Discrete Signature Varieties

This page contains auxiliary files and supplementary code to the following paper:

Carlo Bellingeri, Raul Penaguiao: Discrete Signature Varieties

ARXIV: https://arxiv.org/abs/2303.13377 CODE: https://github.com/raulpenaguiao/discrete_signature_varieties_macaulay2

ABSTRACT: Discrete signatures are invariants computed from time series corresponding to the discretised version of the signature of paths. We study the algebraic varieties arising from their images, the discrete signature varieties. We introduce them and compute their dimension in many cases. From a particular subclass of these varieties, we derive a partial solution to the Chen-Chow theorem for complex-valued time series.

• Section 3 - Degree and dimension of discrete signature varieties
• Section 4 - dimension computation in the limit case

Project page created: 16/04/2025

Project contributors: Carlo Bellingeri, Raul Penaguiao

Corresponding author of this page: Raul Penaguiao, raul.penaguiao@proton.me

Software used: Macaulay2 (Version 1.13) and Python (Version 3.12.3)

System setup used: MacBook Pro with macOS Monterey 12.0.1, Processor 2.7 GHz Intel Core i7, Memory 16 GB 2133 MHz LPDDR3

License for code of this project page: MIT License (https://spdx.org/licenses/MIT.html)