36 citations · 208 across the 26 of their papers we have counts for
5 papers · 1 filter
The moving frame method for iterated-integrals: orthogonal invariants
Joscha Diehl, Rosa Preiß, Michael Ruddy +1
Geometric features, robust to noise, of curves in Euclidean space are of great interest for various applications such as machine learning and image analysis. We apply the Fels-Olve…
Generalized iterated-sums signatures
Joscha Diehl, Kurusch Ebrahimi-Fard, Nikolas Tapia
We explore the algebraic properties of a generalized version of the iterated-sums signature, inspired by previous work of F.~Király and H.~Oberhauser. In particular, we show how to…
Tropical time series, iterated-sums signatures and quasisymmetric functions
Joscha Diehl, Kurusch Ebrahimi-Fard, Nikolas Tapia
Aiming for a systematic feature-extraction from time series, we introduce the iterated-sums signature over arbitrary commutative semirings. The case of the tropical semiring is a c…
A quadratic identity in the shuffle algebra and an alternative proof for de Bruijn's formula
Laura Colmenarejo, Joscha Diehl, Miruna-Stefana Sorea
Motivated by a polynomial identity of certain iterated integrals, first observed in [CGM20] in the setting of lattice paths, we prove an intriguing combinatorial identity in the sh…
Areas of areas generate the shuffle algebra
Joscha Diehl, Terry Lyons, Rosa Preiß +1
We consider the anti-symmetrization of the half-shuffle on words, which we call the 'area' operator, since it corresponds to taking the signed area of elements of the iterated-inte…