12 citations · 12 across the 8 of their papers we have counts for
6 papers · 1 filter
Constructions of contractibility in 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…
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…
Moduli Spaces of Morse Functions for Persistence
Michael J. Catanzaro, Justin Curry, Brittany Terese Fasy +5
We consider different notions of equivalence for Morse functions on the sphere in the context of persistent homology, and introduce new invariants to study these equivalence classe…
Stratifications on the Ran space
Jānis Lazovskis
We describe a partial order on finite simplicial complexes. This partial order provides a poset stratification of the product of the Ran space of a metric space and the nonnegative…