- Mallorca - Spain LASAGNE Presentation, May 0 multi-layer SpAtiotemporal Generalized Networks FP7-ICT-0-8. Proposal 383 FET Proactive: Dynamics of Multi-Level Complex Systems Stefan Thurner Coordinator Vito Latora Albert Díaz-Guilera Mario Chavez Cecilia Mascolo UNIVERSITY of BIRMINGHAM Mirco Musolesi
- Mallorca - Spain IFISC PARTICIPANTS (JRU: UIB +CSIC) UIB LASAGNE Maxi San Miguel Raul Toral Jose Ramasco Marina Diakonova CSIC Emilio Hernández-García Víctor M. Eguíluz IFISC EC-Contribution: 34,000 Total EC-Contribution:,077,743
MOTIVATIONS FOR LASAGNE Multiplex networks: fixed set of nodes connected by different types of links. Modelling a blackout in Italy. SV Buldyrev et al. Nature 44, 05 (00) ICT data contain high precision and integrated information on the nature and the evolution -in space and time- of the state of each single component, together with information on different types of interactions between them Need for a coherent theoretical framework to study and model multi-level and multidimensional complex networks in terms of multi-graphs embedded in space and time. http://ifisc.uib-csic.es
LASAGNE OBJECTIVES Objective Representing multi-level complex systems: the algebra of M M l (s, t), a multi-level (l) graph embedded in space (s) and time (t) Objective - Dynamical processes governed by F Dynamical processes taking place on graphs with many layers and with fluctuating links. Objective 3 - Validation d F[ M ( s, t), ] dt Social Networks Brain Networks Transport networks Vespignani, Nature(00) http://ifisc.uib-csic.es
LASAGNE WPs IFISC
LASAGNE WP4: Co-evolution of GNE networks and processes M. Zimmerman, V. M. Eguíluz and M. San Miguel Lecture Notes in Economics and Mathematical Systems 503, (00); Phys. Rev. E. 9, 050- (004) Dynamics of Networks:. Dynamics OF network formation. Dynamics ON the network 3. Co-evolution of agents and network: structure of network is no longer a given but a variable Co-evolution voter model Co-evolution Prisoner s Dilemma Unsatisfied Defectors break any link with neighbouring Defector and establishes a new link Social differentiation: Emergence of Leaders F. Vázquez, et al, Phys. Rev. Lett. 00, 0870 (008) Single component Fragmented net Conformists Exploiters V. Eguíluz et al. American J. Sociology 0, 977 (005)
LASAGNE WP4: Co-evolution of GNE networks and processes fragmentation recombination COEVOLUTION IN AXELROD MODEL p= 3 4 5 7 3 4 5 7 t t+ F=3, q=7
LASAGNE WP4 WP4: Co-evolution of GNE networks and processes Objective: Coupling between dynamics of the GNE and dynamics on the GNE Task 4. Co-evolution dynamics in multi-layer networks Task 4. Node state and link state dynamics Task 4.3 Characterizing phase transitions in co-evolution dynamics Task 4.4 Mobility processes in co-evolution dynamics WP4 Deliverables D 4. Report on the modeling of co-evolution dynamics on multi-layer networks with node and link state dynamics (M8) (D4. Progress report M) D 4.4 Report on phase transitions on co-evolution dynamics (M3) (PR M4) D 4.5 Report on mobility processes in co-evolution dynamics (M3) (PR M4) http://ifisc.uib-csic.es
LASAGNE WP4 Task.: Co-evolution dynamics of multi-layer networks Objective: Investigating a) coupled mechanisms of link creation and destruction in the different layers b) different dynamical processes, running in the different network layers, than the state of the elements of the network Adaptable Connectivity Characterised by (Gross and Blasius, JRS 008): Self-organisation toward critical behaviour Spontaneous division of labour Formation of complex topologies Complex system-level dynamics Context: artificial adaptability, evolutionary engineering (game-theoretic) biological systems (functional requirements in cardiovascular, neural, immune, genetic.. networks) ecosystems and food webs Multi-layered Structure Framework for: Coupled Infrastructure (anticipating cascading failures, robustness under attack, optimisation of resources..) Social and strategic transmission in social settings (virus, opinions).. and much more
LASAGNE WP4 Task.: Co-evolution dynamics of multi-layer networks Example: Opinion Dynamics on Co-evolving Multi-layer Networks Rewiring probability p 3 p Extensions: horizontal variation of topology horizontal propagation of effects of zealotry consequence of multiplicity of levels on timescales/effect of temporal heterogeneity of update by levels heterogeneous activity patterns representation of opinion by levels? p Dynamics Processes are independent of layer Update rules change depending on the level, reflecting effects of different social cultures on opinion-formation e.g. a combination of voter and threshold dynamics
Task 4. Node state and link state dynamics Link state: friendship, trust, communication:phone or skype, salutation Heider s Social balance B U B U
Task 4. Node state and link state dynamics FC net: frozen states i? Link dynamics majority rule i j j J. Fernandez-Gracia et al. arxiv: 09.483 Random net: Frozen or Dynamical traps Hubs tend to freeze
Aij ( t ) Fa ( xi ( t), Aij ( t)) Task 4. Node state and link state dynamics Coevolution : Link state dynamics + network dynamics Ex. Rewire blinker links Coevolution : Coupled link and node state dynamics Ex. : T. Aoki, T. Aoyagi, PRL 09, 0870 (0) Role of? Link creation/annihilation? Ex.: Language (discrete variables) Node state: competence. Link state: Use Coevolution 3: Multilayer/multiplex networks x ( t ) F( x ( t), a ( t), A ( t)) a i A ij ij j ( t ) F ( x ( t), a ( t)) a ( t ) F ( x ( t), A ( t)) b i i ij ij ij ij Questions: ) Two time scales ) Link creation/annihilation? 3) Fragmentation processes Update rules: activity patterns http://ifisc.uib-csic.es
LASAGNE WP4 Task 4.3 Characterizing phase transitions in co-evolution dynamics From the DOW: Co-evolution dynamics of single layer networks are known to feature fragmentation and recombination transitions, while transitions of dynamical processes on the network, such as percolation are known to depend on the dynamics of the network. The task is the general identification and characterization of phase transitions in co-evolution dynamics in multi-layer GNE networks, addressing transition on the network structure and transitions on the dynamical processes running in the different layers.
Topological Network Transitions Axelrod model with link reorganization LASAGNE WP4 Coevolution enrichs the kind of transitions with respect to the ones found in fixed networks fragmentation recombination CollectivePhenomenain Complex Social Networks Vazquez, Gonzalez-Avella, Eguiluz, San Miguel (009) Cascading failure (percolation) in N> interdependent networks is radically different from single networks http://ifisc.uib-csic.es
LASAGNE WP4 Explore variety of transition types occurring in coevolving multilayer networks The simplest strategy is to consider two coevolving networks for which different transitions have already been identified (Axelrod, voter, ) and study how the character of the transitions is affected when linking the networks with interactions or dependencies. Transition precursors: sociotechnical and brain Zou, Donges & Kurths, 0 Climate networks as coevolving multilayer GNE
LASAGNE WP4 WP4.4: Mobility processes in co-evolution dynamics Physical proximity is one of the key ingredients determining the interactions in social system. Thus a proper description of the mobility of persons is essential to describe the connections on social networks. In addition people interacts in different ways (positive, negative interactions) or using different communication channels. This task is designed to explore: the coupling between mobility and type of interactions in spatially distributed networks the relation between social interactions in different communication ion channels and geography. the dynamics in time of these multi-layer layer networks.
LASAGNE WP4 WP4.4: Mobility processes in co-evolution dynamics + The idea is thus to study the coevolution of a multilayer structure ure in which each layer represent social interactions by different channels nels or interactions of different types. From a theoretical perspective, we will analyze models with homophily- guided rewiring rules in the dynamics and with different dynamics s for the homophily evolution in each layer.