Linear Convergence of Adaptively Iterative Thresholding Algorithms for Compressed Sensing

This paper studies the convergence of the adaptively iterative thresholding (AIT) algorithm for compressed sensing. We first introduce a generalized restricted isometry property (gRIP). Then we prove that the AIT algorithm converges to the original sparse solution at a linear rate under a certain gRIP condition in the noise free case. While in the noisy case, its convergence rate is also linear until attaining a certain error bound. Moreover, as by-products, we also provide some sufficient conditions for the convergence of the AIT algorithm based on the two well-known properties, i.e., the coherence property and the restricted isometry property (RIP), respectively. It should be pointed out that such two properties are special cases of gRIP. The solid improvements on the theoretical results are demonstrated and compared with the known results. Finally, we provide a series of simulations to verify the correctness of the theoretical assertions as well as the effectiveness of the AIT algorithm.Comment: 15 pages, 5 figure

Gas kinematics and star formation in the filamentary molecular cloud G47.06+0.26

We performed a multi-wavelength study toward the filamentary cloud G47.06+0.26 to investigate the gas kinematics and star formation. We present the 12CO (J=1-0), 13CO (J=1-0) and C18O (J=1-0) observations of G47.06+0.26 obtained with the Purple Mountain Observation (PMO) 13.7 m radio telescope to investigate the detailed kinematics of the filament. The 12CO (J=1-0) and 13CO (J=1-0) emission of G47.06+0.26 appear to show a filamentary structure. The filament extends about 45 arcmin (58.1 pc) along the east-west direction. The mean width is about 6.8 pc, as traced by the 13CO (J=1-0) emission. G47.06+0.26 has a linear mass density of about 361.5 Msun/pc. The external pressure (due to neighboring bubbles and H II regions) may help preventing the filament from dispersing under the effects of turbulence. From the velocity-field map, we discern a velocity gradient perpendicular to G47.06+0.26. From the Bolocam Galactic Plane Survey (BGPS) catalog, we found nine BGPS sources in G47.06+0.26, that appear to these sources have sufficient mass to form massive stars. We obtained that the clump formation efficiency (CFE) is about 18% in the filament. Four infrared bubbles were found to be located in, and adjacent to, G47.06+0.26. Particularly, infrared bubble N98 shows a cometary structure. CO molecular gas adjacent to N98 also shows a very intense emission. H II regions associated with infrared bubbles can inject the energy to surrounding gas. We calculated the kinetic energy, ionization energy, and thermal energy of two H II regions in G47.06+0.26. From the GLIMPSE I catalog, we selected some Class I sources with an age of about 100000 yr, which are clustered along the filament. The feedback from the H II regions may cause the formation of a new generation of stars in filament G47.06+0.26.Comment: 10 pages, 11 figures, accepted for publication in A&

Multi-Task Pruning for Semantic Segmentation Networks

This paper focuses on channel pruning for semantic segmentation networks. There are a large number of works to compress and accelerate deep neural networks in the classification task (e.g., ResNet-50 on ImageNet), but they cannot be straightforwardly applied to the semantic segmentation network that involves an implicit multi-task learning problem. To boost the segmentation performance, the backbone of semantic segmentation network is often pre-trained on a large scale classification dataset (e.g., ImageNet), and then optimized on the desired segmentation dataset. Hence to identify the redundancy in segmentation networks, we present a multi-task channel pruning approach. The importance of each convolution filter w.r.t the channel of an arbitrary layer will be simultaneously determined by the classification and segmentation tasks. In addition, we develop an alternative scheme for optimizing importance scores of filters in the entire network. Experimental results on several benchmarks illustrate the superiority of the proposed algorithm over the state-of-the-art pruning methods. Notably, we can obtain an about $2\times$ FLOPs reduction on DeepLabv3 with only an about $1\%$ mIoU drop on the PASCAL VOC 2012 dataset and an about $1.3\%$ mIoU drop on Cityscapes dataset, respectively

Nucleophile Promoted Gold Redox Catalysis with diazonium: CBr, C-S and C-P Bond Formation through Catalytic Sandmeyer Coupling

Gold-catalyzed C-heteroatom (C-X) coupling reactions are evaluated without using sacrificial oxidants. Vital to the success of this methodology is the nucleophile-assisted activation of aryldiazonium salts, which could be an effective oxidant to convert Au(I) to Au(III) even without the addition of assisting ligand or photocatalyst. By accelerating reaction kinetics to outcompete C-C homo-coupling or diazonium dediazoniation, gold-catalyzed Sandmeyer reactions were achieved with different nucleophiles, forming C-Br, C-S and C-P bonds in high yields and selectivity