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

A general approach to high-yield biosynthesis of chimeric RNAs bearing various types of functional small RNAs for broad applications.

RNA research and therapy relies primarily on synthetic RNAs. We employed recombinant RNA technology toward large-scale production of pre-miRNA agents in bacteria, but found the majority of target RNAs were not or negligibly expressed. We thus developed a novel strategy to achieve consistent high-yield biosynthesis of chimeric RNAs carrying various small RNAs (e.g. miRNAs, siRNAs and RNA aptamers), which was based upon an optimal noncoding RNA scaffold (OnRS) derived from tRNA fusion pre-miR-34a (tRNA/mir-34a). Multi-milligrams of chimeric RNAs (e.g. OnRS/miR-124, OnRS/GFP-siRNA, OnRS/Neg (scrambled RNA) and OnRS/MGA (malachite green aptamer)) were readily obtained from 1 l bacterial culture. Deep sequencing analyses revealed that mature miR-124 and target GFP-siRNA were selectively released from chimeric RNAs in human cells. Consequently, OnRS/miR-124 was active in suppressing miR-124 target gene expression and controlling cellular processes, and OnRS/GFP-siRNA was effective in knocking down GFP mRNA levels and fluorescent intensity in ES-2/GFP cells and GFP-transgenic mice. Furthermore, the OnRS/MGA sensor offered a specific strong fluorescence upon binding MG, which was utilized as label-free substrate to accurately determine serum RNase activities in pancreatic cancer patients. These results demonstrate that OnRS-based bioengineering is a common, robust and versatile strategy to assemble various types of small RNAs for broad applications

A DEM investigation of water-bridged granular materials at the critical state

The critical state is an important concept for saturated and partially saturated granular materials as the strength and volume become constant and unique under continuous shear. By incorporating the water bridge effect, the mechanical behaviours of wet granular matters can be studied by the discrete element method (DEM). A series of DEM simulations are performed following the conventional triaxial loading path for dry and wet granular materials, and different suction values are applied at various confining stress levels. Unique critical state behaviours have been observed in both macroscopic and microscopic scales. It shows that the confining stress level plays an important role in the critical state behaviour of wet granular materials. The critical stress ratio for a wet material is not a constant value at different stress levels, and it is found that both the critical stress ratio and void ratio in wet granular matters are also much higher with a low confining stress. A framework is proposed by considering both the contact stress and the capillary stress effects to model the critical state lines. At large strain, the coordination number, the mean inter-particle force and fabric anisotropies evolve to constant critical state values for both dry and wet materials. The macro-parameters formulating the critical state stress ratio are found to be associated with the critical state anisotropies in solid skeleton and water phase fabrics, respectively

Center Symmetric Local Multilevel Pattern Based Descriptor and Its Application in Image Matching

This paper presents an effective local image region description method, called CS-LMP (Center Symmetric Local Multilevel Pattern) descriptor, and its application in image matching. The CS-LMP operator has no exponential computations, so the CS-LMP descriptor can encode the differences of the local intensity values using multiply quantization levels without increasing the dimension of the descriptor. Compared with the binary/ternary pattern based descriptors, the CS-LMP descriptor has better descriptive ability and computational efficiency. Extensive image matching experimental results testified the effectiveness of the proposed CS-LMP descriptor compared with other existing state-of-the-art descriptors