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

Personalized Federated Learning via ADMM with Moreau Envelope

Personalized federated learning (PFL) is an approach proposed to address the issue of poor convergence on heterogeneous data. However, most existing PFL frameworks require strong assumptions for convergence. In this paper, we propose an alternating direction method of multipliers (ADMM) for training PFL models with Moreau envelope (FLAME), which achieves a sublinear convergence rate, relying on the relatively weak assumption of gradient Lipschitz continuity. Moreover, due to the gradient-free nature of ADMM, FLAME alleviates the need for hyperparameter tuning, particularly in avoiding the adjustment of the learning rate when training the global model. In addition, we propose a biased client selection strategy to expedite the convergence of training of PFL models. Our theoretical analysis establishes the global convergence under both unbiased and biased client selection strategies. Our experiments validate that FLAME, when trained on heterogeneous data, outperforms state-of-the-art methods in terms of model performance. Regarding communication efficiency, it exhibits an average speedup of 3.75x compared to the baselines. Furthermore, experimental results validate that the biased client selection strategy speeds up the convergence of both personalized and global models.Comment: 15 page

The Role of Weight on Community Structure of Networks

The role of weight on the weighted networks is investigated by studying the effect of weight on community structures. We use weighted modularity $Q^w$ to evaluate the partitions and Weighted Extremal Optimization algorithm to detect communities. Starting from idealized and empirical weighted networks, the distribution or matching between weights and edges are disturbed. Using dissimilarity function $D$ to distinguish the difference between community structures, it is found that the redistribution of weights does strongly affect the community structure especially in dense networks. This indicates that the community structure in networks is a suitable property to reflect the role of weight.Comment: 10 pages, 6 figure

Accuracy and Precision of Methods for Community Identification in Weighted Networks

Based on brief review of approaches for community identification and measurement for sensitivity characterization, the accuracy and precision of several approaches for detecting communities in weighted networks are investigated. In weighted networks, the community structure should take both links and link weights into account and the partition of networks should be evaluated by weighted modularity $Q^w$. The results reveal that link weight has important effects on communities especially in dense networks. Potts model and Weighted Extremal Optimization (WEO) algorithm work well on weighted networks. Then Potts model and WEO algorithms are used to detect communities in Rhesus monkey network. The results gives nice understanding for real community structure.Comment: 14 pages, 15 figure

Novel Swine Influenza Virus Reassortants in Pigs, China

During swine influenza virus surveillance in pigs in China during 2006–2009, we isolated subtypes H1N1, H1N2, and H3N2 and found novel reassortment between contemporary swine and avian panzootic viruses. These reassortment events raise concern about generation of novel viruses in pigs, which could have pandemic potential

Synthesis of covalently crosslinked attapulgite/poly (acrylic acid-co-acrylamide) nanocomposite hydrogels and their evaluation as adsorbent for heavy metal ions

Novel covalently crosslinked attapulgite/poly(acrylic acid-co-acrylamide) (ATP/P(AA-co-AM)) nanocomposite hydrogel was synthesized via a facile "one-pot" two-step approach, with the modified attapulgite (ATP-C=C) nanorods as the sole crosslinker. Orthogonal experiment was designed to investigate the effect of the synthetic condition on the resultant nanocomposite hydrogels. The ATP/P(AA-co-AM)) nanocomposite hydrogels exhibited selective adsorption toward Pb2+ and Cu2+. The adsorbed ions could be easily desorbed, indicating their desired reusability. These excellent features, such as facile preparation, high mechanical stability, high adsorption capacity, and simple reactivation, make them potential adsorbent for the treatment of the heavy metal-contaminated water. (C) 2014 The Korean Society of Industrial and Engineering Chemistry. Published by Elsevier B.V. All rights reserved

Raspberry-Shaped Independent Temperature and pH Dual-Responsive CPMAA@CPNIPAM Yolk/Shell Microspheres for Site-Specific Targeted Delivery of Anticancer Drugs

Raspberry-shaped CPMAA@CPNIPAM yolk/shell microspheres (RS-CPMAA@CPNIPAM), with independent pH sensitive movable cross-linked poly­(methacrylic acid) (CPMAA) cores and temperature responsive cross-linked poly­(<i>N</i>-isopropylacrylamide) (CPNIPAM) shells, have been successfully fabricated as a potential drug delivery system (DDS) for the controlled release of anticancer drugs, via the one-pot two-step “self-removing” approach based on the consecutive radical seeded emulsion copolymerization. Their formation mechanism was also proposed and the hydrogen bonds between amide groups (in NIPAM and its oligomers) with carboxyl groups (in CPMAA) should be the determining factor for the different morphology. Compared with the regular CPMAA@CPNIPAM core/shell microspheres, the RS-CPMAA@CPNIPAM yolk/shell microspheres possessed higher drug-loading capacity and better controlled release performance, with Doxorubicin (DOX) as a model anticancer drug. Most importantly, the novel raspberry-shaped yolk/shell microspheres possessed excellent site-specific targeted release performance, with minimal drug leakage during circulation in the body