hypothesis 2 Our brains create new multilevel structures Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

69. Aggregation – deconstruction downward dynamics in representing systems Level N+1 Level N Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

70. Level N+1 Level N Create a new object at Level N ! Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11 Aggregation – deconstruction downward dynamics in representing systems

71. Level N+1 Level N Create a new level - Level N-1 ! And new objects at this level Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11 Aggregation – deconstruction downward dynamics in representing systems

72. Level N+1 Level N Create a new object at Level N Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11 Aggregation – deconstruction downward dynamics in representing systems

73. Level N+1 Level N Create new objects at Level N+1 Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11 Aggregation – deconstruction downward dynamics in representing systems

74. Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11 Aggregation – deconstruction downward dynamics in representing systems

75. Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11 Aggregation – deconstruction downward dynamics in representing systems

76. Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

78. 1.8 Mereology Parts and wholes goes back millennia to Plato and Aristotle. mereology was coined in 1927 by Stanislaw Lesniewski A mereological system is defined to be composed of objects, X, and a binary relation called parthood, ‘x is a part of y’. Winston, Chaffin and Herrmann gave six types of meronymic relations: 1. component integral object (pedal-bike), 2. member-collection (ship-fleet), 3. portion-mass (slice-pie), 4. stuff-object (steel-car), 5. feature-activity (paying-shopping), and 6. place-area (Everglades-Florida).

79. Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11 1.8 Mereology

80. Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11 1.8 Mereology

81. Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11 1.8 Mereology

82. Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11 1.8 Mereology Paying is part of shopping

83. Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11 Backcloth and traffic Relational simplices support patterns of numbers across their faces representing dynamical aspects of the systems. The simplices form a backcloth for the more dynamic traffic … but there are also backcloth dynamics as relational simplices are formed.

84. Multilevel patterns of numbers on the structure Emergent capability Capabilities Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

85. Multilevel patterns of numbers on the structure Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

86. System dynamics as traffic on a fixed multilevel backcloth Dynamics on the hypernetwork backcloth Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

87. Dynamics Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

88. Backcloth dynamics: System time and System Events Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

89. Backcloth dynamics: System time and System Events Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

90. Planning involves changing relations Backcloth dynamics: System time and System Events Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

91. System dynamics involves changing relations … trajectories of multidimensional events Backcloth dynamics: System time and System Events Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11

92. Example: design

93. Example: designing the future - policy

94. Example: robot soccer 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

95. Example: robot soccer 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

96. Example: robot soccer 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

97. Example: robot soccer 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

98. ‘scoring a goal’ Example: robot soccer 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

99. ‘the old 1-2 move’ ‘scoring a goal’ Example: robot soccer 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

100. ‘The old 1-2’ as a trajectory in multidimensional space Example: robot soccer 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

101. ‘The old 1-2’ as a trajectory in multidimensional space Example: robot soccer 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

102. ‘The old 1-2’ as a trajectory in multidimensional space Example: robot soccer 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

103. ‘The old 1-2’ as a trajectory in multidimensional space Example: robot soccer 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

104. ‘The old 1-2’ as a polyhedral trajectory in multidimensional space Example: robot soccer 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

105. formation of a polyhedron is a structural event Passing ball event Goal scoring event Example: robot soccer 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

107. Example Multilevel dynamics of greenhouse gas reduction. UK carbon emission to cuts - 26% by 2020 80% by 2050 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

108. Example Multilevel dynamics of greenhouse gas reduction. UK carbon emission to cuts - 26% by 2020 80% by 2050 2020 2050 Emissions Tipping point huge change in how people live Huge change for individual human agent’s values & beliefs 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

109. 2020 2050 Emissions major changes in beliefs, values, aspiration and behaviour Huge change for individual human agent’s values & beliefs major changes in emissions time series 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

110. 2020 2050 Emissions major changes in beliefs, values, aspiration and behaviour Huge change for individual human agent’s values & beliefs major changes in emissions time series How can we model the intermediate levels ? 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

111. Agents, Climate Change & Systems of Systems of Systems This is a system of systems of systems Greenhouse gas emissions system Land-use transportation subsystem Building heating subsystem Personal belief subsystem Personal norm and values subsystems Personal aspirations subsystem Personal action subsystem 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

112. Agents, Climate Change & Systems of Systems of Systems 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

113. Agents, Climate Change & Systems of Systems of Systems 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

114. Agents, Climate Change & Systems of Systems of Systems Government Policy ? Agents 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

115. Agents, Climate Change & Systems of Systems of Systems Must apply bottom-up agent based models 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

116. Agents, Climate Change & Systems of Systems of Systems Must apply bottom-up agent based models Create a synthetic micropopulaton - used for TRANSIMS transportation model - agents choose where they live & their travel Add data on beliefs, values, aspirations - can model how people change behaviour 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

117. Agents, Climate Change & Systems of Systems of Systems Model agent interactions on the hypernetworks How people change their beliefs values aspirations 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

118. Agents, Climate Change & Systems of Systems of Systems Model agent interactions on the hypernetworks How people change their beliefs values aspirations How people change their behaviour 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

119. Agents, Climate Change & Systems of Systems of Systems Model agent interactions on the hypernetworks How people change their beliefs values aspirations How people change their behaviour Expect rapid changes – tipping points ? 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

120. Agents, Climate Change & Systems of Systems of Systems Government Policy Agents 1st PhD School on “Mathematical Modelling of Complex Systems”. 18-29 July 2011, Patras, Greece

121. Conclusions (1) Relational simplices are essential to represent systems (2) … and to model systems of systems of systems (3) The dynamics of n-ary assembly relations is fundamental (4) Relational simplices at higher levels to their parts (5) Hypernetworks necessary for multilevel dynamics Hypernetworks, network dynamics, influence of network: current tendency in social research Warsaw University 13-14/12/11