Focus Areas

The workshop will focus on the intersection of complexity science and computational/applied topology. The topics below are especially of interest, but any relevant contribution is welcome.

Mesoscopic analysis of complex networks: The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally de ned quantities of nodes and edges, such as node degrees, edge weights and more recently correlations between neighboring nodes. However, statistical methods quickly become cumbersome when dealing with many-body properties and do not capture the precise mesoscopic structure of complex networks. Computational algebraic topology offers a new and reliable way to let these intermediate structure emerge and thereby show a deep connection between the homological network structure, the network spectral properties and their implications on network dynamics.

 

Topological foundations of complex systems Topology examines spaces based on how they are connected | this allows global properties of spaces and systems to be studied based on very general local models which encompass nearly all situations we encounter in nature. This generality unfortunately often comes at the expense of our ability to predict and understand the behaviour of a system. Building a topological foundation for complex systems involves choosing models which are veri fiable but remain as general as possible. Work in this direction includes the generalization of models from Euclidean space to manifolds to more general spaces such as strati fed spaces.

 

Applications  Some existing applications of topological analysis to complex systems are characterizing dynamical and chaotic systems systems biology (modelling cancer, genomic expression, examining tree root growth),

  • social analysis (modeling political behaviour),
  • modelling rankings in social networks and analysis of games using Hodge theory,
  • visualization of complex scientific data,
  • linguistic and document analysis