Xu's Method Research Articles

Deformed black hole immersed in dark matter spike

If a lot of dark matter particles accumulate near the black hole, then the chances of detecting dark matter signals near a black hole are greatly increased. These effects may be observed by the Event Horizon Telescope (EHT), Tianqin project, Taiji project, Laser Interferometer Space Antenna (LISA) and Laser Interferometer Gravitational-Wave Observatory (LIGO). In this work, we explore the effects of dark matter spikes on black hole space-time. For the Schwarzschild-like black hole case, we consider Newton's approximation and perturbation approximation. This makes it possible to use Xu's method to solve the Einstein field equation, and extend Schwarzschild-like black hole to Kerr-like black hole (BH) via Newman-Janis (NJ) algorithm. By analyzing the dark matter spike on the black hole event horizon (EH), stationary limit surfaces (SLS), ergosphere and energy-momentum tensors (EMT), we found that compared with the dark matter halo, the dark matter spike would have a higher effect on the black hole by several orders of magnitude. Therefore, if there is a dark matter spike near the black hole, it is very possible to test the dark matter model through gravitational wave (GW) observation and EHT observation.

Monitoring microwave ablation using ultrasound backscatter homodyned K imaging: Comparison of estimators

The feasibility of ultrasound backscatter homodyned K model parametric imaging (termed homodyned K imaging) to monitor coagulation zone during microwave ablation was investigated. Two recent estimators for the homodyned K model parameter, RSK (the estimation method based on the signal-to-noise ratio, the skewness, and the kurtosis of the amplitude envelope of ultrasound) and XU (the estimation method based on the first moment of the intensity of ultrasound, X statistics and U statistics), were compared. Firstly, the ultrasound backscattered signals during the microwave ablation of porcine liver ex vivo were processed by the noise-assisted correlation algorithm, envelope detection, sliding window method, digital scan conversion and color mapping to obtain homodyned K imaging. Then 20 porcine livers' microwave ablation experiments ex vivo were used to evaluate the effect of homodyned K imaging in monitoring the coagulation zone. The results showed that the area under the receiver operating characteristic curve of the RSK method was 0.77 ± 0.06 (mean ± standard deviation), and that of the XU method was 0.83 ± 0.08 (mean ± standard deviation). The accuracy to monitor the coagulation zone was (86 ± 10)% (mean ± standard deviation) by the RSK method and (90 ± 8)% (mean ± standard deviation) by the XU method. Compared with the RSK method, the Bland-Altman consistency for the coagulation zone estimated by the XU method and that of actual porcine liver tissue was higher. The time for parameter estimation and imaging by the XU method was less than that by the RSK method. We conclude that ultrasound backscatter homodyned K imaging can be used to monitor coagulation zones during microwave ablation, and the XU method is better than the RSK method.

The Effect of Catastrophic Health Expenditure on Work After Retirement.

Several factors can force retirees to go to paid work. Catastrophic health-care expenditure (CHCE) is one of the driving forces for retirees to go to paid work. This cross-sectional study was based on 6,307 Iran retirees' data. Xu method was used to calculate CHCE, and a logit model was estimated to show the association between CHCE and bridge employment. Other control variables were added to the model. The findings showed that there was positive relationship between CHCE and bridge employment. Retirement pension had negative relationship with work after retirement. Prevalence of work after retirement was higher in people who lived in rural region and increased due to increase in household size. The financial constraint was the main pushing factor for the retiree to go to paid work. Thus, covering retirees with health insurances and identifying and listing diseases that may face the retirees with CHCE are some possible efforts to decrease CHCE.

Regularized gradient-projection methods for equilibrium and constrained convex minimization problems

In this article, based on Marino and Xu's method, an iterative method which combines the regularized gradient-projection algorithm (RGPA) and the averaged mappings approach is proposed for finding a common solution of equilibrium and constrained convex minimization problems. Under suitable conditions, it is proved that the sequences generated by implicit and explicit schemes converge strongly. The results of this paper extend and improve some existing results. MSC: 58E35; 47H09; 65J15

ESTIMATION METHOD OF THE HOMODYNED K-DISTRIBUTION BASED ON THE MEAN INTENSITY AND TWO LOG-MOMENTS.

The homodyned K-distribution appears naturally in the context of random walks and provides a useful model for the distribution of the received intensity in a wide range of non-Gaussian scattering configurations, including medical ultrasonics. An estimation method for the homodyned K-distribution based on the first moment of the intensity and two log-moments (XU method), namely the X and U-statistics previously studied in the special case of the K-distribution, is proposed as an alternative to a method based on the first three moments of the intensity (MI method) or the amplitude (MA method), and a method based on the signal-to-noise ratio (SNR), the skewness and the kurtosis of two fractional orders of the amplitude (labeled RSK method). Properties of the X and U statistics for the homodyned K-distribution are proved, except for one conjecture. Using those properties, an algorithm based on the bisection method for monotonous functions was developed. The algorithm has a geometric rate of convergence. Various tests were performed to study the behavior of the estimators. It was shown with simulated data samples that the estimations of the parameters 1/α and 1/(κ + 1) of the homodyned K-distribution are preferable to the direct estimations of the clustering parameter α and the structure parameter κ (with respective relative root mean squared errors (RMSEs) of 0.63 and 0.13 as opposed to 1.04 and 4.37, when N = 1000). Tests on simulated ultrasound images with only diffuse scatterers (up to 10 per resolution cell) indicated that the XU estimator is overall more reliable than the other three estimators for the estimation of 1/α, with relative RMSEs of 0.79 (MI), 0.61 (MA), 0.53 (XU) and 0.67 (RSK). For the parameter 1/(κ + 1), the relative RMSEs were equal to 0.074 (MI), 0.075 (MA), 0.069 (XU) and 0.100 (RSK). In the case of a large number of scatterers (11 to 20 per resolution cell), the relative RMSEs of 1/α were equal to 1.43 (MI), 1.27 (MA), 1.25 (XU) and 1.33 (RSK), and the relative RMSEs of 1/(κ + 1) were equal to 0.14 (MI), 0.16 (MA), 0.17 (XU) and 0.20 (RSK). The four methods were also tested on simulated ultrasound images with a variable density of periodic scatterers to test images with a coherent component. The addition of noise on ultrasound images was also studied. Results showed that the XU estimator was overall better than the three other ones. Finally, on the simulated ultrasound images, the average computation times per image were equal to 6.0 ms (MI), 8.0 ms (MA), 6.8 ms (XU) and 500 ms (RSK). Thus, a fast, reliable, and novel algorithm for the estimation of the homodyned K-distribution was proposed.

General iterative methods for equilibrium and constrained convex minimization problem

The gradient-projection algorithm (GPA) plays an important role in solving constrained convex minimization problems. Based on Marino and Xu's method [G. Marino and H.-K. Xu, A general method for nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 318 (2006), pp. 43–52], we combine GPA and averaged mapping approach to propose implicit and explicit composite iterative algorithms for finding a common solution of an equilibrium and a constrained convex minimization problem for the first time in this article. Under suitable conditions, strong convergence theorems are obtained.

Refinements of Miller's Algorithm over Weierstrass Curves Revisited

In 1986, Victor Miller described an algorithm for computing the Weil pairing in his unpublished manuscript. This algorithm has then become the core of all pairing-based cryptosystems. Many improvements of the algorithm have been presented. Most of them involve a choice of elliptic curves of a special form to exploit a possible twist during Tate pairing computation. Other improvements involve a reduction of the number of iterations in the Miller's algorithm. For the generic case, Blake, Murty and Xu proposed three refinements to Miller's algorithm over Weierstrass curves. Though their refinements, which only reduce the total number of vertical lines in Miller's algorithm, did not give an efficient computation as other optimizations, they can be applied for computing both Weil and Tate pairings on all pairing-friendly elliptic curves. In this paper, we extend the Blake–Murty–Xu's method and show how to perform an elimination of all vertical lines in Miller's algorithm during computation of Weil/Tate pairings, on general elliptic curves. Experimental results show that our algorithm is faster by ~25% in comparison with the original Miller's algorithm.

Solutions of Navier equations and their representation structure

Navier equations are used to describe the deformation of a homogeneous, isotropic and linear elastic medium in the absence of body forces. Mathematically, the system is a natural vector O ( n , R ) -invariant generalization of the classical Laplace equation. In this paper, we decompose the space of polynomial solutions of Navier equations into a direct sum of irreducible O ( n , R ) -submodules and construct an explicit basis for each irreducible summand. Moreover, we explicitly solve the initial value problems for Navier equations and their wave-type extension—Lamé equations by Fourier expansion and Xu's method of solving flag partial differential equations. Our work might be counted as a continuation of Olver's important work on the algebraic study of elasticity in a certain sense.

ITERATIVE REGULARIZATION AND NONLINEAR INVERSE SCALE SPACE BASED ON TRANSLATION INVARIANT WAVELET SHRINKAGE

In this paper, we present a new class of iterative regularization methods in the setting of Besov spaces, which can be seen as generalizations of J. Xu's method. By incorporating translation invariant wavelet transform, minimizers of the new methods can be understood as the alternative to translation invariant wavelet shrinkage with weight that is dependent on the wavelet decomposition scale and the Besov smooth order. And we generalize the iterative regularization methods to a new class of nonlinear inverse scale spaces with scale and Besov smooth order dependent weight. The numerical results show an excellent denoising effect and improvement over J. Xu's method.