201 citations · 2.4k across the 113 of their papers we have counts for
22 papers · 1 filter
A multiplicative surface signature through its Magnus expansion
Ilya Chevyrev, Joscha Diehl, Kurusch Ebrahimi-Fard +1
In the last decade, the concept of path signature has achieved significant success in data science applications. It offers a powerful set of features that effectively capture and d…
A Survey on the Munthe-Kaas-Wright Hopf Algebra
Kurusch Ebrahimi-Fard, Ludwig Rahm
We survey the Munthe-Kaas--Wright Hopf algebra defined on planar rooted trees. This algebra serves a role akin to that of the Butcher--Connes--Kreimer Hopf algebra on non-planar ro…
Eight times four bialgebras of hypergraphs, cointeractions, and chromatic polynomials
Kurusch Ebrahimi-Fard, Gunnar Fløystad
We consider the bialgebra of hypergraphs, a generalization of Schmitt's Hopf algebra of graphs, and show it has a cointeracting bialgebra. So one has a double bialgebra in the sens…
Algebraic groups in non-commutative probability theory revisited
Ilya Chevyrev, Kurusch Ebrahimi-Fard, Frédéric Patras
The role of coalgebras as well as algebraic groups in non-commutative probability has long been advocated by the school of von Waldenfels and Schürmann. Another algebraic approach…
Signatures of graphs for bicommutative Hopf algebras
Diego Caudillo, Joscha Diehl, Kurusch Ebrahimi-Fard +1
This article approaches the counting of subgraphs, in terms of signature-type functionals defined over combinatorial Hopf algebras of graphs. Well-known algebraic identities that a…
Post-Lie-Magnus expansion and BCH-recursion
Mahdi Jasim Hasan Al-Kaabi, Kurusch Ebrahimi-Fard, Dominique Manchon
We identify the Baker-Campbell-Hausdorff recursion driven by a weight Rota-Baxter operator with the Magnus expansion relativeto the post-Lie structure naturally associated to…