Density functional theory （DFT） was used to calculate molecular descriptors （properties） for 12 fluoro-quinolone with anti-S.pneumoniae activity. Principal component analysis （PCA） and hierarchical cluster analy...Density functional theory （DFT） was used to calculate molecular descriptors （properties） for 12 fluoro-quinolone with anti-S.pneumoniae activity. Principal component analysis （PCA） and hierarchical cluster analysis （HCA） were employed to reduce dimensionality and investigate in which variables should be more effective for classifying fluoroquinolones according to their degree of an-S.pneumoniae activity. The PCA results showed that the variables ELUMO, Q3, Q5, QA, logP, MR, VOL and △EHL of these compounds were responsible for the anti-S.pneumoniae activity. The HCA results were similar to those obtained with PCA.The methodologies of PCA and HCA provide a reliable rule for classifying new fluoroquinolones with antiS.pneumoniae activity. By using the chemometric results, 6 synthetic compounds were analyzed through the PCA and HCA and two of them are proposed as active molecules with anti-S.pneumoniae, which is consistent with the results of clinic experiments.展开更多
In order to more effectively assess the health status of a project, the monitoring indices in a project＇s life cycle are divided into quality index, cost index, time index, satisfaction index, and sustainable develop...In order to more effectively assess the health status of a project, the monitoring indices in a project＇s life cycle are divided into quality index, cost index, time index, satisfaction index, and sustainable development index. Based on the feature of qualitative and quantitative indices combining, the PCA-PR （principal component analysis and pattern recognition） model is constructed. The model first analyzes the principal components of the life-cycle indices system constructed above, and picks up those principal component indices that can reflect the health status of a project at any time. Then the pattern recognition model is used to study these principal components, which means that the real time health status of the project can be divided into five lamps from a green lamp to a red one and the health status lamp of the project can be recognized by using the PR model and those principal components. Finally, the process is shown with a real example and a conclusion consistent with the actual situation is drawn. So the validity of the index system and the PCA-PR model can be confirmed.展开更多
Gauge duality theory was originated by Preund （1987）, and was recently further investigated by Friedlander et al. （2014）. When solving some matrix optimization problems via gauge dual, one is usually able to avoid...Gauge duality theory was originated by Preund （1987）, and was recently further investigated by Friedlander et al. （2014）. When solving some matrix optimization problems via gauge dual, one is usually able to avoid full matrix decompositions such as singular value and/or eigenvalue decompositions. In such an approach, a gauge dual problem is solved in the first stage, and then an optimal solution to the primal problem can be recovered from the dual optimal solution obtained in the first stage. Recently, this theory has been applied to a class of semidefinite programming （SDP） problems with promising numerical results by Friedlander and Mac^to （2016）. We establish some theoretical results on applying the gauge duality theory to robust principal component analysis （PCA） and general SDP. For each problem, we present its gauge dual problem, characterize the optimality conditions for the primal-dual gauge pair, and validate a way to recover a primal optimal solution from a dual one. These results are extensions of Friedlander and Macedo （2016） from nuclear norm regularization to robust PCA and from a special class of SDP which requires the coefficient matrix in the linear objective to be positive definite to SDP problems without this restriction. Our results provide further understanding in the potential advantages and disadvantages of the gauge duality theory.展开更多
基金This work was supported by National Nature Science Foundation of China and China Academy of Engineering Physics （No. 10376021） Provincial National Science Foundation of He＇nan （No. 2004601107）.
文摘Density functional theory （DFT） was used to calculate molecular descriptors （properties） for 12 fluoro-quinolone with anti-S.pneumoniae activity. Principal component analysis （PCA） and hierarchical cluster analysis （HCA） were employed to reduce dimensionality and investigate in which variables should be more effective for classifying fluoroquinolones according to their degree of an-S.pneumoniae activity. The PCA results showed that the variables ELUMO, Q3, Q5, QA, logP, MR, VOL and △EHL of these compounds were responsible for the anti-S.pneumoniae activity. The HCA results were similar to those obtained with PCA.The methodologies of PCA and HCA provide a reliable rule for classifying new fluoroquinolones with antiS.pneumoniae activity. By using the chemometric results, 6 synthetic compounds were analyzed through the PCA and HCA and two of them are proposed as active molecules with anti-S.pneumoniae, which is consistent with the results of clinic experiments.
基金The Social Science Fund of Hebei Province (No.200607011)the Key Science and Technology Project of Hebei Province(No.07213529)
文摘In order to more effectively assess the health status of a project, the monitoring indices in a project＇s life cycle are divided into quality index, cost index, time index, satisfaction index, and sustainable development index. Based on the feature of qualitative and quantitative indices combining, the PCA-PR （principal component analysis and pattern recognition） model is constructed. The model first analyzes the principal components of the life-cycle indices system constructed above, and picks up those principal component indices that can reflect the health status of a project at any time. Then the pattern recognition model is used to study these principal components, which means that the real time health status of the project can be divided into five lamps from a green lamp to a red one and the health status lamp of the project can be recognized by using the PR model and those principal components. Finally, the process is shown with a real example and a conclusion consistent with the actual situation is drawn. So the validity of the index system and the PCA-PR model can be confirmed.
基金supported by Hong Kong Research Grants Council General Research Fund (Grant No. 14205314)National Natural Science Foundation of China (Grant No. 11371192)
文摘Gauge duality theory was originated by Preund （1987）, and was recently further investigated by Friedlander et al. （2014）. When solving some matrix optimization problems via gauge dual, one is usually able to avoid full matrix decompositions such as singular value and/or eigenvalue decompositions. In such an approach, a gauge dual problem is solved in the first stage, and then an optimal solution to the primal problem can be recovered from the dual optimal solution obtained in the first stage. Recently, this theory has been applied to a class of semidefinite programming （SDP） problems with promising numerical results by Friedlander and Mac^to （2016）. We establish some theoretical results on applying the gauge duality theory to robust principal component analysis （PCA） and general SDP. For each problem, we present its gauge dual problem, characterize the optimality conditions for the primal-dual gauge pair, and validate a way to recover a primal optimal solution from a dual one. These results are extensions of Friedlander and Macedo （2016） from nuclear norm regularization to robust PCA and from a special class of SDP which requires the coefficient matrix in the linear objective to be positive definite to SDP problems without this restriction. Our results provide further understanding in the potential advantages and disadvantages of the gauge duality theory.
