Many complex systems are characterised by multi-level properties. That makes the study of their dynamics and of their emerging phenomena a daunting task. The huge amount of data available in modern sciences will support great progress in these studies, even though the nature of the data varies. It is thus crucial to extract as much as possible features from data, including qualitative (topological) ones.
The goal of this project is to provide methods for describing the dynamics of multi-level complex systems. These methods will be driven by the topology of data . To this end, the project will develop new mathematical and computational formalisms accounting for topological effects.
The project brings together scientists from many diverse fields including topology and geometry, statistical physics and information theory, computer science and biology. The proposed methods, obtained through concerted efforts, will cover different aspects of the science of complexity. They will range from foundations, to simulations through modelling and analysis. They are also expected to constitute the building blocks for a new generalized theory of complexity.