Gradient Estimates For The CR Heat Equation On Complete noncompact Pseudo-Hermitian Manifolds

In this paper, we derive local and global Li-Yau type gradient estimates for the positive solutions of the CR heat equation on complete noncompact pseudo-Hermitian manifolds. As applications of the gradient estimates, we give a Harnack inequality for positive solutions of the CR heat equation, and then obtain an upper bound estimate for the corresponding heat kernel.Comment: All comments welcome

Better Sparsifiers for Directed Eulerian Graphs

Spectral sparsification for directed Eulerian graphs is a key component in the design of fast algorithms for solving directed Laplacian linear systems. Directed Laplacian linear system solvers are crucial algorithmic primitives to fast computation of fundamental problems on random walks, such as computing stationary distribution, hitting and commute time, and personalized PageRank vectors. While spectral sparsification is well understood for undirected graphs and it is known that for every graph $G,$ $(1+\varepsilon)$-sparsifiers with $O(n\varepsilon^{-2})$ edges exist [Batson-Spielman-Srivastava, STOC '09] (which is optimal), the best known constructions of Eulerian sparsifiers require $\Omega(n\varepsilon^{-2}\log^4 n)$ edges and are based on short-cycle decompositions [Chu et al., FOCS '18]. In this paper, we give improved constructions of Eulerian sparsifiers, specifically: 1. We show that for every directed Eulerian graph $\vec{G},$ there exist an Eulerian sparsifier with $O(n\varepsilon^{-2} \log^2 n \log^2\log n + n\varepsilon^{-4/3}\log^{8/3} n)$ edges. This result is based on combining short-cycle decompositions [Chu-Gao-Peng-Sachdeva-Sawlani-Wang, FOCS '18, SICOMP] and [Parter-Yogev, ICALP '19], with recent progress on the matrix Spencer conjecture [Bansal-Meka-Jiang, STOC '23]. 2. We give an improved analysis of the constructions based on short-cycle decompositions, giving an $m^{1+\delta}$-time algorithm for any constant $\delta > 0$ for constructing Eulerian sparsifiers with $O(n\varepsilon^{-2}\log^3 n)$ edges

Circular Accessible Depth: A Robust Traversability Representation for UGV Navigation

In this paper, we present the Circular Accessible Depth (CAD), a robust traversability representation for an unmanned ground vehicle (UGV) to learn traversability in various scenarios containing irregular obstacles. To predict CAD, we propose a neural network, namely CADNet, with an attention-based multi-frame point cloud fusion module, Stability-Attention Module (SAM), to encode the spatial features from point clouds captured by LiDAR. CAD is designed based on the polar coordinate system and focuses on predicting the border of traversable area. Since it encodes the spatial information of the surrounding environment, which enables a semi-supervised learning for the CADNet, and thus desirably avoids annotating a large amount of data. Extensive experiments demonstrate that CAD outperforms baselines in terms of robustness and precision. We also implement our method on a real UGV and show that it performs well in real-world scenarios.Comment: 13 pages, 8 figure

A snoRNA modulates mRNA 3' end processing and regulates the expression of a subset of mRNAs.

mRNA 3' end processing is an essential step in gene expression. It is well established that canonical eukaryotic pre-mRNA 3' processing is carried out within a macromolecular machinery consisting of dozens of trans-acting proteins. However, it is unknown whether RNAs play any role in this process. Unexpectedly, we found that a subset of small nucleolar RNAs (snoRNAs) are associated with the mammalian mRNA 3' processing complex. These snoRNAs primarily interact with Fip1, a component of cleavage and polyadenylation specificity factor (CPSF). We have functionally characterized one of these snoRNAs and our results demonstrated that the U/A-rich SNORD50A inhibits mRNA 3' processing by blocking the Fip1-poly(A) site (PAS) interaction. Consistently, SNORD50A depletion altered the Fip1-RNA interaction landscape and changed the alternative polyadenylation (APA) profiles and/or transcript levels of a subset of genes. Taken together, our data revealed a novel function for snoRNAs and provided the first evidence that non-coding RNAs may play an important role in regulating mRNA 3' processing

Numerical simulation of creep fracture evolution in fractured rock masses

The initiation, expansion, and penetration of microscopic cracks in rock is the macroscopic manifestation of creep. This paper investigates mechanical creep characteristics and fracture evolution processes in rock masses with different fracture angles, lengths, and rock bridge dip angles. Single fractures, dual parallel fractures, and fracture groups are considered. The approach comprises discrete element simulation based on continuum mechanics, utilizing the continuous and discontinuous software, GDEM. Single-fracture rock masses are characterized by a progressive fracture development mode dominated by tensile shear failure. The rate of creep and fracture magnitude both increase according to fracture length. With increasing fracture inclination angle, creep rate and fracture magnitude increase and decrease. The creep rate and degree of rupture are highest for fractures inclined at 30°. The dual-fracture rock mass exhibits both tensile crack failure and compressional shear failure. Creep rates are highest, and rupture effects are most apparent at rock bridge inclination angles of 90°. If the rock bridge is too long or too short, the stable creep stage is prolonged, but the creep acceleration stage intensifies due to interaction between fracture-bounded rock masses. The failure mode, in this case, involves collective failure by tension fractures and compressional shear. Creep rate and fracture magnitude increase with the number of fractures, which accelerates rock mass deformation to a certain extent. However, when the number of fractures reaches a certain threshold, a relatively stable structure may become established, slowing down the creep rate, especially during the creep acceleration stage. This study can provide a theoretical basis and reference for investigating the creep rupture law of rock mass engineering and the prevention and control of fractured rock mass geological disasters

Shock control of a low-sweep transonic laminar flow wing

This paper presents a combined experimental and computational study of a low-sweep transonic natural laminar flow (NLF) wing with shock-control bumps (SCBs). A transonic NLF wing with a relatively low sweep angle of 20 deg was chosen for this study. To avoid the complexity of the flow introduced by perforated/slotted walls commonly used for transonic wind-tunnel tests for reducing the wall interference, both experimental tests and computational simulations were conducted with solid wind-tunnel wall conditions. This allows for like-to-like validation of the computational simulation. Optimization of the shock-control bumps was first conducted to design the wind-tunnel test model with bumps. Two critical parameters of the three-dimensional SCBs for shock control (i.e., bump crest position and bump height) were optimized in terms of total drag reduction at the given design point in the wind tunnel. We show that the strong shock wave on the low-sweep NLF wing can be effective controlled by well-designed SCBs deployed along the wing span. The optimized SCBs result in 18.5% pressure drag reduction with 5% viscous drag penalty, and the SCBs also bring some benefits at off-design conditions. The wind-tunnel tests include pressure measurement, particle image velocimetry, and temperature-sensitive paint to provide detailed insight into the shock-control flowfield and to validate the computational simulations. Comparisons include surface pressure profile, velocity distribution, and transition location

Aggregation-Induced Emission Luminogens for Direct Exfoliation of 2D Layered Materials in Ethanol

© 2020 Wiley-VCH GmbH Aggregation-induced emission (AIE) luminogens are an important type of advanced functional materials with fantastic optical properties and have found potential applications in organic electronics, biochemistry, and molecular imaging. Herein, this article presents a novel application of AIE luminogens (AIEgens) for efficient exfoliation of layered transition metal dichalcogenides (TMDs, such as MoS2 and WSe2). From the 1H NMR spectroscopic analysis, the designed AIEgens can insert into the space between layers of MoS2 in ethanol solution and the dynamic molecular rotation against the weak interactions affords large-scale few-layer MoS2 nanosheets (7–8 layers) with enhanced smoothness. The 3D AIEgens play a significant role in preserving the crystal lattice of MoS2 even at high pressure (>15 GPa). More importantly, the new approach can also be used for exfoliation of WSe2 to achieve large-scale few-layer nanosheets. The present work thus provides a facile and high yielding synthetic method for accessing on a large scale 2D layered materials with enhanced properties for high-technology applications

Loss of endothelial hypoxia inducible factor-prolyl hydroxylase 2 induces cardiac hypertrophy and fibrosis

BACKGROUND: Cardiac hypertrophy and fibrosis are common adaptive responses to injury and stress, eventually leading to heart failure. Hypoxia signaling is important to the (patho)physiological process of cardiac remodeling. However, the role of endothelial PHD2 (prolyl-4 hydroxylase 2)/hypoxia inducible factor (HIF) signaling in the pathogenesis of cardiac hypertrophy and heart failure remains elusive. METHODS AND RESULTS: Mice with Egln1Tie2Cre (Tie2-Cre-mediated deletion of Egln1 [encoding PHD2]) exhibited left ventricular hypertrophy evident by increased thickness of anterior and posterior wall and left ventricular mass, as well as cardiac fibrosis. Tamoxifen-induced endothelial Egln1 deletion in adult mice also induced left ventricular hypertrophy and fibrosis. Additionally, we observed a marked decrease of PHD2 expression in heart tissues and cardiovascular endothelial cells from patients with cardiomyopathy. Moreover, genetic ablation of Hif2a but not Hif1a in Egln1Tie2Cre mice normalized cardiac size and function. RNA sequencing analysis also demonstrated HIF-2α as a critical mediator of signaling related to cardiac hypertrophy and fibrosis. Pharmacological inhibition of HIF-2α attenuated cardiac hypertrophy and fibrosis in Egln1Tie2Cre mice. CONCLUSIONS: The present study defines for the first time an unexpected role of endothelial PHD2 deficiency in inducing cardiac hypertrophy and fibrosis in an HIF-2α– dependent manner. PHD2 was markedly decreased in cardiovascular endothelial cells in patients with cardiomyopathy. Thus, targeting PHD2/HIF-2α signaling may represent a novel therapeutic approach for the treatment of pathological cardiac hypertrophy and failure

Simultaneous heat and water recovery from flue gas by membrane condensation: experimental investigation

A tubular ceramic membrane is investigated as the condenser for simultaneous heat and water recovery from flue gas. The effects of the operational parameters, such as fluid (gas and water) flow rates, temperatures of flue gas and coolant water, and flue gas humidity on the process performance in terms of mass and heat transfer across the membrane are studied. Particularly, the overall heat transfer coefficient is also evaluated. As the gas flow rate increases, water and heat transfer efficiencies and recoveries decline due to the reduced residence time. Increasing the water flow rate or lowing the coolant temperature can effectively improve mass and heat transfer efficiencies and recoveries. Increasing the temperature of the inlet gas can enhance water and heat fluxes and recoveries, but does not improve the overall heat transfer efficiency. The rise in flue gas humidity can dramatically improve water and heat transfer rates and the overall heat transfer coefficient, but has little effect on water and heat recoveries. These results offer a general guideline in optimising the operational parameters in low-grade heat recovery with membrane heat exchangers, and it may greatly advance the development of membrane condensation technology for practical low-grade heat recovery