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  1. We study how to optimize the latent space of neural shape generators that map latent codes to 3D deformable shapes. The key focus is to look at a deformable shape generator from a differential geometry perspective. We define a Riemannian metric based on as-rigid-as-possible and as-conformal-as-possible deformation energies. Under this metric, we study two desired properties of the latent space: 1) straight-line interpolations in latent codes follow geodesic curves; 2) latent codes disentangle pose and shape variations at different scales. Strictly enforcing the geometric interpolation property, however, only applies if the metric matrix is a constant. We show how to achieve this property approximately by enforcing that geodesic interpolations are axis-aligned, i.e., interpolations along coordinate axis follow geodesic curves. In addition, we introduce a novel approach that decouples pose and shape variations via generalized eigendecomposition. We also study efficient regularization terms for learning deformable shape generators, e.g., that promote smooth interpolations. Experimental results on benchmark datasets show that our approach leads to interpretable latent codes, improves the generalizability of synthetic shapes, and enhances performance in geodesic interpolation and geodesic shooting.

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    Free, publicly-accessible full text available December 5, 2024
  2. Abstract

    Site‐selective and partial decoration of supported metal nanoparticles (NPs) with transition metal oxides (e.g., FeOx) can remarkably improve its catalytic performance and maintain the functions of the carrier. However, it is challenging to selectively deposit transition metal oxides on the metal NPs embedded in the mesopores of supporting matrix through conventional deposition method. Herein, a restricted in situ site‐selective modification strategy utilizing poly(ethylene oxide)‐block‐polystyrene (PEO‐b‐PS) micellar nanoreactors is proposed to overcome such an obstacle. The PEO shell of PEO‐b‐PS micelles interacts with the hydrolyzed tungsten salts and silica precursors, while the hydrophobic organoplatinum complex and ferrocene are confined in the hydrophobic PS core. The thermal treatment leads to mesoporous SiO2/WO3‐xframework, and meanwhile FeOxnanolayers are in situ partially deposited on the supported Pt NPs due to the strong metal‐support interaction between FeOxand Pt. The selective modification of Pt NPs with FeOxmakes the Pt NPs present an electron‐deficient state, which promotes the mobility of CO and activates the oxidation of CO. Therefore, mesoporous SiO2/WO3‐x‐FeOx/Pt based gas sensors show a high sensitivity (31 ± 2 in 50 ppm of CO), excellent selectivity, and fast response time (3.6 s to 25 ppm) to CO gas at low operating temperature (66 °C, 74% relative humidity).

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