DescriptionF. Unger: Recent works in Topological Data Analysis have analyzed biological neural networks by understanding them as directed graphs and analyzing their flag complex. The significance of their findings was always with respect to comparable Erdös-Renyi-Graphs (ER-Graphs), despite them lacking a large enough flag complex to support more complex topological structures to begin with. This raises the question: Are these topological findings just a byproduct of the large number of simplices? We propose a different null-model than ER-Graphs of comparable size and density: We require additionally a comparable number of simplices in its flag complex. In this talk we’ll present a first step towards that: Whilst also retaining the underlying undirected graph, we develop a Monte-Carlo-Markov-Chain-based sampling algorithm able to uniformly sample from our proposed null-model. As a first result, we present that the connectome of C.Elegans does not only give rise to a higher number of simplices when compared to comparable ER-graphs (already known), but additionally has more topological features not only compared to an ER-graph, but also compared to our (connectivity-restrained) null-model. This suggests significance and purpose of topological methods beyond simplex count analysis.
|Period||29 Jun 2022|
|Held at||Swiss Federal Institute of Technology in Lausanne, Switzerland|
|Degree of Recognition||International|