🚨 New pub out at Entropy MDPI, developing topology-informed methods to identify interesting gene expression patterns in scRNA-seq datasets. Fun Oxford Mathematics x Ludwig Cancer Oxford collab led by Renee Hoekzema, Lewis Marsh, Otto Sumray, Helen Byrne, and Heather Harrington. Quick 🧵:

I'm very excited to announce that our latest pre-print just went up on the arxiv, joint work with Heather Harrington and Ulrike Tillmann. Grounded persistent path homology: a stable, topological descriptor for weighted digraphs arxiv.org/abs/2210.11274

If you're in need to find points nearby, But afraid that your computer will fry, Don't be a fool! Use the right tool! A ball tree is the right guy.

Baby #2 is due any day now, and I am too wired to do the intelligent thing (i.e., sleep). So please join me, the wonderful Otto Sumray, and Heather Harrington on a journey through some fun machine learning & representation theory. 1/11

Really pleased to finally share my preprint: Diffusion Geometry (1/4) Diffusion geometry defines Riemannian geometry for data and probability spaces! arxiv.org/abs/2405.10858

Arguably one of the least utilised but most powerful features of persistent homology (PH) is functoriality. Large swathes of data come pre-divided into distinguished, disjoint subsets (a priori/via clustering). A functorial PH pipeline lets us analyse how these subsets interact!

1/5 Very happy to share our work on flexible, multiscale cell type assignment for subcellular spatial transcriptomics, now in nature nature.com/articles/s4158…