Quantum Error Correction of Time-Correlated Errors

The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of quantum systems; an error corrected during the previous cycle may reoccur later due to physical processes specific for each physical implementation of the qubits. In this paper we study quantum error correction for a restricted class of time-correlated errors in a spin-boson model. The algorithm we propose allows the correction of two errors per error correction cycle, provided that one of them is time-correlated. The algorithm can be applied to any stabilizer code when the two logical qubits $\mid 0_L>$ and $\mid 1_L>$ are entangled states of $2^{n}$ basis states in $\mathcal{H}_{2^n}$.Comment: 14 pages, 3 figure

Epigenomic and Transcriptional Regulation of Hepatic Metabolism by REV-ERB and Hdac3

Metabolic activities are regulated by the circadian clock, and disruption of the clock exacerbates metabolic diseases including obesity and diabetes. Transcriptomic studies in metabolic organs suggested that the circadian clock drives the circadian expression of important metabolic genes. Here we show that histone deacetylase 3 (HDAC3) is recruited to the mouse liver genome in a circadian manner. Histone acetylation is inversely related to HDAC3 binding, and this rhythm is lost when HDAC3 is absent. Diurnal recruitment of HDAC3 corresponds to the expression pattern of REV-ERBα, an important component of the circadian clock. REV-ERBα colocalizes with HDAC3 near genes regulating lipid metabolism, and deletion of HDAC3 or Rev-erbα in mouse liver causes hepatic steatosis. Thus, genomic recruitment of HDAC3 by REV-ERBα directs a circadian rhythm of histone acetylation and gene expression required for normal hepatic lipid homeostasis. In addition, we reported that the REV-ERBα paralog, REV-ERBβ also displays circadian binding similar to that of REV-ERBα. REV-ERBβ also recruits HDAC3 and protects the circadian clock and hepatic lipid homeostasis in the absence of REV-ERBα. REV-ERBs are indeed essential components of the circadian clock. Furthermore, we discovered that REV-ERBs competes with RORα for genomic binding at Bmal1 and Npas2 genes, and drives a diurnal binding of RORα. We then identified thousands of competing sites by RORα ChIP-seq, many of which are in close proximity of clock and metabolic genes. We also discovered many RORα binding sites with no rhythmic RORα binding or rhythmic RORα binding in-phase with REV-ERBs. Collectively, these findings indicate that REV-ERBs, HDAC3 and potentially RORα mediate the epigenomic and transcriptional regulation of liver metabolism by the circadian clock

Theory and development of a camera-based noncontact vibration measurement system

Title from PDF of title page; abstract from research PDF (University of Missouri--Columbia, viewed on June 25, 2014).Dramatic advancement in technologies for high-speed high-resolution digital cameras in recent years enables the development of camera-based full-field noncontact measurement systems for vibration testing of flexible multibody systems undergoing large rigid-body motion and elastic/plastic deformations. A few of such systems exist in today's metrology market, but they are inconvenient for use and prohibitively expensive. Most seriously, they are not really appropriate for structural vibration testing because their measurement accuracy is low due to several technical reasons, including inappropriate setting of cameras and experimental setup because of user's innocence of video-grammetry, non-precise corner detection and other problems of image processing techniques, and inaccurate modeling and calibration of cameras. This thesis develops and puts together a complete set of necessary techniques for the development of a camerabased noncontact full-field vibration measurement system using inexpensive off-the-shelf digital cameras. An optimal combination of appropriate methods for corner detection, camera calibration, lens distortion modeling, and measurement applications is proposed and numerically and experimentally verified. Moreover, we derive/improve some image processing methods and 3D reconstruction algorithms to improve vibration measurement accuracy. The proposed methods include: 1) a corner detection method for processing 2D images with sub-pixel resolutions, 2) an improved flexible camera calibration method for easy and fast calibration with high accuracy, 3) a lens distortion model for correcting radial, decentering, and thin prism distortions, 4) a set of guidelines for setting up cameras and experiments for measurement, and 5) algorithms for measurement applications. The proposed corner detection method improves Foerstner's corner detector, which improved Moravec's and Harris's corner detectors. The proposed camera calibration method improves Zhang's flexible technique, which works without knowing the object's 3D geometry or computer vision. The method only requires the camera to observe a planar pattern (e.g., a checker board) shown at two or more independent orientations by arbitrarily moving the planar pattern (or the camera). Estimation of the camera's intrinsic parameters (i.e., focal length, principal point, the skewness parameter and aspect ratios of the two image axes, and lens distortion parameters) and extrinsic parameters (i.e., camera's location and orientation with respect to the referential world coordinate system) consists of an approximate initial guess based on linear closed-form solutions and then nonlinear optimization for refinement. This approach is between the photogrammetric calibration and the self-calibration. Compared with photogrammetric calibration techniques that use expensive calibration objects of two or three orthogonal planes, the proposed technique is easy to use and flexible. To examine the proposed methods and their combined effects against high measurement accuracy, two Canon EOS-7D DSLR cameras are used for theoretical studies and experimental verifications. Numerical and experimental results show that the recommended methods together with our improved image processing techniques is feasible for the development of a camera-based noncontact full-field vibration measurement system with high precision and low cost. This camera-based measurement instrument has the potential for developing new structural testing techniques and can open new possibilities for research and development in mechanical and aerospace engineering, computer science, animal science, and many other fields

A simple entanglement measure for multipartite pure states

A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.Comment: 8 pages LaTe