Neural ordinary differential equations are an attractive option for modelling temporal
dynamics. However, a fundamental issue is that the solution to an ordinary differential …

Iterated-integral signatures and log signatures are sequences calculated from a path that
characterizes its shape. They originate from the work of KT Chen and have become …

In data science, one is often confronted with a time series representing measurements of
some quantity of interest. Usually, in a first step, features of the time series need to be …

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 …

The signature transform is a'universal nonlinearity'on the space of continuous vector-valued
paths, and has received attention for use in machine learning on time series. However, real …

We study a family of shuffling operators on the symmetric group $ S_n $, which includes the
top-to-random shuffle. The general shuffling scheme consists of removing one card at a time …

Over the course of three different collaborative projects, we gather evidence of how Hopf, Lie
and pre-Lie, Zinbiel and dendriform, as well as Tortkara algebras appear in and influence …

Abstract Models that can effectively represent structured Electronic Healthcare Records
(EHR) are central to an increasing range of applications in healthcare. Due to the sequential …

The amalgamation of rough path theory and machine learning for sequential data has been
a topic of increasing interest over the last ten or so years. The unity of these two subject …

We study an infinite family of shuffling operators on the symmetric group Sn, which includes
the well-studied top-to-random shuffle. The general shuffling scheme consists of removing …