Macroscopic Analysis of Large-scale Systems

Transcription

1 MPI MIS WV Seminar Leipzig, 12 th November 2013 Macroscopic Analysis of Large-scale Systems Robin Lamarche-Perrin Reviewers: Bernard Moulin and Éric Fleury Examiners: Salima Hassas and Brigitte Plateau Supervisors: Yves Demazeau and Jean-Marc Vincent

2 The Analysis of Large-scale Systems 2 System Analysis Observer

3 The Analysis of Large-scale Systems 3 System Large-scale Distributed Nondeterministic Analysis Observer

4 The Analysis of Large-scale Systems 4 System Large-scale Distributed Nondeterministic Microscopic Observation Microscopic Representation Analysis Observer

5 The Analysis of Large-scale Systems 5 System Large-scale Distributed Nondeterministic Microscopic Observation Microscopic Representation Too complex Analysis Observer

6 The Analysis of Large-scale Systems 6 System Large-scale Distributed Nondeterministic Microscopic Observation Microscopic Representation Abstraction Method Macroscopic Representation OK! Analysis Observer

7 The Analysis of Large-scale Systems 7 System Large-scale Distributed Nondeterministic Microscopic Observation Microscopic Representation Abstraction Method Macroscopic Representation OK! Analysis How to generate consistent abstractions out of microscopic data? Observer

8 Analysis of International Relations 8 Geographer International System

9 Analysis of International Relations 9 Hypothesis: media constitute an adequate instrument to observe the national level [Grasland et al., 2011] Geographer International System Media Microscopic Representation

10 Analysis of International Relations 10 Hypothesis: media constitute an adequate instrument to observe the national level [Grasland et al., 2011] Geographer International System Media Microscopic Representation Data Aggregation Macroscopic Representation

11 Data from Print Media 11 The GEOMEDIA Database (ANR CORPUS GUI-AAP-04) THE GUARDIAN THE TIMES OF INDIA Paper 1 Paper 2 Paper newspapers 1,944,000 papers Japan Madrid French Spain GEOGRAPHIC INFORMATION 193 countries (UN members)

12 Data from Print Media 12 The GEOMEDIA Database (ANR CORPUS GUI-AAP-04) THE GUARDIAN THE TIMES OF INDIA Paper 1 Paper 2 Paper newspapers 1,944,000 papers Japan Madrid French Spain GEOGRAPHIC INFORMATION 193 countries (UN members) India Spain

13 Data from Print Media 13 The GEOMEDIA Database (ANR CORPUS GUI-AAP-04) THE GUARDIAN THE TIMES OF INDIA Paper 1 Paper 2 Paper newspapers 1,944,000 papers Japan Madrid French Spain GEOGRAPHIC INFORMATION 193 countries (UN members) 30 th May th May th July 2012 TEMPORAL INFORMATION 889 days / 127 weeks (from the 3 rd May 2011 to today)

14 Time Microscopic Representation of the International System 14 Newspaper LE MONDE Space USA Libya Syria France Israel... Total 2 May May May May May June June June June July July July July Aug Total

15 Time Microscopic Representation of the International System 15 Newspaper LE MONDE t π Israel France Syria Libya USA Space... Total 2 May May May May May June June June June July July July July Aug Total Number of observed citations v π, t

16 Time Microscopic Representation of the International System 16 Newspaper LE MONDE t π Israel France Syria Libya USA Space... Total 2 May May May May May June June June June July July July July Aug Total Number of observed citations v., t v π,. v.,. v π, t Number of expected citations v π, t = v π,. v., t v.,.

17 Time Geographical Representation 17 t Israel France Syria Libya USA Space... Total 2 May May May May May June June June June July July July July Aug Total ρ π, t Observed-to-expected ratio of citation number = v π, t v π, t Spatial variation of the ratio at date t = v π, t v.,. v π,. v., t

18 Detection of Media Events 18 x 2.9 x 2.2 Newspaper LE MONDE in July 2011 MICROSCOPIC REPRESENTATION x 1.7 x 1.3 x 0.8

19 Detection of Media Events 19 x 2.9 x 2.2 Newspaper LE MONDE in July 2011 MICROSCOPIC REPRESENTATION National Event x 1.7 x 1.3 x 0.8 National Event

20 Detection of Media Events 20 x 2.9 x 2.2 Newspaper LE MONDE in July 2011 MICROSCOPIC REPRESENTATION x 1.7 x 1.3 x 0.8 National Events

21 Detection of Media Events 21 x 2.9 x 2.2 Newspaper LE MONDE in July 2011 MICROSCOPIC REPRESENTATION x 1.7 x 1.3 x 0.8 International Event

22 Time Data Aggregation 22 π 1 π 2 π 3 Space t USA Libya Syria France Israel REPRÉSENTATION MICROSCOPIQUE... Total 2 May May May May May June June June June July July July July Aug Total National Events

23 Time Data Aggregation 23 π 1 π 2 π 3 Space USA Aggregate Israel... Total t 2 May May May May May June June June June July July July July Aug Total International Event

24 P1: The Semantics of Geographical Aggregates 24 Geographer

25 P1: The Semantics of Geographical Aggregates 25 Geographer

26 P1: The Semantics of Geographical Aggregates 26 Geographer Latin America

27 P1: The Semantics of Geographical Aggregates 27 Geographer Latin America

28 P1: The Semantics of Geographical Aggregates 28? Geographer Latin America

29 P1: The Semantics of Geographical Aggregates 29? Geographer Latin America Problem 1: How to generate abstractions that are meaningful for the observer?

30 P2: The Levels of Representation 30 x 2.9 x 2.2 Newspaper LE MONDE in July 2011 MICROSCOPIC REPRESENTATION x 1.7 x 1.3 x 0.8

31 P2: The Levels of Representation 31 x 2.9 x 2.2 Newspaper LE MONDE in July 2011 MESOSCOPIC REPRESENTATION x 1.7 x 1.3 x 0.8

32 P2: The Levels of Representation 32 x 2.9 x 2.2 Newspaper LE MONDE in July 2011 MACROSCOPIC REPRESENTATION x 1.7 x 1.3 x 0.8

33 P2: The Levels of Representation 33 x 2.9 x 2.2 Newspaper LE MONDE in July 2011 MACROSCOPIC REPRESENTATION National Event x 1.7 x 1.3 x 0.8 International Event National Event

34 P2: The Levels of Representation 34 x 2.9 x 2.2 Newspaper LE MONDE in July 2011 MULTIRESOLUTION REPRESENTATION National Event x 1.7 x 1.3 x 0.8 International Event National Event

35 P2: The Levels of Representation 35 x 2.9 x 2.2 Newspaper LE MONDE in July 2011 MULTIRESOLUTION REPRESENTATION National Event x 1.7 x 1.3 x 0.8 Problem 2: How to find the representation levels that are relevant for the analysis? International Event National Event

36 P3: The Computation of the Best Representations 36 The number of possible representations exponentially depends on the size of the microscopic representation.

37 P3: The Computation of the Best Representations 37 Le nombre de représentations possibles representation dépend exponentiellement in an efficient de la way? taille de la représentation microscopique Problem 3 : How to compute the optimal

38 And for Other Dimensions? 38 MICROSCOPIC REPRESENTATION Newspaper LE MONDE regarding Syria Frequency on the whole period

39 And for Other Dimensions? 39 MICROSCOPIC REPRESENTATION Week-scale Events Newspaper LE MONDE regarding Syria Frequency on the whole period

40 And for Other Dimensions? 40 MULTIRESOLUTION REPRESENTATION Month-scale Events Newspaper LE MONDE regarding Syria Frequency on the whole period

41 Outline 41 P0 P1 P2 P3 To characterize the aggregation process The algebra of possible partitions To preserve the system s semantics A constrained partitioning method To aggregate according to several dimension Some constraints expressing the system s topology To evaluate and compare the representations Some measures of complexity and information To offer several granularity levels The optimization of a compromise To compute the best representations A generic algorithm of constrained optimization

42 My Approach 42 P0 P1 P2 P3 To characterize the aggregation process The algebra of possible partitions To preserve the system s semantics A constrained partitioning method To aggregate according to several dimension Some constraints expressing the system s topology To evaluate and compare the representations Some measures of complexity and information To offer several granularity levels The optimization of a compromise To compute the best representations A generic algorithm of constrained optimization

43 My Approach 43 P0 P1 P2 P3 To characterize the aggregation process The algebra of possible partitions To preserve the system s semantics A constrained partitioning method To aggregate according to several dimension Some constraints expressing the system s topology To evaluate and compare the representations Some measures of complexity and information To offer several granularity levels The optimization of a compromise To compute the best representations A generic algorithm of constrained optimization

44 The Aggregation Process 44 Partitioning Aggregation Microscopic Representation Partitioned Representation Aggregated Representation

45 Set of Possible Partitions 45

46 Set of Possible Partitions 46 Algebraic Structure A partial order on the set of possible partitions the refinement relation

47 Set of Possible Partitions 47 Algebraic Structure A partial order on the set of possible partitions the refinement relation Microscopic representation

48 Set of Possible Partitions 48 Entirely aggregated representation Algebraic Structure A partial order on the set of possible partitions the refinement relation Microscopic representation

49 Set of Possible Partitions 49 Entirely aggregated representation Algebraic Structure A partial order on the set of possible partitions the refinement relation Microscopic representation

50 Set of Possible Partitions 50 Entirely aggregated representation Algebraic Structure A partial order on the set of possible partitions the refinement relation Microscopic representation

51 My Approach 51 P0 P1 P2 P3 To characterize the aggregation process The algebra of possible partitions To preserve the system s semantics A constrained partitioning method To aggregate according to several dimension Some constraints expressing the system s topology To evaluate and compare the representations Some measures of complexity and information To offer several granularity levels The optimization of a compromise To compute the best representations A generic algorithm of constrained optimization

52 Problems and Objectives 52 Set of possible partitions Geographical Semantics Temporal Semantics Geographer

53 Problems and Objectives 53 Set of possible partitions Geographical Semantics Temporal Semantics Geographer Constraints Set of admissible partitions

54 Constrained Partitioning 54 At the instances level [Davidson and Basu, 2007] must-link cannot-link

55 Constrained Partitioning 55 At the instances level [Davidson and Basu, 2007] must-link cannot-link At the parts level [Lamarche-Perrin et al., IAT 2013] Non-admissible Partitions At the partitions level [Lamarche-Perrin et al., IAT 2013] Non-admissible parts

56 Preserving the Neighborhood Relation 56 Admissible Parts: set of connected countries regarding the adjacency graph Examples of admissible parts

57 The WUTS Hierarchy [Grasland and Didelon, 2007] 57 Admissible Parts: set of countries that are politically, culturally and economically consistent

58 The WUTS Hierarchy [Grasland and Didelon, 2007] 58 Admissible Parts: set of countries that are politically, culturally and economically consistent Level 1

59 The WUTS Hierarchy [Grasland and Didelon, 2007] 59 Level 2 Admissible Parts: set of countries that are politically, culturally and economically consistent Level 1

60 The WUTS Hierarchy [Grasland and Didelon, 2007] 60 Level 2 Level 3 Admissible Parts: set of countries that are politically, culturally and economically consistent Level 1

61 The WUTS Hierarchy [Grasland and Didelon, 2007] 61 Level 2 Level 3 Admissible Parts: set of countries that are politically, culturally and economically consistent Level 1 Examples of admissible parts

62 Aggregating according to a Hierarchy 62 Admissible Parts (nodes of the hierarchy) Admissible Partitions (cuts of the hierarchy)

63 Aggregating according to a Hierarchy 63 Admissible Parts (nodes of the hierarchy) Admissible Partitions (cuts of the hierarchy)

64 Aggregating according to a Hierarchy 64 Admissible Parts (nodes of the hierarchy) Admissible Partitions (cuts of the hierarchy)

65 Preserving the Order of Time 65 Admissible Parts: time intervals Examples of admissible parts t 1 t 2 t 3 t 4 t 5 t 6 t 7 t 8 t 9 t 10 t 11 t 12 temps

66 Aggregating according to a Total Order 66 Admissible Parts (time intervals) Admissible Partitions (interval sequences)

67 Complexity of Algebraic Structures 67 Non-constrained partitions Admissible partitions according to a total order Admissible partitions according to a hierarchy Less constrained More complex More constrained Less complex

68 My Approach 68 P0 P1 P2 P3 To characterize the aggregation process The algebra of possible partitions To preserve the system s semantics A constrained partitioning method To aggregate according to several dimension Some constraints expressing the system s topology To evaluate and compare the representations Some measures of complexity and information To offer several granularity levels The optimization of a compromise To compute the best representations A generic algorithm of constrained optimization

69 Objectives and Difficulties 69 Which admissible partition is the best partition for a particular dataset?

70 Objectives and Difficulties 70 MICROSCOPIC REPRESENTATION Which admissible partition is the best partition for a particular dataset? TOO COMPLEX TO SCALE-UP

71 Objectives and Difficulties 71 ENTIRELY AGGREGATED REPRESENTATION Which admissible partition is the best partition for a particular dataset? GIVES TOO FEW INFORMATION

72 Objectives and Difficulties 72 WHICH ONE TO CHOOSE? Which admissible partition is the best partition for a particular dataset?

73 Complexity and Information 73 MICROSCOPIC REPRESENTATION AGGREGATED REPRESENTATION

74 Complexity and Information 74 Heterogeneous Small-size MICROSCOPIC REPRESENTATION AGGREGATED REPRESENTATION

75 Complexity and Information 75 Heterogeneous Small-size HIGH information loss LOW complexity reduction MICROSCOPIC REPRESENTATION AGGREGATED REPRESENTATION

76 Complexity and Information 76 Heterogeneous Small-size HIGH information loss LOW complexity reduction MICROSCOPIC REPRESENTATION Homogeneous Large-size AGGREGATED REPRESENTATION

77 Complexity and Information 77 Heterogeneous Small-size HIGH information loss LOW complexity reduction LOW information loss HIGH complexity reduction MICROSCOPIC REPRESENTATION Homogeneous Large-size AGGREGATED REPRESENTATION

78 Complexity and Information 78 Preserve the information (No aggregation) Reduce the complexity (Aggregation) MICROSCOPIC REPRESENTATION AGGREGATED REPRESENTATION

79 Quality Measures 79 [Lamarche-Perrin et al., ECCS 2012] Complexity depends on the tasks we want to fulfill and the description tools that are available to do so [Bonabeau and Dessalles, 1997] Information loss is measured by the KL-divergence between two probabilistic distributions [Kullback et Leibler, 1951] Information Loss Complexity

80 Quality Measures 80 [Lamarche-Perrin et al., ECCS 2012] Complexity depends on the tasks we want to fulfill and the description tools that are available to do so Information loss is measured by the KL-divergence between two probabilistic distributions [Bonabeau and Dessalles, 1997] [Kullback et Leibler, 1951] Information Loss Number of represented aggregates: T X = X Complexity

81 Quality Measures 81 [Lamarche-Perrin et al., ECCS 2012] Complexity depends on the tasks we want to fulfill and the description tools that are available to do so Information loss is measured by the KL-divergence between two probabilistic distributions [Bonabeau and Dessalles, 1997] [Kullback et Leibler, 1951] Information Loss Number of represented aggregates: T X = X Kullback-Leibler Divergence D X = X X x X v x v Ω log 2 v x X v X Complexity

82 Measures Decomposability 82 Number of represented aggregates: T X = X Kullback-Leibler Divergence D X = X X x X v x v Ω log 2 v x X v X Additive Decomposability: The quality of a partition is the sum of the qualities of its parts [Jackson et al., 2005] [Csiszár, 2008] Q 1,2, 3,4 = Q 1,2 + Q 3,4

83 Information Loss Optimizing the Partition Qualities 83 Two criteria that should be optimized Compromise of Quality: CQL α = α T T max 1 α D D max Complexity

84 Information Loss Optimizing the Partition Qualities 84 Two criteria that should be optimized Compromise of Quality: CQL α = α T T max 1 α D D max 25% Complexity

85 Information Loss Optimizing the Partition Qualities 85 Two criteria that should be optimized Compromise of Quality: CQL α = α T T max 1 α D D max Minimal Loss 25% Complexity

86 Information Loss Optimizing the Partition Qualities 86 Two criteria that should be optimized Compromise of Quality: CQL α = α T T max 1 α D D max 15% Complexity

87 Information Loss Optimizing the Partition Qualities 87 Two criteria that should be optimized Compromise of Quality: CQL α = α T T max 1 α D D max Minimal complexity 15% Complexity

88 Information Loss Optimizing the Partition Qualities 88 Two criteria that should be optimized Compromise of Quality: CQL α = α T T max 1 α D D max Complexity

89 Characterizing Different Datasets 89

90 My Approach 90 P0 P1 P2 P3 To characterize the aggregation process The algebra of possible partitions To preserve the system s semantics A constrained partitioning method To aggregate according to several dimension Some constraints expressing the system s topology To evaluate and compare the representations Some measures of complexity and information To offer several granularity levels The optimization of a compromise To compute the best representations A generic algorithm of constrained optimization

91 Objectives 91 Set of admissible partitions Quality Measures T X = Ω X D X = X X v x v Ω x X log 2 v x X v X CQL α = α T T max 1 α D D max

92 Objectives 92 Set of admissible partitions Quality Measures T X = Ω X D X = X X v x v Ω x X log 2 v x X v X CQL α = α T T max 1 α D D max The Admissible Optimal Partitions Problem: Which admissible partitions optimize a given compromise of quality? A well-known constrained optimization problem

93 Exponential Algorithmic Complexity 93 Non-constrained Set Ordered Set Hierarchical Set Number of admissible partitions (n = size of the system) e n log n 2 n c n [Berend and Tassa, 2010] [Lamarche-Perrin et al., IAT 2013]

94 Toward an Efficient Algorithm 94 Classical clustering techniques uses some heuristics to find local optima [Halkidi et al., 2001] In our case: The admissibility constraints allow to reduce the complexity of the optimization problem The algebraic properties of the quality measures allow to efficiently compare the partitions We look for the global optima

95 Toward an Efficient Algorithm 95 Classical clustering techniques uses some heuristics to find local optima [Halkidi et al., 2001] In our case: The admissibility constraints allow to reduce the complexity of the optimization problem The algebraic properties of the quality measures allow to efficiently compare the partitions We look for the global optima

96 Idea of the Algorithm 96 Decomposition according to the refinement relation DIVIDE AND CONQUER Recursion according to the decomposability of measures [Lamarche-Perrin et al., IAT 2013]

97 Execution of the Algorithm 97 Decomposition Recursion Decomposition Recursion Decomposition

98 Execution of the Algorithm 98 Decomposition Recursion Record the intermediary results Decomposition Recursion Decomposition

99 Execution of the Algorithm 99 Decomposition Recursion Decomposition Record the intermediary results Avoid redundant evaluation within the algebraic structure Recursion Decomposition

100 Execution Time (milliseconds) Execution Time (milliseconds) Complexity of the Algorithm 100 The algorithm spatial and temporal complexity directly depend on the algebraic properties of the set of admissible partitions the more constrained, the less complex According to a hierarchy According to a total order Linear Complexity Quadratic Complexity System s size System s size

101 EXPERIMENTS AND RESULTS

102 The Syrian civil war according to LE MONDE 102 [Giraud, Grasland, Lamarche-Perrin et al., ECTQG 2013] 0%

103 The Syrian civil war according to LE MONDE 103 [Giraud, Grasland, Lamarche-Perrin et al., ECTQG 2013] Violent clashes in Homs First meeting of the Friends of Syria Houla massacre 0%

104 The Syrian civil war according to LE MONDE 104 [Giraud, Grasland, Lamarche-Perrin et al., ECTQG 2013] 1%

105 The Syrian civil war according to LE MONDE 105 [Giraud, Grasland, Lamarche-Perrin et al., ECTQG 2013] 5%

106 The Syrian civil war according to LE MONDE 106 [Giraud, Grasland, Lamarche-Perrin et al., ECTQG 2013] 10%

107 The Syrian civil war according to LE MONDE 107 [Giraud, Grasland, Lamarche-Perrin et al., ECTQG 2013] 20%

108 The Syrian civil war according to LE MONDE 108 [Giraud, Grasland, Lamarche-Perrin et al., ECTQG 2013] Beginning of the siege of Homs Houla massacre Battles of Damascus and Aleppo 20%

109 The Syrian civil war according to LE MONDE 109 [Giraud, Grasland, Lamarche-Perrin et al., ECTQG 2013] 30%

110 The Syrian civil war according to LE MONDE 110 [Giraud, Grasland, Lamarche-Perrin et al., ECTQG 2013] Source: Wikipedia Timeline of the Syrian civil war Siege of Homs 30% SIEGE OF HOMS Revel offensive Decrease in fighting Syrian army offensive Battles of Damascus and Aleppo

111 The Syrian civil war according to LE MONDE 111 [Giraud, Grasland, Lamarche-Perrin et al., ECTQG 2013] 70%

112 The Syrian civil war according to LE MONDE 112 [Giraud, Grasland, Lamarche-Perrin et al., ECTQG 2013] 70% Battles of Damascus and Aleppo Global increasing of the media attention

113 The Syrian civil war according to 4 newspapers 113 [Giraud, Grasland, Lamarche-Perrin et al., ECTQG 2013] LE MONDE THE TIMES OF INDIA THE FINANCIAL TIMES THE WASHINGTON POST

114 The Syrian civil war according to 4 newspapers 114 [Giraud, Grasland, Lamarche-Perrin et al., ECTQG 2013] LE MONDE Irregular variations of the media attention THE TIMES OF INDIA Irregular variations of the media attention THE FINANCIAL TIMES THE WASHINGTON POST Regular media attention Significant macro-variation

115 Aggregation of Execution Traces Hierarchical structure of the grid computing [Schnorr et al., 2013] [Lamarche-Perrin, Schnorr et al., TSI 2013] Microscopic treemap representation 115 Detection of multi-scale anomalies Aggregated treemap representations

116 Aggregation of Execution Traces 116 [Pagano, Dosimont et al., 2013] Optimal temporal representation Stable phase Stable phase Initialization Perturbation Time Complexity Reduction Information Loss

117 OUTCOMES AND PERSPECTIVES

118 Summary of the Contributions 118 P1 Algebraic structures that express the system s semantic properties P2 A compromise of quality to generate multi-resolution representations CQL α = α T T max 1 α D D max P2 Graphs of quality to choose the representations granularity P3 A generic aggregation algorithm with polynomial complexity 30%

119 Summary of the Hypotheses 119 Microscopic observation tools P0 Aggregation according to partitions P1 Hierarchical or ordered systems P2 Decomposable quality measures

120 Theoretical Perspectives 120 Aggregation of other structures Multidimensional aggregation and commutativity Aggregation of causal relations, of lexical networks Aggregation of the state space of a Markov process Some measures to evaluate representations Measures from information theory and complexity science Measures of cognitive efficiency [Tufte, 1983] Other criteria to evaluate representations

121 Application Perspectives 121 In social science Urban structures, micro/macro economics, social networks THE GEOMEDIA DATABASE IS AVAILABLE! In computer science and AI Exascale computing, embedded systems, sensor networks, multi-agent systems, swarm intelligence In other fields? Biology, neuroscience, physics

122 Epistemological Perspectives 122 What is a macroscopic phenomenon? Is it a real object or just an abstraction? Are upward and downward causations possible? What is the concept of epistemological emergence? What is the place of the observer? Internal or external observation? What is the probe effect? Is a self-observation possible?

123 THANKS FOR YOUR ATTENTION «Aujourd hui nous sommes confrontés à un autre infini : l infiniment complexe. Mais cette fois, plus d instrument.» Joël de Rosnay, Le macroscope, 1975

124 LIST OF PUBLICATIONS Peer-reviewed Journals (being accepted) Lamarche-Perrin, Demazeau et Vincent. Building the Best Macroscopic Representations of Complex Multi-Agent Systems. Transaction on Computational Collective Intelligence (TCCI), Lamarche-Perrin, Schnorr, Vincent et Demazeau. Agrégation de traces pour la visualisation de grands systèmes distribués. Technique et Science Informatiques (TSI), International Peer-reviewed Conferences with Proceedings Lamarche-Perrin, Demazeau et Vincent. The Best-partitions Problem: How to Build Meaningful Aggregations. Intelligent Agent Technology (IAT), Atlanta, Giraud, Grasland, Lamarche-Perrin, Demazeau et Vincent. Identification of International Media Events by Spatial and Temporal Aggregation of RSS Flows of Newspapers. European Colloquium in Theoretical and Quantitative Geography (ECTQG), Dourdan, Lamarche-Perrin, Demazeau and Vincent. How to Build the Best Macroscopic Description of your Multi-agent System? Practical Applications of Agents and Multi-Agent Systems (PAAMS), Salamanca, French Peer-reviewed Conferences with Proceedings Lamarche-Perrin, Demazeau et Vincent. Organisation, agrégation et visualisation d'informations médiatiques. Colloque annuel du Collège des Sciences du Territoire, Paris, Lamarche-Perrin, Demazeau et Vincent. Observation macroscopique et émergence dans les SMA de très grande taille. Journées Francophones des Systèmes Multi-Agents (JFSMA), Valenciennes, 2011.

125 Non-decomposable Measures 125 Q 1,2, 3,4 Q 1,2 + Q 3,4 The recursive approach is no longer possible The quality of a part cannot be defined Do non-decomposable quality measures have a meaning to evaluate the aggregation process?

126 Non-disjoint and Non-covering Parts 126 Partitioning Aggregation Data Overlapping Data Suppression Microscopic Representation Partitioned Representation Aggregated Representation Effect on the algorithmic complexity?

127 Microscopic Observation 127 Macroscopic Representation Analysis Observer System Abstraction Method MACRO MICRO Individuals Microscopic Observation Microscopic Representation 127

128 The Probe Effect 128 Macroscopic Representation Analysis Observer System + Observation Tools Abstraction Method MACRO MICRO System Probe Effect Microscopic Observation Microscopic Representation 128

129 Macroscopic Observation 129 Analysis Macroscopic Observation Macroscopic Representation Observer System Abstraction Method MACRO AGGREGATION PROCESS MICRO Individuals Microscopic Observation Microscopic Representation 129

130 Application Perspectives 130 Multi-agent Systems [Lamarche-Perrin et al., JFSMA 2011] Sensor Networks Multi-scale simulation [Gil-Quijano et al., 2012]

131 Space Other Topological Structures 131 Aggregation of Events [Mattern, 1989] Aggregation according to a Graph Time Aggregation of an Interaction Matrix CHE BEL GBR FRA ESP ESP X FRA 14 X Corresponding Algebras GBR X 6 9 BEL X 5 CHE X [Lamarche-Perrin et al., CIST 2011]

132 Algorithmic Complexity 132 Find the complexity classes that are associated to other dimensions, other semantics, other topologies, etc. Set Admissible Parts Admissible Partitions Temporal Complexity Spatial Complexity Non-contrained 2 n e n log n 3 n 2 n Ordered n 2 2 n n 2 n 2 Hierarchical Ο n Ο c n Ο n Ο n Other topologies????

133 Multidimensional Aggregation 133 Microscopic Representation Aggregated Representation

134 Macroscopic Probes Aggregation of Causal Structures 134 Discovery of source 1 Exploitation of source 1 Macroscopic Observation Discovery of sources 2 and 3 Global time Exploitation of sources 2 and 3