Identification of Pharmacophoric Fragments of DYRK1A Inhibitors Using Machine Learning Classification Models

Dual-specific tyrosine phosphorylation regulated kinase 1 (DYRK1A) has been regarded as a potential therapeutic target of neurodegenerative diseases, and considerable progress has been made in the discovery of DYRK1A inhibitors. Identification of pharmacophoric fragments provides valuable information for structure- and fragment-based design of potent and selective DYRK1A inhibitors. In this study, seven machine learning methods along with five molecular fingerprints were employed to develop qualitative classification models of DYRK1A inhibitors, which were evaluated by cross-validation, test set, and external validation set with four performance indicators of predictive classification accuracy (CA), the area under receiver operating characteristic (AUC), Matthews correlation coefficient (MCC), and balanced accuracy (BA). The PubChem fingerprint-support vector machine model (CA = 0.909, AUC = 0.933, MCC = 0.717, BA = 0.855) and PubChem fingerprint along with the artificial neural model (CA = 0.862, AUC = 0.911, MCC = 0.705, BA = 0.870) were considered as the optimal modes for training set and test set, respectively. A hybrid data balancing method SMOTETL, a combination of synthetic minority over-sampling technique (SMOTE) and Tomek link (TL) algorithms, was applied to explore the impact of balanced learning on the performance of models. Based on the frequency analysis and information gain, pharmacophoric fragments related to DYRK1A inhibition were also identified. All the results will provide theoretical supports and clues for the screening and design of novel DYRK1A inhibitors.     

Explicit generalized zolotarev polynomials with complex coefficients

We give explicitly a class of polynomials with complex coefficients of degreen which deviate least from zero on [−1, 1] with respect to the max-norm among all polynomials which have the same,m + 1, 2m ≤n, first leading coefficients. Form=1, we obtain the polynomials discovered by Freund and Ruschewyh. Furthermore, corresponding results are obtained with respect to weight functions of the type 1/√ρl, whereρl is a polynomial positive on [−1, 1].     

水稻糙米粗蛋白近红外光谱定量分析模型的优化研究

筛选有代表性的191份糙米样品为试材,其中42份来自国家稻种资源库、149份来自水旱稻杂交产生的DH系,蛋白质含量变幅5.90％～14.50％,采用偏最小二乘法(PLS)建立模型,并构造模型的评价参数——目标函数[R/(1+RMSECV)], 同时借助校正集和验证集两个载荷向量得分二维空间投影图,对近红外定量模型进行评价和优化。结果表明: 在5 000～9 000 cm-1范围内,预处理方法为一阶导数,校正模型和外部检验的目标函数值分别为0.701和0.687;两载荷向量得分直观分布图显示样品的聚类结果与目标函数筛选结果一致,也进一步验证了目标函数是模型评价和优化的有效指标。     

The Friedberg–Lee symmetry and minimal seesaw model

The Friedberg–Lee (FL) symmetry is generated by a transformation of a fermionic field q to q+ξz. This symmetry puts very restrictive constraints on allowed terms in a Lagrangian. Applying this symmetry to N fermionic fields, we find that the number of independent fields is reduced to N−1 if the fields have gauge interaction or the transformation is a local one. Using this property, we find that a seesaw model originally with three generations of left- and right-handed neutrinos, with the left-handed neutrinos unaffected but the right-handed neutrinos transformed under the local FL translation, is reduced to an effective theory of minimal seesaw which has only two right-handed neutrinos. The symmetry predicts that one of the light neutrino masses must be zero.     

Clustering Rules: A Comparison of Partitioning and Hierarchical Clustering Algorithms

Previous research has resulted in a number of different algorithms for rule discovery. Two approaches discussed here, the ‘all-rules’ algorithm and multi-objective metaheuristics, both result in the production of a large number of partial classification rules, or ‘nuggets’, for describing different subsets of the records in the class of interest. This paper describes the application of a number of different clustering algorithms to these rules, in order to identify similar rules and to better understand the data.     

Examples of non-conjugated holomorphic vector fields and foliations

We consider germs of holomorphic vector fields near the origin of with a saddle-node singularity, and the induced singular foliations. In a previous article we described the invariants addressing the analytical classification of these vector fields. They split into three parts: a formal, an orbital and a tangential component. For a fixed formal class, the orbital invariant (associated to the foliation) was obtained by Martinet and Ramis; we give it an integral representation. We then derive examples of non-orbitally conjugated foliations by the use of a “first-step” normal form, whose first-significative jet is an invariant. The tangential invariant also admits an integral representation, hence we derive explicit examples of vector fields, inducing the same foliation, that are not mutually conjugated. In addition, we provide a family of normal forms for vector fields orbitally equivalent to the model of Poincaré-Dulac.     

The GHS inequality and the Riemann hypothesis

LetV(t) be the even function on (–, ) which is related to the Riemann xi-function by (x/2)=4 _– exp(ixt–V(t))dt. In a proof of certain moment inequalities which are necessary for the validity of the Riemann Hypothesis, it was previously shown thatV'(t)/t is increasing on (0, ). We prove a stronger property which is related to the GHS inequality of statistical mechanics, namely thatV' is convex on [0, ). The possible relevance of the convexity ofV' to the Riemann Hypothesis is discussed.Communicated by Richard Varga.     

Gaining insight into student satisfaction using comprehensible data mining techniques

As a consequence of the heightened competition on the education market, the management of educational institutions often attempts to collect information on what drives student satisfaction by e.g. organizing large scale surveys amongst the student population. Until now, this source of potentially very valuable information remains largely untapped. In this study, we address this issue by investigating the applicability of different data mining techniques to identify the main drivers of student satisfaction in two business education institutions. In the end, the resulting models are to be used by the management to support the strategic decision making process. Hence, the aspect of model comprehensibility is considered to be at least equally important as model performance. It is found that data mining techniques are able to select a surprisingly small number of constructs that require attention in order to manage student satisfaction.     

Temperley-Lieb planar algebra modules arising from the ADE planar algebras

A Hilbert module over a planar algebra P is essentially a Hilbert module over a canonically defined algebra spanned by the annular tangles in P. It follows that any planar algebra Q containing P is a module over P, and in particular, any subfactor planar algebra is a module over the Temperley-Lieb planar algebra with the same modulus. We describe a positivity result that allows us to describe irreducible Temperley-Lieb planar algebra modules, and apply the result to decompose the planar algebras determined by the Coxeter graphs A_n (n?3), D_n (n?4), E₆, E₇, and E₈.