Impact assessment of the rational selection of training and test sets on the predictive ability of QSAR models

This study performed an analysis of the influence of the training and test set rational selection on the quality and predictively of the quantitative structure–activity relationship (QSAR) model. The study was carried out on three different datasets of Influenza Neuraminidase (H1N1) inhibitors. The three datasets were divided into training and test sets using three rational selection methods: based on k-means, Kennard–Stone algorithm and Activity and the results were compared with Random selection. Then, a total of 31,490 mathematical models were developed and those models that presented a determination coefficient higher than: r²_train > 0.8, r²_loo > 0.7, r²_test > 0.5 and minimum standard deviation (SD) and minimum root-mean square error (RMS) were selected. The selected models were validated using the internal leave-one-out method and the predictive capacity was evaluated by the external test set. The results indicate that random selection could lead to erroneous results. In return, a rational selection allows for obtaining more reliable conclusions. The QSAR models with major predictive power were found using the k-means algorithm and selection by activity.     

一类满足可补性质的双重Stone代数

该文构造了一个从布尔代数范畴到满足可补性质的双重Ｓｔｏｎｅ 代数范畴的函子，并证明了这个函子有一个等价的左伴随函子．     

REPRESENTATION OF POSETS

In this paper we give new criterions for left distributive posets to have neatest representations. We also illustrate a construction that would embed left distributive posets into representable semilattices.     

磷酸铵镁结石患者尿微晶组分分析及其与结石形成的关系

采用X射线衍射(XRD)、傅里叶变换红外光谱(FTIR)、纳米粒度仪、扫描电子显微镜(SEM)和透射电子显微镜(TEM)研究了磷酸铵镁结石患者尿液中微晶的组分、形貌、粒径和Zeta电位,并对其结石进行了组分分析.结果表明,结石类型、尿微晶组分和尿液pH三者之间存在密切的联系:磷酸铵镁结石病人的尿液pH值较高,通常在6....     

Niveloids and their extensions: Risk measures on small domains

Given a functional defined on a nonempty subset of an Archimedean Riesz space with unit, necessary and sufficient conditions are obtained for the existence of a (convex or concave) niveloid that extends the functional to the entire space. In the language of mathematical finance, this problem is equivalent to the one of verifying if the policy adopted by a regulator is consistent with monetary risk measurement, when only partial information is available.     

A Bishop–Stone–Weierstrass Theorem for （M2（C））^n

In this paper, we shall give an elementary proof of a Bishop–Stone–Weierstrass theorem for （M2（C））n with respect to its pure states. To be more precise, we shall show that the pure-state Bishop hull of a unital subalgebra （not necessarily self-adjoint） of （M2（C））n is equal to itself.     

Study of titanium adsorption on perfect and defected BC3 nanotubes using density functional theory

Density functional theory calculations were used to study the titanium (Ti) adsorption on perfect and defected (4, 0) BC₃ nanotubes, considering Stone–Wales and vacancy defects. The binding energy values for these nanotubes were larger than the corresponding values for carbon nanotubes. The charge transfer from the Ti atom to nanotube was observed for all systems studied. The most exothermic binding process occurred for the Ti adsorption on a native V_B defect, which showed minimum structural deformation with respect to a perfect BC₃ tube. In the case of a nanotube with a reconstructed carbon vacancy, the adsorption of Ti generated a half-metallic anti-ferromagnet. The results obtained in this paper are relevant for spintronics and hydrogen adsorption applications.     

Topological group criterion for in compact-open-like topologies, II

We continue from “part I” our address of the following situation. For a Tychonoff space Y, the “second epi-topology” σ is a certain topology on C(Y), which has arisen from the theory of categorical epimorphisms in a category of lattice-ordered groups. The topology σ is always Hausdorff, and σ interacts with the point-wise addition + on C(Y) as: inversion is a homeomorphism and + is separately continuous. When is + jointly continuous, i.e. σ is a group topology? This is so if Y is Lindelöf and Čech-complete, and the converse generally fails. We show in the present paper: under the Continuum Hypothesis, for Y separable metrizable, if σ is a group topology, then Y is (Lindelöf and) Čech-complete, i.e. Polish. The proof consists in showing that if Y is not Čech-complete, then there is a family of compact sets in βY which is maximal in a certain sense.