Optimal surface profile design of deployable mesh reflectors via a force density strategy

Based on a force density method coupled with optimal design of node positions, a novel approach for optimal surface profile design of mesh reflectors is presented. Uniform tension is achieved by iterations on coefficients of force density. The positions of net nodes are recalculated in each iteration so that the faceting RMS error of the reflector surface is minimized. Applications of both prime focus and offset configurations are demonstrated. The simulation results show the effectiveness of the proposed approach

Entanglement Entropy: Helicity versus Spin

For a massive spin 1/2 field, we present the reduced spin and helicity density matrix, respectively, for the same pure one particle state. Their relation has also been developed. Furthermore, we calculate and compare the corresponding entanglement entropy for spin and helicity within the same inertial reference frame. Due to the distinct dependence on momentum degree of freedom between spin and helicity states, the resultant helicity entropy is different from that of spin in general. In particular, we find that both helicity entanglement for a spin eigenstate and spin entanglement for a right handed or left handed helicity state do not vanish and their Von Neumann entropy has no dependence on the specific form of momentum distribution as long as it is isotropic.Comment: 3 pages, title changed, typos corrected, version to appear in Int. J. Quant. In

Helicity Entanglement of Moving Bodies

We investigate the Lorentz transformation of the reduced helicity density matrix for a pair of massive spin 1/2 particles. The corresponding Wootters concurrence shows no invariant meaning, which implies that we can generate helicity entanglement simply by the transformation from one reference frame to another. The difference between the helicity and spin case is also discussed.Comment: 3 pages, 1 figure, version to appear in Int. J. Quant. In

PRL1, an RNA-Binding Protein, Positively Regulates the Accumulation of miRNAs and siRNAs in Arabidopsis

The evolutionary conserved WD-40 protein PRL1 plays important roles in immunity and development. Here we show that PRL1 is required for the accumulation of microRNAs (miRNAs) and small interfering RNAs (siRNAs). PRL1 positively influences the processing of miRNA primary transcripts (pri-miRNAs) and double-stranded RNAs (dsRNAs). Furthermore, PRL1 interacts with the pri-miRNA processor, DCL1, and the dsRNA processors (DCL3 and DCL4). These results suggest that PRL1 may function as a general factor to promote the production of miRNAs and siRNAs. We also show that PRL1 is an RNA-binding protein and associates with pri-miRNAs in vivo. In addition, prl1 reduces pri-miRNA levels without affecting pri-miRNA transcription. These results suggest that PRL1 may stabilize pri-miRNAs and function as a co-factor to enhance DCL1 activity. We further reveal the genetic interaction of PRL1 with CDC5, which interacts with PRL1 and regulates transcription and processing of pri-miRNAs. Both miRNA and pri-miRNA levels are lower in cdc5 prl1 than those in either cdc5 or prl1. However, the processing efficiency of pri-miRNAs in cdc5 prl1 is similar to that in cdc5 and slightly lower than that in prl1. Based on these results, we propose that CDC5 and PRL1 cooperatively regulate pri-miRNA levels, which results in their synergistic effects on miRNA accumulation, while they function together as a complex to enhance DCL1 activity

microRNA biogenesis, degradation and activity in plants

microRNAs (miRNAs) are important regulators of gene expression. After excised from primary miRNA transcript by dicer-like1 (DCL1, an RNAse III enzyme), miRNAs bind and guide their effector protein named argonaute 1 (AGO1) to silence the expression of target RNAs containing their complementary sequences in plants. miRNA levels and activities are tightly controlled to ensure their functions in various biological processes such as development, metabolism and responses to abiotic and biotic stresses. Studies have identified many factors that involve in miRNA accumulation and activities. Characterization of these factors in turn greatly improves our understanding of the processes related to miRNAs. Here, we review recent progress of mechanisms underlying miRNA expression and functions in plants

microRNA biogenesis, degradation and activity in plants

microRNAs (miRNAs) are important regulators of gene expression. After excised from primary miRNA transcript by dicer-like1 (DCL1, an RNAse III enzyme), miRNAs bind and guide their effector protein named argonaute 1 (AGO1) to silence the expression of target RNAs containing their complementary sequences in plants. miRNA levels and activities are tightly controlled to ensure their functions in various biological processes such as development, metabolism and responses to abiotic and biotic stresses. Studies have identified many factors that involve in miRNA accumulation and activities. Characterization of these factors in turn greatly improves our understanding of the processes related to miRNAs. Here, we review recent progress of mechanisms underlying miRNA expression and functions in plants

On Polynomial-time Path-following Interior-point Methods with Local Superlinear Convergence

Interior-point methods provide one of the most popular ways of solving convex optimization problems. Two advantages of modern interior-point methods over other approaches are: (1) robust global convergence, and (2) the ability to obtain high accuracy solutions in theory (and in practice, if the algorithms are properly implemented, and as long as numerical linear system solvers continue to provide high accuracy solutions) for well-posed problem instances. This second ability is typically demonstrated by asymptotic superlinear convergence properties. In this thesis, we study superlinear convergence properties of interior-point methods with proven polynomial iteration complexity. Our focus is on linear programming and semidefinite programming special cases. We provide a survey on polynomial iteration complexity interior-point methods which also achieve asymptotic superlinear convergence. We analyze the elements of superlinear convergence proofs for a dual interior-point algorithm of Nesterov and Tun\c{c}el and a primal-dual interior-point algorithm of Mizuno, Todd and Ye. We present the results of our computational experiments which observe and track superlinear convergence for a variant of Nesterov and Tun\c{c}el's algorithm