A second‐order ensemble method based on a blended backward differentiation formula timestepping scheme for time‐dependent Navier–Stokes equations

We present a second‐order ensemble method based on a blended three‐step backward differentiation formula (BDF) timestepping scheme to compute an ensemble of Navier–Stokes equations. Compared with the only existing second‐order ensemble method that combines the two‐step BDF timestepping scheme and a special explicit second‐order Adams–Bashforth treatment of the advection term, this method is more accurate with nominal increase in computational cost. We give comprehensive stability and error analysis for the method. Numerical examples are also provided to verify theoretical results and demonstrate the improved accuracy of the method. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 34–61, 2017     

经方量化归经研究中的向量矩阵应用

在经方量化归经研究中发现,药物组成的归经量化问题,若以五维向量表示更能体现其药物的归经方向和归经比例.利用向量矩阵分析方法给出了方剂归经量化的一种全新的量化模型体系,并以此研究方剂归经的量化规律及其应用特点.     

Estimation of the limit of detection using information theory measures

Definitions of the limit of detection (LOD) based on the probability of false positive and/or false negative errors have been proposed over the past years. Although such definitions are straightforward and valid for any kind of analytical system, proposed methodologies to estimate the LOD are usually simplified to signals with Gaussian noise. Additionally, there is a general misconception that two systems with the same LOD provide the same amount of information on the source regardless of the prior probability of presenting a blank/analyte sample. Based upon an analogy between an analytical system and a binary communication channel, in this paper we show that the amount of information that can be extracted from an analytical system depends on the probability of presenting the two different possible states. We propose a new definition of LOD utilizing information theory tools that deals with noise of any kind and allows the introduction of prior knowledge easily. Unlike most traditional LOD estimation approaches, the proposed definition is based on the amount of information that the chemical instrumentation system provides on the chemical information source. Our findings indicate that the benchmark of analytical systems based on the ability to provide information about the presence/absence of the analyte (our proposed approach) is a more general and proper framework, while converging to the usual values when dealing with Gaussian noise.     

Quantification of human growth hormone by amino acid composition analysis using isotope dilution liquid-chromatography tandem mass spectrometry

We describe an accurate method for protein quantification based on conventional acid hydrolysis and an isotope dilution-HPLC-mass spectrometry (ID-HPLC-MS) method. Sample purity was confirmed using capillary zone electrophoresis, HPLC and MS. The analyte protein, human growth hormone (hGH), was effectively hydrolyzed by incubation with 8 M hydrochloric acid at 130 °C for 48 h, where at least 1 μM of hGH was treated to avoid possible degradation of released amino acids during hydrolysis. Using a reversed-phase column, the analytes (isoleucine, phenylalanine, proline and valine) were separated within 5 min using an isocratic eluent comprising 10% acetonitrile containing 0.1% trifluoroacetic acid. The detection limit (signal to noise ratio of 3) of amino acids was 5.5-6.2 fmol per injection. The quantification precision (RSD) of amino acids for intra- and inter-day assays was less than 0.98% and 0.39%, respectively. Comparison with other biochemical and instrumental methods revealed substantially higher accuracy and reproducibility of the ID-HPLC-MS/MS method as expected. The optimized hydrolysis and analytical conditions in our study were suitable for accurate quantification of hGH.     

Large deviation theory for a homogenized and “corrected” elliptic ODE

We study a one-dimensional elliptic problem with highly oscillatory random diffusion coefficient. We derive a homogenized solution and a so-called Gaussian corrector. We also prove a “pointwise” large deviation principle (LDP) for the full solution and approximate this LDP with a more tractable form. Applications to uncertainty quantification are considered.     

A Study of Hyperbolicity of Kinetic Stochastic Galerkin System for the Isentropic Euler Equations with Uncertainty

The authors study the fluid dynamic behavior of the stochastic Galerkin (SG for short) approximation to the kinetic Fokker-Planck equation with random uncertainty. While the SG system at the kinetic level is hyperbolic, its fluid dynamic limit, as the Knudsen number goes to zero and the underlying kinetic equation approaches to the uncertain isentropic Euler equations, is not necessarily hyperbolic, as will be shown in the case study fashion for various orders of the SG approximations.     

不确定结构时域响应分析的多项式维数分解法

针对具有不确定参数结构,提出时域不确定性传播和量化的多项式维数分解法,确定了结构响应统计量的演变过程.首先,采用参数概率模型来描述结构参数的不确定性,建立结构动力学方程,将结构响应表达为不确定参数的函数;进一步,将所关心的结构响应采用成员函数进行维数分解,并利用正交多项式基底对成员函数进行Fourier展开;最后,应用降维积分方法进行展开系数的求解,给出了响应均值和标准差的计算表达式.在数值算例中,将本文方法与蒙特卡洛方法进行对比,结果表明所建立方法具有较高的求解效率和计算精度.     

Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids

Quantitative predictions of the behavior of many deterministic systems are uncertain due to ubiquitous heterogeneity and insufficient characterization by data. We present a computational approach to quantify predictive uncertainty in complex phenomena, which is modeled by (partial) differential equations with uncertain parameters exhibiting multi-scale variability. The approach is motivated by flow in random composites whose internal architecture (spatial arrangement of constitutive materials) and spatial variability of properties of each material are both uncertain. The proposed two-scale framework combines a random domain decomposition (RDD) and a probabilistic collocation method (PCM) on sparse grids to quantify these two sources of uncertainty, respectively. The use of sparse grid points significantly reduces the overall computational cost, especially for random processes with small correlation lengths. A series of one-, two-, and three-dimensional computational examples demonstrate that the combined RDD–PCM approach yields efficient, robust and non-intrusive approximations for the statistics of diffusion in random composites.     

Is mortality or interest rate the most important risk in annuity models? A comparison of sensitivity analysis methods

Demographic and financial factors are key risk-drivers for insurance companies and pension funds. This paper proposes a systematic investigation for deepening our understanding how these risk drivers affect the annuity cost. We employ local and global sensitivity methods. For local sensitivity, we derive closed form expressions for the differential importance measures of perturbed annuities and connect them to the entropy of the annuity cost. For global sensitivity, we compare variance-based, moment-independent sensitivity measures and Shapley effects. In particular, moment-independent sensitivity measures and Shapley effects are compared for the first time in the case of dependent risk factors. Our framework encompasses and extends several previous results on the sensitivity analysis of annuity models. From a methodological viewpoint, the techniques compared in this paper can support analysts in building annuity models and in verifying the impact of risk drivers in their models. Numerical results using the U.S. 1990 and the U.K. 1990–1994 mortality tables show that the demographic factor is the most important risk source in low-interest rate contexts. However, when uncertainty on the two risk sources is taken into account, the financial factor becomes the global key-driver of risk. Also, interactions among the two factors appear quantitatively significant.