Goodness-Of-Fit Tests Based on Estimated Expectations of Probability Integral Transformed Order Statistics

New goodness-of-fit tests, based on bootstrap estimated expectations of probability integral transformed order statistics, are derived for the location-scale model. The resulting test statistics are location and scale invariant, and are sensitive to discrepancies at the tails of the hypothesized distribution. The limiting null distributions of the test statistics are derived in terms of functionals of a certain Gaussian process, and the tests are shown to be consistent against a broad family of alternatives. Critical points for all sample sizes are provided for tests of normality. A simulation study shows that the proposed tests are more powerful than established tests such as Shapiro-Wilk, Cramér-von Mises and Anderson-Darling, for a wide range of alternative distributions.     

Bioactivity of SiO2-CaO-P2O5-Na2O glasses containing zinc-iron oxide

Glasses with composition x(ZnO,Fe₂O₃)(65 − x)SiO₂20(CaO,P₂O₅)15Na₂O (6 ≤ x ≤ 21 mol%) were prepared by melt-quenching technique. Bioactivity of the glasses was investigated in vitro by examining apatite formation on the surface of glasses treated in acellular simulated body fluid (SBF) with ion concentrations nearly equal to those in human blood plasma. Formation of bioactive apatite layer on the samples treated in SBF was confirmed by using Fourier transform infrared reflection (FTIR) spectroscopy, grazing incidence X-ray diffraction (GI-XRD) and scanning electron microscope (SEM) equipped with energy dispersive X-ray spectrometer. Development of an apatite structure on the surface of the SBF treated glass samples as functions of composition and time could be established using the GI-XRD data. FTIR spectra of the glasses treated in SBF show features at characteristic vibration frequencies of apatite after 1-day of immersion in SBF. SEM observations revealed that the spherical particles formed on the glass surface were made of calcium and phosphorus with the Ca/P molar ratio being close to 1.67, corresponding to the value in crystalline apatite. Increase in bioactivity with increasing zinc-iron oxide content was observed. The results have been used to understand the evolution of the apatite surface layer as a function of glass composition and immersion time in SBF.     

Optimal testing strategies in overlapped design process

Testing is an important activity in product development. Past studies, which are developed to determine the optimal scheduling of tests, often focused on single-stage testing of sequential design process. This paper presents an analytical model for the scheduling of tests in overlapped design process, where a downstream stage starts before the completion of upstream testing. We derive optimal stopping rules for upstream and downstream stages’ testing, together with the optimal time elapsed between beginning the upstream tests and beginning the downstream development. We find that the cost function is first convex then concave increasing with respect to upstream testing duration. A one-dimensional search algorithm is then proposed for finding the unique optimum that minimizes the overall cost. Moreover, the impact of different model parameters, such as the problem-solving capacity and opportunity cost, on the optimal solution is discussed. Finally, we compare the testing strategies in overlapped process with those in sequential process, and get some additional results. The methodology is illustrated with a case study at a handset design company.     

On the effectiveness of a generalization of Miller’s primality theorem

Berrizbeitia and Olivieri showed in a recent paper that, for any integer r$r$, the notion of ω$\omega$-prime to base a$a$ leads to a primality test for numbers n≡1$n\equiv 1$ mod r$r$, that under the Extended Riemann Hypothesis (ERH) runs in polynomial time. They showed that the complexity of their test is at most the complexity of the Miller primality test (MPT), which is O((logn)^4+o(1))$O\left({(logn)}^{4+o\left(1\right)}\right)$. They conjectured that their test is more effective than the MPT if r$r$ is large.     

A Non-Linear SGS Model Based On The Spatial Velocity Increment

A new subgrid scale (SGS) modelling concept for large-eddy simulation (LES) of incompressible flow is proposed based on the three-dimensional spatial velocity increment δ u _i . The new model is inspired by the structure function formulation developed by Métais and Lesieur [39] and applied in the context of the scale similarity type formulation. First, the similarity between the SGS stress tensor τ _ij and the velocity increment tensor Q _ij = δ u _i δ u _j is analyzed analytically and numerically using a priori tests of fully developed pipe flow at Re _τ = 180. Both forward and backward energy transfers between resolved and unresolved scales of the flow are well predicted with a SGS model based on Q _ij . Secondly, a posteriori tests are performed for two families of turbulent shear flows. LES of fully developed pipe flow up to Re _τ = 520 and LES of round turbulent jet at Re _D = 25000 carried out with a dynamic version of the model provide promising results that confirm the power of this approach for wall-bounded and free shear flows.     

数域上的最小k次非剩余

1964年王元院士在有理数域上建立了素数模的最小正k次非剩余的一些结果.本文将其中在广义Riemann猜想下的条件结果推广到代数数域.     

15Nmethacetin test to control liver function of infants with formerly very low birth weight

Abstract

Hepatic detoxification capacities of three groups of infants aged about two were estimated using the [¹⁵N]methacetin elimination test, as well as standard serum parameters:

1. Formerly hypotrophically born infants still too small for their age (n = 23)

2. Patients suffering from severe liver diseases (n = 15)

3. Patients without liver diseases (n = 14).

17 of the infants of group 1 showed ¹⁵N elimination rates as low as the rates of the liver-diseased patients of group 2. Compared to the infants of group 3, who had normal values, the findings reflect diminished hepatic monooxygenases activities in groups 1 and 2. On the other hand, the serum parameters of the infants of group 1 did not deviate from normal values estimated in group 3. Here only group 2 showed pathological values. Consequently, the [¹⁵N]methacetin test seems to be more sensitive in controlling hepatic parameters of growth retardations than the usual serum parameters used here. Further investigations have to answer the question to which proportion intrauterine malnutrition and postnatal effects, such as environmental living conditions, contribute to the retardation of liver function development in combination with growth retardation.     

Determination of 13CO2/12CO2 Ratio by IRMS and NDIRS

Abstract

Breath tests using ¹³C-labelled substrates require the measurement of ¹³CO₂/¹²CO₂ ratio in breath gas samples. Next to isotope ratio mass spectrometry (IRMS), which is very sensitive but also complex and expensive, alternatively isotope selective nondispersive infrared spectrometry (NDIRS) can be used to determine the ¹³CO₂/¹²CO₂ ratio in expired breath. In this study we compared NDIRS- with IRMS-results to investigate whether the less expensive and very simply to operate NDIRS works as reliable as IRMS. For this purpose we applicated 1-¹³C-Phenylalanine to patients with advanced liver cirrhosis and healthy volunteers and took duplicated breath samples for IRMS and NDIRS at selected time points. Our data show a good correlation between these two methods for a small number of samples as required for simple breath tests. Longer series, where repeated measurements are required on the NDIRS instrument lead to a decreasing correlation. This indicates the superiority of IRMS concerning ¹³CO₂-kinetics over longer time periods.     

Bayesian Binary Segmentation Procedure for a Poisson Process With Multiple Changepoints

We observe n events occurring in (0, T] taken from a Poisson process. The intensity function of the process is assumed to be a step function with multiple changepoints. This article proposes a Bayesian binary segmentation procedure for locating the changepoints and the associated heights of the intensity function. We conduct a sequence of nested hypothesis tests using the Bayes factor or the BIC approximation to the Bayes factor. At each comparison in the binary segmentation steps, we need only to compare a singlechangepoint model to a no-changepoint model. Therefore, this method circumvents the computational complexity we would normally face in problems with an unknown (large) number of dimensions. A simulation study and an analysis on a real dataset are given to illustrate our methods.     

皮肤毛孔照片诊断标准评价的潜在分类变量模型研究

本文在无金标准情况下探讨皮肤毛孔标准照片制定的合理性和可行性,对医师诊断正确性进行评价。按照毛孔粗大程度制定分类为5水平的毛孔标准照片。对128名女性志愿者制作鼻翼毛孔照片,5位年资相近的皮肤科医师按照诊断标准和标准照片对128例自愿者照片进行独立的等级评分。诊断结果数据采用潜在分类变量模型(Latent Class Model,LCM)进行分析,分别拟合5位医师诊断条件概率一致的模型和诊断条件概率不一致的模型。计算医师诊断的条件概率和后验概率。潜变量分析结果提示诊断标准过于细化且分类模糊,依据条件概率将原始分类重新划分为3类的模型较好地拟合了诊断数据。运用客观和准确的能够真实反应和区分个体情况的诊断标准是诊断试验评价的基础和前提。潜在分类模型能够有效地处理无金标准的诊断重复性或一致性研究数据。