Tripartite Entanglement in Noninertial Frame

The tripartite entanglement is examined when one of the three parties moves with a uniform acceleration with respect to other parties. As Unruh effect indicates, the tripartite entanglement exhibits a decreasing behavior with increasing the acceleration. Unlike the bipartite entanglement, however, the tripartite entanglement does not completely vanish in the infinite acceleration limit. If the three parties, for example, share the Greenberger-Horne-Zeilinger or W-state initially, the corresponding $\pi$-tangle, one of the measures for tripartite entanglement, is shown to be $\pi/6 \sim 0.524$ or 0.176 in this limit, respectively. This fact indicates that the tripartite quantum information processing may be possible even if one of the parties approaches to the Rindler horizon. The physical implications of this striking result are discussed in the context of black hole physics.Comment: 19 pages, 5 figure

Inherited crustal deformation along the East Gondwana margin revealed by seismic anisotropy tomography

The mechanisms of continental growth are a crucial part of plate tectonic theory, yet a clear understanding of the processes involved remains elusive. Here we determine seismic Rayleigh wave phase anisotropy variations in the crust beneath the southern Tasmanides of Australia, a Paleozoic accretionary margin. Our results reveal a complex, thick-skinned pervasive deformation that was driven by the tectonic interaction between the proto-Pacific Ocean and the ancient eastern margin of Gondwana. Stress-induced effects triggered by the collision and entrainment of a microcontinent into the active subduction zone are evident in the anisotropy signature. The paleofracturing trend of failed rifting between Australia and Antarctica is also recorded in the anisotropy pattern as well as a tightly curved feature in central Tasmania. The observed patterns of anisotropy correlate well with recent geodynamic and kinematic models of the Tasmanides and provide a platform from which the spatial extent of deformational domains can be refined

An algorithm to compute the polar decomposition of a 3 × 3 matrix

We propose an algorithm for computing the polar decomposition of a 3 × 3 real matrix that is based on the connection between orthogonal matrices and quaternions. An important application is to 3D transformations in the level 3 Cascading Style Sheets specification used in web browsers. Our algorithm is numerically reliable and requires fewer arithmetic operations than the alternative of computing the polar decomposition via the singular value decomposition

Development and validation of a clinical prediction rule for chest wall syndrome in primary care.

Chest wall syndrome (CWS), the main cause of chest pain in primary care practice, is most often an exclusion diagnosis. We developed and evaluated a clinical prediction rule for CWS. Data from a multicenter clinical cohort of consecutive primary care patients with chest pain were used (59 general practitioners, 672 patients). A final diagnosis was determined after 12 months of follow-up. We used the literature and bivariate analyses to identify candidate predictors, and multivariate logistic regression was used to develop a clinical prediction rule for CWS. We used data from a German cohort (n = 1212) for external validation. From bivariate analyses, we identified six variables characterizing CWS: thoracic pain (neither retrosternal nor oppressive), stabbing, well localized pain, no history of coronary heart disease, absence of general practitioner's concern, and pain reproducible by palpation. This last variable accounted for 2 points in the clinical prediction rule, the others for 1 point each; the total score ranged from 0 to 7 points. The area under the receiver operating characteristic (ROC) curve was 0.80 (95% confidence interval 0.76-0.83) in the derivation cohort (specificity: 89%; sensitivity: 45%; cut-off set at 6 points). Among all patients presenting CWS (n = 284), 71% (n = 201) had a pain reproducible by palpation and 45% (n = 127) were correctly diagnosed. For a subset (n = 43) of these correctly classified CWS patients, 65 additional investigations (30 electrocardiograms, 16 thoracic radiographies, 10 laboratory tests, eight specialist referrals, one thoracic computed tomography) had been performed to achieve diagnosis. False positives (n = 41) included three patients with stable angina (1.8% of all positives). External validation revealed the ROC curve to be 0.76 (95% confidence interval 0.73-0.79) with a sensitivity of 22% and a specificity of 93%. This CWS score offers a useful complement to the usual CWS exclusion diagnosing process. Indeed, for the 127 patients presenting CWS and correctly classified by our clinical prediction rule, 65 additional tests and exams could have been avoided. However, the reproduction of chest pain by palpation, the most important characteristic to diagnose CWS, is not pathognomonic