Maximum principles for a class of nonlinear second order elliptic differential equations

In this paper we investigate maximum principles for functionals defined on solutions to special partial diff'erential equations of elliptic type, extending results by Payne and Philippin. We apply such maximum principles to investigate one overdetermined problem.     

A regression approach to ROC surface, with applications to Alzheimer’s disease

We consider the estimation of three-dimensional ROC surfaces for continuous tests given covariates.Three way ROC analysis is important in our motivating example where patients with Alzheimer’s disease are usually classified into three categories and should receive different category-specific medical treatment.There has been no discussion on how covariates affect the three way ROC analysis.We propose a regression framework induced from the relationship between test results and covariates.We consider several practical cases and the corresponding inference procedures.Simulations are conducted to validate our methodology.The application on the motivating example illustrates clearly the age and sex effects on the accuracy for Mini-Mental State Examination of Alzheimer’s disease.     

Reconstructing the relaxation dynamics induced by an unknown heat bath

In quantum state tomography, one potential source of error is uncontrolled contact of the system with a heat bath whose detailed properties are not known, and whose impact on the system moreover varies between different runs of the experiment. Precisely these variations provide a handle for reconstructing the system?s effective relaxation dynamics. I propose a pertinent estimation scheme which is based on a steepest-descent ansatz and maximum likelihood. After reconstructing the relaxation dynamics, the original quantum state of the system can be constrained to a curve in state space.     

Folded overlapping variance estimators for simulation

We propose and analyze a new class of estimators for the variance parameter of a steady-state simulation output process. The new estimators are computed by averaging individual estimators from “folded” standardized time series based on overlapping batches composed of consecutive observations. The folding transformation on each batch can be applied more than once to produce an entire set of estimators. We establish the limiting distributions of the proposed estimators as the sample size tends to infinity while the ratio of the sample size to the batch size remains constant. We give analytical and Monte Carlo results showing that, compared to their counterparts computed from nonoverlapping batches, the new estimators have roughly the same bias but smaller variance. In addition, these estimators can be computed with order-of-sample-size work.     

Computationally Efficient Changepoint Detection for a Range of Penalties

In the multiple changepoint setting, various search methods have been proposed, which involve optimizing either a constrained or penalized cost function over possible numbers and locations of changepoints using dynamic programming. Recent work in the penalized optimization setting has focused on developing an exact pruning-based approach that, under certain conditions, is linear in the number of data points. Such an approach naturally requires the specification of a penalty to avoid under/over-fitting. Work has been undertaken to identify the appropriate penalty choice for data-generating processes with known distributional form, but in many applications the model assumed for the data is not correct and these penalty choices are not always appropriate. To this end, we present a method that enables us to find the solution path for all choices of penalty values across a continuous range. This permits an evaluation of the various segmentations to identify a suitable penalty choice. The computational complexity of this approach can be linear in the number of data points and linear in the difference between the number of changepoints in the optimal segmentations for the smallest and largest penalty values. Supplementary materials for this article are available online.     

Dynamic Behavior of Surfactants in Solution

Adsorption of various surfactants at the gas liquid interface is studied with equilibrium and dynamic surface tension measurements. The Wilhelmey plate method and maximum bubble pressure method are used for this study. Dynamic surface tension of solutions of different surfactants, sodium lauryl sulfate (SLS), polyoxyethylene glycol 4‐tert‐octyl phenyl ether (Triton X 100), poly‐oxyethylene(20) cetyl ether (Brij 58), and tetraethylene glycol mono‐n‐dodecyl ether (Brij 30), is measured at different concentrations. Adsorption of different surfactants is compared on the basis of equilibrium and dynamic behavior. Effectiveness and efficiency of different surfactants is found from equilibrium surface tension measurement. A new parameter is defined to quantify the dynamic behavior of adsorption, which gives the concentration of surfactant needed to reduce surface tension to half of its maximum reduction within a defined time available for adsorption. The dynamics of surfactant solution is quantified by using this parameter.     

Ill-posed problems in rheology

Experimental data are always noisy and often incomplete. This leads to ambiguities if one wants to infer from the data some functions, which are related to the measured quantity through an integral equation of the first kind. In rheology many of such so-called ill-posed problems appear. Two techniques to treat such problems, the regularization method and the maximum entropy method, are applied to the determination of the relaxation spectrum from data of small oscillatory shear flow. With simulated data from a reference spectrum it is discussed how the inferred spectrum depends on the region, in which data are available. It turns out that information about the asymptotic behavior of the measured quantity can be of great help in determining the full spectrum also from incomplete data.Dedicated to Prof. Dr. J. Meissner on the occasion of his 60th birthday.     

带有二元连接函数的半参数模型

提出了一种新的带有二元连接函数的广义半参数模型,即二元连接模型(简称为BLM).使用轮廓似然方法估计模型的参数和非参数部分,并给出了计算算法.证明了所得的未知参数的估计量为n~(1/2)-相合,渐近正态且具有渐近最小方差,给出了实际数据分析和模拟研究,最终采用局部功效方法来检验非参数部分的线性性.     

On an Inequality of Pual Turan Concerning Polynomials-Ⅱ

Let P(z) be a polynomial of degree n and for any complex number α, let D_αP(z) = nP(z)+(α- z) P′(z) denote the polar derivative of the polynomial P(z) with respect to α. In this paper, we obtain inequalities for the polar derivative of a polynomial having all zeros inside a circle. Our results shall generalize and sharpen some well-known results of Turan, Govil, Dewan et al. and others.     

END样本最近邻密度估计的强相合速度

本文研究了扩展负相依(END)样本最近邻密度估计的强相合性问题.利用END序列的Bernstein型不等式和截尾的方法,获得了END样本最近邻密度估计的强相合速度,推广了NA样本和ND样本最近邻密度估计的相应结果.