BMI Progress Reports 2021 // Prof. Hess Bellwald's Lab: S. Ebli & C. Hacker, Topological methods in neuroscience

Historically topology studies shapes up to deformation, providing insight into the global structure of geometric objects. Recently, topological methods have been successfully applied to analyze high dimensional data in various settings in biology.

In this talk we will present two topological methods that can be applied to neuroscience data.

The first method applies to the analysis of connectomes. It is a generalization of the node2vec algorithm, which has previously been used to study structural and functional connectomes. It has been shown that analyzing brain networks through the lens of higher dimensional structures, called simplices, can be more informative than using just the structure given by pairwise interactions. To this end, we suggest a method that aims at understanding higher dimensional structures in networks by obtaining a vectorized representation of these structures, in a similar way to node2vec.

The second method applies to a class of recurrent neural networks used for modelling neural activity, called combinatorial threshold-linear networks (CTLNs). The dynamics of these networks is determined by the structure of a directed graph. We propose a topologically inspired method to reduce the size of the dynamical system.  Moreover, we will see how from the reduced dynamical system we can predict properties of the dynamics in the original network.