Objective / propose to investigate random directed graphs which incorporate a 'popularity measure' into their construction. We assign each vertex a random 'weight' which represents its relative 'attractiveness'. The simplest case leads to compound random mappings. It is expected that results for compound random mappings will contribute to the development of a theoretical framework for Bayesian inference for epidemic processes on contact networks. I also propose to investigate random models that incorporate arbitrary degree distributions. This provides another method of incorporating a 'popularity measure' into the model. By considering arbitrary degree distributions it is possible to mimic the highly skewed degree distributions seen in many networks such as the World Wide Web. Such models can be used for simulating and testing network algorithms. There are also connections between the analysis of epidemic processes and the analysis of algorithms in cryptology which may be elucidated by this investigation. To investigate the proposed non-uniform random digraph models I need to gain expertise in non-combinatorial techniques. I expect to acquire it through collaboration and interaction with the probability, applied statistics, and statistical physics groups at Heriot-Watt University. In addition, I would like to explore with the applied scientists at Heriot-Watt the potential applications of these random digraph models to a broad range of problems in both epidemic processes and communication networks. This training will enable me to return to my home institution to lead and direct a new multidisciplinary research group focusing on these applications of random digraphs. This project enhances European excellence in science by addressing the problem of fragmentation within the European Research Area and by fostering links between centres of excellence in discrete mathematics in Poznan and in probability, statistics and mathematical physics at Heriot-Watt. Fields of science natural sciencesmathematicsapplied mathematicsmathematical physicsnatural sciencesmathematicsapplied mathematicsstatistics and probabilitybayesian statisticsnatural sciencescomputer and information sciencescomputer securitycryptographynatural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theorynatural sciencescomputer and information sciencesinternetworld wide web Keywords epidemic processes random mappings and their generalisations Programme(s) FP6-MOBILITY - Human resources and Mobility in the specific programme for research, technological development and demonstration "Structuring the European Research Area" under the Sixth Framework Programme 2002-2006 Topic(s) MOBILITY-2.1 - Marie Curie Intra-European Fellowships (EIF) Call for proposal FP6-2002-MOBILITY-5 See other projects for this call Funding Scheme EIF - Marie Curie actions-Intra-European Fellowships Coordinator HERIOT-WATT UNIVERSITY EU contribution No data Address Riccarton EDINBURGH United Kingdom See on map Total cost No data
