WP1 Statistical physics of critical events in complex networks and multi- networks

Workpackage number:

1

Start date or starting event:

3 months

Participant number:

CO1

CR2

CR3

CR4

CR5

Person-months per participant:

21

3

3

1

3

Objectives
O1.1. To develop  a theory of critical events in complex networks.
O1.2. To develop  models  of  critical multi-network systems.

Description of work
The theoretical methodology will be mainly grounded in:

1. the theory of complex networks (graph theory, evolving networks paradigm)
2. the theory of phase transitions (scaling hypothesis, renormalization group theory, mean field approach)

The analytic studies will be verified by numerical simulations of investigated networks. Several minor tasks will be organized around the two major directions:
T1.1. Description of static and dynamic correlations functions for network structure and nodes internal  dynamics. We will check if special kinds of fluctuation-dissipation theorems exist that join correlation functions with network susceptibility to external forces and allow to predict network response in the face of environmental perturbations. We will also look for other thermodynamical relations like Claussius-Clapeyron equations eventually Maxwell or Onsager relations to predict the behaviour of a complex network in the critical regime.
T1.2. Models of coupled networks. To investigate multi-networks we need a preliminary reliable characterization of such systems. Deferent models of coupled networks will be analyzed from the point of view structural and critical properties. In the first approximation various kinds of ferromagnetic and anti-ferromagnetic coupling will be considered to find the phase diagram of  coupled complex networks. 

Deliverables
D1.1. Methods for characterization critical phenomena in complex networks.  
D1.2. Models of network-network interactions.
D1.3. Catalogue of critical events in complex networks.

Milestones and expected results
Expected results concern the quantitative description of parameters that characterise critical events in complex networks, their dynamic evolution (in sense of a new phase spreading) and their control (foreseeing).
We expect to get D1.1 after 18 months and D1.2 after 35 months. The Consortium Board after 18 months, that will take place slightly before the beginning of WP4, will act as milestone for D1.3.
Investigations performed here will be tested against real-world problems in WP4.