Inverse maximum flow problems under the weighted Hamming distance

In this paper, we consider inverse maximum flow problem under the weighted Hamming distance. Four models are studied: the problem under sum-type weighted Hamming distance; the problem under bottleneck-type weighted Hamming distance and two mixed types of problems. We present their respective combinatorial algorithms that all run in strongly polynomial times.Research supported by the National Natural Science Foundation of China (60021201), and the Hong Kong Research Grant Council under CERG CityU 9041091 and CUHK 103105.     

未知参数多项式相位信号的最优检测及性能

根据Neyman-Pearson(NP)准则,利用广义似然比检验方法,给出了未知参数多项式相位信号的最优检测器。在相位多项式次数分别为1或2时,周期图、chirp傅里叶变换检测即为对应的最优检测器。推导了检验统计量的概率密度函数以及虚警概率和检测概率,揭示了多项式相位信号检测中信号能量噪声比、信号参数空间中搜索点数、虚警概率和检测概率之间的关系。仿真结果验证了理论分析的有效性。     

The Lamperti Transforms of Self-Similar Gaussian Processes and Their Exponentials

We present results on the second order behavior and the expected maximal increments of Lamperti transforms of self-similar Gaussian processes and their exponentials. The Ornstein Uhlenbeck processes driven by fractional Brownian motion (fBM) and its exponentials have been recently studied in Ref.^{[ 20} Matsui , M. ; Shieh , N.-R. On the exponentials of fractional Ornstein-Uhlenbeck processes . Electron. J. Probab. 2009 , 14 , 594 – 611 .[Crossref], [Web of Science ®] , [Google Scholar] ^] and Ref.^{[ 21} Matsui , M. ; Shieh , N.-R. On the exponential process associated with a CARMA-type process. Stochastics , 2012 . doi: 10.1080/17442508.2012.654791 .[Taylor &; Francis Online] , [Google Scholar] ^], where we essentially make use of some particular properties, e.g., stationary increments of fBM. Here, the treated processes are fBM, bi-fBM, and sub-fBM; the latter two are not of stationary increments. We utilize decompositions of self-similar Gaussian processes and effectively evaluate the maxima and correlations of each decomposed process. We also present discussion on the usage of the exponential stationary processes for stochastic modeling.     

Hyper-Graeco-Latin Squares and Fractional Factorial Designs

A Latin square of order s is an arrangement of the s letters in an s × s square so that every letter appears exactly once in every row and exactly once in every column. Copeland and Nelson (2000) used two examples to show that a Latin square can be chosen such that it corresponds to a fractional factorial design. In this article, we are going to study this topic more precisely. Furthermore, we will explore the relationship between fractional factorial designs and hyper-Graeco-Latin squares in general, where s is a prime or a power of a prime.     

一类带有限制的网络瓶颈容量扩张问题

在一些物理网络中,当设施（边的容量等）建立后,由于需求增加,需要调整网络的容量来提高服务水平。调整优化的过程中既要考虑扩张成本,同时也要考虑需要调整的总边数,以尽可能小的影响人们的正常生活。本文研究对于一个给定的网络G,已知边e_i的初始容量和单位容量扩张成本,在预算成本和扩张总边数的约束下,如何有效地扩张边的容量至x_i,使得系统的容量最大,即max{min_ei∈T x_i,T是网络G中的生成树。首先求解两个与之相关的模型,然后通过分析两个相关模型与原问题之间的联系与区别,提出了原问题的多项式时间算法。最后,通过算例说明算法的步骤,并分析了不同参数值对系统容量的影响。     

Analysis of inaccurate data with mixture measurement error models

Measurement error, the difference between a measured (observed) value of quantity and its true value, is perceived as a possible source of estimation bias in many surveys. To correct for such bias, a validation sample can be used in addition to the original sample for adjustment of measurement error. Depending on the type of validation sample, we can either use the internal calibration approach or the external calibration approach. Motivated by Korean Longitudinal Study of Aging (KLoSA), we propose a novel application of fractional imputation to correct for measurement error in the analysis of survey data. The proposed method is to create imputed values of the unobserved true variables, which are mis-measured in the main study, by using validation subsample. Furthermore, the proposed method can be directly applicable when the measurement error model is a mixture distribution. Variance estimation using Taylor linearization is developed. Results from a limited simulation study are also presented.     

A beta-inflated mean regression model with mixed effects for fractional response variables

Abstract

In this article we propose a new mixed-effects regression model for fractional bounded response variables. Our model allows us to incorporate covariates directly to the expected value, so we can quantify exactly the influence of these covariates in the mean of the variable of interest rather than to the conditional mean. Estimation is carried out from a Bayesian perspective. Due to the complexity of the augmented posterior distribution, we use a Hamiltonian Monte Carlo algorithm, the No-U-Turn sampler, implemented using the Stan software. A simulation study was performed showing that our model has a better performance than other traditional longitudinal models for bounded variables. Finally, we applied our beta-inflated mean mixed-effects regression model to real data which consists of utilization of credit lines in the peruvian financial system.     

Minimum aberration blocking schemes for 128-run designs

Several criteria have been proposed for ranking blocked fractional factorial designs. For large fractional factorial designs, the most appropriate minimum aberration criterion was one proposed by Cheng and Wu (2002). We justify this assertion and propose a novel construction method to overcome the computational challenge encountered in large fractional factorial designs. Tables of minimum aberration blocked designs are presented for N=128 runs and n=8–64 factors.