On the integrability of Wilson loops in AdS_5 x S^5: Some periodic ansatze

Wilson loops are calculated within the AdS/CFT correspondence by finding a classical solution to the string equations of motion in AdS_5 x S^5 and evaluating its action. An important fact is that this sigma-model used to evaluate the Wilson loops is integrable, a feature that has gained relevance through the study of spinning strings carrying large quantum numbers and spin-chains. We apply the same techniques used to solve the equations for spinning strings to find the minimal surfaces describing a wide class of Wilson loops. We focus on different cases with periodic boundary conditions on the AdS_5 and S^5 factors and find a rich array of solutions. We examine the different phases that appear in the problem and comment on the applicability of integrability to the general problem.Comment: LaTex, 49 pages, 8 figure

An efficient shortest path routing algorithm in the data centre network DPillar

DPillar has recently been proposed as a server-centric data centre network and is combinatorially related to the well-known wrapped butterfly network. We explain the relationship between DPillar and the wrapped butterfly network before proving a symmetry property of DPillar. We use this symmetry property to establish a single-path routing algorithm for DPillar that computes a shortest path and has time complexity O(klog(n))O(klog⁡(n)), where k parameterizes the dimension of DPillar and n the number of ports in its switches. Moreover, our algorithm is trivial to implement, being essentially a conditional clause of numeric tests, and improves significantly upon a routing algorithm earlier employed for DPillar. A secondary and important effect of our work is that it emphasises that data centre networks are amenable to a closer combinatorial scrutiny that can significantly improve their computational efficiency and performance

Quantitative real-time polymerase chain reaction for detecting \u3ci\u3eMycoplasma hyosynoviae\u3c/i\u3e and \u3ci\u3eMycoplasma hyorhinis\u3c/i\u3e in pen-based oral, tonsillar, and nasal fluids

Mycoplasma (M.) hyorhinis and M. hyosynoviae are pathogens known to cause disease in pigs post-weaning. Due to their fastidious nature, there is increased need for culture-independent diagnostic platforms to detect these microorganisms. Therefore, this study was performed to develop and optimize quantitative real-time PCR (qPCR) assays to rapidly detect M. hyorhinis and M. hyosynoviae in pen-based oral fluids as well as nasal and tonsillar fluids as proxies for samples used in swine herd surveillance. Two methods of genomic DNA extraction, automated versus manual, were used to compare diagnostic test performance. A wean-to-finish longitudinal study was also carried out to demonstrate the reproducibility of using pen-based oral fluids. Overall, pen-based oral and tonsillar fluids were more likely to be positive for both types of bacteria whereas only M. hyorhinis was detected in nasal fluids. DNA extraction protocols were shown to significantly influence test result. Although the initial detection time somewhat differed, both organisms were repeatedly detected in the longitudinal study. Overall, this study evaluated two qPCR methods for rapid and specific detection of either mycoplasma. Results from the present investigation can serve as a foundation for future studies to determine the prevalence of the two microorganisms, environmental load, and effectiveness of veterinary interventions for infection control

Ferromagnetism in the Mott insulator Ba2NaOsO6

Results are presented of single crystal structural, thermodynamic, and reflectivity measurements of the double-perovskite Ba2NaOsO6. These characterize the material as a 5d^1 ferromagnetic Mott insulator with an ordered moment of ~0.2 Bohr magnetons per formula unit and TC = 6.8(3) K. The magnetic entropy associated with this phase transition is close to Rln2, indicating that the quartet groundstate anticipated from consideration of the crystal structure is split, consistent with a scenario in which the ferromagnetism is associated with orbital ordering.Comment: 5 pages, 5 figures, added reference

Quark--anti-quark potential in N=4 SYM

We construct a closed system of equations describing the quark--anti-quark potential at any coupling in planar N=4 supersymmetric Yang-Mills theory. It is based on the Quantum Spectral Curve method supplemented with a novel type of asymptotics. We present a high precision numerical solution reproducing the classical and one-loop string predictions very accurately. We also analytically compute the first 7 nontrivial orders of the weak coupling expansion. Moreover, we study analytically the generalized quark--anti-quark potential in the limit of large imaginary twist to all orders in perturbation theory. We demonstrate how the QSC reduces in this case to a one-dimensional Schrodinger equation. In the process we establish a link between the Q-functions and the solution of the Bethe-Salpeter equation.Comment: 31 pages, 1 figure; v2: minor correcton

Commutator Leavitt path algebras

For any field K and directed graph E, we completely describe the elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E),L_K(E)]. We then use this result to classify all Leavitt path algebras L_K(E) that satisfy L_K(E)=[L_K(E),L_K(E)]. We also show that these Leavitt path algebras have the additional (unusual) property that all their Lie ideals are (ring-theoretic) ideals, and construct examples of such rings with various ideal structures.Comment: 24 page

Water Abundance in Molecular Cloud Cores

We present Submillimeter Wave Astronomy Satellite (SWAS) observations of the 1_{10}-1_{01} transition of ortho-water at 557 GHz toward 12 molecular cloud cores. The water emission was detected in NGC 7538, Rho Oph A, NGC 2024, CRL 2591, W3, W3(OH), Mon R2, and W33, and was not detected in TMC-1, L134N, and B335. We also present a small map of the water emission in S140. Observations of the H_2^{18}O line were obtained toward S140 and NGC 7538, but no emission was detected. The abundance of ortho-water relative to H_2 in the giant molecular cloud cores was found to vary between 6x10^{-10} and 1x10^{-8}. Five of the cloud cores in our sample have previous water detections; however, in all cases the emission is thought to arise from hot cores with small angular extents. The water abundance estimated for the hot core gas is at least 100 times larger than in the gas probed by SWAS. The most stringent upper limit on the ortho-water abundance in dark clouds is provided in TMC-1, where the 3-sigma upper limit on the ortho-water fractional abundance is 7x10^{-8}.Comment: 5 pages, 3 Postscript figures, uses aastex.cls, emulateapj5.sty (included), and apjfonts.sty (included

The Distribution of Water Emission in M17SW

We present a 17-point map of the M17SW cloud core in the 1_{10}-1_{01} transition of ortho-water at 557 GHz obtained with the Submillimeter Wave Astronomy Satellite. Water emission was detected in 11 of the 17 observed positions. The line widths of the water emission vary between 4 and 9 km s^{-1}, and are similar to other emission lines that arise in the M17SW core. A direct comparison is made between the spatial extent of the water emission and the ^{13}CO J = 5\to4 emission; the good agreement suggests that the water emission arises in the same warm, dense gas as the ^{13}CO emission. A spectrum of the H_2^{18}O line was also obtained at the center position of the cloud core, but no emission was detected. We estimate that the average abundance of ortho-water relative to H_2 within the M17 dense core is approximately 1x10^{-9}, 30 times smaller than the average for the Orion core. Toward the H II region/molecular cloud interface in M17SW the ortho-water abundance may be about 5 times larger than in the dense core.Comment: 4 pages, 3 Postscript figures, uses aastex.cls, emulateapj5.sty (included), and apjfonts.sty (included