Nonparametric regression with current status data

We apply nonparametric regression to current status data, which often arises in survival analysis and reliability analysis. While no parametric assumption on the distributions has been imposed, most authors have employed parametric models like linear models to measure the covariate effects on failure times in regression analysis with current status data. We construct a nonparametric estimator of the regression function by modifying the maximum rank correlation (MRC) estimator. Our estimator can deal with the cases where the other estimators do not work. We present the asymptotic bias and the asymptotic distribution of the estimator by adapting a result on equicontinuity of degenerate U-processes to the setup of this paper.     

Lagrangian decomposition of block-separable mixed-integer all-quadratic programs

The purpose of this paper is threefold. First we propose splitting schemes for reformulating non-separable problems as block-separable problems. Second we show that the Lagrangian dual of a block-separable mixed-integer all-quadratic program (MIQQP) can be formulated as an eigenvalue optimization problem keeping the block-separable structure. Finally we report numerical results on solving the eigenvalue optimization problem by a proximal bundle algorithm applying Lagrangian decomposition. The results indicate that appropriate block-separable reformulations of MIQQPs could accelerate the running time of dual solution algorithms considerably.The work was supported by the German Research Foundation (DFG) under grant NO 421/2-1Mathematics Subject Classification (2000): 90C22, 90C20, 90C27, 90C26, 90C59     

Optimization with binet matrices

This paper deals with linear and integer programming problems in which the constraint matrix is a binet matrix. Linear programs can be solved with the generalized network simplex method, while integer programs are converted to a matching problem. It is also proved that an integral binet matrix has strong Chvátal rank 1.     

面积平均p叶函数的最小模估计及其应用

假设,在单位圆盘△={z:|z|<1}内是面积平均p叶函数.关于|f'/f|2的平均增长,Hayman和Duren等对其进行了详细的研究.注意到,这种增长涉及到f(z)的最小模m(r)=min|z|=r|f(z)|.本文首先估计m(r),然后给出一些相关的应用,其中包括|f'/f|2的平均增长估计,|f(eiθ)|-λ的可积性以及一个新的Bazilevic定理,这个新的定理涉及到f的最大增长方向和最小增长方向.我们得到的某些结果是不可改进的.     

Field Performance Prediction and IR Imaging Simulation Based on Measured System Level Parameters*

Traditionally, the Minimum Resolvable Temperature Difference (MRTD) and the Johnson criteria are used to predict the field performance of IR imaging system. However this method generally leads to far too pessimistic range predictions. For the improvement of the prediction accuracy of the field performance, a novel approach to predict field performance is proposed based on the three-dimensional infrared scene generated by Vega software. Further, this approach utilizes the measured system level parameters to characterize the signal transfer process, noise, and the blur effect of the output image instead of theoretical model. By controlling the target range in the simulated image, a simulation experiment is performed, and the range corresponding to the 75% correct probability of discrimination is achieved by the statistical method. Comparisons with the real experimental result show that this method can give more accurate range prediction than the target acquisition (TA) model based on the MRTD.* Foundation Item: The project supported by The Research Fund for the Doctoral Program of Higher Education(No. 20030701003) and National Natural Science Foundation of China (No: 60277005, 60477038).     

Sensitivity of the Hermite rank

The Hermite rank appears in limit theorems involving long memory. We show that a Hermite rank higher than one is unstable when the data is slightly perturbed by transformations such as shift and scaling. We carry out a “near higher order rank analysis” to illustrate how the limit theorems are affected by a shift perturbation that is decreasing in size. We also consider the case where the deterministic shift is replaced by centering with respect to the sample mean. The paper is a companion of Bai and Taqqu (2017) which discusses the instability of the Hermite rank in the statistical context.     

When is a matrix unitary or Hermitian plus low rank?

Hermitian and unitary matrices are two representatives of the class of normal matrices whose full eigenvalue decomposition can be stably computed in quadratic computing complexity once the matrix has been reduced, for instance, to tridiagonal or Hessenberg form. Recently, fast and reliable eigensolvers dealing with low‐rank perturbations of unitary and Hermitian matrices have been proposed. These structured eigenvalue problems appear naturally when computing roots, via confederate linearizations, of polynomials expressed in, for example, the monomial or Chebyshev basis. Often, however, it is not known beforehand whether or not a matrix can be written as the sum of a Hermitian or unitary matrix plus a low‐rank perturbation. In this paper, we give necessary and sufficient conditions characterizing the class of Hermitian or unitary plus low‐rank matrices. The number of singular values deviating from 1 determines the rank of a perturbation to bring a matrix to unitary form. A similar condition holds for Hermitian matrices; the eigenvalues of the skew‐Hermitian part differing from 0 dictate the rank of the perturbation. We prove that these relations are linked via the Cayley transform. Then, based on these conditions, we identify the closest Hermitian or unitary plus rank k matrix to a given matrix A, in Frobenius and spectral norm, and give a formula for their distance from A. Finally, we present a practical iteration to detect the low‐rank perturbation. Numerical tests prove that this straightforward algorithm is effective.     

New concept of organic homo‐rank compounds and its application in estimating enthalpy of formation of mono‐substituted alkanes

Based on the topological characteristics of distance matrices and adjacency matrices of molecular graphs, a new concept of organic homo‐rank compounds was proposed. Based on this concept, compounds can be classified into new groups other than the traditional homologues. Furthermore, novel structure–property relationship approach named as homo‐rank compounds method can be developed. The feasibility of homo‐rank compounds method was explored by estimating the enthalpy of formation of organic compounds. The group contribution index (GCI_X) and group polarizability potential index (GPI_X) of substituents X were defined and determined for mono‐substituted alkanes RX (X includes 20 substituents). The research results show that the enthalpies of formation of organic homo‐rank compounds and their isomers can be correlated very well with the parameters GCI_X and GPI_X. Combining the method of homologues with that of homo‐rank compounds, a general and simple quantitative correlation equation (8) was established to estimate the enthalpy of formation for RX, and the calculation precision is within the chemical accuracy ‘1 kcal/mol’. For 242 samples of RX, the average absolute deviation between the experimental and the calculated values is 2.42 kJ/mol. In addition, the enthalpies of formation of more than 2800 samples of RX were estimated. The approaches of organic homo‐rank compounds and organic homologues are independent of but complementary to each other. The combination of these two methods can help us to understand the organic molecular structure–property relationships more deeply, and to investigate these relationships more conveniently and accurately. Copyright © 2015 John Wiley & Sons, Ltd.     

Power-law and exponential rank distributions: A panoramic Gibbsian perspective

Rank distributions are collections of positive sizes ordered either increasingly or decreasingly. Many decreasing rank distributions, formed by the collective collaboration of human actions, follow an inverse power-law relation between ranks and sizes. This remarkable empirical fact is termed Zipf’s law, and one of its quintessential manifestations is the demography of human settlements — which exhibits a harmonic relation between ranks and sizes. In this paper we present a comprehensive statistical-physics analysis of rank distributions, establish that power-law and exponential rank distributions stand out as optimal in various entropy-based senses, and unveil the special role of the harmonic relation between ranks and sizes. Our results extend the contemporary entropy-maximization view of Zipf’s law to a broader, panoramic, Gibbsian perspective of increasing and decreasing power-law and exponential rank distributions — of which Zipf’s law is one out of four pillars.