By slicing the region of the response (Li, 1991, SIR) and applying local kernel regression (Xia et al., 2002, MAVE) to each slice, a new dimension reduction method is proposed. Compared with the traditional inverse regression methods, e.g. sliced inverse regression (Li, 1991), the new method is free of the linearity condition (Li, 1991) and enjoys much improved estimation accuracy. Compared with the direct estimation methods (e.g., MAVE), the new method is much more robust against extreme values and can capture the entire central subspace (Cook, 1998b, CS) exhaustively. To determine the CS dimension, a consistent crossvalidation (CV) criterion is developed. Extensive numerical studies including one real example confirm our theoretical findings.

No abstract

A two‐faced synthesis: Biphasic grafting at a Pickering emulsion interface leads to the formation of Janus colloids (see scheme; ATRP: atom transfer radical polymerization), which form Janus composite colloids by the preferential growth of desired materials in specific regions of the original colloids. This approach is general and can be extended to the synthesis of a huge family of such colloids.

In this paper we propose a dimension reduction method for estimating the directions in a multiple-index regression based on information extraction. This extends the recent work of Yin and Cook [X. Yin, R.D. Cook, Direction estimation in single-index regression, Biometrika 92 (2005) 371-384] who introduced the method and used it to estimate the direction in a single-index regression. While a formal extension seems conceptually straightforward, there is a fundamentally new aspect of our extension: We are able to show that, under the assumption of elliptical predictors, the estimation of multiple-index regressions can be decomposed into successive single-index estimation problems. This significantly reduces the computational complexity, because the nonparametric procedure involves only a one-dimensional search at each stage. In addition, we developed a permutation test to assist in estimating the dimension of a multiple-index regression.

We report a Johnson hexadecahedronal coordination cage, constructed via 10 Ni4-p-tert-butylthiacalix[4]arene (Ni4-TC4A) units as vertices and 16 5-(pyridin-4-yl)isophthalate (PIP) ligands as tiles. It features a gyroelongated square bipyramidal geometry, equivalent to two square pyramids pillared by a square antiprism, a J17 Johnson solid. Remarkably, the cage compound exhibits a much higher uptake capacity of C3H8 than CH4, representing a promising material for separation of these two gases. In contrast, Co4-TC4A units are linked by PIP ligands and rare {Co4O4Cl2} clusters, providing a one-dimensional bamboo stick-like polymer.