We study how to establish spectral independence, a key concept in sampling, without relying on total influence bounds, by applying an approximate inverse of the influence matrix. Our method gives constant upper bounds on spectral independence for two well-studied Gibbs distributions known to have unbounded total influences:

Rapid eye movement (REM) sleep without atonia (RSWA) is a critical diagnostic criterion for REM sleep behavior disorder (RBD). Current clinical practices rely on time-consuming manual annotation, increasing workload, and introducing variability. Existing automated methods, including CNN, LSTM, Transformer, and their combinations, fail to fully exploit the inherent physiological relationship between sleep staging and RSWA detection, while also facing challenges such as severe data imbalance and the complex fusion of multichannel signals. To address these limitations, we propose a multi-task learning framework that jointly optimizes both tasks. Our Multi-scale Information Attention Bottleneck Network (MIABNet) backbone improves multichannel fusion. Building upon MIABNet, the Multi-task RBD Network (MtRBD) implements dynamic feature enhancement, facilitating cross-task information flow while preserving physiological relationships. On the clinical CZ-RBD dataset collected from 30 patients over 59 nights at Shanghai Changzheng Hospital, our framework achieved the accuracy of 83.0% for sleep staging and 93.6% for RSWA detection, with an accuracy of 77.6% for critical RSWA event identification, outperforming single-task methods in cross-subject validation. Through modality selection and Grad-CAM visualization, we enhance clinical interpretability, providing reliable support for early detection of RBD and related neurodegenerative diseases.

Stroke is the second leading cause of disability and mortality worldwide. Extensive researches on rehabilitation assessment for stroke survivors using wearable plantar pressure sensors often suffer from troublesome processes and unsatisfactory results due to excessive sensors and sparse pressure sensing structures. To address this, we developed an automatic assessment system for the recovery stage of stroke patients based solely on smart high-density flexible wearable plantar pressure insoles and an ensemble learning classification algorithm (ELCA). This system quantitatively evaluates the stroke patient's recovery progress. The data from 37 stroke patients were collected using self-developed smart insoles, from which multidimensional high-order features were extracted. ELCA employing seven basic classifiers was then developed to quantitatively assess recovery stages. Finally, the leave-one-out method was used to evaluate the performance of classifiers. The results show the ELCA has the best performance, achieving an accuracy, specificity, and sensitivity of up to 91.890/0, 97.30%, and 91.89% respectively, preliminarily demonstrating the system possesses excellent capabilities in quantitatively assessing rehabilitation progress. This solution is expected to provide an objective and practical method for long-term home rehabilitation monitoring of stroke patients.