Circular Chromatic Indices of Regular Graphs

The circular chromatic index of a graph G, written , is the minimum r permitting a function such that whenever e and are adjacent. It is known that for any , there is a 3‐regular simple graph G with . This article proves the following results: Assume is an odd integer. For any , there is an n‐regular simple graph G with . For any , there is an n‐regular multigraph G with .     

Measuring rank correlation coefficients between financial time series: A GARCH-copula based sequence alignment algorithm

This paper presents a novel four-stage algorithm for the measurement of the rank correlation coefficients between pairwise financial time series. In first stage returns of financial time series are fitted as skewed-t distributions by the generalized autoregressive conditional heteroscedasticity model. In the second stage, the joint probability density function (PDF) of the fitted skewed-t distributions is computed using the symmetrized Joe–Clayton copula. The joint PDF is then utilized as the scoring scheme for pairwise sequence alignment in the third stage. After solving the optimal sequence alignment problem using the dynamic programming method, we obtain the aligned pairs of the series. Finally, we compute the rank correlation coefficients of the aligned pairs in the fourth stage. To the best of our knowledge, the proposed algorithm is the first to use a sequence alignment technique to pair numerical financial time series directly, without initially transforming numerical values into symbols. Using practical financial data, the experiments illustrate the method and demonstrate the advantages of the proposed algorithm.     

Regularized generalized canonical correlation analysis for multiblock or multigroup data analysis

This paper presents an overview of methods for the analysis of data structured in blocks of variables or in groups of individuals. More specifically, regularized generalized canonical correlation analysis (RGCCA), which is a unifying approach for multiblock data analysis, is extended to be also a unifying tool for multigroup data analysis. The versatility and usefulness of our approach is illustrated on two real datasets.     

《例说循环论证之谬误》注

指出《例说循环论证之谬误》中的第二个例子并非循环论证,并给出例子说明相关问题中更有可能产生循环论证之处。     

Optimized projections for compressed sensing via rank-constrained nearest correlation matrix

Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper a novel formulation of the optimization problem is proposed, in the form of a rank-constrained nearest correlation matrix problem. Furthermore, improvements for three existing optimization algorithms are introduced, which are shown to be particular instances of the proposed formulation. Simulation results show notable improvements and superior robustness in sparse signal recovery.     

On spatial contagion and multivariate GARCH models

We propose a method for defining and measuring spatial contagion between two financial markets via conditional copulas. Some theoretical results on monotonicity and asymptotic properties of Gaussian copulas with respect to conditioning are presented. Next, we combine the spatial contagion approach with time series models. We investigate which model from a large family of multivariate GARCH is the best tool for modelling spatial contagion. In an empirical study, we show that among models designed for general fit, a two‐step model fitting procedure reduces the ability to describe the contagion effect. This is a feature of copula‐GARCH models. Copyright © 2013 John Wiley & Sons, Ltd.     

用矩阵方程法求解循环卷积的改进算法

从循环卷积的定义出发,描述了用以m为变量的方法求解循环卷积的步骤.特别详述了其中的矩阵方程法,指出了该方法的不足——含有冗余项,提出了矩阵方程法的改进算法,消除了冗余项,简化了矩阵方程,给出了矩阵方程内部各列的构成规律.实例表明该方法简便、有效.     

状态方程法预测四元系超额体积

利用ＦＲＫＳ立方状态方程和改进的ＬＬ混合规则，拟合二元系超额体系的实验数据，得到二元参数。在不引入任何多元参数的情况下，直接用二元参数预测四元系的超额体积。对四元系的计算结果表明，该方法能给出较好的预测结果。     

A novel approach to the determination of the crosslink density in rubber materials with the dipolar correlation effect in low magnetic fields

We present a novel NMR approach to the determination of crosslink densities in rubber materials. The method is based on the dipolar correlation effect (DCE) on the stimulated echo examined in a series of rubber samples and linear polyisoprene. The parameter evaluated from the echo attenuation curves is the mean‐squared dipolar fluctuation associated with anisotropic reorientations of macromolecular backbones. The contributions to the DCE of the constraints due to excluded volume effects and chemical crosslinks are estimated. A strong dependence of the mean‐squared dipolar fluctuation on the crosslink density of rubber combined with the simplicity of performing the measurements with inexpensive low‐field instruments suggests that the DCE is a useful tool for routine applications. The potential and problems of performing DCE measurements in low‐magnetic‐field conditions are discussed in detail. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2207–2216, 2001     

圆形管道振动分析及实验研究

应用摄动地和波动分析法研究圆形管道的振动；利用MASP编辑管道动态振型，通过实验对理论指导的正确性加以验证。