More about the kernel convergence and the ideal convergence

Let I 2N be an ideal and let XI = span{χI ： I ∈ I}, and let pI be the quotient norm of l∞/XI. In this paper, we show first that for each proper ideal I 2N, the ideal convergence deduced by I is equivalent to pI-kernel convergence. In addition, let K = {x＊oχ（·） ： x＊∈ p（e）}, where p（x） = lim supn→∞1/n（∑k=1n｜x（k）｜, and let Iμ = {A N ： μ（A） = 0} for all μ = x＊oχ（·） ∈ K. Then Iμ is a proper ideal. We also show that the ideal convergence deduced by the proper ideal Iμ, the p-kernel convergence and the statistical convergence are also equivalent.     

An empirical study on information spillover effects between the Chinese copper futures market and spot market

This study employs a parametric approach based on TGARCH and GARCH models to estimate the VaR of the copper futures market and spot market in China. Considering the short selling mechanism in the futures market, the paper introduces two new notions: upside VaR and extreme upside risk spillover. And downside VaR and upside VaR are examined by using the above approach. Also, we use Kupiec’s [P.H. Kupiec, Techniques for verifying the accuracy of risk measurement models, Journal of Derivatives 3 (1995) 73-84] backtest to test the power of our approaches. In addition, we investigate information spillover effects between the futures market and the spot market by employing a linear Granger causality test, and Granger causality tests in mean, volatility and risk respectively. Moreover, we also investigate the relationship between the futures market and the spot market by using a test based on a kernel function. Empirical results indicate that there exist significant two-way spillovers between the futures market and the spot market, and the spillovers from the futures market to the spot market are much more striking.     

Equivalences among Z2s-linear Hadamard codes

The ${\mathbb{Z}}_{2^s}$-additive codes are subgroups of ${\mathbb{Z}}_{2^s}^n$, and can be seen as a generalization of linear codes over ${\mathbb{Z}}_2$ and ${\mathbb{Z}}_4$. A ${\mathbb{Z}}_{2^s}$-linear Hadamard code is a binary Hadamard code which is the Gray map image of a ${\mathbb{Z}}_{2^s}$-additive code. A partial classification of these codes by using the dimension of the kernel is known. In this paper, we establish that some ${\mathbb{Z}}_{2^s}$-linear Hadamard codes of length $2^t$ are equivalent, once $t$ is fixed. This allows us to improve the known upper bounds for the number of such nonequivalent codes. Moreover, up to $t=11$, this new upper bound coincides with a known lower bound (based on the rank and dimension of the kernel). Finally, when we focus on $s\in \{2,3\}$, the full classification of the ${\mathbb{Z}}_{2^s}$-linear Hadamard codes of length $2^t$ is established by giving the exact number of such codes.     

Diffusion maps for changing data

Graph Laplacians and related nonlinear mappings into low dimensional spaces have been shown to be powerful tools for organizing high dimensional data. Here we consider a data set X in which the graph associated with it changes depending on some set of parameters. We analyze this type of data in terms of the diffusion distance and the corresponding diffusion map. As the data changes over the parameter space, the low dimensional embedding changes as well. We give a way to go between these embeddings, and furthermore, map them all into a common space, allowing one to track the evolution of X in its intrinsic geometry. A global diffusion distance is also defined, which gives a measure of the global behavior of the data over the parameter space. Approximation theorems in terms of randomly sampled data are presented, as are potential applications.     

Bootstrapping the nonparametric ARCH regression model

In this paper we introduce the nonparametric AR(1)–ARCH(1) model and show weak consistency of the Nadaraya–Watson estimators for the model. We propose a residual and a wild bootstrap method and prove weak consistency of the bootstrap estimators.     

Improved prediction of drug-target interactions using regularized least squares integrating with kernel fusion technique

Identification of drug-target interactions (DTI) is a central task in drug discovery processes. In this work, a simple but effective regularized least squares integrating with nonlinear kernel fusion (RLS-KF) algorithm is proposed to perform DTI predictions. Using benchmark DTI datasets, our proposed algorithm achieves the state-of-the-art results with area under precision–recall curve (AUPR) of 0.915, 0.925, 0.853 and 0.909 for enzymes, ion channels (IC), G protein-coupled receptors (GPCR) and nuclear receptors (NR) based on 10 fold cross-validation. The performance can further be improved by using a recalculated kernel matrix, especially for the small set of nuclear receptors with AUPR of 0.945. Importantly, most of the top ranked interaction predictions can be validated by experimental data reported in the literature, bioassay results in the PubChem BioAssay database, as well as other previous studies. Our analysis suggests that the proposed RLS-KF is helpful for studying DTI, drug repositioning as well as polypharmacology, and may help to accelerate drug discovery by identifying novel drug targets.     

基于模糊多核学习的改进支持向量机算法研究

针对传统SVM对噪声点和孤立点敏感的问题,以及不能解决样本特征规模大、含有异构信息、在特征空间中分布不平坦的问题,将模糊隶属度融入多核学习中,提出了一种模糊多核学习的方法。通过实验验证了模糊多核学习比传统SVM、模糊支持向量机以及多核学习具有更好的分类效果,从而验证了所提方法能够有效的克服传统SVM对噪声点敏感以及数据分布不平坦的问题。     

Estimation of source spectra profiles and simultaneous determination of polycomponent in mixtures from ultraviolet spectra data using kernel independent component analysis and support vector regression

A method that use kernel independent component analysis (KICA) and support vector regression (SVR) was proposed for estimation of source ultraviolet (UV) spectra profiles and simultaneous determination of polycomponents in mixtures. In KICA-SVR procedure, the UV source spectra profiles were estimated using KICA, then the mixing matrix of the components were calculated using the estimated sources, and the calibration model was build using SVR based on the calculated mixing matrix. A simulated UV dataset of three-component mixtures was used to test the ability of KICA for estimating source spectra profiles from spectra data of mixtures. It was found that KICA has the potential power to estimate pure UV spectra profiles, and correlation coefficient of estimated sources correspond to the real adopted ones are better compared with that by FastICA and Infomax ICA. An UV dataset of polycomponent vitamin B was processed using the proposed KICA-SVR method. The results show that the estimated source spectra profiles are correlative with the real UV spectra of the components and chemically interpretable, and accurate results were obtained.     

图形软件包(GKS-RMX86)——GKS在iRMX86操作系统下的实现

本文提出了一种图形软件包GKS-RMX86,并说明了iRMX 86操作系统如何支持它作工。文中还介绍了一种速度快且易于理解的新裁剪算法。