Superconvergent postprocessing of C0C^0 interior penalty method

This paper focuses on the superconvergence analysis of the Hessian recovery technique for the $C^0$ Interior Penalty Method (C0IP) in solving the biharmonic equation. We establish interior error estimates for C0IP method that serve as the superconvergent analysis tool. Using the argument of superconvergence by difference quotient, we prove superconvergent results of the recovered Hessian matrix on translation-invariant meshes. The Hessian recovery technique enables us to construct an asymptotically exact ${\it a\, posteriori}$ error estimator for the C0IP method. Numerical experiments are provided to support our theoretical results

Exploiting Visual Semantic Reasoning for Video-Text Retrieval

Video retrieval is a challenging research topic bridging the vision and language areas and has attracted broad attention in recent years. Previous works have been devoted to representing videos by directly encoding from frame-level features. In fact, videos consist of various and abundant semantic relations to which existing methods pay less attention. To address this issue, we propose a Visual Semantic Enhanced Reasoning Network (ViSERN) to exploit reasoning between frame regions. Specifically, we consider frame regions as vertices and construct a fully-connected semantic correlation graph. Then, we perform reasoning by novel random walk rule-based graph convolutional networks to generate region features involved with semantic relations. With the benefit of reasoning, semantic interactions between regions are considered, while the impact of redundancy is suppressed. Finally, the region features are aggregated to form frame-level features for further encoding to measure video-text similarity. Extensive experiments on two public benchmark datasets validate the effectiveness of our method by achieving state-of-the-art performance due to the powerful semantic reasoning.Comment: Accepted by IJCAI 2020. SOLE copyright holder is IJCAI (International Joint Conferences on Artificial Intelligence), all rights reserved. http://static.ijcai.org/2020-accepted_papers.htm

Unfitted finite element method for the quad-curl interface problem

In this paper, we introduce a novel unfitted finite element method to solve the quad-curl interface problem. We adapt Nitsche's method for curlcurl-conforming elements and double the degrees of freedom on interface elements. To ensure stability, we incorporate ghost penalty terms and a discrete divergence-free term. We establish the well-posedness of our method and demonstrate an optimal error bound in the discrete energy norm. We also analyze the stiffness matrix's condition number. Our numerical tests back up our theory on convergence rates and condition numbers

Manifold Path Guiding for Importance Sampling Specular Chains

Complex visual effects such as caustics are often produced by light paths containing multiple consecutive specular vertices (dubbed specular chains), which pose a challenge to unbiased estimation in Monte Carlo rendering. In this work, we study the light transport behavior within a sub-path that is comprised of a specular chain and two non-specular separators. We show that the specular manifolds formed by all the sub-paths could be exploited to provide coherence among sub-paths. By reconstructing continuous energy distributions from historical and coherent sub-paths, seed chains can be generated in the context of importance sampling and converge to admissible chains through manifold walks. We verify that importance sampling the seed chain in the continuous space reaches the goal of importance sampling the discrete admissible specular chain. Based on these observations and theoretical analyses, a progressive pipeline, manifold path guiding, is designed and implemented to importance sample challenging paths featuring long specular chains. To our best knowledge, this is the first general framework for importance sampling discrete specular chains in regular Monte Carlo rendering. Extensive experiments demonstrate that our method outperforms state-of-the-art unbiased solutions with up to 40x variance reduction, especially in typical scenes containing long specular chains and complex visibility.Comment: 14 pages, 19 figure

Shapes of distal tibiofibular syndesmosis are associated with risk of recurrent lateral ankle sprains

Distal tibiofibular syndesmosis (DTS) has wide anatomic variability in depth of incisura fibularis and shape of tibial tubercles. We designed a 3-year prospective cohort study of 300 young physical training soldiers in an Army Physical Fitness School. Ankle computed tomography (CT) scans showed that 56% of the incisura fibularis were a "C" shape, 25% were a "1" shape, and 19% were a "Gamma"shape. Furthermore, we invited a randomly selected subcohort of 6 participants in each shape of DTS to undergo a three-dimensional (3D) laser scanning. The "1" shape group showed widest displacement range of the DTS in the y-axis, along with the range of motion (ROM) on the position more than 20 degrees of the ankle dorsiflexion, inversion and eversion. During the 3-year study period, 23 participants experienced recurrent lateral ankle sprains. 7 cases of the incisura fibularis were "C" shape, 13 cases were "1" shape, and 3 cases were "Gamma"shape. The "1" shape showed highest risk among the three shapes in incident recurrent lateral ankle sprains. We propose that it is possible to classify shapes of DTS according to the shapes of incisura fibularis, and people with "1" shape may have more risk of recurrent lateral ankle sprains