Scope & Goals Mapping Complex Dynamical Systems to Networks Current Trends: Network Modeling of Complex Dynamical Systems Bosiljka Tadi´ c Department of Theoretical Physics Jožef Stefan Institute, Ljubljana , Slovenia ICCS Workshop “Networks” Krakow June 23-25, 2008 Tadi´ c Dynamic Phenomena on Networks
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Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
Network Modeling of Complex DynamicalSystems
Bosiljka Tadic
Department of Theoretical PhysicsJožef Stefan Institute, Ljubljana , Slovenia
ICCS Workshop “Networks” Krakow June 23-25, 2008
Tadic Dynamic Phenomena on Networks
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
Outline
1 Scope & Goals
2 Mapping Complex Dynamical Systems to Networks
3 Current Trends:More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
Tadic Dynamic Phenomena on Networks
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
THE MAIN IDEA:
⊲In Complex Dynamical Systems:
Local interactions ⇒ Global properties
⊲Representing a Complex Dynamical System by a Network(Graph) then enables use of formal methods:
Graph Theory and Algorithms;
Statistical Physics of Complex Networks;
⊲This approach of quantitative study of complexity is particularlyuseful in biological and social systems, ecology, economy, etc...but also in physics of new functional materials and soft matterphysics, where no exact theories are available!
Tadic Dynamic Phenomena on Networks
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
Dynamic State Variables on Networks:
⊲Network function: Dynamic State variables attached to Nodes⊲Nodes activity through interactions ⇒ Noise signals
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Active Nodes Noise SignalsTadic Dynamic Phenomena on Networks
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
Mapping CDS to Networks creates Problems...
⊲Mapping CDS ⇒ Network is not unique:
Choise of graph elements (Nodes, Links) and Dynamic.var
Constraints with (given) local, global, mesoscopic structure
⊲Some CDS are Networks, structure dyn.changing, or unknown:
How that structure affects the network function?
⊲ Can we overcome such problems and how?
Depending on the puprose of the resarch & availableresources, comp.power, time, ...
Tadic Dynamic Phenomena on Networks
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
Outline
1 Scope & Goals
2 Mapping Complex Dynamical Systems to Networks
3 Current Trends:More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
Tadic Dynamic Phenomena on Networks
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
NETWORKS FROM EMPIRICAL DATA
⊲Data-Driven Models: New network types & Their properties
New classes of E-Social Networks Bipartitivity...different node types
Gene Networks Characteristic Subgraphs Id.Modularity rel. to Function
Protein Interaction Networks Mesoscopic structure ∼∼
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
Outline
1 Scope & Goals
2 Mapping Complex Dynamical Systems to Networks
3 Current Trends:More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
Tadic Dynamic Phenomena on Networks
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
FINE STRUCTURE OF NETWORKS
⊲Finding networks structure at local, mesoscopic & global scale ;⊲Modules ⇔Function; Network-of-networks: interacting networks
Pajek
Tadic Dynamic Phenomena on Networks
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
Outline
1 Scope & Goals
2 Mapping Complex Dynamical Systems to Networks
3 Current Trends:More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
Tadic Dynamic Phenomena on Networks
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
METHODS TO EXPLORE NETWORKS
⊲As new networks being discovered (i.e., from CDS), demandsgrow to adjust/develop appropriate algorithms to explore them
New network features require suitablemethods for a quantitative study:
Finding relevant network partition;
Search for dynamical subgraphs(motifs, modules, paths, cycles, trees...)
Visualization related to network type;
Spectra of Aij & other related matrices;
Tadic Dynamic Phenomena on Networks
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
Outline
1 Scope & Goals
2 Mapping Complex Dynamical Systems to Networks
3 Current Trends:More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
Tadic Dynamic Phenomena on Networks
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
DYNAMICS ON/OF NETWORKS
Dynamic var.update ⇔Noise sugnal;
Mirror participation of nodes and otherstructural elements in the dynamics;
Dynamics depends on Structure andcan be used for (noninvasive) structurecharacterization; Need more systematicquantification of Structure ⇔ Dynamics;
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
Outline
1 Scope & Goals
2 Mapping Complex Dynamical Systems to Networks
3 Current Trends:More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
Tadic Dynamic Phenomena on Networks
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
APPLICATIONS OF NETWORK THEORY
Nano-science: Networks of GoldNano-Particles as conducting films
E-social interactions: Social networksemerging through communicationnetworks/Agents and Subjects play asimilar role...
...
conduction paths
Tadic Dynamic Phenomena on Networks
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
Outline
1 Scope & Goals
2 Mapping Complex Dynamical Systems to Networks
3 Current Trends:More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
Tadic Dynamic Phenomena on Networks
Scope & GoalsMapping Complex Dynamical Systems to Networks
Current Trends:
More Networks from DataNetworks’ Fine StructureMore Formal Methods for Network Analysis & VisualizationDynamical Processes on NetworksApplied Networks++New Theoretical Approaches
THEORETICAL MODELS BEYOND SIMPLE SF...
Grown vs. Fluctuating networks Rate Eqs. vs. Stat.Phys.Constraints: given mesoscopic structure; Given degree, CC, ...given spectral properties...Multi—networks == interacting networks diff. nature, or topology—graphs == weighted networks; Links b. any pair—partite networks! vs. Links b.partitionsAdaptive networks: Dynamic variablesinteract ⇒ Network updates optimization principle