A new error analysis for parabolic Dirichlet boundary control problems

In this paper, we consider the finite element approximation to a parabolic Dirichlet boundary control problem and establish new a priori error estimates. In the temporal semi-discretization we apply the DG(0) method for the state and the variational discretization for the control, and obtain the convergence rates $O(k^{\frac{1}{4}})$ and $O(k^{\frac{3}{4}-\varepsilon})$ $(\varepsilon>0)$ for the control for problems posed on polytopes with $y_0\in L^2(\Omega)$, $y_d\in L^2(I;L^2(\Omega))$ and smooth domains with $y_0\in H^{\frac{1}{2}}(\Omega)$, $y_d\in L^2(I;H^1(\Omega))\cap H^{\frac{1}{2}}(I;L^2(\Omega))$, respectively. In the fully discretization of the optimal control problem posed on polytopal domains, we apply the DG(0)-CG(1) method for the state and the variational discretization approach for the control, and derive the convergence order $O(k^{\frac{1}{4}} +h^{\frac{1}{2}})$, which improves the known results by removing the mesh size condition $k=O(h^2)$ between the space mesh size $h$ and the time step $k$. As a byproduct, we obtain a priori error estimate $O(h+k^{1\over 2})$ for the fully discretization of parabolic equations with inhomogeneous Dirichlet data posed on polytopes, which also improves the known error estimate by removing the above mesh size condition

On the Pareto Front of Multilingual Neural Machine Translation

In this work, we study how the performance of a given direction changes with its sampling ratio in Multilingual Neural Machine Translation (MNMT). By training over 200 multilingual models with various model sizes, data sizes, and language directions, we find it interesting that the performance of certain translation direction does not always improve with the increase of its weight in the multi-task optimization objective. Accordingly, scalarization method leads to a multitask trade-off front that deviates from the traditional Pareto front when there exists data imbalance in the training corpus, which poses a great challenge to improve the overall performance of all directions. Based on our observations, we propose the Double Power Law to predict the unique performance trade-off front in MNMT, which is robust across various languages, data adequacy, and the number of tasks. Finally, we formulate the sample ratio selection problem in MNMT as an optimization problem based on the Double Power Law. In our experiments, it achieves better performance than temperature searching and gradient manipulation methods with only 1/5 to 1/2 of the total training budget. We release the code at https://github.com/pkunlp-icler/ParetoMNMT for reproduction.Comment: NeurIPS 202

Motion-aware Memory Network for Fast Video Salient Object Detection

Previous methods based on 3DCNN, convLSTM, or optical flow have achieved great success in video salient object detection (VSOD). However, they still suffer from high computational costs or poor quality of the generated saliency maps. To solve these problems, we design a space-time memory (STM)-based network, which extracts useful temporal information of the current frame from adjacent frames as the temporal branch of VSOD. Furthermore, previous methods only considered single-frame prediction without temporal association. As a result, the model may not focus on the temporal information sufficiently. Thus, we initially introduce object motion prediction between inter-frame into VSOD. Our model follows standard encoder--decoder architecture. In the encoding stage, we generate high-level temporal features by using high-level features from the current and its adjacent frames. This approach is more efficient than the optical flow-based methods. In the decoding stage, we propose an effective fusion strategy for spatial and temporal branches. The semantic information of the high-level features is used to fuse the object details in the low-level features, and then the spatiotemporal features are obtained step by step to reconstruct the saliency maps. Moreover, inspired by the boundary supervision commonly used in image salient object detection (ISOD), we design a motion-aware loss for predicting object boundary motion and simultaneously perform multitask learning for VSOD and object motion prediction, which can further facilitate the model to extract spatiotemporal features accurately and maintain the object integrity. Extensive experiments on several datasets demonstrated the effectiveness of our method and can achieve state-of-the-art metrics on some datasets. The proposed model does not require optical flow or other preprocessing, and can reach a speed of nearly 100 FPS during inference.Comment: 12 pages, 10 figure

Evaluation of five satellite top-of-atmosphere albedo products over land

Five satellite top-of-atmosphere (TOA) albedo products over land were evaluated in this study including global products from the Advanced Very High Resolution Radiometer (AVHRR) (TAL-AVHRR), Moderate Resolution Imaging Spectroradiometer (MODIS) (TAL-MODIS), and Clouds and the Earth’s Radiant Energy System (CERES); one regional product from the Climate Monitoring Satellite Application Facility (CM SAF); and one harmonized product termed Diagnosing Earth’s Energy Pathways in the Climate system (DEEP-C). Results showed that overall, there is good consistency among these five products, particularly after the year 2000. The differences among these products in the high-latitude regions were relatively larger. The percentage differences among TAL-AVHRR, TAL-MODIS, and CERES were generally less than 20%, while the differences between TAL-AVHRR and DEEP-C before 2000 were much larger. Except for the obvious decrease in the differences after 2000, the differences did not show significant changes over time, but varied among different regions. The differences between TAL-AVHRR and the other products were relatively large in the high-latitude regions of North America, Asia, and the Maritime Continent, while the differences between DEEP-C and CM SAF in Europe and Africa were smaller. Interannual variability was consistent between products after 2000, before which the differences among the three products were much larger

The effects of grain structure on electromigration failure of the lead-free solder bump

This paper carries out an electromigration (EM) acceleration test on ball grid array (BGA) samples with Sn96.5/Ag3.0/Cu0.5 solder bumps under constant temperature, and characterizes the structure of β-Sn grains in the lead-free solder bumps. The EM failure modes of the solder bumps of different grain structures were analysed, aiming to disclose the effect of grain structure on the EM failure. Considering the driving forces of the EM (i.e. electron wind force, stress gradient, temperature gradient and atomic density gradient), the atomic density integral (ADI) method was introduced to simulate the void formation and failure lifetime of the EM. The simulation results show that solder bump reliability and failure mode are greatly affected by grain orientation, in that the EM failure occurs rapidly when the c-axis of grain structure of the solder bump is strongly misaligned, or almost perpendicular, to the current direction. The double grain solder bump with grain boundary parallel to current direction boasts a small EM failure and thus a long lifetime

Efficient purification and assembly of ribonucleoprotein complex for interaction analysis by MST assay coupled with GaMD simulations

Here, we describe a generic protocol for monitoring protein-RNA interaction using a cleavable GFP fusion of a recombinant RNA-binding protein. We detail each expression and purification step, including high salt and heparin column for contaminant RNA removal. After the assembly of RNA into the ribonucleoprotein complex, the MicroScale Thermophoresis assay enables the binding affinity to be obtained quickly with a small amount of sample. Further Gaussian accelerated molecular dynamics simulations allow us to analyze protein:RNA interactions in detail

1-[(2,3,4,5,6-Penta­fluoro­phen­yl)ethyn­yl]ferrocene

The mol­ecular structure of the title compound, [Fe(C5H5)(C13H4F5)], consists of a ferrocenyl group and a 2,3,4,5,6-penta­fluoro­benzene group linked through an ethyne spacer. The crystal packing is dominated by inter­molecular C—H⋯F hydrogen bonds, C—F⋯π inter­actions between the penta­fluoro­benzene groups [F⋯centroid distances = 3.882 (2) and 3.884 (2) Å] and π–π inter­actions between the penta­fluoro­benzene and cyclo­penta­dienyl rings [centroid–centroid distance = 3.741 (1) Å]

A Triple-Network Dynamic Connection Study in Alzheimer's Disease

© 2022 Meng, Wu, Liang, Zhang, Xu, Yang and Meng. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY). https://creativecommons.org/licenses/by/4.0/Alzheimer's disease (AD) was associated with abnormal organization and function of large-scale brain networks. We applied group independent component analysis (Group ICA) to construct the triple-network consisting of the saliency network (SN), the central executive network (CEN), and the default mode network (DMN) in 25 AD, 60 mild cognitive impairment (MCI) and 60 cognitively normal (CN) subjects. To explore the dynamic functional network connectivity (dFNC), we investigated dynamic time-varying triple-network interactions in subjects using Group ICA analysis based on k-means clustering (GDA-k-means). The mean of brain state-specific network interaction indices (meanNII) in the three groups (AD, MCI, CN) showed significant differences by ANOVA analysis. To verify the robustness of the findings, a support vector machine (SVM) was taken meanNII, gender and age as features to classify. This method obtained accuracy values of 95, 94, and 77% when classifying AD vs. CN, AD vs. MCI, and MCI vs. CN, respectively. In our work, the findings demonstrated that the dynamic characteristics of functional interactions of the triple-networks contributed to studying the underlying pathophysiology of AD. It provided strong evidence for dysregulation of brain dynamics of AD.Peer reviewedFinal Published versio