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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.
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.
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.
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.
Accurate monitoring of a patient's heart rate is a key element in the medical observation and health monitoring. In particular, its importance extends to the identification of sleep-related disorders. Various methods have been established that involve sensor-based recording of physiological signals followed by automated examination and analysis. This study attempts to evaluate the efficacy of a non-invasive HR monitoring framework based on an accelerometer sensor specifically during sleep. To achieve this goal, the motion induced by thoracic movements during cardiac contractions is captured by a device installed under the mattress. Signal filtering techniques and heart rate estimation using the symlets6 wavelet are part of the implemented computational framework described in this article. Subsequent analysis indicates the potential applicability of this system in the prognostic domain, with an average error margin of approximately 3 beats per minute. The results obtained represent a promising advancement in non-invasive heart rate monitoring during sleep, with potential implications for improved diagnosis and management of cardiovascular and sleep-related disorders.
The scoring of sleep stages is an essential part of sleep studies. The main objective of this research is to provide an algorithm for the automatic classification of sleep stages using signals that may be obtained in a non-obtrusive way. After reviewing the relevant research, the authors selected a multinomial logistic regression as the basis for their approach. Several parameters were derived from movement and breathing signals, and their combinations were investigated to develop an accurate and stable algorithm. The algorithm was implemented to produce successful results: the accuracy of the recognition of Wake/NREM/REM stages is equal to 73%, with Cohen's kappa of 0.44 for the analyzed 19324 sleep epochs of 30 seconds each. This approach has the advantage of using the only movement and breathing signals, which can be recorded with less effort than heart or brainwave signals, and requiring only four derived parameters for the calculations. Therefore, the new system is a significant improvement for non-obtrusive sleep stage identification compared to existing approaches.
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.
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.
The scoring of sleep stages is one of the essential tasks in sleep analysis. Since a manual procedure requires considerable human and financial resources, and incorporates some subjectivity, an automated approach could result in several advantages. There have been many developments in this area, and in order to provide a comprehensive overview, it is essential to review relevant recent works and summarise the characteristics of the approaches, which is the main aim of this article. To achieve it, we examined articles published between 2018 and 2022 that dealt with the automated scoring of sleep stages. In the final selection for in-depth analysis, 125 articles were included after reviewing a total of 515 publications. The results revealed that automatic scoring demonstrates good quality (with Cohen's kappa up to over 0.80 and accuracy up to over 90%) in analysing EEG/EEG + EOG + EMG signals. At the same time, it should be noted that there has been no breakthrough in the quality of results using these signals in recent years. Systems involving other signals that could potentially be acquired more conveniently for the user (e.g. respiratory, cardiac or movement signals) remain more challenging in the implementation with a high level of reliability but have considerable innovation capability. In general, automatic sleep stage scoring has excellent potential to assist medical professionals while providing an objective assessment.
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.
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.
Recognizing Human Activity of Daily Living Using a Flexible Wearable for 3D Spine Pose Tracking
(2023)
The World Health Organization recognizes physical activity as an influencing domain on quality of life. Monitoring, evaluating, and supervising it by wearable devices can contribute to the early detection and progress assessment of diseases such as Alzheimer’s, rehabilitation, and exercises in telehealth, as well as abrupt events such as a fall. In this work, we use a non-invasive and non-intrusive flexible wearable device for 3D spine pose measurement to monitor and classify physical activity. We develop a comprehensive protocol that consists of 10 indoor, 4 outdoor, and 8 transition states activities in three categories of static, dynamic, and transition in order to evaluate the applicability of the flexible wearable device in human activity recognition. We implement and compare the performance of three neural networks: long short-term memory (LSTM), convolutional neural network (CNN), and a hybrid model (CNN-LSTM). For ground truth, we use an accelerometer and strips data. LSTM reached an overall classification accuracy of 98% for all activities. The CNN model with accelerometer data delivered better performance in lying down (100%), static (standing = 82%, sitting = 75%), and dynamic (walking = 100%, running = 100%) positions. Data fusion improved the outputs in standing (92%) and sitting (94%), while LSTM with the strips data yielded a better performance in bending-related activities (bending forward = 49%, bending backward = 88%, bending right = 92%, and bending left = 100%), the combination of data fusion and principle components analysis further strengthened the output (bending forward = 100%, bending backward = 89%, bending right = 100%, and bending left = 100%). Moreover, the LSTM model detected the first transition state that is similar to fall with the accuracy of 84%. The results show that the wearable device can be used in a daily routine for activity monitoring, recognition, and exercise supervision, but still needs further improvement for fall detection.
Apnea is a sleep disorder characterized by breathing interruptions during sleep, impacting cardiorespiratory function and overall health. Traditional diagnostic methods, like polysomnography (PSG), are unobtrusive, leading to noninvasive monitoring. This study aims to develop and validate a novel sleep monitoring system using noninvasive sensor technology to estimate cardiorespiratory parameters and detect sleep apnea. We designed a seamless monitoring system integrating noncontact force-sensitive resistor sensors to collect ballistocardiogram signals associated with cardiorespiratory activity. We enhanced the sensor’s sensitivity and reduced the noise by designing a new concept of edge-measuring sensor using a hemisphere dome and mechanical hanger to distribute the force and mechanically amplify the micromovement caused by cardiac and respiration activities. In total, we deployed three edge-measuring sensors, two deployed under the thoracic and one under the abdominal regions. The system is supported with onboard signal preprocessing in multiple physical layers deployed under the mattress. We collected the data in four sleeping positions from 16 subjects and analyzed them using ensemble empirical mode decomposition (EMD) to avoid frequency mixing. We also developed an adaptive thresholding method to identify sleep apnea. The error was reduced to 3.98 and 1.43 beats/min (BPM) in heart rate (HR) and respiration estimation, respectively. The apnea was detected with an accuracy of 87%. We optimized the system such that only one edge-measuring sensor can measure the cardiorespiratory parameters. Such a reduction in the complexity and simplification of the instruction of use shows excellent potential for in-home and continuous monitoring.
Unintrusive health monitoring systems is important when continuous monitoring of the patient vital signals is required. In this paper, signals obtained from accelerometers placed under a bed are processed with ballistocardiography algorithms and compared with synchronized electrocardiographic signals.
Background
This is a systematic review protocol to identify automated features, applied technologies, and algorithms in the electronic early warning/track and triage system (EW/TTS) developed to predict clinical deterioration (CD).
Methodology
This study will be conducted using PubMed, Scopus, and Web of Science databases to evaluate the features of EW/TTS in terms of their automated features, technologies, and algorithms. To this end, we will include any English articles reporting an EW/TTS without time limitation. Retrieved records will be independently screened by two authors and relevant data will be extracted from studies and abstracted for further analysis. The included articles will be evaluated independently using the JBI critical appraisal checklist by two researchers.
Discussion
This study is an effort to address the available automated features in the electronic version of the EW/TTS to shed light on the applied technologies, automated level of systems, and utilized algorithms in order to smooth the road toward the fully automated EW/TTS as one of the potential solutions of prevention CD and its adverse consequences.
The present work proposes the use of modern ICT technologies such as smartphones, NFCs, internet, and web technologies, to help patients in carrying out their therapies. The implemented system provides a calendar with a reminder of the assumptions, ensures the drug identification through NFC, allows remote assistance from healthcare staff and family members to check and manage the therapy in real-time. The system also provides centralized information on the patient's therapeutic situation, helpful in choosing new compatible therapies.
While driving, stress is caused by situations in which the driver estimates their ability to manage the driving demands as insufficient or loses the capability to handle the situation. This leads to increased numbers of driver mistakes and traffic violations. Additional stressing factors are time pressure, road conditions, or dislike for driving. Therefore, stress affects driver and road safety. Stress is classified into two categories depending on its duration and the effects on the body and psyche: short-term eustress and constantly present distress, which causes degenerative effects. In this work, we focus on distress. Wearable sensors are handy tools for collecting biosignals like heart rate, activity, etc. Easy installation and non-intrusive nature make them convenient for calculating stress. This study focuses on the investigation of stress and its implications. Specifically, the research conducts an analysis of stress within a select group of individuals from both Spain and Germany. The primary objective is to examine the influence of recognized psychological factors, including personality traits such as neuroticism, extroversion, psychoticism, stress and road safety. The estimation of stress levels was accomplished through the collection of physiological parameters (R-R intervals) using a Polar H10 chest strap. We observed that personality traits, such as extroversion, exhibited similar trends during relaxation, with an average heart rate 6% higher in Spain and 3% higher in Germany. However, while driving, introverts, on average, experienced more stress, with rates 4% and 1% lower than extroverts in Spain and Germany, respectively.
Introduction. Despite its high accuracy, polysomnography (PSG) has several drawbacks for diagnosing obstructive sleep apnea (OSA). Consequently, multiple portable monitors (PMs) have been proposed. Objective. This systematic review aims to investigate the current literature to analyze the sets of physiological parameters captured by a PM to select the minimum number of such physiological signals while maintaining accurate results in OSA detection. Methods. Inclusion and exclusion criteria for the selection of publications were established prior to the search. The evaluation of the publications was made based on one central question and several specific questions. Results. The abilities to detect hypopneas, sleep time, or awakenings were some of the features studied to investigate the full functionality of the PMs to select the most relevant set of physiological signals. Based on the physiological parameters collected (one to six), the PMs were classified into sets according to the level of evidence. The advantages and the disadvantages of each possible set of signals were explained by answering the research questions proposed in the methods. Conclusions. The minimum number of physiological signals detected by PMs for the detection of OSA depends mainly on the purpose and context of the sleep study. The set of three physiological signals showed the best results in the detection of OSA.
The massive use of patient data for the training of artificial intelligence algorithms is common nowadays in medicine. In this scientific work, a statistical analysis of one of the most used datasets for the training of artificial intelligence models for the detection of sleep disorders is performed: sleep health heart study 2. This study focuses on determining whether the gender and age of the patients have a relevant influence to consider working with differentiated datasets based on these variables for the training of artificial intelligence models.
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.
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.
This paper compares two popular scripting implementations for hardware prototyping: Python scripts exe- cut from User-Space and C-based Linux-Driver processes executed from Kernel-Space, which can provide information to researchers when considering one or another in their implementations. Conclusions exhibit that deploying software scripts in the kernel space makes it possible to grant a certain quality of sensor information using a Raspberry Pi without the need for advanced real-time operational systems.
Healthy and good sleep is a prerequisite for a rested mind and body. Both form the basis for physical and mental health. Healthy sleep is hindered by sleep disorders, the medically diagnosed frequency of which increases sharply from the age of 40. This chapter describes the formal specification of an on-course practical implementation for a non-invasive system based on biomedical signal processing to support the diagnosis and treatment of sleep-related diseases. The system aims to continuously monitor vital data during sleep in a patient’s home environment over long periods by using non-invasive technologies. At the center of the development is the MORPHEUS Box (MoBo), which consists of five main conceptualizations: the MoBo core, the MoBo-HW, the MoBo algorithm, the MoBo API, and the MoBo app. These synergistic elements aim to support the diagnosis and treatment of sleep-related diseases. Although there are related developments in individual aspects concerning the system, no comparative approach is known that gives a similar scope of functionality, deployment flexibility, extensibility, or the possibility to use multiple user groups. With the specification provided in this chapter, the MORPHEUS project sets a good platform, data model, and transmission strategies to bring an innovative proposal to measure sleep quality and detect sleep diseases from non-invasive sensors.
The actual task of electrocardiographic examinations is to increase the reliability of diagnosing the condition of the heart. Within the framework of this task, an important direction is the solution of the inverse problem of electrocardiography, based on the processing of electrocardiographic signals of multichannel cardio leads at known electrode coordinates in these leads (Titomir et al. Noninvasiv electrocardiotopography, 2003), (Macfarlane et al. Comprehensive Electrocardiology, 2nd ed. (Chapter 9), 2011).