A combination of modified particle swarm optimization algorithm and support vector machine for gene selection and tumor classification

In the analysis of gene expression profiles, the number of tissue samples with genes expression levels available is usually small compared with the number of genes. This can lead either to possible overfitting or even to a complete failure in analysis of microarray data. The selection of genes that are really indicative of the tissue classification concerned is becoming one of the key steps in microarray studies. In the present paper, we have combined the modified discrete particle swarm optimization (PSO) and support vector machines (SVM) for tumor classification. The modified discrete PSO is applied to select genes, while SVM is used as the classifier or the evaluator. The proposed approach is used to the microarray data of 22 normal and 40 colon tumor tissues and showed good prediction performance. It has been demonstrated that the modified PSO is a useful tool for gene selection and mining high dimension data.     

一维〔M（tmp）〕_2ReO_4（M＝Ni、Cu、Pd）聚合物的能带结构

用紧束缚ＥＨＴ晶体轨道方法对一维〔Ｍ（ｔｍｐ）〕_２ＲｅＯ_４（Ｍ＝Ｎｉ、Ｃｕ、Ｐｄ）聚合物进行了能带计算，利用键向量近似方法对能带的结构及组成进行了讨论。结果表明，该类型聚合物具有不同的导电机理，并进一步研究了环平面间的成键性质及转角改变对聚合物导电性能的影响。     

Complexation of well-controlled low-molecular weight polyelectrolytes with antisense oligonucleotides

The influences of polymer-related properties such as molecular weight, charge density, counter ion, and hydrophilic block on the complexation of polyelectrolytes and a fluorescein-labeled oligonucleotide (ON) were investigated. A series of well-defined and well-controlled 2-(N,N-dimethylamino)ethyl methacrylate (DMAEMA) polymers and block copolymers were prepared using living anionic and radical polymerization methods. Fluorescence measurement was used to reveal the effects of polymer molecular weight, charge density, and counter ion type on the complexation. PolyDMAEMA samples having double molecular weights of the chosen oligonucleotide gave the optimal complexation performance. Kinetic studies showed that high-molecular weight/high-charge density polymer samples produced very stable complexes. The fully charged polyDMAEMA displayed the strongest binding with the ON. These complexes were therefore less sensitive to the changes in the environment. PolyDMAEMA–DMSQ samples had slightly higher complexation ability than polyDMAEMA–MCQ (DMSQ: dimethylsulfate quat; MCQ: methylchloride quat). Both poly(DMAEMA-b-HEMA) and poly(DMAEMA–MCQ-b-PEG) block copolymers showed good complexation ability and steric stability [HEMA: 2-hydroxyethyl methacrylate; PEG: poly(ethylene glycol)]. PEG, but not HEMA block, enhanced the effectiveness of polyDMAEMA–MCQ binding with the ON.     

从电子工业“脊梁”到全面开花的镓元素

镓是第一个根据化学元素周期律预言并在自然界中证实的元素，是室温下电导率和热导率均为最大的液态物质，镓在电子工业中得到了广泛应用，被誉为电子工业“脊梁”。近十几年来，镓的更多应用潜力被发掘出来，在电子工业、散热、增材制造、柔性机器、生物医学等领域均有重要的应用前景。     

Mathematical studies of Kekulé structures

The perfect matching vector and forcing and the Kekulé-vector of cata-benzenoids are defined. Two theorems are given which set the sufficient and necessary conditions for HKZ-vector (Harary et al. J Math Chem 6:295, 1991) and Kekulé-vector in cata-benzenoids. Additional two theorems are obtained which give sharp bounds for the modules of HKZ- and Kekulé vectors. Dedicated to Professor Tadeusz Marek Krygowski on the happy occasion of his 70th birthday.     

基于SVR和k-近邻群的组合预测在QSAR中的应用

为提高定量构效关系(QSAR)研究的预测精度,发展了一种新的基于支持向量机回归(SVR)非线性筛选分子结构描述符、基于k-近邻群的非线性组合预测方法.首先以均方误差(MSE)最小为原则,以留一法通过多轮末尾淘汰实施分子结构描述符的非线性SVR汰选并给出最优核函数和相应保留描述符;其次基于待测样本与训练样本保留描述符向量的欧氏距离,以不同k-近邻群子模型双重留一法预测值反映样本集的异质性;然后基于MSE最小,以留一法通过多轮末尾淘汰实施近邻群子模型的非线性SVR汰选并给出最优核函数和相应保留子模型;最后基于保留子模型以双重留一法实施组合预测.以取代苯胺和苯酚类化合物对大型溞的QSAR实例验证表明:新方法在所有参比模型中预测精度最高,且能更精细地反映描述符与化合物毒性间的非线性关系,具结构风险最小、非线性、适于小样本,能有效克服过拟合、维数灾和局极小,非线性筛选描述符和子模型,非线性组合预测,自动选择最优核函数及其相应参数,泛化推广能力优异、预测精度高等诸多优点,在QSAR研究中有广泛应用前景.     

Tractability frontiers in probabilistic team semantics and existential second-order logic over the reals

Probabilistic team semantics is a framework for logical analysis of probabilistic dependencies. Our focus is on the axiomatizability, complexity, and expressivity of probabilistic inclusion logic and its extensions. We identify a natural fragment of existential second-order logic with additive real arithmetic that captures exactly the expressivity of probabilistic inclusion logic. We furthermore relate these formalisms to linear programming, and doing so obtain PTIME data complexity for the logics. Moreover, on finite structures, we show that the full existential second-order logic with additive real arithmetic can only express NP properties. Lastly, we present a sound and complete axiomatization for probabilistic inclusion logic at the atomic level.     

增量式Huber-支持向量回归机算法研究

传统的面向支持向量回归的一次性建模算法中样本增加时,均需从头开始学习,而增量式算法可以充分利用上一阶段的学习成果。SVR的增量算法通常基于ε-不敏感损失函数,该损失函数对大的异常值比较敏感,而Huber损失函数对异常值敏感度低。所以在有噪声的情况下,Huber损失函数是比ε-不敏感损失函数更好的选择,在现实情况当中。基于此,本文提出了一种基于Huber损失函数的增量式Huber-SVR算法,该算法能够持续地将新样本信息集成到已经构建好的模型中,而不是重新建模。与增量式ε-SVR算法和增量式RBF算法相比,在对真实数据进行预测建模时,增量式Huber-SVR算法具有更高的预测精度。     

Single machine group scheduling with ordered criteria

The single machine group scheduling problem is considered. Jobs are classified into several groups on the basis of group technology, i.e. jobs of the same group have to be processed jointly. A machine set-up time independent of the group sequence is needed between each two consecutive groups. A schedule specifies the sequence of groups and the sequence of jobs in each group. The quality of a schedule is measured by the criteriaF ₁, ...,F _m ordered by their relative importance. The objective is to minimize the least important criterionF _m subject to the schedule being optimal with respect to the more important criterionF _m–1 which is minimized on the set of schedules minimizing criterionF _m–2 and so on. The most important criterion isF ₁, which is minimized on the set of all feasible schedules. An approach to solve this multicriterion problem in polynomial time is presented if functionsF ₁, ...,F _m have special properties. The total weighted completion time and the total weighted exponential time are the examples of functionsF ₁, ...,F _m–1 and the maximum cost is an example of functionF _m for which our approach can be applied.The research of the authors was partially supported by a KBN Grant No. 3 P 406 003 05, the Fundamental Research Fund of Belarus, Project N 60-242, and the Deutsche Forschungsgemeinschaft, Project Schema, respectively. The paper was completed while the first author was visiting the University of Melbourne.     

Standard pseudo-Hermitian structure on manifolds and seifert fibration

A strictly pseudoconvex pseudo-Hermitian manifoldM admits a canonical Lorentz metric as well as a canonical Riemannian metric. Using these metrics, we can define a curvaturelike function onM. AsM supports a contact form, there exists a characteristic vector field dual to the contact structure. If induces a local one-parameter group ofCR transformations, then a strictly pseudoconvex pseudo-Hermitian manifoldM is said to be a standard pseudo-Hermitian manifold. We study topological and geometric properties of standard pseudo-Hermitian manifolds of positive curvature or of nonpositive curvature . By the definition, standard pseudo-Hermitian manifolds are calledK-contact manifolds by Sasaki. In particular, standard pseudo-Hermitian manifolds of constant curvature turn out to be Sasakian space forms. It is well known that a conformally flat manifold contains a class of Riemannian manifolds of constant curvature. A sphericalCR manifold is aCR manifold whose Chern-Moser curvature form vanishes (equivalently, Weyl pseudo-conformal curvature tensor vanishes). In contrast, it is emphasized that a sphericalCR manifold contains a class of standard pseudo-Hermitian manifolds of constant curvature (i.e., Sasakian space forms). We shall classify those compact Sasakian space forms. When 0, standard pseudo-Hermitian closed aspherical manifolds are shown to be Seifert fiber spaces. We consider a deformation of standard pseudo-Hermitian structure preserving a sphericalCR structure.Dedicated to Professor Sasao Seiya for his sixtieth birthday