Topics:

• Complex systems
• Network models and properties
• Statistical network analysis methods

Description:

These lectures aim to introduce the audience to the fundamental properties of complex systems, and their modelling in terms of networks (or graphs). Broadly speaking, complexity refers to the emergent collective behaviour of natural or socio-economic systems made of large numbers of units interacting with each other. Such "macroscopic" behaviour is often hard to predict based on the "microscopic" rules of interaction between units. For instance, how could the same virus be eradicated in one population and cause an epidemic in another? How could the same actors trading seamlessly on one day find themselves in the middle of a market crash on the next?

We can often make sense of such puzzles by representing complex systems as a network, i.e., a set of nodes and links representing the units and interactions of a system, respectively. This workshop will provide an introduction to the key mathematical properties of complex networks, highlighting benchmark models such as the renowned Barabási-Albert model of scale-free networks.

Participants will gain insights into how the topology of a network can influence the outcomes of dynamical processes occurring within it. Additionally, we will delve into statistical methodologies designed to identify the most impactful nodes and links within empirical network data. Throughout the series, we will engage with real-world case studies and examples drawn from various disciplines, including Epidemiology, Finance, and the Social Sciences.

About the instructor:

Giacomo Livan is Associate Professor at the Physics Department of the University of Pavia (Italy). He obtained a PhD from the University of Pavia in 2012, after which he joined the Abdus Salam International Centre for Theoretical Physics as a postdoctoral fellow. In 2014 he joined the Computer Science Department of University College London (UCL). In 2016 he obtained a Fellowship from the UK research council in Engineering and Physical Sciences (EPSRC), and got promoted to Associate Professor at UCL in 2021. He eventually returned to the University of Pavia in 2023, while retaining an honorary appointment at UCL. Livan's research focuses on interdisciplinary applications of Statistical Physics and Network Theory to the analysis of socio-economic complex systems, with applications ranging from finance to opinion dynamics and bibliometrics. His work has been published in some of the most impactful multidisciplinary academic venues, such as PNAS and Nature Communications.  

Schedule:

Thursday, 28. November 2024 (F21/03.48)

10:30h - 12:00h: The basics (definitions, adjacency matrix, degree distributions, centrality measures)

13:15h - 14:45h: Benchmark models and their properties (Erdos-Renyi, Barabasi-Albert, Watts-Strogats; how topology determines resilience against attacks and diffusion processes, e.g. epidemics/contagion)

15:15h - 16:45h: Statistical analysis of networks (methods to identify statistically relevant nodes & links, null network models, community detection) 

Friday, 29. November 2024 (F21/02.41)

12:30h - 14:00h: Examples and applications (e.g., DebtRank, economic complexity, ecology, opinion dynamics)