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Institute
- Institut für Angewandte Forschung - IAF (115) (remove)
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.
The class of square matrices of order n having a negative determinant and all their minors up to order n-1 nonnegative is considered. A characterization of these matrices is presented which provides an easy test based on the Cauchon algorithm for their recognition. Furthermore, the maximum allowable perturbation of the entry in position (2,2) such that the perturbed matrix remains in this class is given. Finally, it is shown that all matrices lying between two matrices of this class with respect to the checkerboard ordering are contained in this class, too.
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.
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.
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.
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.
Nowadays, the importance of early active patient mobilization in the recovery and rehabilitation phase has increased significantly. One way to involve patients in the treatment is a gamification-like approach, which is one of the methods of motivation in various life processes. This article shows a system prototype for patients who require physical activity because of active early mobilization after medical interventions or during illness. Bedridden patients and people with a sedentary lifestyle (predominantly lying in bed) are also potential users. The main idea for the concept was non-contact system implementation for the patients making them feel effortless during its usage. The system consists of three related parts: hardware, software, and game application. To test the relevance and coherence of the system, it was used by 35 people. The participants were asked to play a video game requiring them to make body movements while lying down. Then they were asked to take part in a small survey to evaluate the system's usability. As a result, we offer a prototype consisting of hardware and software parts that can increase and diversify physical activity during active early mobilization of patients and prevent the occurrence of possible health problems due to predominantly low activity. The proposed design can be possibly implemented in hospitals, rehabilitation centers, and even at home.
This study investigates the application of Force Sensing Resistor (FSR) sensors and machine learning algorithms for non-invasive body position monitoring during sleep. Although reliable, traditional methods like Polysomnography (PSG) are invasive and unsuited for extended home-based monitoring. Our approach utilizes FSR sensors placed beneath the mattress to detect body positions effectively. We employed machine learning techniques, specifically Random Forest (RF), K-Nearest Neighbors (KNN), and XGBoost algorithms, to analyze the sensor data. The models were trained and tested using data from a controlled study with 15 subjects assuming various sleep positions. The performance of these models was evaluated based on accuracy and confusion matrices. The results indicate XGBoost as the most effective model for this application, followed by RF and KNN, offering promising avenues for home-based sleep monitoring systems.
Monitoring heart rate and breathing is essential in understanding the physiological processes for sleep analysis. Polysomnography (PSG) system have traditionally been used for sleep monitoring, but alternative methods can help to make sleep monitoring more portable in someone's home. This study conducted a series of experiments to investigate the use of pressure sensors placed under the bed as an alternative to PSG for monitoring heart rate and breathing during sleep. The following sets of experiments involved the addition of small rubber domes - transparent and black - that were glued to the pressure sensor. The resulting data were compared with the PSG system to determine the accuracy of the pressure sensor readings. The study found that the pressure sensor provided reliable data for extracting heart rate and respiration rate, with mean absolute errors (MAE) of 2.32 and 3.24 for respiration and heart rate, respectively. However, the addition of small rubber hemispheres did not significantly improve the accuracy of the readings, with MAEs of 2.3 bpm and 7.56 breaths per minute for respiration rate and heart rate, respectively. The findings of this study suggest that pressure sensors placed under the bed may serve as a viable alternative to traditional PSG systems for monitoring heart rate and breathing during sleep. These sensors provide a more comfortable and non-invasive method of sleep monitoring. However, the addition of small rubber domes did not significantly enhance the accuracy of the readings, indicating that it may not be a worthwhile addition to the pressure sensor system.
Sleep analysis using a Polysomnography system is difficult and expensive. That is why we suggest a non-invasive and unobtrusive measurement. Very few people want the cables or devices attached to their bodies during sleep. The proposed approach is to implement a monitoring system, so the subject is not bothered. As a result, the idea is a non-invasive monitoring system based on detecting pressure distribution. This system should be able to measure the pressure differences that occur during a single heartbeat and during breathing through the mattress. The system consists of two blocks signal acquisition and signal processing. This whole technology should be economical to be affordable enough for every user. As a result, preprocessed data is obtained for further detailed analysis using different filters for heartbeat and respiration detection. In the initial stage of filtration, Butterworth filters are used.
Cardiovascular diseases (CVD) are leading contributors to global mortality, necessitating advanced methods for vital sign monitoring. Heart Rate Variability (HRV) and Respiratory Rate, key indicators of cardiovascular health, are traditionally monitored via Electrocardiogram (ECG). However, ECG's obtrusiveness limits its practicality, prompting the exploration of Ballistocardiography (BCG) as a non-invasive alternative. BCG records the mechanical activity of the body with each heartbeat, offering a contactless method for HRV monitoring. Despite its benefits, BCG signals are susceptible to external interference and present a challenge in accurately detecting J-Peaks. This research uses advanced signal processing and deep learning techniques to overcome these limitations. Our approach integrates accelerometers for long-term BCG data collection during sleep, applying Discrete Wavelet Transforms (DWT) and Ensemble Empirical Mode Decomposition (EEMD) for feature extraction. The Bi-LSTM model, leveraging these features, enhances heartbeat detection, offering improved reliability over traditional methods. The study's findings indicate that the combined use of DWT, EEMD, and Bi-LSTM for J-Peak detection in BCG signals is effective, with potential applications in unobtrusive long-term cardiovascular monitoring. Our results suggest that this methodology could contribute to HRV monitoring, particularly in home settings, enhancing patient comfort and compliance.
Gamification is one of the recognized methods of motivating people in various life processes, and it has spread to many spheres of life, including healthcare. This article proposes a system design for long-term care patients using the method mentioned. The proposed system aims to increase patient engagement in the treatment and rehabilitation process via gamification. Literature research on available and earlier proposed systems was conducted to develop a suited system design. The primary target group includes bedridden patients and a sedentary lifestyle (predominantly lying in bed). One of the main criteria for selecting a suitable option was its contactless realization for the mentioned target groups in long-term care cases. As a result, we developed the system design for hardware and software that could prevent bedsores and other health problems from occurring because of low activity. The proposed design can be tested in hospitals, nursing homes, and rehabilitation centers.
Evaluation of a Contactless Accelerometer Sensor System for Heart Rate Monitoring During Sleep
(2024)
The monitoring of a patient's heart rate (HR) is critical in the diagnosis of diseases. In the detection of sleep disorders, it also plays an important role. Several techniques have been proposed, including using sensors to record physiological signals that are automatically examined and analysed. This work aims to evaluate using a contactless HR monitoring system based on an accelerometer sensor during sleep. For this purpose, the oscillations caused by chest movements during heart contractions are recorded by an installation mounted under the bed mattress. The processing algorithm presented in this paper filters the signals and determines the HR. As a result, an average error of about 5 bpm has been documented, i.e., the system can be considered to be used for the forecasted domain.
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.
Sleep is an essential part of human existence, as we are in this state for approximately a third of our lives. Sleep disorders are common conditions that can affect many aspects of life. Sleep disorders are diagnosed in special laboratories with a polysomnography system, a costly procedure requiring much effort for the patient. Several systems have been proposed to address this situation, including performing the examination and analysis at the patient's home, using sensors to detect physiological signals automatically analysed by algorithms. This work aims to evaluate the use of a contactless respiratory recording system based on an accelerometer sensor in sleep apnea detection. For this purpose, an installation mounted under the bed mattress records the oscillations caused by the chest movements during the breathing process. The presented processing algorithm performs filtering of the obtained signals and determines the apnea events presence. The performance of the developed system and algorithm of apnea event detection (average values of accuracy, specificity and sensitivity are 94.6%, 95.3%, and 93.7% respectively) confirms the suitability of the proposed method and system for further ambulatory and in-home use.
Sleep is essential to physical and mental health. However, the traditional approach to sleep analysis—polysomnography (PSG)—is intrusive and expensive. Therefore, there is great interest in the development of non-contact, non-invasive, and non-intrusive sleep monitoring systems and technologies that can reliably and accurately measure cardiorespiratory parameters with minimal impact on the patient. This has led to the development of other relevant approaches, which are characterised, for example, by the fact that they allow greater freedom of movement and do not require direct contact with the body, i.e., they are non-contact. This systematic review discusses the relevant methods and technologies for non-contact monitoring of cardiorespiratory activity during sleep. Taking into account the current state of the art in non-intrusive technologies, we can identify the methods of non-intrusive monitoring of cardiac and respiratory activity, the technologies and types of sensors used, and the possible physiological parameters available for analysis. To do this, we conducted a literature review and summarised current research on the use of non-contact technologies for non-intrusive monitoring of cardiac and respiratory activity. The inclusion and exclusion criteria for the selection of publications were established prior to the start of the search. Publications were assessed using one main question and several specific questions. We obtained 3774 unique articles from four literature databases (Web of Science, IEEE Xplore, PubMed, and Scopus) and checked them for relevance, resulting in 54 articles that were analysed in a structured way using terminology. The result was 15 different types of sensors and devices (e.g., radar, temperature sensors, motion sensors, cameras) that can be installed in hospital wards and departments or in the environment. The ability to detect heart rate, respiratory rate, and sleep disorders such as apnoea was among the characteristics examined to investigate the overall effectiveness of the systems and technologies considered for cardiorespiratory monitoring. In addition, the advantages and disadvantages of the considered systems and technologies were identified by answering the identified research questions. The results obtained allow us to determine the current trends and the vector of development of medical technologies in sleep medicine for future researchers and research.
The respiratory rate is a vital sign indicating breathing illness. It is necessary to analyze the mechanical oscillations of the patient's body arising from chest movements. An inappropriate holder on which the sensor is mounted, or an inappropriate sensor position is some of the external factors which should be minimized during signal registration. This paper considers using a non-invasive device placed under the bed mattress and evaluates the respiratory rate. The aim of the work is the development of an accelerometer sensor holder for this system. The normal and deep breathing signals were analyzed, corresponding to the relaxed state and when taking deep breaths. The evaluation criterion for the holder's model is its influence on the patient's respiratory signal amplitude for each state. As a result, we offer a non-invasive system of respiratory rate detection, including the mechanical component providing the most accurate values of mentioned respiratory rate.