Robust Recovery of Subspace Structures by Low-Rank Representation

In this work we address the subspace recovery problem. Given a set of data samples (vectors) approximately drawn from a union of multiple subspaces, our goal is to segment the samples into their respective subspaces and correct the possible errors as well. To this end, we propose a novel method termed Low-Rank Representation (LRR), which seeks the lowest-rank representation among all the candidates that can represent the data samples as linear combinations of the bases in a given dictionary. It is shown that LRR well solves the subspace recovery problem: when the data is clean, we prove that LRR exactly captures the true subspace structures; for the data contaminated by outliers, we prove that under certain conditions LRR can exactly recover the row space of the original data and detect the outlier as well; for the data corrupted by arbitrary errors, LRR can also approximately recover the row space with theoretical guarantees. Since the subspace membership is provably determined by the row space, these further imply that LRR can perform robust subspace segmentation and error correction, in an efficient way.Comment: IEEE Trans. Pattern Analysis and Machine Intelligenc

Schwarzschild-de Sitter Metric and Inertial Beltrami Coordinates

Under consideration of coordinate conditions, we get the Schwarzschild-Beltrami-de Sitter (S-BdS) metric solution of the Einstein field equations with a cosmological constant $\Lambda$. A brief review to the de Sitter invariant special relativity (dS-SR), and de Sitter general relativity (dS-GR, or GR with a $\Lambda$) is presented. The Beltrami metric $B_{\mu\nu}$ provides inertial reference frame for the dS-spacetime. By examining the Schwarzschild-de Sitter (S-dS) metric $g_{\mu\nu}^{(M)}$ existed in literatures since 1918, we find that the existed S-dS metric $g_{\mu\nu}^{(M)}$ describes some mixing effects of gravity and inertial-force, instead of a pure gravity effect arisen from "solar mass" $M$ in dS-GR. In this paper, we solve the vacuum Einstein equation of dS-GR, with the requirement of gravity-free metric $g_{\mu\nu}^{(M)}|_{M\rightarrow 0}=B_{\mu\nu}$. In this way we find S-BdS solution of dS-GR, written in inertial Beltrami coordinates. This is a new form of S-dS metric. Its physical meaning and possible applications are discussed.Comment: 16 pages, 1 figur

High Resolution Detection of Synchronously Determining Tilt Angle and Displacement of Test Plane by Blu-Ray Pickup Head

AbstractWe present an optical design for Blu-ray pickup head that can synchronously detect a linear displacement and two-dimensional (2D) angular tilt of the test plane. In order to enhance the accuracy of tilt angle and discriminate more tilted orientations, a high resolution detector (177×177 pixels) is used as the photo detector of the Blu-ray pickup head. The horizontal beam expander is used to make the laser beam be more uniform to improve the accuracy of signal at the photo detector. The signal at the high resolution detector of the pickup head used astigmatic detection is comprised of two displacement signals and one angular signal. The displacement of the test plane is ascertained from the rate of change in the length of semi-major and semi-minor axis for elliptical beam shape on the high resolution detector. The tilt of the test plane is obtained from the brightest position of beam shape. It is not only able to judge the tilt angle for four orientations (α, β, 45°and 135°), but also the tilt angle for four orientations (30°, 60°, 120°and 150°). The smaller pixel size will help to improve the accuracy in the 2D angle measurement further

Stable Agrobacterium-mediated transformation of the halophytic Leymus chinensis (Trin.)

In this study, an efficient procedure for stable Agrobacterium-mediated transformation of Leymus chinensis (Trin.) was established. Agrobacterium tumefaciens strain EHA105, harboring a binary vector pCAMBIA2300, was used for transformation, along with a sweet potato 2-cysteine peroxiredoxin (2-Cys Prx) gene under the control of the stress-inducible sweet potato anionic peroxidase 2 (SWPA2) promoter and the neomycin phosphotransferase (nptII) gene under the control of the cauliflower mosaic virus (CaMV) 35 S promoter. We found that a one-month-old callus derived from mature seeds could be efficiently transformed. Seven-day preculture followed by inoculation with the addition of 100 μmolL-1 acetosyringone (AS) and then a 3 day co-cultivation were performed before selection. Selection of transgenic shoots was done in the presence of 150 mgL-1 kanamycin (KM). An optical density at a wavelength of 600 nm (OD600) of approximately 0.4 for A. tumefaciens infection solution and 20 min of infection time gave the highest transformation efficiency. Polymerase chain reaction (PCR) analysis of KM-resistant plants and newly regenerated rhizomes revealed stable transformation of the 2-Cys Prx gene and the nptII gene, with the highest transformation frequency of 4.93%. RT-RCR analysis was conducted using salt stressed transgenic plants, and the results suggested that 2-Cys Prx had low transcription levels under non-stressed conditions, and increased transcription after 6 h of 200 mM NaCl stress. This gene continued to demonstrate high levels of transcription until 6 h after withdrawal of stress, with a slow recovery. The method reported herein provides a direct opportunity for improvement of the quality traits of L. chinensis via genetic transformation.Keywords: Leymus chinensis, Agrobacterium-mediated transformation, 2-Cys peroxiredoxin, gene transformatio