145 research outputs found

    On Convergence of the Inexact Rayleigh Quotient Iteration with the Lanczos Method Used for Solving Linear Systems

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    For the Hermitian inexact Rayleigh quotient iteration (RQI), the author has established new local general convergence results, independent of iterative solvers for inner linear systems. The theory shows that the method locally converges quadratically under a new condition, called the uniform positiveness condition. In this paper we first consider the local convergence of the inexact RQI with the unpreconditioned Lanczos method for the linear systems. Some attractive properties are derived for the residuals, whose norms are ξk+1\xi_{k+1}'s, of the linear systems obtained by the Lanczos method. Based on them and the new general convergence results, we make a refined analysis and establish new local convergence results. It is proved that the inexact RQI with Lanczos converges quadratically provided that ξk+1ξ\xi_{k+1}\leq\xi with a constant ξ1\xi\geq 1. The method is guaranteed to converge linearly provided that ξk+1\xi_{k+1} is bounded by a small multiple of the reciprocal of the residual norm rk\|r_k\| of the current approximate eigenpair. The results are fundamentally different from the existing convergence results that always require ξk+1<1\xi_{k+1}<1, and they have a strong impact on effective implementations of the method. We extend the new theory to the inexact RQI with a tuned preconditioned Lanczos for the linear systems. Based on the new theory, we can design practical criteria to control ξk+1\xi_{k+1} to achieve quadratic convergence and implement the method more effectively than ever before. Numerical experiments confirm our theory.Comment: 20 pages, 8 figures. arXiv admin note: text overlap with arXiv:0906.223

    On the Convergence of Ritz Pairs and Refined Ritz Vectors for Quadratic Eigenvalue Problems

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    For a given subspace, the Rayleigh-Ritz method projects the large quadratic eigenvalue problem (QEP) onto it and produces a small sized dense QEP. Similar to the Rayleigh-Ritz method for the linear eigenvalue problem, the Rayleigh-Ritz method defines the Ritz values and the Ritz vectors of the QEP with respect to the projection subspace. We analyze the convergence of the method when the angle between the subspace and the desired eigenvector converges to zero. We prove that there is a Ritz value that converges to the desired eigenvalue unconditionally but the Ritz vector converges conditionally and may fail to converge. To remedy the drawback of possible non-convergence of the Ritz vector, we propose a refined Ritz vector that is mathematically different from the Ritz vector and is proved to converge unconditionally. We construct examples to illustrate our theory.Comment: 20 page

    Магнитный контроль параметров ферромагнитных объектов методом высших гармоник

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    В данной работе объектом исследования являются контрольные образцы тороидальной формы из ферромагнитных сталей различных марок, изготовленные согласно ГОСТ 8.377-80, магнитные параметры которых исследуются с помощью разработанной многопараметровой установки для измерения магнитных характеристик MS-1.In this work, the object of the study is the control samples of toroidal shape of ferromagnetic steels of different brands, made according to GOST 8.377-80, the magnetic parameters of which are investigated using the developed multiparameter installation for measuring the magnetic characteristics of MS-1

    Digital Health Solutions to Reduce the Burden of Atherosclerotic Cardiovascular Disease Proposed by the CARRIER Consortium

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    Digital health is a promising tool to support people with an elevated risk for atherosclerotic cardiovascular disease (ASCVD) and patients with an established disease to improve cardiovascular outcomes. Many digital health initiatives have been developed and employed. However, barriers to their large-scale implementation have remained. This paper focuses on these barriers and presents solutions as proposed by the Dutch CARRIER (ie, Coronary ARtery disease: Risk estimations and Interventions for prevention and EaRly detection) consortium. We will focus in 4 sections on the following: (1) the development process of an eHealth solution that will include design thinking and cocreation with relevant stakeholders; (2) the modeling approach for two clinical prediction models (CPMs) to identify people at risk of developing ASCVD and to guide interventions; (3) description of a federated data infrastructure to train the CPMs and to provide the eHealth solution with relevant data; and (4) discussion of an ethical and legal framework for responsible data handling in health care. The Dutch CARRIER consortium consists of a collaboration between experts in the fields of eHealth development, ASCVD, public health, big data, as well as ethics and law. The consortium focuses on reducing the burden of ASCVD. We believe the future of health care is data driven and supported by digital health. Therefore, we hope that our research will not only facilitate CARRIER consortium but may also facilitate other future health care initiatives

    Rapid screening for chromosomal aneuploidies using array-MLPA

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    <p>Abstract</p> <p>Background</p> <p>Chromosome abnormalities, especially trisomy of chromosome 21, 13, or 18 as well as sex chromosome aneuploidy, are a well-established cause of pregnancy loss. Cultured cell karyotype analysis and FISH have been considered reliable detectors of fetal abnormality. However, results are usually not available for 3-4 days or more. Multiplex ligation-dependent probe amplification (MLPA) has emerged as an alternative rapid technique for detection of chromosome aneuploidies. However, conventional MLPA does not allow for relative quantification of more than 50 different target sequences in one reaction and does not detect mosaic trisomy. A multiplexed MLPA with more sensitive detection would be useful for fetal genetic screening.</p> <p>Methods</p> <p>We developed a method of array-based MLPA to rapidly screen for common aneuploidies. We designed 116 universal tag-probes covering chromosomes 13, 18, 21, X, and Y, and 8 control autosomal genes. We performed MLPA and hybridized the products on a 4-well flow-through microarray system. We determined chromosome copy numbers by analyzing the relative signals of the chromosome-specific probes.</p> <p>Results</p> <p>In a blind study of 161 peripheral blood and 12 amniotic fluid samples previously karyotyped, 169 of 173 (97.7%) including all the amniotic fluid samples were correctly identified by array-MLPA. Furthermore, we detected two chromosome X monosomy mosaic cases in which the mosaism rates estimated by array-MLPA were basically consistent with the results from karyotyping. Additionally, we identified five Y chromosome abnormalities in which G-banding could not distinguish their origins for four of the five cases.</p> <p>Conclusions</p> <p>Our study demonstrates the successful application and strong potential of array-MLPA in clinical diagnosis and prenatal testing for rapid and sensitive chromosomal aneuploidy screening. Furthermore, we have developed a simple and rapid procedure for screening copy numbers on chromosomes 13, 18, 21, X, and Y using array-MLPA.</p

    Array-based technology and recommendations for utilization in medical genetics practice for detection of chromosomal abnormalities

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    Laboratory evaluation of patients with developmental delay/intellectual disability, congenital anomalies, and dysmorphic features has changed significantly in the last several years with the introduction of microarray technologies. Using these techniques, a patient’s genome can be examined for gains or losses of genetic material too small to be detected by standard G-banded chromosome studies. This increased resolution of microarray technology over conventional cytogenetic analysis allows for identification of chromosomal imbalances with greater precision, accuracy, and technical sensitivity. A variety of array-based platforms are now available for use in clinical practice, and utilization strategies are evolving. Thus, a review of the utility and limitations of these techniques and recommendations regarding present and future application in the clinical setting are presented in this study
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