子空间比较法研究拓扑块的变量关系及变量选择

用子空间比较法研究由不同拓扑指数构成的块变量之间的关系,提出了一种变量选择的新方法.以530种烷烃的5大类拓扑指数为样本进行比较,得到了反映拓扑块变量间线性相关关系的夹角余弦值,以及这些子空间所对应的结构信息.结合子空间比较的结果选择变量,对上述烷烃的沸点值进行回归,R=0.9948,S=4.08,交互检验预测误差LOO=4.38     

结构描述符正交化及典型相关分析在饱和醇、醚质谱分类中的应用

结构描述符正交化及典型相关分析在饱和醇、醚质谱分类中的应用;饱和醇醚;模式识别;质谱分类变量;块变量;典型相关分析     

基于分子结构预测气相色谱程序升温保留指数

从拓扑指数出发,研究了分子结构与气相色谱程序升温保留指数之间的关系。对所选择的部分分子结构,利用主成分回归(PCR)的相关系数R=0.9998,标准偏差S=9.987,交互检验(leave one out cross-valida-tion)所得标准偏差S=11.17。同时,对同一柱型不同升温速率条件下的保留指数之间的关系、同一升温速率不同柱型条件下保留指数之间的关系进行了初步探讨,建立的模型线性关系明显。     

Multivariate Association of Graph-Theoretic Variables and Physicochemical Properties

Abstract

We used canonical correlation analysis to examine the multivariate association between two distinct data sets commonly measured or calculated for approximately 600 chemicals: (1) measured or calculated values of select physieochemical properties (i.e., K _ow, boiling point, heat of vaporization, molecular weight, water solubility, molecular volume, hydrogen bonding potential, and vapor pressure) and (2) calculated algorithmically-derived variables (i.e., topological and neighborhood indices derived from graph theory). Canonical correlation analysis identified eight highly significant associations between linear combinations of graph-theoretic variables and linear combinations of physicochemical properties. The set of graph theoretic variables was significantly related to all physieochemical properties, explaining 55% to 99% of the variation in these properties.     

Asymptotically independent topological indices on random trees

Topological indices are graph invariants used in computational chemistry to encode molecules. A frequent problem when performing structure-activity studies is that topological indices are inter-correlated. We consider a simple topological index and show asymptotic independence for a random tree model. This continues previous work on the correlation among topological indices. These findings suggest that a size-dependence in a certain class of distance-based topological indices can be eliminated.AMS subject classification: 05C80, 60E10, 92E10     

Discrimination between linear and non-linear models describing retention data of alkylbenzenes in gas-chromatography

Summary Detailed statistical analysis is presented to describe the retention indices of alkylbenzenes as a function of their physical (boiling point, modrefraction) and topological (connectivity and complexity indices) properties. With the help of several statistical characteristics (examination of residuals, F test, partial F test, termination criteria, correlation indices) a discrimination is made among different models. A nonlinear equation was chosen which describes the retention data on slightly polar phases with the practically attainable precision. A comparison with literature sources shows that this equation provides the smallest residual error and, hence, it can be applied for prediction purposes. A correlation was found between the preexponential factor in the simple exponential model and the polarity of stationary phases on the Tarján scale.     

Structural interpretation of the topological index. 2. The molecular connectivity index, the Kappa index, and the atom-type E-State index

The structural interpretation is extended to the topological indices describing cyclic structures. Three representatives of the topological index, such as the molecular connectivity index, the Kappa index, and the atom-type E-State index, are interpreted by mining out, through projection pursuit combining with a number theory method generating uniformly distributed directions on unit sphere, the structural features hidden in the spaces spanned by the three series of indices individually. Some interesting results, which can hardly be found by individual index, are obtained from the multidimensional spaces by several topological indices. The results support quantitatively the former studies on the topological indices, and some new insights are obtained during the analysis. The combinations of several molecular connectivity indices describe mainly three general categories of molecular structure information, which include degree of branching, size, and degree of cyclicity. The cyclicity can also be coded by the combination of chi cluster and path/cluster indices. The Kappa shape indices encode, in combination, significant information on size, the degree of cyclicity, and the degree of centralization/separation in branching. The size, branch number, and cyclicity information has also been mined out to interpret atom-type E-State indices. The structural feature such as the number of quaternary atoms is searched out to be an important factor. The results indicate that the collinearity might be a serious problem in the applications of the topological indices.     

Isomer discrimination by topological information approach

A comparative analysis of ten topological indices is made. No index is found to discriminate isomers uniquely. A combined topological index, named the superindex, consisting of a number of topological indices is proposed. Information theory is applied to express all components of the superindex on a common quantitative scale. The superindex is tested on the sample of 427 graphs consisting of all acyclic, monocyclic, and bicyclic graphs with 4–8 vertices.     

环烷烃及烷烃的折光指数与结构的关系研究

A new structure information autocorrelation topological index tX is designed and developed based on the vertex degree of molecular topology and autocorrelation function of mathematics. Quantitative structure property the relationships for estimating the refractive index of cycloalkane and alkane are set up based on multiple linear regression. The vertex degree is defined as βi .The structure information autocorrelation topological index tX is set up with the βi. The refractive index （nD）, for the 64 cycloalkanes, are correlated with this topological indices. The index, for the 27 alkanes, are also correlated with this topological indices. The calculated results showed that the calculated refractive index of cycloalkanes and alkanes are in good agreement with the experimental data, with the mean velative deviation 0.25%. With the established model, the refractive index of the other 5 alkanes are predicted.     

Some novel neighborhood degree sum-based versus degree-based topological indices in QSPR analysis of alkanes from n-butane to nonanes

The topological indices are reported to be very useful in various QSPR studies as these indices can be utilized as a tool to predict the physicochemical properties of a diverse set of chemical compounds. The objective of this communication is twofold. First, to introduce some neighborhood degree sum-based topological indices and perform a comparative QSPR analysis of the indices with their corresponding degree-based topological indices to analyze the usefulness of the new indices. Second, to investigate isomer discrimination ability of the newly defined indices on the basis of degeneracy test. Neighborhood degree sum-based topological indices not only consider the degree of each atom in the molecule but also the degrees of its neighboring atoms. Moreover, these indices are expected to provide information about how connected and dense the neighborhoods of atoms are within the molecule. In this study, we observe that the proposed neighborhood degree sum-based topological indices exhibit better correlation with some physicochemical properties of Octane Isomers and 66 alkanes as compared to their corresponding degree-based topological indices. Also, the supremacy in terms of sensitivity of the neighbourhood degree sum-based topological indices as compared to the classical degree-based ones is established.     

拓扑指数与手性化合物构效关系研究

传统的拓扑指数仅考虑原子间的连接关系,不能区分手性信息．故本研究对Am指数与分子连接性指数进行了扩展,并将其用于3-苯基哌啶类手性化合物的构效关系研究．扩展后的拓扑指数构造的数学模型优于用传统的Am指数与分子连接性指数得到的模型．同时进行了变量的两两相关性测试,结果显示所选3个变量之间的相关性较小．通过交叉验证,证明手性拓扑指数所得到的数学模型是稳定的．并进一步运用人工神经网络,得到了满意的结果．     

甲基烷烃结构与色谱保留指数相关性的拓扑指数法研究

计算了207个甲基烷烃的127个拓扑指数变量,把变量选择方法GAPLS方法引入到定量结构与气相色谱保留关系研究中,对127个拓扑指数变量进行选择,得到了含7个变量的化合物的定量结构与色谱保留指数关系(QSRR)模型,其复相关系数的平方为0.99998,标准偏差为2.88。交互验证的复相关系数为0.99997,交互验证的预测标准偏差为2.95,表明该模型具有良好的稳定性和可靠性。对获得的7个变量进行了合理的结构解释,表明甲基烷烃色谱保留指数完全能用拓扑指数来精确表征。     

The variable connectivity index 1chi(f) versus the traditional molecular descriptors: a comparative study of 1chi(f) against descriptors of CODESSA.

In this study we compared the prediction abilities of the variable connectivity index 1chi(f) (not included in CODESSA) with topological indices available from CODESSA. We selected the boiling points of n = 100 alcohols as the property and examined the pool of 56 topological indices. Prediction capabilities of the developed models were evaluated by classical training/test set approach. RMS errors calculated from the prediction set for the MLR models obtained from CODESSA software with 1, 2, 3, 4, and 5 parameters were 9.06, 5.69, 5.40, 4.9, and 3.37 degrees C, respectively. Using the variable connectivity index with weights x = 0.10 and y = -0.92 for carbon and oxygen atom respectively, we obtain regression BP = 38.12 1chi(f) - 37.56 with the correlation coefficient r = 0.9915, RMS error 4.21 degrees C calculated from the test set, and Fisher ratio F = 5691. Prediction capability of the variable connectivity index was better than for MLR regression model with up to four parameters.