arXiv cs.AI· Timothy Oladunni, Farouk Ganiyu Adewumi·· 12 小时前AI 评分22
Attractor Domain Theory（ADT）：基于可穿戴 PPG 验证的心血管吸引子分析数学框架
Attractor Domain Theory: A Mathematical Framework for Cardiovascular Attractor Analysis with Wearable Photoplethysmography (PPG) Validation
AI 导读
研究提出 Attractor Domain Theory（ADT），用几何、遍历与变分三种表示算子刻画延迟嵌入重建的心血管动力学，并给出条件域分解与域变换不可能性定理。
正文 · 原文
Abstract:The cardiac attractor provides a phase-space representation of cardiovascular dynamics reconstructed from scalar observations under standard delay-embedding conditions. We introduce Attractor Domain Theory (ADT), a theory in which linked mathematical transformations expose distinct properties of reconstructed dynamics: the Geometry Domain is obtained through the delay-reconstruction transformation, while Ergodic and Variational transformations act on that geometry to characterize long-horizon organization and localized finite-time deformation. Thus, ADT specifies a three-representation operator architecture for reconstructed dynamics rather than retrospectively grouping existing nonlinear features; the architecture is proposed as an operational organization, not as a uniqueness or exhaustiveness theorem. A Conditional Domain Decomposition quantifies endpoint-specific incremental information with an explicit residual, and a domain-transformation impossibility theorem establishes that a property cannot be exactly recovered when an operator maps property-distinct inputs to the same representation. Empirical evaluation includes PPG analysis across 176{,}742 segments with 18 patient-level held-out BIDMC records (AUC 0.757 [0.686--0.828]) and an independent ECG analysis of 5{,}000 PTB-XL records (AUC 0.719 [0.686--0.750]). Cross-observation transfer is property-specific: the Lyapunov exponent shows subject-level ECG--PPG agreement ($\rho=0.703$, 95\% CI [0.503, 0.836]), whereas the predicted class-wide separation of invariant and observation-coupled descriptors is not supported ($p=0.54$). These results provide empirical support for attractor-domain analysis across cardiovascular measurements while leaving cross-observation recoverability as a property-specific empirical question.
| Subjects: | Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2606.22039 [cs.AI] |
| (or arXiv:2606.22039v3 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2606.22039 arXiv-issued DOI via DataCite |
Submission history
From: Timothy Oladunni [view email]
[v1]
Sat, 20 Jun 2026 13:32:32 UTC (33 KB)
[v2]
Wed, 29 Jul 2026 18:28:36 UTC (931 KB)
[v3]
Thu, 22 Oct 2026 23:54:33 UTC (443 KB)
来源：arXiv cs.AI · arxiv.org