Since 2010, I teach the course “Complexity in Social Systems” at the Physics Department of the University of Torino, Italy.
The course provides an introduction to the following subjects:
Introduction to Complex Systems;
Network theory: metrics (definition of a network, adjacency matrix, degree distribution, clustering coefficient, motifs). Network theory: models (Erdos Renji); Network theory: metrics (distance and diameter, betweennes and closeness). Network theory: models (Watts-Strogatz and small world effect); Network theory: models (Barabasi-Albert, growth and preferential attachment). Power laws and Page Rank algorithms; Percolation on a network. Random walk and resilience
Introduction to computational epidemiology: compartmental models in homogeneous mixing. Deterministic SIR model; Stochastic SIR model, definition of R0, early stage approximation, epidemic threshold, vaccination; introduction to epidemic spreading on contact networks, SIR model on a network; Epidemic spreading on homogeneous and heterogeneous contact networks. Degree block approximation. Introduction to the metapopulation models. Global invasion threshold for homogeneous networks. Introduction to Global invasion threshold for heterogeneous networks; Introduction to temporal networks, simulations of epidemic spreading on temporal networks;
Opinion dynamics. Relation between physics and sociology. Thermodynamical limit, Voter model on a lattice, on a small world network and on a generic network. Consensus time. Invasion model. Community detection and modularity. Newmann algorithm for community detection; Gossip diffusion. Innovation diffusion. Axelrod model, Deffuant model.