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In this paper, we derive a Riccati-type equation applicable to (sub-)static Einstein spaces and examine its various applications. Specifically, within the framework of conformally compactifiable manifolds, we prove a splitting theorem for the Riemannian universal covering. Furthermore, we demonstrate two distinct methods by which the Riccati equation can establish the connectivity of the conformal boundary under the static Einstein equation. Additionally, for compact static triples possessing positive scalar curvature, we establish the compactness of the universal covering., Comment: Lemma 1 and Theorem 3 were originally presented in a prior paper by S. Borghini and M. Fogagnolo. An explanation of the motivation behind Lemma 1 was added

Multiple cameras can provide comprehensive multi-view video coverage of a person. Fusing this multi-view data is crucial for tasks like behavioral analysis, although it traditionally requires camera calibration, a process that is often complex. Moreover, previous studies have overlooked the challenges posed by self-occlusion under multiple views and the continuity of human body shape estimation. In this study, we introduce a method to reconstruct the 3D human body from multiple uncalibrated camera views. Initially, we utilize a pre-trained human body encoder to process each camera view individually, enabling the reconstruction of human body models and parameters for each view along with predicted camera positions. Rather than merely averaging the models across views, we develop a neural network trained to assign weights to individual views for all human body joints, based on the estimated distribution of joint distances from each camera. Additionally, we focus on the mesh surface of the human body for dynamic fusion, allowing for the seamless integration of facial expressions and body shape into a unified human body model. Our method has shown excellent performance in reconstructing the human body on two public datasets, advancing beyond previous work from the SMPL model to the SMPL-X model. This extension incorporates more complex hand poses and facial expressions, enhancing the detail and accuracy of the reconstructions. Crucially, it supports the flexible ad-hoc deployment of any number of cameras, offering significant potential for various applications. Our code is available at https://github.com/AbsterZhu/MUC.

Mid-infrared semiconductor lasers in photonic integrated circuits are of considerable interest for a variety of industrial, environmental, and medical applications. However, photonic integration technologies in the mid-infrared lag far behind the near-infrared range. Here we present the monolithic integration of mid-infrared quantum cascade lasers with low-loss passive waveguides via butt-coupling. The passive waveguide losses are experimentally evaluated to be only 1.2 +- 0.3 dB/cm, with negligible butt-coupling losses. We demonstrate continuous-wave lasing at room temperature of these active-to-passive waveguide coupled devices. Moreover, we report a frequency comb operation paving the way toward on-chip, mid-infrared, dual-comb sensors.

Blind face restoration usually synthesizes degraded low-quality data with a pre-defined degradation model for training, while more complex cases could happen in the real world. This gap between the assumed and actual degradation hurts the restoration performance where artifacts are often observed in the output. However, it is expensive and infeasible to include every type of degradation to cover real-world cases in the training data. To tackle this robustness issue, we propose Diffusion-based Robust Degradation Remover (DR2) to first transform the degraded image to a coarse but degradation-invariant prediction, then employ an enhancement module to restore the coarse prediction to a high-quality image. By leveraging a well-performing denoising diffusion probabilistic model, our DR2 diffuses input images to a noisy status where various types of degradation give way to Gaussian noise, and then captures semantic information through iterative denoising steps. As a result, DR2 is robust against common degradation (e.g. blur, resize, noise and compression) and compatible with different designs of enhancement modules. Experiments in various settings show that our framework outperforms state-of-the-art methods on heavily degraded synthetic and real-world datasets., Comment: Accepted to CVPR 2023

For an asymptotically Poincare-Einstein manifold with a lower Ricci curvature bound, we establish a sharp inequality relating the type II Yamabe invariant of the interior and the Yamabe invariant of its conformal infinity

For a Poincare-Einstein manifold under certain restrictions, X. Chen, M. Lai and F. Wang proved a sharp inequality relating Yamabe invariants. We show that the inequality is true without any restriction.

Semiconductor lasers with ultra-low thresholds and minimal footprints are a topic of active research. Such devices require a combination of high quality factor laser cavities with small active region volumes, which drives the quest for novel cavity geometries exploiting nano-optic concepts. For high-reflectivity coated ridge lasers, where light is tightly confined in the waveguide, a low threshold can only be achieved by strongly reducing the diffraction losses arising at the laser facet. We show here that, somewhat counter-intuitively, opening a carefully designed aperture in a metallic facet coating can simultaneously enhance both its transmission and modal reflectivity by correcting the phase front at the subwavelength scale. Numerical simulations and experimental results demonstrate a reduction of optical mirror loss by up to 40% while the transmission is increased by four orders of magnitude. Applying this approach to both facets of a short cavity quantum cascade laser, we achieve laser operation at room temperature with an electrical dissipation of only 143 mW. Such light sources are especially suitable for portable and battery-operated chemical agent sensing applications operating in the mid-infrared wavelength range, where multiple greenhouse and pollutant gases have their fundamental absorption lines. Our work suggests possibilities for further applications including frequency comb dispersion engineering, and can be implemented in a broad range of optoelectronic systems., Comment: 8 pages, 3 figures