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Wearable devices have become commonplace tools for tracking behavioral and physiological parameters in real-world settings. Nonetheless, the practical utility of these data for clinical and research applications, such as sleep analysis, is hindered by their noisy, large-scale, and multidimensional characteristics. Here, we develop a neural network algorithm that predicts sleep stages by tracking topological features (TFs) of wearable data and model-driven clock proxies (CPs) reflecting the circadian propensity for sleep. To evaluate its accuracy, we apply it to motion and heart rate data from the Apple Watch worn by young subjects undergoing polysomnography (PSG) and compare the predicted sleep stages with the corresponding ground truth PSG records. The neural network that includes TFs and CPs along with raw wearable data as inputs shows improved performance in classifying Wake/REM/NREM sleep. For example, it shows significant improvements in identifying REM and NREM sleep (AUROC/AUPRC improvements >13% and REM/NREM accuracy improvement of 12%) compared with the neural network using only raw data inputs. We find that this improvement is mainly attributed to the heart rate TFs. To further validate our algorithm on a different population, we test it on elderly subjects from the Multi-ethnic Study of Atherosclerosis cohort. This confirms that TFs and CPs contribute to the improvements in Wake/REM/NREM classification. We next compare the performance of our algorithm with previous state-of-the-art wearable-based sleep scoring algorithms and find that our algorithm outperforms them within and across different populations. This study demonstrates the benefits of combining topological data analysis and mathematical modeling to extract hidden inputs of neural networks from puzzling wearable data. 

Mathematical models have a long and influential history in the study of human circadian rhythms. Accurate predictive models for the human circadian light response have been used to study the impact of a host of light exposures on the circadian system. However, generally, these models do not account for the physiological basis of these rhythms. We illustrate a new paradigm for deriving models of the human circadian light response. Beginning from a high-dimensional model of the circadian neural network, we systematically derive low-dimensional models using an approach motivated by experimental measurements of circadian neurons. This systematic reduction allows for the variables and parameters of the derived model to be interpreted in a physiological context. We fit and validate the resulting models to a library of experimental measurements. Finally, we compare model predictions for experimental measurements of light levels and discuss the differences between our model’s predictions and previous models. Our modeling paradigm allows for the integration of experimental measurements across the single-cell, tissue, and behavioral scales, thereby enabling the development of accurate low-dimensional models for human circadian rhythms.