Covering skew-supermodular functions by hypergraphs of minimum total size

The paper presents results related to a theorem of Szigeti on covering symmetric skew-supermodular set functions by hypergraphs. We prove the following generalization using a variation of Schrijver’s supermodular colouring theorem: if p₁ and p₂ are skew-supermodular functions with the same maximum value, then it is possible to find in polynomial time a hypergraph of minimum total size that covers both p₁ and p₂. We also give some applications concerning the connectivity augmentation of hypergraphs.     

传递对准中测量延迟的补偿方法

采用“速度 姿态”匹配方式，提出了一种解决传递对准中主惯导数据测量延迟现象的方法。该方法将主惯导数据测量延迟时间扩展为卡尔曼滤波器的一个状态变量，并同时考虑了测量延迟时间对速度和姿态测量量的影响。在主惯导数据存在测量延迟的情况下，推导了速度、姿态测量方程，最后对提出的方法进行了仿真。仿真结果表明，该方法可以加快滤波器的收敛速度，提高传递对准的对准精度。     

Flow and heat transfer over a backward-facing step with a cylinder mounted near its top corner

A study was made to see if it is possible to enhance the heat transfer in the downstream region of a backward-facing step, where heat transfer is normally deteriorated, by the insertion of a cylinder near the top corner of the step. Cylinder size and streamwise position of the cylinder were kept constant but the cross-stream position of the cylinder was changed in three steps. Results of the heat transfer experiment, flow visualization, and measurement of the averaged and fluctuating flow fields were reported. When the cylinder was mounted at a position, a little higher than the top surface of the step, a jet-like flow pattern emerged in the averaged velocity profile beneath the cylinder and the recirculating flow was intensified. Therefore, the velocity of recirculating flow near the wall is increased at some streamwise positions. Additionally, the velocity fluctuation was intensified not only in the shear layer between the jet-like flow and the recirculating flow regions but also in the near wall region, resulting in the effective augmentation of heat transfer in this case. Therefore, it is concluded that the mounting of a cylinder is effective in the enhancement of deteriorated heat transfer in the recirculating flow region, if its is mounted in a proper position.     

A New Algorithm for Simulating a Correlation Matrix Based on Parameter Expansion and Reparameterization

The correlation matrix (denoted by R) plays an important role in many statistical models. Unfortunately, sampling the correlation matrix in Markov chain Monte Carlo (MCMC) algorithms can be problematic. In addition to the positive definite constraint of covariance matrices, correlation matrices have diagonal elements fixed at one. In this article, we propose an efficient two-stage parameter expanded reparameterization and Metropolis-Hastings (PX-RPMH) algorithm for simulating R. Using this algorithm, we draw all elements of R simultaneously by first drawing a covariance matrix from an inverse Wishart distribution, and then translating it back to a correlation matrix through a reduction function and accepting it based on a Metropolis-Hastings acceptance probability. This algorithm is illustrated using multivariate probit (MVP) models and multivariate regression (MVR) models with a common correlation matrix across groups. Via both a simulation study and a real data example, the performance of the PX-RPMH algorithm is compared with those of other common algorithms. The results show that the PX-RPMH algorithm is more efficient than other methods for sampling a correlation matrix.     

An Artificial Allocations Based Solution to the Label Switching Problem in Bayesian Analysis of Mixtures of Distributions

Label switching is a well-known problem occurring in MCMC outputs in Bayesian mixture modeling. In this article we propose a formal solution to this problem by considering the space of the artificial allocation variables. We show that there exist certain subsets of the allocation space leading to a class of nonsymmetric distributions that have the same support with the symmetric posterior distribution and can reproduce it by simply permuting the labels. Moreover, we select one of these distributions as a solution to the label switching problem using the simple matching distance between the artificial allocation variables. The proposed algorithm can be used in any mixture model and its computational cost depends on the length of the simulated chain but not on the parameter space dimension. Real and simulated data examples are provided in both univariate and multivariate settings. Supplemental material for this article is available online.     

Variational Bayes Estimation of Discrete-Margined Copula Models With Application to Time Series

We propose a new variational Bayes (VB) estimator for high-dimensional copulas with discrete, or a combination of discrete and continuous, margins. The method is based on a variational approximation to a tractable augmented posterior and is faster than previous likelihood-based approaches. We use it to estimate drawable vine copulas for univariate and multivariate Markov ordinal and mixed time series. These have dimension rT, where T is the number of observations and r is the number of series, and are difficult to estimate using previous methods. The vine pair-copulas are carefully selected to allow for heteroscedasticity, which is a feature of most ordinal time series data. When combined with flexible margins, the resulting time series models also allow for other common features of ordinal data, such as zero inflation, multiple modes, and under or overdispersion. Using six example series, we illustrate both the flexibility of the time series copula models and the efficacy of the VB estimator for copulas of up to 792 dimensions and 60 parameters. This far exceeds the size and complexity of copula models for discrete data that can be estimated using previous methods. An online appendix and MATLAB code implementing the method are available as supplementary materials.