mar753 - Networks and Complexity (Complete module description)

Students are able to independently apply the various approaches for complex systems modeling and data analysis. Their knowledge of the fundamentals of these methods allows them to adapt and expand them for new problems. Students have an overview of the phenomena that occur in complex, networked systems. Their understanding allows them to analyze robustness and vulnerability of complex systems from different perspectives.

This module uses concrete examples to explain various network-based methods for analyzing complex systems. Lectures introduce problems from  science and society, then develop the necessary theory to solve the problem (for simple examples) with pen and paper.

In this way we build up experience with hands-on methods but also a deeper understanding of principles of complex systems.

The topics are organized into four main sections:

Network Algorithms. Problem-solving approaches from computer science used to quickly determine network properties: shortest paths, optimal routes, etc. (Programming skills are not required for this.)

Network Physics. Approaches from physics for analyzing large, sometimes unknown, systems: statistical models of networks, phase transitions, and critical states. Static network properties. Robustness against attacks and fault tolerance of networks.

Dynamics of Complex Systems. Approaches from the theory of dynamical systems: critical transitions, methods for simplification, and model reduction.

Spectral Theory of Networks. The study of networks using algebraic methods: self-organization and pattern formation, an introduction to high-performance data analysis methods, and connections to information theory and statistical physics.

A.L. Barabasi and M. Posfai: Network Science

S.N. Dorogovtsev: Lectures on Complex Networks

E. Estrada and P. Knight: A first course in Network Theory

V. Latora, V. Nicosia and G. Russo: Complex   Networks: Principles, Methods, and Applications

C. Moore and S. Mertens: The Nature of Computation

M. Newman: Networks

S. Strogatz: Nonlinear Dynamics and Chaos

Portfolio or practical exercise or oral examination as determined by the lecturer

1 graded examination

Portfolio or practical exercise or oral examination