On the convergence rate and some applications of regularized ranking algorithms

This paper studies the ranking problem in the context of the regularization theory that allows a simultaneous analysis of a wide class of ranking algorithms. Some of them were previously studied separately. For such ones, our analysis gives a better convergence rate compared to the reported in the literature. We also supplement our theoretical results with numerical illustrations and discuss the application of ranking to the problem of estimating the risk from errors in blood glucose measurements of diabetic patients.     

Smoothing Properties and Approximation of Time Derivatives for Parabolic Equations: Variable Time Steps

We study smoothing properties and approximation of time derivatives for time discretization schemes with variable time steps for a homogeneous parabolic problem formulated as an abstract initial value problem in a Banach space. The time stepping methods are based on using rational approximations to the exponential function which are A()-stable for suitable (0,/2] with unit bounded maximum norm. First- and second-order approximations of time derivatives based on using difference quotients are considered. Smoothing properties are derived and error estimates are established under the so-called increasing quasi-quasiuniform assumption on the time steps.     

残差绝对值之和最小准则下回归方程的求法

本应用线性规划方法,解决了“残差绝对值之和最小”,“最大偏差最小”准则下回归方程的求法,这种方法对于建立多元线性回归方程、多项式回归方程和可以线性化的回归方程都是有效的。     

The influence of space irradiated PIN photodetector on BER in satellite laser communication system

By analyzing the radiation dose on PIN photodetectors in space radiation environment, the variation of photocurrent and dark current after radiation is obtained. On the basis, the bit error rate of satellite laser communication based on space radiation dose of PIN photodetectors is established. According to simulation, when radiation dose is about 1.6 × 10³ Gy and 7 × 10⁴ Gy, bit error rate reaches 10⁻⁶ induced by 50 MeV and 10 MeV protons separately; and when radiation dose is within the range of 5 × 10 Gy–6 × 10⁵ Gy, electrons and gamma-ray irradiation also cause increase in bit error rate to 10⁻⁶. The principle of damage dose on bit error rate is investigated, and the influence of decision threshold on bit error rate is further discussed. The result shows that when radiation dose is 1 MGy, if decision threshold is increased from 4.3 × 10⁻⁷ A to 5.5 × 10⁻⁷ A, bit error rate will decrease about 4 orders of magnitude. Hence, a proper decision threshold can improve system bit error rate efficiently.     

Minimax kernels for density estimation with biased data

This paper considers the asymptotic properties of two kernel estimates % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaacamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E82!\[\tilde f_{_n }\]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaqcamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E83!\[\hat f_{_n }\], which have been proposed by Bhattacharyya et al. (1988, Comm. Statist. Theory Methods, A17, 3629–3644) and Jones (1991, Biometrika, 78, 511–519), respectively, for estimating the underlying density f at a point under a general selection biased model. The asymptotic optimality of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaqcamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E83!\[\hat f_{_n }\]and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaacamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E82!\[\tilde f_{_n }\]is measured by the corresponding asymptotic minimax mean squared errors under a compactly supported Lipschitz continuous family of the underlying densities. It is shown that, in general, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaqcamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E83!\[\hat f_{_n }\]is a superior local estimate than % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaacamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E82!\[\tilde f_{_n }\]in the sense that the asymptotic minimax risk of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaqcamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E83!\[\hat f_{_n }\]is lower than that of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaacamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E82!\[\tilde f_{_n }\]. The minimax kernels and bandwidths of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciqa-zgagaqcamaaBaaaleaadaWgaaadbaGaa8NBaaqabaaa% leqaaaaa!3E83!\[\hat f_{_n }\]are computed explicity and shown to have simple forms and depend on the weight functions of the model.     

Global Error Bound for the Generalized Linear Complementarity Problem over a Polyhedral Cone

In this paper, the global error bound estimation for the generalized linear complementarity problem over a polyhedral cone (GLCP) is considered. To obtain a global error bound for the GLCP, we first develop some equivalent reformulations of the problem under milder conditions and then characterize the solution set of the GLCP. Based on this, an easily computable global error bound for the GLCP is established. The results obtained in this paper can be taken as an extension of the existing global error bound for the classical linear complementarity problems. This work was supported by the Research Grant Council of Hong Kong, a Chair Professor Fund of The Hong Kong Polytechnic University, the Natural Science Foundation of China (Grant No. 10771120) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.     

Error Estimates for Semi-Discrete and Fully Discrete Galerkin Finite Element Approximations of the General Linear Second-Order Hyperbolic Equation

In this article, we derive error estimates for the semi-discrete and fully discrete Galerkin approximations of a general linear second-order hyperbolic partial differential equation with general damping (which includes boundary damping). The results can be applied to a variety of cases (e.g. vibrating systems of linked elastic bodies). The results generalize pioneering work of Dupont and complement a recent article by Basson and Van Rensburg.     

Error and jitter effect studies on the SLED for the BEPC Ⅱ-linac

An RF pulse compressor is a device used to convert a long RF pulse to a short one with a much higher peak RF magnitude. SLED can be regarded as the earliest RF pulse compressor to be used in large-scale linear accelerators. It has been widely studied around the world and applied in the BEPC and BEPC linac for many years. During routine operation, error and jitter effects will deteriorate the performance of SLED, either on the output electromagnetic wave amplitude or phase. The error effects mainly include the frequency drift induced by cooling water temperature variation and the frequency/Q 0 /β unbalances between the two energy storage cavities caused by mechanical fabrication or microwave tuning. The jitter effects refer to the PSK switching phase and time jitters. In this paper, we re-derive the generalized formulae for the conventional SLED used in the BEPC linac, and the error and jitter effects on SLED performance are also investigated.     

Total error and uncertainty: Friends or foes?

Guidelines ISO 17025 and ISO 15189 aim to improve the quality-assurance scheme of laboratories. Reliable analytical results are of central importance due to the critical decisions that are taken with them. ISO 17025 and ISO 15189 therefore require that analytical methods be validated and that laboratories can routinely provide the measurement uncertainty of the results of measurements. To evaluate the fitness of purpose of analytical methods, total error is increasingly applied to assess the reliability of results generated by analytical methods. However, the ISO requirement to estimate measurement uncertainty seems opposed to the concept of total error, leading to delays in laboratories implementing ISO 17025 and ISO 15189 and confusion for the analysts. This article therefore aims to clarify the divergences between total error and measurement uncertainty, but also to discuss their main similarities and emphasize their implementation.     

薄层色谱扫描仪波长示值误差校准方法

目前我国没有薄层色谱扫描仪国家检定规程,一些地方或部门标准中的波长示值误差项目计量方法可操作性不强。通过对比现有标准,提出了一种薄层色谱扫描仪波长示值误差计量方法。该方法利用计量单位使用的钬玻璃波长滤光片作为计量标准器,操作步骤与样品测试类似,波长示值误差的扩展不确定度为0.6 nm(k=2),满足校准要求。该法降低了计量操作难度,可作为计量人员的参考依据。