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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.
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 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).
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.
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.
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.
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.
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.
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.
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.