Workpackage : WP9
Statistical analysis of real networks - collaboration and exchange visits.
Start date or start event : 1 month

Objectives :

1. Promote the COPIRA group as a partner with the leading European research centres.
2. Collaboration on software packages for Monte-Carlo simulations of various systems of random geometry including dynamical triangulations, simplicial gravity, and scale-free networks.
3. Collaboration on software construction to collect data from existing sociological, biological, ecological networks and networks in telecommunication (Internet, WWW etc.).
4. Bring the knowledge about this rapidly developing research area to scientific community and students of the Jagellonian University.

Description :
Theory of random geometry had a great impact on fundamental research. It provided a non-perturbative formulation of string theory and quantum gravity. The theory naturally combines randomness of quantum physics and geometrical nature of gravity. In recent years, the analytical and numerical methods of the theory have found application in many areas ranging far beyond fundamental research, for example, in biology, where they are used in description of bio-membranes, or ecological or biochemical random graphs. The methods are also applicable in sociology, telecommunication, linguistics etc., - everywhere where problems can be formulated in terms of abstract random graphs of networks. The researchers of the COPIRA group have already developed many original analytical methods for studying problems related to random geometry as for instance field theoretical methods (matrix models) and numerical methods, like for example Monte-Carlo algorithms, to generate random graphs.
Number of visits :

• 1st yr - 2 visits (Paris,NBI),
• 2nd yr - 3 visits (Utrecht,Edinbourgh),
• 3rd yr - 1 visit (Bielefeld) , (3-4 days each visit)

Partners involved :

• Niels Bohr Institute, Copenhagen, Denmark,
• Spinoza Institute, Utrecht, The Netherlands,
• LPT, Universite Paris-Sud, Orsay, France,
• Heriot-Watt University, Edinburgh, Scottland,
• University of Bielefeld, Germany.

Deliverables :

1. Report on the status of the collaboration and obtained results.
2. Lecture course for undergraduate and graduate students.

Milestones and expected results :

1. Collaboration on the Monte-Carlo software for generating and analysing random graphs.
2. Promotion of the COPIRA group as a full partner in the network of the European collaboration.
3. Creating the COPIRA group as a leading centre in Europe constructing software for the Monte Carlo simulations of random geometries.
4. Common publications in renowned journals.
5. Seminars delivered in the collaborating institutions.