A note on inversion of Toeplitz matrices

AbstractIt is shown that the invertibility of a Toeplitz matrix can be determined through the solvability of two standard equations. The inverse matrix can be denoted as a sum of products of circulant matrices and upper triangular Toeplitz matrices. The stability of the inversion formula for a Toeplitz matrix is also considered

A modified T. Chan’s preconditioner for Toeplitz systems

AbstractWe present a modified T. Chan’s preconditioner for solving Toeplitz linear systems by the preconditioned conjugate gradient (PCG) method in this paper. Especially, we give some results when the matrices are Hermitian positive definite Toeplitz matrices. The operation and convergence of the PCG method are discussed. Numerical examples presented illustrate the effectiveness of the preconditioner obtained

An Efficient Variational Method for Image Restoration

Image restoration is one of the most fundamental issues in imaging science. Total variation regularization is widely used in image restoration problems for its capability to preserve edges. In this paper, we consider a constrained minimization problem with double total variation regularization terms. To solve this problem, we employ the split Bregman iteration method and the Chambolle’s algorithm. The convergence property of the algorithm is established. The numerical results demonstrate the effectiveness of the proposed method in terms of peak signal-to-noise ratio (PSNR) and the structure similarity index (SSIM)

Split Bregman Iteration Algorithm for Image Deblurring Using Fourth-Order Total Bounded Variation Regularization Model

We propose a fourth-order total bounded variation regularization model which could reduce undesirable effects effectively. Based on this model, we introduce an improved split Bregman iteration algorithm to obtain the optimum solution. The convergence property of our algorithm is provided. Numerical experiments show the more excellent visual quality of the proposed model compared with the second-order total bounded variation model which is proposed by Liu and Huang (2010)

Movable Fiber-Integrated Hybrid Plasmonic Waveguide on Metal Film

A waveguide structure consisting of a tapered nanofiber on a metal film is proposed and analyzed to support highly localized hybrid plasmonic modes. The hybrid plasmonic mode can be efficiently excited through the in-line tapered fiber based on adiabatic conversion and collected by the same fiber, which is very convenient in the experiment. Due to the ultrasmall mode area of plasmonic mode, the local electromagnetic field is greatly enhanced in this movable waveguide, which is potential for enhanced coherence light emitter interactions, such as waveguide quantum electrodynamics, single emitter spectrum and nonlinear optics

Modes of Antiviral Action of Chemical Portions and Constituents from Woad Root Extract against Influenza Virus A FM1

Woad root has been used for the prevention of influenza for hundreds of years in many Asian countries. In this study, the antiviral modes of clemastanin B (CB), epigoitrin, phenylpropanoid portion (PEP), and the mixture of phenylpropanoids, alkaloids, and organic acid portions (PEP + ALK + OA) from wood root extract against influenza virus A FM1 were investigated. The results revealed that CB, epigoitrin, PEP, and PEP + ALK + OA exert their anti-influenza activity via inhibiting the virus multiplication, prophylaxis, and blocking the virus attachment. The primary mode of action of PEP and PEP + ALK + OA is the inhibition of virus replication. The inhibitory effect on virus attachment and multiplication is the main modes for epigoitrin. All the compounds or chemical portions from woad root extract tested in this study do not have direct virucidal activity. Our results provided the comprehensive analysis of the antiviral mechanism of wood root extract

National incidence of traumatic fractures in China: a retrospective survey of 512 187 individuals

Background Traumatic fractures place a substantial burden on health-care systems worldwide. Although detailed information about incidence, distribution, and risk factors for traumatic fractures is vital for planning and prevention, in China, national data are unavailable. We aimed to do an up-to-date national survey on the population-weighted incidence of traumatic fractures in China. Methods The China National Fracture Study (CNFS) was a retrospective epidemiological study that recruited a nationally representative sample from eight provinces, 24 urban cities, and 24 rural counties in China using stratified random sampling and the probability proportional to size method. All eligible household members who had lived in their current residence for 6 months or longer were personally interviewed by trained research teams about traumatic fractures of the trunk, arms, or legs (not including the skull, sternum, and ribs) that had occurred in 2014. Telephone surveys were used for participants who were non-contactable after repeated visits. Fracture cases were verified by clinical records, medical history, and radiographs by orthopaedic surgeons and radiologists. We estimated incidence rates for traumatic fractures for the overall population and for subgroups by age and sex, as well as by demographic factors such as ethnic origin, occupation, geographical region, and residency category. We also studied potential associations between fractures and various factors of interest, such as age, ethnic origin, education, smoking, alcohol drinking, sleep time per day, and history of previous fracture. Data were weighted during statistical analysis to ascertain the national incidence rate. This study is registered with the Chinese Clinical Trial Registry, number ChiCTR-EPR-15005878. Findings Between Jan 19, 2015, and May 16, 2015, 535 836 individuals were selected and invited to participate in the study. Questionnaires from 23 649 (4%) individuals were excluded due to missing items, insufficient responses, or logical errors. Following exclusions, 512 187 (96%) individuals participated in the CNFS, consisting of 259 649 (51%) boys and men and 252 538 (49%) girls and women. Of these individuals, 1763 individuals had experienced traumatic fractures during 2014 (n=1833). The population-weighted incidence rate of traumatic fractures of the trunk, arms, or legs was 3·21 (95% CI 2·83–3·59) per 1000 population in 2014 (3·65, 3·12–4·18 in men and 2·75, 2·46–3·04 in women). For all ages, sleeping less than 7 h per day was identified as a risk factor for traumatic fractures. We identified previous fracture history as a risk factor for adults aged 15 years and older. Alcohol consumption incurred a risk effect for men aged 15 years and older and women aged 15–64 years. Interpretation Our results provide detailed information about fracture incidence, distribution, and risk factors, which can now be used as an up-to-date clinical evidence base for national health-care planning and preventive efforts in China and elsewhere. Specific public health policies that focus on decreasing alcohol consumption, prohibiting drunk driving, promoting smoking cessation, and encouraging individuals to obtain sufficient sleep and maintain a healthy bodyweight should be urgently implemented to help reduce the risk of traumatic fractures

Whole-genome sequencing of native sheep provides insights into rapid adaptations to extreme environments

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