9 papers
Higher-order rich clubs and configuration models on general directed hypergraphs
Jason P. Smith, Celia Hacker, Jānis Lazovskis +3
Detecting structure in complex networks, especially those arising from physical systems, is a central problem across the sciences. One approach is via rich club analysis, which ide…
A constructive proof for the simple connectedness of finite subset spaces
Jānis Lazovskis
The space of all finite non-empty subsets of a topological space , also known as the Ran space of , is weakly contractible for path connected. We consider subspaces $\mat…
Stability of 0-dimensional persistent homology in enriched and sparsified point clouds
Jānis Lazovskis, Ran Levi, Juliano Morimoto
We give bounds for dimension 0 persistent homology and codimension 1 homology of Vietoris--Rips, alpha, and cubical complex filtrations from finite sets related by enrichment (addi…
Pruning vineyards: updating barcodes and representative cycles by removing simplices
Barbara Giunti, Jānis Lazovskis
The barcode of a filtration and its representative cycles encode rich information often useful in data analysis. However, obtaining them can be computationally expensive. Therefore…
DONUT -- Creation, Development, and Opportunities of a Database
Barbara Giunti, Jānis Lazovskis, Bastian Rieck
DONUT is a database of papers about practical, real-world uses of Topological Data Analysis (TDA). Its original seed was planted in a group chat formed during the HIM Spring School…
An application of neighbourhoods in digraphs to the classification of binary dynamics
Pedro Conceição, Dejan Govc, Jānis Lazovskis +3
A binary state on a graph means an assignment of binary values to its vertices. For example, if one encodes a network of spiking neurons as a directed graph, then the spikes produc…