Data-driven slicing for dimension reduction in regressions:A likelihood-ratio approach

To efficiently estimate the central subspace in sufficient dimension reduction,response discretization via slicing its range is one of the most used methodologies when inverse regression-based methods are applied.However,existing slicing schemes are almost all ad hoc and not widely accepted.Thus,how to define datadriven schemes with certain optimal properties is a longstanding problem in this field.The research described here is then twofold.First,we introduce a likelihood-ratio-based framework for dimension reduction,subsuming the popularly used methods including the sliced inverse regression,the sliced average variance estimation and the likelihood acquired direction.Second,we propose a regularized log likelihood-ratio criterion to obtain a data-driven slicing scheme and derive the asymptotic properties of the estimators.A simulation study is carried out to examine the performance of the proposed method and that of existing methods.A data set concerning concrete compressive strength is also analyzed for illustration and comparison.

可定制多孔玻璃表面的溶解制造策略

玻璃表面微纳结构的设计和制造在实现所需功能方面具有重要意义.然而,玻璃固有的硬度和脆性给传统制造方法带来了不便.因此,开发一种简单且可控的制造策略对于制备具备功能应用的微纳结构玻璃至关重要.在本文中,我们提出了一种创新方法,利用可溶性氯化钠颗粒作为前驱体模板,在玻璃表面上创建可定制的多孔结构.通过我们的先导成型策略,成功利用可溶性氯化钠颗粒的潜力作为前驱体模板,从而便于制造量身定制的多孔玻璃表面.通过调节这些颗粒的大小和组合,我们实现了对所得多孔玻璃的连续调控,范围从超亲水(1°)到超疏水(142°).值得注意的是,制备的多孔玻璃表面表现出显著的亲油性,展示了在油水分离和自清洁等多种应用方面的巨大潜力.最重要的是,即使经过了10次制造迭代,玻璃表面的疏水-亲油功能依然完好,凸显了我们策略的耐久性和可重复性.这种方法为实现玻璃的特殊功能提供了方便且具有成本效益的途径,为不同领域的进展铺平了道路.

Quantum Implementation of Numerical Methods for Convection-Diffusion Equations:Toward Computational Fluid Dynamics

We present quantum numerical methods for the typical initial boundary value problems(IBVPs)of convection-diffusion equations in fluid dynamics.The IBVP is discretized into a series of linear systems via finite difference methods and explicit time marching schemes.To solve these discrete systems in quantum computers,we design a series of quantum circuits,including four stages of encoding,amplification,adding source terms,and incorporating boundary conditions.In the encoding stage,the initial condition is encoded in the amplitudes of quantum registers as a state vector to take advantage of quantum algorithms in space complexity.In the following three stages,the discrete differential operators in classical computing are converted into unitary evolutions to satisfy the postulate in quantum systems.The related arithmetic calculations in quantum amplitudes are also realized to sum up the increments from these stages.The proposed quantum algorithm is implemented within the open-source quantum computing framework Qiskit[2].By simulating one-dimensional transient problems,including the Helmholtz equation,the Burgers’equation,and Navier-Stokes equations,we demonstrate the capability of quantum computers in fluid dynamics.

偏正态混合模型的惩罚极大似然估计

在分析具有异质性和非对称性数据时,偏正态混合模型提供一种比经典的Gauss混合模型更为灵活的建模方式.然而,由于无界的似然函数和发散的形状参数,该模型的极大似然估计并未被正确定义,进一步导致不理想的推断过程.为同时解决这两个问题,本文基于惩罚似然提出一种新的估计方案,并证明在混合分布的类别个数大于或等于真实的类别个数时,相应的惩罚极大似然估计是强相合的.同时,本文也提出相应的惩罚EM (expectation maximization)算法来计算惩罚估计.最后,通过模拟分析与现有方法比较研究估计方法在有限样本下的表现,并采用两个实例说明方法的有效性.

Pairwise distance-based heteroscedasticity test for regressions

In this study,we propose nonparametric testing for heteroscedasticity in nonlinear regression models based on pairwise distances between points in a sample.The test statistic can be formulated such that Ustatistic theory can be applied to it.Although the limiting null distribution of the statistic is complicated,we can derive a computationally feasible bootstrap approximation for such a distribution;the validity of the introduced bootstrap algorithm is proven.The test can detect any local alternatives that are different from the null at a nearly optimal rate in hypothesis testing.The convergence rate of this test statistic does not depend on the dimension of the covariates,which significantly alleviates the impact of dimensionality.We provide three simulation studies and a real-data example to evaluate the performance of the test and demonstrate its applications.

A combined p-value test for the mean difference of high-dimensional data

This paper proposes a novel method for testing the equality of high-dimensional means using a multiple hypothesis test. The proposed method is based on the maximum of standardized partial sums of logarithmic p-values statistic. Numerical studies show that the method performs well for both normal and non-normal data and has a good power performance under both dense and sparse alternative hypotheses. For illustration, a real data analysis is implemented.

高雷诺数流固声耦合的大涡模拟

高雷诺数流固声耦合的大涡模拟是湍流和计算流体力学的前沿领域.它可以用于飞机、潜艇和新能源汽车的舱内噪声预测.本文设计了槽道湍流激励下的平板-空腔系统作为典型案例,研究了大涡模拟方法用于高雷诺数流固声耦合系统的可能性.我们的数值结果表明,基于动态Smagorinsky模型的大涡模拟方法得到的振动声学响应与直接数值模拟接近,但是在高频部分低估了振动声学响应,并在低频部分高估响应.其主要原因在于大涡模拟未能准确预测壁面压力时空能谱,而时空能谱决定了流固声耦合系统的振动声学响应.通过Corcos模型激励的Euler-Bernoulli梁的理论分析,我们确认了不准确壁面压力时空能谱影响振动声学响应的机制.最后,本文工作表明了有必要通过发展新型的亚格子项模型,提升壁面压力时空能谱的预测精度,最终实现大涡模拟方法对高雷诺数流固声耦合系统的准确预测.

Stable correlation and robust feature screening

In this paper,we propose a new correlation,called stable correlation,to measure the dependence between two random vectors.The new correlation is well defined without the moment condition and is zero if and only if the two random vectors are independent.We also study its other theoretical properties.Based on the new correlation,we further propose a robust model-free feature screening procedure for ultrahigh dimensional data and establish its sure screening property and rank consistency property without imposing the subexponential or sub-Gaussian tail condition,which is commonly required in the literature of feature screening.We also examine the finite sample performance of the proposed robust feature screening procedure via Monte Carlo simulation studies and illustrate the proposed procedure by a real data example.