Biology has entered the age of Big Data. The technical revolution has transformed the field,
and extracting meaningful information from large biological data sets is now a central …

Two general challenges faced by data analysis are the existence of noise and the extraction
of meaningful information from collected data. In this study, we used a multiscale framework …

Despite the obvious similarities between the metrics used in topological data analysis and
those of optimal transport, an optimal-transport based formalism to study persistence …

We show that an embedding in Euclidean space based on tropical geometry generates
stable sufficient statistics for barcodes. In topological data analysis, barcodes are multiscale …

We study the persistent homology of both functional data on compact topological spaces
and structural data presented as compact metric measure spaces. One of our goals is to …

Rapid developments in high-throughput sequencing have accumulated a wealth of cancer
genomics data (44, 12), which has led to the use of phylogenetic methods becoming an …

Let $ X $ be a closed subspace of a metric space $ M $. Under mild hypotheses, one can
estimate the Betti numbers of $ X $ from a finite set $ P\subset M $ of points approximating …

Rapid developments in high-throughput sequencing have accumulated a wealth of cancer
genomics data [44, 12], which has led to the use of phylogenetic methods becoming an …