Vincenzo Galgano

Novel Research in Biological Artificial Intelligence Expressions of interest and nominations for a Max Planck Director to lead research in the field of Biological Artificial Intelligence.

Novel Research in Biological Artificial Intelligence: Expressions of interest and nominations for a Max Planck Director to lead research in the field of Biological Artificial Intelligence @mpi-cbg.de and @csbdresden.bsky.social. More information: www.mpi-cbg.de/news-outreac...

Highlights to come from Brunów, Poland, but here we all are! All current and upcoming members. A wonderful couple of days getting to know more about each others’ work. All three groups together: @haharrington.bsky.social, Türkü Özlüm Çelik, and @aidadoesmath.bsky.social 🩵🩵🩵

Using the software FRUITS, we apply the discrete signature to a knotted protein dataset. We show that discrete signatures have high correlation with aminoacid sequence similarity and knot depth.

The discrete signature map is invariant under consecutive repetitions and translations of time-points. We show that actually it is injective up to these two relations. This makes the discrete landscape feature map more than descriptive than the (continuous) landscape feature map.

To a persistence landscape we associate the time-series of its critical points, of which we compute the discrete signature. We show that the resulting discrete feature map is uniformly continuous.

The resulting "feature map" is still stable, but loses injectivity because the Chen signature map is invariant under tree-like equivalence of paths. We address this by proposing a discrete alternative.

The landscape embedding associates a path to a barcode, and this map is stable and injective. Chevyrev, Nanda and Oberhauser compose it with the Chen signature map, which assigns to a path a sequence of tensors of increasing order.

Discrete signature tensors for persistence landscapes Signature tensors of paths are a versatile tool for data analysis and machine learning. Recently, they have been applied to persistent homology, by embedding barcodes into spaces of paths. Among the d...

Very excited that my paper "Discrete signature tensors for persistence landscapes" with @haharrington.bsky.social and Daniel Tolosa is now on arXiv! We use discrete signature tensors to vectorise barcodes, and we showcase such approach on a knotted protein dataset.

arxiv.org/abs/2505.02800

Very excited that our Oxford members and postdocs on the collaboration grant @mpi-cbg.de @csbdresden.bsky.social @oxfordmathematics.bsky.social joined our research retreat!

Fulvio Gesmundo @fulges.bsky.social from the Université de Toulouse visited Vincenzo @vincgalg.bsky.social this week to work on tensor geometry. Fulvio works on tensor decomposition, ie rewriting tensors to make them usable for computations. Happy to have you with us Fulvio!

The ELBE Postdoc Program is closing for applications tomorrow (Feb 14th). We're looking for strong backgrounds in applied math, compbio/compsci/bioinformatics, theoretical physics/biophysics, and/or cell/dev bio, and a big interest in interdisciplinary research: www.csbdresden.de/join-us/as-a...

Along with Pierpaola Santarsierso from Bologna, Francesco Galuppi visited us from Warsaw, an algebraic geometer interested in the signature tensors of paths. Lots of work and discussions with Vincenzo Galgano and others, as well as tapas, pizzas, and a beautiful party hosted by Ali 🩵

And here’s Pierpaola Santarsierso! From the University of Bologna and also an algebraic geometer and tensor decomposition pro, telling us why tensors are useful in an age of giant data. We loved having you both here and no doubt we’ll see you again soon 😎