Group-Sparse Signal Denoising: Non-Convex Regularization, Convex Optimization

Convex optimization with sparsity-promoting convex regularization is a standard approach for estimating sparse signals in noise. In order to promote sparsity more strongly than convex regularization, it is also standard practice to employ non-convex optimization. In this paper, we take a third approach. We utilize a non-convex regularization term chosen such that the total cost function (consisting of data consistency and regularization terms) is convex. Therefore, sparsity is more strongly promoted than in the standard convex formulation, but without sacrificing the attractive aspects of convex optimization (unique minimum, robust algorithms, etc.). We use this idea to improve the recently developed 'overlapping group shrinkage' (OGS) algorithm for the denoising of group-sparse signals. The algorithm is applied to the problem of speech enhancement with favorable results in terms of both SNR and perceptual quality.Comment: 14 pages, 11 figure

Two-photon Exchange Corrections to Single Spin Asymmetry of Neutron and 3^3He

In a simple hadronic model, the two-photon exchange contributions to the single spin asymmetries for the nucleon and the $^3$He are estimated. The results show that the elastic contributions of two-photon exchange to the the single spin asymmetries for the nucleon are rather small while those for the $^3$He are relatively large. Besides the strong angular dependence, the two-photon contributions to the single spin asymmetry for the $^3$He are very sensitive to the momentum transfer.Comment: 11 pages, 8 figure

HEN1 recognizes 21-24 nt small RNA duplexes and deposits a methyl group onto the 2' OH of the 3' terminal nucleotide.

microRNAs (miRNAs) and small interfering RNAs (siRNAs) in plants bear a methyl group on the ribose of the 3' terminal nucleotide. We showed previously that the methylation of miRNAs and siRNAs requires the protein HEN1 in vivo and that purified HEN1 protein methylates miRNA/miRNA* duplexes in vitro. In this study, we show that HEN1 methylates both miRNA/miRNA* and siRNA/siRNA* duplexes in vitro with a preference for 21-24 nt RNA duplexes with 2 nt overhangs. We also demonstrate that HEN1 deposits the methyl group on to the 2' OH of the 3' terminal nucleotide. Among various modifications that can occur on the ribose of the terminal nucleotide, such as 2'-deoxy, 3'-deoxy, 2'-O-methyl and 3'-O-methyl, only 2'-O-methyl on a small RNA inhibits the activity of yeast poly(A) polymerase (PAP). These findings indicate that HEN1 specifically methylates miRNAs and siRNAs and implicate the importance of the 2'-O-methyl group in the biology of RNA silencing

General relations of heavy quark-antiquark potentials induced by reparameterization invariance

A set of general relations between the spin-independent and spin-dependent potentials of heavy quark and anti-quark interactions are derived from reparameterization invariance in the Heavy Quark Effective Theory. It covers the Gromes relation and includes some new interesting relations which are useful in understanding the spin-independent and spin-dependent relativistic corrections to the leading order nonrelativistic potential.Comment: 11 pages, TUIMP-TH-93/54, CCAST-93-3

A New Approach to Linear/Nonlinear Distributed Fusion Estimation Problem

Disturbance noises are always bounded in a practical system, while fusion estimation is to best utilize multiple sensor data containing noises for the purpose of estimating a quantity--a parameter or process. However, few results are focused on the information fusion estimation problem under bounded noises. In this paper, we study the distributed fusion estimation problem for linear time-varying systems and nonlinear systems with bounded noises, where the addressed noises do not provide any statistical information, and are unknown but bounded. When considering linear time-varying fusion systems with bounded noises, a new local Kalman-like estimator is designed such that the square error of the estimator is bounded as time goes to $\infty$. A novel constructive method is proposed to find an upper bound of fusion estimation error, then a convex optimization problem on the design of an optimal weighting fusion criterion is established in terms of linear matrix inequalities, which can be solved by standard software packages. Furthermore, according to the design method of linear time-varying fusion systems, each local nonlinear estimator is derived for nonlinear systems with bounded noises by using Taylor series expansion, and a corresponding distributed fusion criterion is obtained by solving a convex optimization problem. Finally, target tracking system and localization of a mobile robot are given to show the advantages and effectiveness of the proposed methods.Comment: 9 pages, 3 figure

A Note on the Generalization of the GEMS Approach

This paper is a supplement of our earlier work JHEP 0410 (2004) 011[gr-qc/0409107].We map the vector potential of charged black holes into GEMS and find that its effect on the thermal spectrum is the same as that on the black hole side, i.e., it will induce a chemical potential in the thermal spectrum which is the same as that in the charged black holes.We also argue that the generalization of GEMS approach to non-stationary motions is not possible.Comment: Latex file, 10 pages, no figure; v2: minor corrections; v3: revised with title changed, one new section added and references adde