Jeanne Lin | Searcharxiv

arXiv2026

Fingertip Micro-Motion as a Source of Respiratory Information During Sleep Using Triaxial Accelerometers

Objective: Triaxial accelerometers (TAAs) are widely used in homecare medicine. This study investigates whether TAA signals recorded at the fingertip encode respiratory information, particularly instantaneous respiratory rate (IRR) and respiratory effort, during sleep. Method: We propose an antiderivative-based nonlinear transformation to convert TAA signals into a respiratory surrogate, termed TAA-resp. To quantify the embedded respiratory-induced motion, a modern time-frequency analysis tool is applied to derive an index, referred to as the respiratory motion index (RMI). The proposed TAA-resp and RMI are validated on a dataset comprising 39 full-night recordings with simultaneous polysomnography (PSG) and a fingertip TAA measurements. Criteria for labeling TAA-resp signal quality as good, moderate, or poor are established, and expert annotations are obtained. Result: On average, TAA-resp over 22.2% $\pm$ 15.6% of full-night recordings encodes high-quality respiratory information, reaching up to 58.9% in some cases. TAA-resp shows stronger correlation with thoracic and abdominal motion than with airflow, indicating predominant capture of respiratory effort. High-quality TAA-resp offers an accurate IRR estimate with root mean square error $0.027 \pm 0.022$ Hz. RMI is higher for high-quality segments and lower for poor-quality segments, and its distribution aligns with physiology, with higher values during REM, N2, and N3 sleep and in the absence of apnea or hypopnea events. In leave-one-subject-out cross-validation, RMI predicts quality labels with 0.74 sensitivity and 0.75 specificity. Conclusion: Fingertip-mounted TAAs encode meaningful respiratory information. Leveraging this underutilized signal may enhance home-based sleep monitoring in channel-limited settings.

physics.med-ph↗

arXiv2024

On the extinction of multiple shocks in scalar viscous conservation laws

We are interested in the dynamics of interfaces, or zeros, of shock waves in general scalar viscous conservation laws with a locally Lipschitz continuous flux function, such as the modular Burgers' equation. We prove that all interfaces coalesce within finite time, leaving behind either a single interface or no interface at all. Our proof relies on mass and energy estimates, regularization of the flux function, and an application of the Sturm theorems on the number of zeros of solutions of parabolic problems. Our analysis yields an explicit upper bound on the time of extinction in terms of the initial condition and the flux function. Moreover, in the case of a smooth flux function, we characterize the generic bifurcations arising at a coalescence event with and without the presence of odd symmetry. We identify associated scaling laws describing the local interface dynamics near collision. Finally, we present an extension of these results to the case of anti-shock waves converging to asymptotic limits of opposite signs. Our analysis is corroborated by numerical simulations in the modular Burgers' equation and its regularizations.

math.AP↗