11:00 Mon 2 July – RED 351
11:00 Wed 4 July – RED 351 |
11:00 Fri 6 July – RED 351
11:00 Mon 9 July – RED 351 |

**Biography. **Saeed Osat is a PhD Student at Skoltech working with Jacob Biamonte and others towards the development of an information theory of networked and complex systems. Before joining Skoltech, Osat published several papers on complex network theory, including

**Optimal percolation on multiplex networks, **Saeed Osat and others, *Nature Communications* 8 (1), 1540 (2017)

Email. Saeed.Osat@skoltech.ru

**Synopsis. **Complex network science represents one of the most diverse and widely applicable areas in modern science. Virtually all areas of applied science and engineering can benefit from incorporating aspects of modern network analysis.

This excitement is based on the surprising discovery that the networks representing a variety of physical systems share common attributes. A wide class of network models and tools are now available to study networks and these tools are applying to an ever-widening array of scientific questions. Originally based on statistical physics, these methods have long applied to various problems ranging from understanding the flow of traffic, to information in social networks, to biological networks, to understanding non-trivial patterns in the connectivity of the WWW and much more. In these four lectures, I will introduce some of the basics of network science, starting from definitions and leading to some of the seminal findings.

**Lecture 1. Basics (Monday 2 July). **Most of the real world complex systems i.e. from transportation networks to fine-grained brain networks consist of many constituents which interact with each other according to a complicated interaction pattern. Network science provides us with tools to analyze and gain insight about the collective behavior of such complex systems. This lecture introduces briefly the core definitions of network science. Beginning with graphs we will recall several network descriptors. The lecture concludes with a brief review of several important real-world complex networks and their structural properties.

**Lecture 2. Random Graph Models (Wednesday 4 July). **Instead of studying each of the real complex networks separately, its better to define graph models that mimic real systems in terms of structure and dynamics. This lecture attempts to answer the following questions. Which random graph models grasp the basic topological structures of real networks? How we can implant some topologically important sub-structures in random graph model? Are there any growing models that end up with the same structure that we have in mind?

**Lecture 3. Dynamics on Networks (Friday 6 July). **Given a graph with known structure, it is important to be able to follow a process which takes place on top of that network. In this lecture, we will study percolation process on top of a given network. Generating functionology is the tool which is suitable to study percolation as a branching process. We will end this lecture by introducing a Message-Passing approach which not only is the best way to recover the phase diagram of percolation of real networks, but it will help us to relate the spectrum of the graph to the dynamics that runs on top of it (spectral graph theory).

**Lecture 4. Multiplexity (Monday 9 July). **First attempts to attain a full physical description of real networks in terms of graphs was not satisfactory enough. Forgetting about potentially different kind of links(different interaction pattern; multiplexity) induce detrimental effects on results of the analysis. What is outcomes of multiplexity? We will introduce the concept of multiplexity and how physics of multiplexity is able to disclose unprecedentedly unknown facts about interconnected networks.

**References. **

- Newman, Mark EJ.
**The structure and function of complex networks**.*SIAM review*45.2 (2003): 167-256. - Newman, Mark.
. Oxford University Press, 2010.*Networks: an introduction* - Cohen, Reuven, and Shlomo Havlin.
. Cambridge University Press, 2010.*Complex networks: structure, robustness and function* - Barrat, Alain, Alessandro Vespignani, and Marc Barthélemy.
**Dynamical processes on complex networks**. Cambridge University Press, 2008.