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The module’s objective is to familiarise students with the mathematical modelling of urban systems using the principles of complexity science. Among the various modelling techniques available, only two will be introduced: spatial interaction models and network science. These are widely used to model emergent patterns from the local interactions. In particular, we will look at modelling flows between areas, taking into account the characteristics at the different locations and their spatial distribution. Additionally, the course will cover encoding various types of interactions, understanding the roles of different agents (such as people or places), and analysing how the global structure of the system influences diverse processes.

The skills learnt in this course can be applied to a wide range of systems. During the course we will look at transport systems and the modelling of flows related to commuting patterns. We will assess the role of transport nodes using centrality measures, and the resilience of the system using global measures. The framework is exemplified on social systems as well, where techniques such as community detection are more natural.

Prerequisites: basic knowledge of Python, or a good knowledge of another programming language. The student should be able to understand and modify the codes given in the course in Python. Basic linear algebra will be reviewed, but it is strongly advised to review matrices and vectors before the start of the course.