Hypothesis testing for the generalized multivariate modified Bessel model

In this paper, we consider hypothesis testing problems in which the involved samples are drawn from generalized multivariate modified Bessel populations. This is a much more general distribution that includes both the multivariate normal and multivariate-t distributions as special cases. We derive the distribution of the Hotelling's T²-statistic for both the one- and two-sample problems, as well as the distribution of the Scheffe's T²-statistic for the Behrens–Fisher problem. In all cases, the non-null distribution of the corresponding F-statistic follows a new distribution which we introduce as the non-central F-Bessel distribution. Some statistical properties of this distribution are studied. Furthermore, this distribution was utilized to perform some power calculations for tests of means for different models which are special cases of the generalized multivariate modified Bessel distribution, and the results compared with those obtained under the multivariate normal case. Under the null hypothesis, however, the non-central F-Bessel distribution reduces to the central F-distribution obtained under the classical normal model.     

大视场短焦距镜头CCD摄像系统的畸变校正

从光学测量角度出发,结合计算机视觉中的摄像机标定方法,解决了大视场短焦距镜头CCD摄像系统的畸变校正问题。与摄像机标定不同,畸变校正中仅标定内部参数,外部参数作为已知条件。采用线性畸变模型,由最小二乘法解线性方程组得到摄像系统畸变模型的畸变系数。介绍了数字图像中像素间距和光学中心的标定方法。通过比较由标定参数得到的畸变图像和摄像机采集的畸变图像对实验标定精度进行评定,实验结果表明边缘视场(112°)的标定精度达到了0 75%。     

工业CT图像均匀性校正

在工业CT图像重建过程中,射束硬化使得图像出现“杯状”伪影,阵列探测器响应不一致使得图像出现环状伪影、带状伪影和点伪影,影响图像均匀性.本文分析了射束硬化的原理和探测器响应不一致的数学模型,并通过实验,对探测器响应进行多挡板定标得到校正系数表.利用查表插值的方法对投影数据进行均匀性校正,消除上述伪影.     

Methods in carbon K-edge NEXAFS: Experiment and analysis

Near-edge X-ray absorption spectroscopy (NEXAFS) is widely used to probe the chemistry and structure of surface layers. Moreover, using ultra-high brilliance polarised synchrotron light sources, it is possible to determine the molecular alignment of ultra-thin surface films. However, the quantitative analysis of NEXAFS data is complicated by many experimental factors and, historically, the essential methods of calibration, normalisation and artefact removal are presented in the literature in a somewhat fragmented manner, thus hindering their integrated implementation as well as their further development. This paper outlines a unified, systematic approach to the collection and quantitative analysis of NEXAFS data with a particular focus upon carbon K-edge spectra. As a consequence, we show that current methods neglect several important aspects of the data analysis process, which we address with a combination of novel and adapted techniques. We discuss multiple approaches in solving the issues commonly encountered in the analysis of NEXAFS data, revealing the inherent assumptions of each approach and providing guidelines for assessing their appropriateness in a broad range of experimental situations.     

Estimation of entropy and other functionals of a multivariate density

For a multivariate density f with respect to Lebesgue measure , the estimation of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa8qaaeaacaWGkbGaaiikaiaadAgacaGGPaGaamOzaiaadsgacqaH% 8oqBaSqabeqaniabgUIiYdaaaa!4404!\[\int {J(f)fd\mu } \], and in particular % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa8qaaeaacaWGMbWaaWbaaSqabeaacaaIYaaaaOGaamizaiabeY7a% TbWcbeqab0Gaey4kIipaaaa!41E4!\[\int {f^2 d\mu } \] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Waa8qaaeaacaWGMbGaciiBaiaac+gacaGGNbGaamOzaiaadsgacqaH% 8oqBaSqabeqaniabgUIiYdaaaa!44AC!\[\int {f\log fd\mu } \], is studied. These two particular functionals are important in a number of contexts. Asymptotic bias and variance terms are obtained for the estimators % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaybyaeqaleqabaGaey4jIKnaneaacaWGjbaaaOGaeyypa0Zaa8qa% aeaacaWGkbGaaiikamaawagabeWcbeqaaiabgEIizdqdbaGaamOzaa% aakiaacMcacaWGKbGaamOramaaBaaaleaacaWGobaabeaaaeqabeqd% cqGHRiI8aaaa!4994!\[\mathop I\limits^ \wedge = \int {J(\mathop f\limits^ \wedge )dF_N } \] and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaybyaeqaleqabaGaeSipIOdaneaacaWGjbaaaOGaeyypa0Zaa8qa% aeaacaWGkbGaaiikamaawagabeWcbeqaaiabgEIizdqdbaGaamOzaa% aakiaacMcadaGfGbqabSqabeaacqGHNis2a0qaaiaadAgaaaGccaWG% KbGaeqiVd0galeqabeqdcqGHRiI8aaaa!4C40!\[\mathop I\limits^ \sim = \int {J(\mathop f\limits^ \wedge )\mathop f\limits^ \wedge d\mu } \], where % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaybyaeqaleqabaGaey4jIKnaneaacaWGMbaaaaaa!3E9C!\[{\mathop f\limits^ \wedge }\] is a kernel density estimate of f and F _n is the empirical distribution function based on the random sample X ₁ ,..., X _n from f. For the two functionalsmentioned above, a first order bias term for Î can be made zero by appropriate choices of non-unimodal kernels. Suggestions for the choice of bandwidth are given; for % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaybyaeqaleqabaGaey4jIKnaneaacaWGjbaaaOGaeyypa0Zaa8qa% aeaadaGfGbqabSqabeaacqGHNis2a0qaaiaadAgaaaGccaWGKbGaam% OramaaBaaaleaacaWGobaabeaaaeqabeqdcqGHRiI8aaaa!476C!\[\mathop I\limits^ \wedge = \int {\mathop f\limits^ \wedge dF_N } \], a study of optimal bandwidth is possible.This research was supported by an NSERC Grant and a UBC Killam Research Fellowship.     

交替三线性分解算法结合高效液相色谱法同时测定水杨酸与龙胆酸

利用交替三线性分解算法(ATLD)与高效液相色谱法相结合,在色谱保留时间为0.662 8~0.949 5min(间隔1/150 min)、紫外吸收波长为268~332 nm(间隔2 nm)且在未知干扰物2,3-二羟基苯甲酸存在下,同时测定了水溶液中光谱及色谱严重重叠的水杨酸(SA)和龙胆酸(GA)的含量,回收率分别为(102.2±6.7)%,(102.1±4.1)%,分辨结果与实际结果一致。研究结果表明:该方法定量快速准确、实验操作步骤简单,说明ATLD算法收敛快速稳定,对复杂体系中组分数估计不敏感,能有效解决色谱中的二阶校正问题。     

人工神经网络及其在分析化学中的应用

人工神经网络是一种新兴的计算方法，有着广阔的发展前途，目前在分析化学领域已经有了多方面的应用。本文简要介绍了人工神经网络的原理及其在分析化学中的应用。     

Multivariate calibration of near infrared spectra by orthogonal WAVElet correction using a genetic algorithm

Orthogonal WAVElet correction (OWAVEC) is a pre-processing method aimed at simultaneously accomplishing two essential needs in multivariate calibration, signal correction and data compression, by combining the application of an orthogonal signal correction algorithm to remove information unrelated to a certain response with the great potential that wavelet analysis has shown for signal processing. In the previous version of the OWAVEC method, once the wavelet coefficients matrix had been computed from NIR spectra and deflated from irrelevant information in the orthogonalization step, effective data compression was achieved by selecting those largest correlation/variance wavelet coefficients serving as the basis for the development of a reliable regression model. This paper presents an evolution of the OWAVEC method, maintaining the first two stages in its application procedure (wavelet signal decomposition and direct orthogonalization) intact but incorporating genetic algorithms as a wavelet coefficients selection method to perform data compression and to improve the quality of the regression models developed later. Several specific applications dealing with diverse NIR regression problems are analyzed to evaluate the actual performance of the new OWAVEC method. Results provided by OWAVEC are also compared with those obtained with original data and with other orthogonal signal correction methods.     

Improved accuracy of quantitative XPS analysis using predetermined spectrometer transmission functions with UNIFIT 2004

The accuracy of quantitative XPS analysis can be improved using predetermined transmission functions. Two different calibration methods are used for estimating the transmission function T(E) of a photoelectron spectrometer, applying a survey spectra approach (SSA) and a quantified peak‐area approach (QPA) to minimize the quantification error. For the SSA method, Au, Ag and Cu spectra measured with the Metrology Spectrometer II have been used. The new QPA method was built up from Au 4f, Au 4d, Au 4p_3/2, Ag 3d, Ag 3p_3/2, Cu 3p, Cu 2p_3/2, Ge 3p and Ge 2p_3/2 standard peak areas, applying adequate ionization cross‐sections and mean free path lengths for different pass energies (10 and 50 eV), lens modes (large area, large area XL, small area 150) and x‐ray sources (Al/Mg Twin and Al Mono). In the energy range 200–1500 eV a transmission function T(E) = a₀ + b₁E (where a₀, b₁ and b₂ are variable parameters) was found to give an appropriate approximation for eight tested spectrometer settings, implementing the largest changes in the case of pass energy variations. Determination and application of the transmission functions were integrated in the XPS analysis software (UNIFIT 2004) and tested by means of an Ni90Cr10 alloy. The results demonstrate the practicability of the SSA and QPA methods, giving decreased errors of <8% in comparison with errors up to 38% obtained using Wagner's sensitivity factors. Copyright © 2005 John Wiley & Sons, Ltd.     

Two different strategies for the fluorimetric determination of piroxicam in serum

Two different spectrofluorimetric methods for the determination of piroxicam (PX) in serum are presented and discussed. One of them is based on the use of three-way fluorescence data and multivariate calibration performed with parallel factor analysis (PARAFAC) and self-weighted alternating trilinear decomposition (SWATLD). This methodology exploits the so-called second-order advantage of the three-way data, allowing to obtain the concentration of the studied analyte in the presence of any number of uncalibrated (serum) components. The method was developed following two different procedures: internal standard addition and external calibration with standard solutions, which were compared and discussed. The second approach investigated is based on the combination of solid-phase extraction (SPE) and room temperature fluorimetry. Both methods here presented yield satisfactory results. The concentration range in which PX could be determined in serum was 1–10 μg ml⁻¹. The limits of quantification for the experimental solutions using the chemometric approach were 0.09 μg ml⁻¹ for the standard addition mode and 0.12 μg ml⁻¹ using external calibration (both for PARAFAC and SWATLD algorithms). In the solid-surface fluorimetric method, the calibration graph was linear up to 0.22 μg ml⁻¹ and the limit of quantification was 0.02 μg ml⁻¹.