4 papers
Path signatures of ODE solutions
Francesco Galuppi, Giovanni Moreno, Pierpaola Santarsiero
The signature of a path is a sequence of tensors which allows to uniquely reconstruct the path. By employing the geometric theory of nonlinear systems of ordinary differential equa…
Decomposing Tensor Spaces via Path Signatures
Carlos Améndola, Francesco Galuppi, Ãngel David RÃos Ortiz +2
The signature of a path is a sequence of tensors whose entries are iterated integrals, playing a key role in stochastic analysis and applications. The set of all signature tensors…
Symmetric rank of some reducible forms
Liena Colarte-Gómez, Francesco Galuppi
In this paper, we study the symmetric rank of products of linear forms and an irreducible quadratic form. The main result presents a new, non-trivial lower bound for the rank, and…
Rank and symmetries of signature tensors
Francesco Galuppi, Pierpaola Santarsiero
The signature of a path is a sequence of tensors which allows to uniquely reconstruct the path. In this paper we propose a systematic study of basic properties of signature tensors…