Збережено в:
| Автор: | |
|---|---|
| Формат: | Recurso digital |
| Мова: | Англійська |
| Опубліковано: |
Zenodo
2026
|
| Предмети: | |
| Онлайн доступ: | https://doi.org/10.5281/zenodo.19600331 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| _version_ | 1866901668002529280 |
|---|---|
| author | Vázquez Broquá, Juan Ignacio |
| author_facet | Vázquez Broquá, Juan Ignacio |
| contents | <p>We introduce Geometric Transfer Entropy (GTE), a measure of directional<br>information flow between time series that preserves the grade structure of the<br>Clifford-algebraic embedding underlying the Geometric Signal Dynamics (GSD)<br>programme. Building on the kinematic embedding and geometric product of Vázquez<br>Broquá (2026a), the spectral bivector identity of Vázquez Broquá (2026b), the joint<br>embedding for cointegration of Vázquez Broquá (2026c), and the antisymmetric<br>entropy HAS of Vázquez Broquá (2026d), we define GTEX→Y (τ ) as the sum of<br>two grade-resolved channels: a scalar channel T(0)X→Y that captures transfer of alignment/level information, and a bivector channel T(2)X→Y that captures transfer of rotational information (velocity, curvature, phase). The net flow ΦXY = GTEX→Y −GTEY →X decomposes analogously into a scalar and a rotational flow, ΦXY = Φ(0) XY + Φ(2) XY . Across seven benchmark systems, GTE recovers the classical Schreiber transfer entropy on level-coupled linear systems, detects velocity-coupled systems four times more strongly than Schreiber TE, and correctly identifies the direction<br>of coupling in stochastic oscillators where classical TE reverses sign. The bivariate signature (Φ(0), Φ<br>(2)) produces a taxonomy of dynamical coupling mechanisms and yields geometric diagnostics of cointegration, common confounding, and pure rotational transfer that classical information flow measures cannot provide.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19600331 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Geometric Transfer Entropy: A Grade-Resolved Directional Information Flow for Dynamical Coupling of Time Series Vázquez Broquá, Juan Ignacio transfer entropy clifford algebra geometric signal dynamics directional coupling non-commutative information cointegration coupled oscillators <p>We introduce Geometric Transfer Entropy (GTE), a measure of directional<br>information flow between time series that preserves the grade structure of the<br>Clifford-algebraic embedding underlying the Geometric Signal Dynamics (GSD)<br>programme. Building on the kinematic embedding and geometric product of Vázquez<br>Broquá (2026a), the spectral bivector identity of Vázquez Broquá (2026b), the joint<br>embedding for cointegration of Vázquez Broquá (2026c), and the antisymmetric<br>entropy HAS of Vázquez Broquá (2026d), we define GTEX→Y (τ ) as the sum of<br>two grade-resolved channels: a scalar channel T(0)X→Y that captures transfer of alignment/level information, and a bivector channel T(2)X→Y that captures transfer of rotational information (velocity, curvature, phase). The net flow ΦXY = GTEX→Y −GTEY →X decomposes analogously into a scalar and a rotational flow, ΦXY = Φ(0) XY + Φ(2) XY . Across seven benchmark systems, GTE recovers the classical Schreiber transfer entropy on level-coupled linear systems, detects velocity-coupled systems four times more strongly than Schreiber TE, and correctly identifies the direction<br>of coupling in stochastic oscillators where classical TE reverses sign. The bivariate signature (Φ(0), Φ<br>(2)) produces a taxonomy of dynamical coupling mechanisms and yields geometric diagnostics of cointegration, common confounding, and pure rotational transfer that classical information flow measures cannot provide.</p> |
| title | Geometric Transfer Entropy: A Grade-Resolved Directional Information Flow for Dynamical Coupling of Time Series |
| topic | transfer entropy clifford algebra geometric signal dynamics directional coupling non-commutative information cointegration coupled oscillators |
| url | https://doi.org/10.5281/zenodo.19600331 |