Open Access

Background: Polysomnography (PSG) is the gold standard for detecting obstructive sleep apnea (OSA). However, this technique has many disadvantages when using it outside the hospital or for daily use. Portable monitors (PMs) aim to streamline the OSA detection process through deep learning (DL). Materials and methods: We studied how to detect OSA events and calculate the apnea-hypopnea index (AHI) by using deep learning models that aim to be implemented on PMs. Several deep learning models are presented after being trained on polysomnography data from the National Sleep Research Resource (NSRR) repository. The best hyperparameters for the DL architecture are presented. In addition, emphasis is focused on model explainability techniques, concretely on Gradient-weighted Class Activation Mapping (Grad-CAM). Results: The results for the best DL model are presented and analyzed. The interpretability of the DL model is also analyzed by studying the regions of the signals that are most relevant for the model to make the decision. The model that yields the best result is a one-dimensional convolutional neural network (1D-CNN) with 84.3% accuracy. Conclusion: The use of PMs using machine learning techniques for detecting OSA events still has a long way to go. However, our method for developing explainable DL models demonstrates that PMs appear to be a promising alternative to PSG in the future for the detection of obstructive apnea events and the automatic calculation of AHI.

In order to ensure sufficient recovery of the human body and brain, healthy sleep is indispensable. For this purpose, appropriate therapy should be initiated at an early stage in the case of sleep disorders. For some sleep disorders (e.g., insomnia), a sleep diary is essential for diagnosis and therapy monitoring. However, subjective measurement with a sleep diary has several disadvantages, requiring regular action from the user and leading to decreased comfort and potential data loss. To automate sleep monitoring and increase user comfort, one could consider replacing a sleep diary with an automatic measurement, such as a smartwatch, which would not disturb sleep. To obtain accurate results on the evaluation of the possibility of such a replacement, a field study was conducted with a total of 166 overnight recordings, followed by an analysis of the results. In this evaluation, objective sleep measurement with a Samsung Galaxy Watch 4 was compared to a subjective approach with a sleep diary, which is a standard method in sleep medicine. The focus was on comparing four relevant sleep characteristics: falling asleep time, waking up time, total sleep time (TST), and sleep efficiency (SE). After evaluating the results, it was concluded that a smartwatch could replace subjective measurement to determine falling asleep and waking up time, considering some level of inaccuracy. In the case of SE, substitution was also proved to be possible. However, some individual recordings showed a higher discrepancy in results between the two approaches. For its part, the evaluation of the TST measurement currently does not allow us to recommend substituting the measurement method for this sleep parameter. The appropriateness of replacing sleep diary measurement with a smartwatch depends on the acceptable levels of discrepancy. We propose four levels of similarity of results, defining ranges of absolute differences between objective and subjective measurements. By considering the values in the provided table and knowing the required accuracy, it is possible to determine the suitability of substitution in each individual case. The introduction of a “similarity level” parameter increases the adaptability and reusability of study findings in individual practical cases.

In this article, the collection of classes of matrices presented in [J. Garloff, M. Adm, ad J. Titi, A survey of classes of matrices possessing the interval property and related properties, Reliab. Comput. 22:1-14, 2016] is continued. That is, given an interval of matrices with respect to a certain partial order, it is desired to know whether a special property of the entire matrix interval can be inferred from some of its element matrices lying on the vertices of the matrix interval. The interval property of some matrix classes found in the literature is presented, and the interval property of further matrix classes including the ultrametric, the conditionally positive semidefinite, and the infinitely divisible matrices is given for the first time. For the inverse M-matrices the cardinality of the required set of vertex matrices known so far is significantly reduced.

Matrix methods for the computation of bounds for the range of a complex polynomial and its modulus over a rectangular region in the complex plane are presented. The approach relies on the expansion of the given polynomial into Bernstein polynomials. The results are extended to multivariate complex polynomials and rational functions.

In this paper, rectangular matrices whose minors of a given order have the same strict sign are considered and sufficient conditions for their recognition are presented. The results are extended to matrices whose minors of a given order have the same sign or are allowed to vanish. A matrix A is called oscillatory if all its minors are nonnegative and there exists a positive integer k such that A^k has all its minors positive. As a generalization, a new type of matrices, called oscillatory of a specific order, is introduced and some of their properties are investigated.