Binscatter is very popular in applied microeconomics. It provides a flexible, yet parsimonious way of visualizing and summarizing large data sets in regression settings, and it is often used for informal evaluation of substantive hypotheses such as linearity or monotonicity of the regression function. This paper presents a foundational, thorough analysis of binscatter: we give an array of theoretical and practical results that aid both in understanding current practices (i.e., their validity or lack thereof) and in offering theory-based guidance for future applications. Our main results include principled number of bins selection, confidence intervals and bands, hypothesis tests for parametric and shape restrictions of the regression function, and several other new methods, applicable to canonical binscatter as well as higher-order polynomial, covariateadjusted and smoothness-restricted extensions thereof. In particular, we highlight important methodological problems related to covariate adjustment methods used in current practice. We also discuss extensions to clustered data. Our results are illustrated with simulated and real data throughout. Companion general-purpose software packages for Stata and R are provided. Finally, from a technical perspective, new theoretical results for partitioning-based series estimation are obtained that may be of independent interest. AbstractThis supplement collects all technical proofs, more general theoretical results than those reported in the main paper, and other methodological and numerical results. New theoretical results for partitioning-based series estimation are obtained that may be of independent interest. See also Stata and R companion software available at https://sites.google.com/site/nppackages/binsreg/ where replication files are also provided.

Dislocations are commonly present and important in metals but their effects have not been fully recognized in oxide ceramics. The large strain energy raised by the rigid ionic/covalent bonding in oxide ceramics leads to dislocations with low density (∼106 mm−2), thermodynamic instability and spatial inhomogeneity. In this paper, we report ultrahigh density (∼109 mm−2) of edge dislocations that are uniformly distributed in oxide ceramics with large compositional complexity. We demonstrate the dislocations are progressively and thermodynamically stabilized with increasing complexity of the composition, in which the entropy gain can compensate the strain energy of dislocations. We also find cracks are deflected and bridged with ∼70% enhancement of fracture toughness in the pyrochlore ceramics with multiple valence cations, due to the interaction with enlarged strain field around the immobile dislocations. This research provides a controllable approach to establish ultra-dense dislocations in oxide ceramics, which may open up another dimension to tune their properties.

Ceria (CeO 2 ) nanotube arrays with precisely defined size and density were directly synthesized on glass and cordierite substrates using a ZnO nanorods-assisted hydrothermal method. Eliminating the procedures of template removal and film coating, the one-step synthesis approach could greatly broaden the applications for materials with tubular structures. The proper concentration of cerium nitrate precursor solution acts a vital role to adjust the instantaneous precipitation of CeO 2 and dissolution of ZnO templates. The as-prepared CeO 2 tube arrays were characterized by scanning electron microscopy (SEM), transmission electron microscopy (TEM) and powder X-ray diffraction (XRD) techniques, which reveal a regular tubular structure with the average diameter of 500 nm and length of 3 mm. The automotive exhaust catalytic performance of CeO 2 tube arrays prepared on the cordierite was evaluated. Compared with the ceria nanoparticles film, the target CeO 2 tubes exhibit improved catalytic activities at a low start-up temperature for oxycarbide and hydrocarbon. Furthermore, the palladium-decorated CeO 2 tubes exhibit a higher catalytic activity for the degradation of oxynitride than that of palladium/ceria particles/cordierite.

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With the introduction of poly ethylene glycol (PEG) (10000), relatively well dispersed and oriented ZnO microrod arrays and ZnO microsphere arrays were successfully synthesized on unmodified indium tin oxide (ITO) substrate by a hydrothermal method. The growth behaviors of the two different kinds of ZnO arrays were experimentally investigated with variations of PEG addition and the precursor solution’s concentration. The PEG-assisted growth mechanism of ZnO microrod arrays and ZnO microsphere arrays has also been carefully discussed. Both the dissolved state of PEG and the interaction between PEG and ZnO crystalline grains were found to play important roles in the fabrication of the two different ZnO structure arrays. The research on PEG-assisted growth mechanism for these two kinds of ZnO structure arrays will provide more theoretical references for preparations of ZnO one-dimensional rod arrays and other kinds of assembled structures on the substrate.