Advanced Methods for Complex Systems II

Provided by: 



PhD in Economics, Networks and Business Analytics (ENBA)









Educational Goals: 

The second part of the course ÒAdvanced Methods for Complex SystemsÓ focuses on advanced practical applications of the concepts introduced in the first part. In particular, emphasis will be put on the successful areas of pattern detection and network reconstruction from partial information. Network pattern detection is the identification of robust empirical patterns (like scale invariance, clustering, assortatitvity, reciprocity, motifs, etc.) that are widespread across real-world networks and that deviate systematically from some null hypothesis formalised in terms of a suitable random graph model. The models introduced in part I will then be used here for pattern detection purposes. The problem of community detection will also be covered, with an emphasis on the differences between finding communities in network data and in correlation matrices constructed from (e.g. financial or neural) time series databases. The problem of network reconstruction from partial topological information will be addressed concentrating on the reconstruction of financial and interbank networks from node-specific properties, with the purpose of improving stress tests and systemic risk estimates in real markets and offering better tools to policy makers. The statistical physics methods recently found by central banks to be the best-performing reconstruction techniques will be reviewed in detail. The course will include a combination of recent and ongoing research in the NETWORKS unit at IMT Lucca, thereby offering directions for possible PhD projects in this area.


Solid mathematical background, scientific curiosity, interest in multidisciplinarity, successful completion of the course ÒAdvanced Methods for Complex Systems IÓ. Note: completion of this second part of the course is not required in order to move on to the third part (parts II and III can be understood in parallel independently of each other, after part I is completed), although it would surely provide a useful overview of practical motivations for part III.
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