41 citations · 58 across the 7 of their papers we have counts for
8 papers
Conjugation, loop and closure invariants of the iterated-integrals signature
Joscha Diehl, Rosa Preiß, Jeremy Reizenstein
Given a feature set for the shape of a closed loop, it is natural to ask which features in that set do not change when the starting point of the path is moved. For example, in two…
A structure theorem for streamed information
Cristopher Salvi, Joscha Diehl, Terry Lyons +2
We identify the free half shuffle algebra of Schützenberger (1958) with an algebra of real-valued functionals on paths, where the half shuffle emulates integration of a functional…
From Hopf algebras to rough paths and regularity structures
Rosa Preiß
Lyon's rough paths give an algebraic and analytic framework for Stieltjes integrals in a regime of low regularity where the usual Riemann-Stieltjes integral does not converge. Befo…
Smooth rough paths, their geometry and algebraic renormalization
Carlo Bellingeri, Peter K. Friz, Sylvie Paycha +1
We introduce the class of "smooth rough paths" and study their main properties. Working in a smooth setting allows us to discard sewing arguments and focus on algebraic and geometr…
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…
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…
Signatures of paths transformed by polynomial maps
Laura Colmenarejo, Rosa Preiß
We characterize the signature of piecewise continuously differentiable paths transformed by a polynomial map in terms of the signature of the original path. For this aim, we define…
A Rough Path Perspective on Renormalization
Yvain Bruned, Ilya Chevyrev, Peter K. Friz +1
We develop the algebraic theory of rough path translation. Particular attention is given to the case of branched rough paths, whose underlying algebraic structure (Connes-Kreimer,…