Browsing by Author "Wang, Tao"

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    Bernstein Polynomial Model for Nonparametric Multivariate Density
    (Taylor and Francis, 2019) Wang, Tao; Guan, Zhong
    In this paper, we study the Bernstein polynomial model for estimating the multivariate distribution functions and densities with bounded support. As a mixture model of multivariate beta distributions, the maximum (approximate) likelihood estimate can be obtained using EM algorithm. A change-point method of choosing optimal degrees of the proposed Bernstein polynomial model is presented. Under some conditions, the optimal rate of convergence in the mean -divergence of new density estimator is shown to be nearly parametric. The method is illustrated by an application to a real data set. Finite sample performance of the proposed method is also investigated by simulation study and is shown to be much better than the kernel density estimate but close to the parametric ones. Keywords: Approximate Bernstein polynomial model; beta mixture; maximum likelihood; multivariate density estimation; nonparametric model
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    Reaction selectivity of homochiral versus heterochiral intermolecular reactions of prochiral terminal alkynes on surfaces
    (Nature Communications, 2019) Wang, Tao; Huang, Jianmin; Feng, Lin; Zhang, Wenzhao; Han, Dong; Xu, Qian; Zhu, Junfa; Lv, Haifeng; Shan, Huan; Mao, Yahui; Wang, Jinyi; Du, Pingwu; Zhao, Aidi; Wu, Xiaojun; Tait, Steven
    Controlling selectivity between homochiral and heterochiral reaction pathways on surfaces remains a great challenge. Here, competing reactions of a prochiral alkyne on Ag(111): two-dimensional (2D) homochiral Glaser coupling and heterochiral cross-coupling with a Bergman cyclization step have been examined. We demonstrate control strategies in steering the reactions between the homochiral and heterochiral pathways by tuning the precursor substituents and the kinetic parameters, as confirmed by high-resolution scanning probe microscopy (SPM). Control experiments and density functional theory (DFT) calculations reveal that the template effect of organometallic chains obtained under specific kinetic conditions enhances Glaser coupling between homochiral molecules. In contrast, for the reaction of free monomers, the kinetically favorable reaction pathway is the cross-coupling between two heterochiral molecules (one of them involving cyclization). This work demonstrates the application of kinetic control to steer chiral organic coupling pathways at surfaces.