Network Dimension as Damage Indicator in Biosystems


Jakob Renner

Wednesday, 25.04.2018, 17:00
WW8, Raum 2.018, Dr.-Mack-Str. 77, Fürth

The complexity of biosystems can be accurately captured by the connectivity pattern of a network. Despite accumulated damage many biological systems are able to maintain minimal functionality. Instead of catastrophic failure a gradual breakdown of function can be observed. Structural brain networks, but as well fibre networks in connective tissue like collagen, show a hierarchical modular architecture. Network models reproducing this organisational principle posses a finite topological dimension. Recently it has been shown that this parameter is able to connect structure and function in models of activity propagation.
This study tries to clarify the picture between structural resilience and functional resilience by investigating the evolution of the topological dimension under damage. As damage process we use simple bond percolation and a scalar elasticity model on two related network architectures. Their resilience properties are investigated using standard tools from percolation theory.
We find that hierarchical modular networks break in a modular way. It is therefore impossible to define a critical point at which the network disintegrates. Additionally the statistics of finite components differ greatly in size in comparison to standard network models. The topological dimension shows a continuous decrease under random damage, which is attributed to the hierarchical modular architecture. Moreover the topological dimension is able to identify physically relevant points in the quasi-static stress strain curve of the scalar elasticity model.