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Random Directed Graph Models with Applications to Epidemic Processes and Communication Networks


/ 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.

Field of science

  • /natural sciences/mathematics/pure mathematics/discrete mathematics
  • /natural sciences/computer and information sciences/computer security/cryptography
  • /natural sciences/mathematics/applied mathematics/mathematical physics
  • /natural sciences/computer and information sciences/internet/world wide web
  • /natural sciences/mathematics/applied mathematics/statistics and probability/bayesian statistics

Call for proposal

See other projects for this call

Funding Scheme

EIF - Marie Curie actions-Intra-European Fellowships


United Kingdom