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Sleep disorders can impact daily life, affecting physical, emotional, and cognitive well-being. Due to the time-consuming, highly obtrusive, and expensive nature of using the standard approaches such as polysomnography, it is of great interest to develop a noninvasive and unobtrusive in-home sleep monitoring system that can reliably and accurately measure cardiorespiratory parameters while causing minimal discomfort to the user’s sleep. We developed a low-cost Out of Center Sleep Testing (OCST) system with low complexity to measure cardiorespiratory parameters. We tested and validated two force-sensitive resistor strip sensors under the bed mattress covering the thoracic and abdominal regions. Twenty subjects were recruited, including 12 males and 8 females. The ballistocardiogram signal was processed using the 4th smooth level of the discrete wavelet transform and the 2nd order of the Butterworth bandpass filter to measure the heart rate and respiration rate, respectively. We reached a total error (concerning the reference sensors) of 3.24 beats per minute and 2.32 rates for heart rate and respiration rate, respectively. For males and females, heart rate errors were 3.47 and 2.68, and respiration rate errors were 2.32 and 2.33, respectively. We developed and verified the reliability and applicability of the system. It showed a minor dependency on sleeping positions, one of the major cumbersome sleep measurements. We identified the sensor under the thoracic region as the optimal configuration for cardiorespiratory measurement. Although testing the system with healthy subjects and regular patterns of cardiorespiratory parameters showed promising results, further investigation is required with the bandwidth frequency and validation of the system with larger groups of subjects, including patients.
In 1970, B.A. Asner, Jr., proved that for a real quasi-stable polynomial, i.e., a polynomial whose zeros lie in the closed left half-plane of the complex plane, its finite Hurwitz matrix is totally nonnegative, i.e., all its minors are nonnegative, and that the converse statement is not true. In this work, we explain this phenomenon in detail, and provide necessary and sufficient conditions for a real polynomial to have a totally nonnegative finite Hurwitz matrix.
Probabilistic Short-Term Low-Voltage Load Forecasting using Bernstein-Polynomial Normalizing Flows
(2021)
The transition to a fully renewable energy grid requires better forecasting of demand at the low-voltage level. However, high fluctuations and increasing electrification cause huge forecast errors with traditional point estimates. Probabilistic load forecasts take future uncertainties into account and thus enables various applications in low-carbon energy systems. We propose an approach for flexible conditional density forecasting of short-term load based on Bernstein-Polynomial Normalizing Flows where a neural network controls the parameters of the flow. In an empirical study with 363 smart meter customers, our density predictions compare favorably against Gaussian and Gaussian mixture densities and also outperform a non-parametric approach based on the pinball loss for 24h-ahead load forecasting for two different neural network architectures.
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.
Sleep is extremely important for physical and mental health. Although polysomnography is an established approach in sleep analysis, it is quite intrusive and expensive. Consequently, developing a non-invasive and non-intrusive home sleep monitoring system with minimal influence on patients, that can reliably and accurately measure cardiorespiratory parameters, is of great interest. The aim of this study is to validate a non-invasive and unobtrusive cardiorespiratory parameter monitoring system based on an accelerometer sensor. This system includes a special holder to install the system under the bed mattress. The additional aim is to determine the optimum relative system position (in relation to the subject) at which the most accurate and precise values of measured parameters could be achieved. The data were collected from 23 subjects (13 males and 10 females). The obtained ballistocardiogram signal was sequentially processed using a sixth-order Butterworth bandpass filter and a moving average filter. As a result, an average error (compared to reference values) of 2.24 beats per minute for heart rate and 1.52 breaths per minute for respiratory rate was achieved, regardless of the subject’s sleep position. For males and females, the errors were 2.28 bpm and 2.19 bpm for heart rate and 1.41 rpm and 1.30 rpm for respiratory rate. We determined that placing the sensor and system at chest level is the preferred configuration for cardiorespiratory measurement. Further studies of the system’s performance in larger groups of subjects are required, despite the promising results of the current tests in healthy subjects.
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.
Further applications of the Cauchon algorithm to rank determination and bidiagonal factorization
(2018)
For a class of matrices connected with Cauchon diagrams, Cauchon matrices, and the Cauchon algorithm, a method for determining the rank, and for checking a set of consecutive row (or column) vectors for linear independence is presented. Cauchon diagrams are also linked to the elementary bidiagonal factorization of a matrix and to certain types of rank conditions associated with submatrices called descending rank conditions.
Positive systems play an important role in systems and control theory and have found applications in multiagent systems, neural networks, systems biology, and more. Positive systems map the nonnegative orthant to itself (and also the non-positive orthant to itself). In other words, they map the set of vectors with zero sign variation to itself. In this article, discrete-time linear systems that map the set of vectors with up to k-1 sign variations to itself are introduced. For the special case k = 1 these reduce to discrete-time positive linear systems. Properties of these systems are analyzed using tools from the theory of sign-regular matrices. In particular, it is shown that almost every solution of such systems converges to the set of vectors with up to k-1 sign variations. It is also shown that these systems induce a positive dynamics of k-dimensional parallelotopes.
Sustainable technologies are being increasingly used in various areas of human life. While they have a multitude of benefits, they are especially useful in health monitoring, especially for certain groups of people, such as the elderly. However, there are still several issues that need to be addressed before its use becomes widespread. This work aims to clarify the aspects that are of great importance for increasing the acceptance of the use of this type of technology in the elderly. In addition, we aim to clarify whether the technologies that are already available are able to ensure acceptable accuracy and whether they could replace some of the manual approaches that are currently being used. A two-week study with people 65 years of age and over was conducted to address the questions posed here, and the results were evaluated. It was demonstrated that simplicity of use and automatic functioning play a crucial role. It was also concluded that technology cannot yet completely replace traditional methods such as questionnaires in some areas. Although the technologies that were tested were classified as being “easy to use”, the elderly population in the current study indicated that they were not sure that they would use these technologies regularly in the long term because the added value is not always clear, among other issues. Therefore, awareness-raising must take place in parallel with the development of technologies and services.