21 citations · 96 across the 15 of their papers we have counts for
18 papers
Explicit and Effectively Symmetric Runge-Kutta Methods
Daniil Shmelev, Kurusch Ebrahimi-Fard, Nikolas Tapia +1
Symmetry is a key property of numerical methods. The geometric properties of symmetric schemes make them an attractive option for integrating Hamiltonian systems, whilst their abil…
Perturbative renormalisation of the model via generalized Wick maps
Nils Berglund, Tom Klose, Nikolas Tapia
We consider the perturbative renormalisation of the model from Euclidean Quantum Field Theory for any, possibly non-integer dimension . The so-called BPHZ renormalisat…
An introduction to tensors for path signatures
Jack Beda, Goncalo dos Reis, Nikolas Tapia
We present a fit-for-purpose introduction to tensors and their operations. It is envisaged to help the reader become acquainted with its underpinning concepts for the study of path…
On expected signatures and signature cumulants in semimartingale models
Peter K. Friz, Paul P. Hager, Nikolas Tapia
The concept of signatures and expected signatures is vital in data science, especially for sequential data analysis. The signature transform, a Cartan type development, translates…
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…
Free generators and Hoffman's isomorphism for the two-parameter shuffle algebra
Leonard Schmitz, Nikolas Tapia
Signature transforms have recently been extended to data indexed by two and more parameters. With free Lyndon generators, ideas from -algebras and a novel two-pa…