Weak lensing goes bananas: What flexion really measures

In weak gravitational lensing, the image distortion caused by shear measures the projected tidal gravitational field of the deflecting mass distribution. To lowest order, the shear is proportional to the mean image ellipticity. If the image sizes are not small compared to the scale over which the shear varies, higher-order distortions occur, called flexion. For ordinary weak lensing, the observable quantity is not the shear, but the reduced shear, owing to the mass-sheet degeneracy. Likewise, the flexion itself is unobservable. Rather, higher-order image distortions measure the reduced flexion, i.e., derivatives of the reduced shear. We derive the corresponding lens equation in terms of the reduced flexion and calculate the resulting relation between brightness moments of source and image. Assuming an isotropic distribution of source orientations, estimates for the reduced shear and flexion are obtained; these are then tested with simulations. In particular, the presence of flexion affects the determination of the reduced shear. The results of these simulations yield the amount of bias of the estimators, as a function of the shear and flexion. We point out and quantify a fundamental limitation of the flexion formalism, in terms of the product of reduced flexion and source size. If this product increases above the derived threshold, multiple images of the source are formed locally, and the formalism breaks down. Finally, we show how a general (reduced) flexion field can be decomposed into its four components: two of them are due to a shear field, carrying an E- and B-mode in general. The other two components do not correspond to a shear field; they can also be split up into corresponding E- and B-modes.Comment: 17 pages, 6 figures, submitted to A&

Estimate of dark halo ellipticity by lensing flexion

Aims. The predictions of the ellipticity of the dark matter halos from models of structure formation are notoriously difficult to test with observations. A direct measurement would give important constraints on the formation of galaxies, and its effect on the dark matter distribution in their halos. Here we show that galaxy-galaxy flexion provides a direct and potentially powerful method for determining the ellipticity of (an ensemble of) elliptical lenses. Methods. We decompose the spin-1 flexion into a radial and a tangential component. Using the ratio of tangential-to- radial flexion, which is independent of the radial mass profile, the mass ellipticity can be estimated. Results. An estimator for the ellipticity of the mass distribution is derived and tested with simulations. We show that the estimator is slightly biased. We quantify this bias, and provide a method to reduce it. Furthermore, a parametric fitting of the flexion ratio and orientation provides another estimate for the dark halo ellipticity, which is more accurate for individual lenses Overall, galaxy-galaxy flexion appears as a powerful tool for constraining the ellipticity of mass distributions.Comment: 6 pages,5 figures, submitted to AA, comments welcom

Does using a femoral nerve block for total knee replacement decrease postoperative delirium?

<p>Abstract</p> <p>Background</p> <p>The effect of peripheral nerve blocks on postoperative delirium in older patients has not been studied. Peripheral nerve blocks may reduce the incidence of postoperative opioid use and its side effects such as delirium via opioid-sparing effect.</p> <p>Methods</p> <p>A prospective cohort study was conducted in patients who underwent total knee replacement. Baseline cognitive function was assessed using the Telephone Interview for Cognitive Status. Postoperative delirium was measured using the Confusion Assessment Method postoperatively. Incidence of postoperative delirium was compared in two postoperative management groups: femoral nerve block ± patient-controlled analgesia and patient-controlled analgesia only. In addition, pain levels (using numeric rating scales) and opioid use were compared in two groups.</p> <p>Results</p> <p>85 patients were studied. The overall incidence of postoperative delirium either on postoperative day one or day two was 48.1%. Incidence of postoperative delirium in the femoral nerve block group was lower than patient controlled analgesia only group (25% vs. 61%, <it>P </it>= 0.002). However, there was no significant difference between the groups with respect to postoperative pain level or the amount of intravenous opioid use.</p> <p>Conclusions</p> <p>Femoral nerve block reduces the incidence of postoperative delirium. These results suggest that a larger randomized control trial is necessary to confirm these preliminary findings.</p

Regression analysis for peak designation in pulsatile pressure signals

Following recent studies, the automatic analysis of intracranial pressure (ICP) pulses appears to be a promising tool for forecasting critical intracranial and cerebrovascular pathophysiological variations during the management of many disorders. A pulse analysis framework has been recently developed to automatically extract morphological features of ICP pulses. The algorithm is able to enhance the quality of ICP signals, to segment ICP pulses, and to designate the locations of the three ICP sub-peaks in a pulse. This paper extends this algorithm by utilizing machine learning techniques to replace Gaussian priors used in the peak designation process with more versatile regression models. The experimental evaluations are conducted on a database of ICP signals built from 700 h of recordings from 64 neurosurgical patients. A comparative analysis of different state-of-the-art regression analysis methods is conducted and the best approach is then compared to the original pulse analysis algorithm. The results demonstrate a significant improvement in terms of accuracy in favor of our regression-based recognition framework. It reaches an average peak designation accuracy of 99% using a kernel spectral regression against 93% for the original algorithm

Optical conductivity of the nonsuperconducting cuprate La(8-x)Sr(x)Cu(8)O(20)

La(8-x)Sr(x)Cu(8)O(20) is a non-superconducting cuprate, which exhibits a doubling of the elementary cell along the c axis. Its optical conductivity sigma (omega) has been first measured here, down to 20 K, in two single crystals with x = 1.56 and x = 2.24. Along c, sigma (omega) shows, in both samples, bands due to strongly bound charges, thus confirming that the cell doubling is due to charge ordering. In the ab plane, in addition to the Drude term one observes an infrared peak at 0.1 eV and a midinfrared band at 0.7 eV. The 0.1 eV peak hardens considerably below 200 K, in correspondence of an anomalous increase in the sample dc resistivity, in agreement with its polaronic origin. This study allows one to establish relevant similarities and differences with respect to the spectrum of the ab plane of the superconducting cuprates.Comment: Revised version submitted to Phys. Rev. B, including the elimination of Fig. 1 and changes to Figs. 4 and

DFT Study of Planar Boron Sheets: A New Template for Hydrogen Storage

We study the hydrogen storage properties of planar boron sheets and compare them to those of graphene. The binding of molecular hydrogen to the boron sheet (0.05 eV) is stronger than that to graphene. We find that dispersion of alkali metal (AM = Li, Na, and K) atoms onto the boron sheet markedly increases hydrogen binding energies and storage capacities. The unique structure of the boron sheet presents a template for creating a stable lattice of strongly bonded metal atoms with a large nearest neighbor distance. In contrast, AM atoms dispersed on graphene tend to cluster to form a bulk metal. In particular the boron-Li system is found to be a good candidate for hydrogen storage purposes. In the fully loaded case this compound can contain up to 10.7 wt. % molecular hydrogen with an average binding energy of 0.15 eV/H2.Comment: 19 pages, 7 figures, and 3 table

In situ evidence for the structure of the magnetic null in a 3D reconnection event in the Earth's magnetotail

Magnetic reconnection is one of the most important processes in astrophysical, space and laboratory plasmas. Identifying the structure around the point at which the magnetic field lines break and subsequently reform, known as the magnetic null point, is crucial to improving our understanding reconnection. But owing to the inherently three-dimensional nature of this process, magnetic nulls are only detectable through measurements obtained simultaneously from at least four points in space. Using data collected by the four spacecraft of the Cluster constellation as they traversed a diffusion region in the Earth's magnetotail on 15 September, 2001, we report here the first in situ evidence for the structure of an isolated magnetic null. The results indicate that it has a positive-spiral structure whose spatial extent is of the same order as the local ion inertial length scale, suggesting that the Hall effect could play an important role in 3D reconnection dynamics.Comment: 14 pages, 4 figure

Comparative efficacy of ultrasound-guided and stimulating popliteal-sciatic perineural catheters for postoperative analgesia

Perineural catheter insertion using ultrasound guidance alone is a relatively new approach. Previous studies have shown that ultrasound-guided catheters take less time to place with high placement success rates, but the analgesic efficacy compared with the established stimulating catheter technique remains unknown. We tested the hypothesis that popliteal-sciatic perineural catheter insertion relying exclusively on ultrasound guidance results in superior postoperative analgesia compared with stimulating catheters. Preoperatively, subjects receiving a popliteal-sciatic perineural catheter for foot or ankle surgery were assigned randomly to either ultrasound guidance (bolus via needle with non-stimulating catheter insertion) or electrical stimulation (bolus via catheter). We used 1.5% mepivacaine 40 mL for the primary surgical nerve block and 0.2% ropivacaine (basal 8 mL·hr−1; bolus 4 mL; 30 min lockout) was infused postoperatively. The primary outcome was average surgical pain on postoperative day one. Forty of the 80 subjects enrolled were randomized to each treatment group. One of 40 subjects (2.5%) in the ultrasound group failed catheter placement per protocol vs nine of 40 (22.5%) in the stimulating catheter group (P = 0.014). The difference in procedural duration (mean [95% confidence interval (CI)]) was −6.48 (−9.90 - −3.05) min, with ultrasound requiring 7.0 (4.0-14.1) min vs stimulation requiring 11.0 (5.0-30.0) min (P &lt; 0.001). The average pain scores of subjects who provided data on postoperative day one were somewhat higher for the 33 ultrasound subjects than for the 26 stimulation subjects (5.0 [1.0-7.8] vs 3.0 [0.0-6.5], respectively; P = 0.032), a difference (mean [95%CI]) of 1.37 (0.03-2.71). For popliteal-sciatic perineural catheters, ultrasound guidance takes less time and results in fewer placement failures compared with stimulating catheters. However, analgesia may be mildly improved with successfully placed stimulating catheters. Clinical trial registration number NCT00876681

New monotonicity formulas for Ricci curvature and applications. I

Original manuscript November 21, 2011We prove three new monotonicity formulas for manifolds with a lower Ricci curvature bound and show that they are connected to rate of convergence to tangent cones. In fact, we show that the derivative of each of these three monotone quantities is bounded from below in terms of the Gromov–Hausdorff distance to the nearest cone. The monotonicity formulas are related to the classical Bishop–Gromov volume comparison theorem and Perelman’s celebrated monotonicity formula for the Ricci flow. We will explain the connection between all of these. Moreover, we show that these new monotonicity formulas are linked to a new sharp gradient estimate for the Green function that we prove. This is parallel to the fact that Perelman’s monotonicity is closely related to the sharp gradient estimate for the heat kernel of Li–Yau. In [CM4] one of the monotonicity formulas is used to show uniqueness of tangent cones with smooth cross-sections of Einstein manifolds. Finally, there are obvious parallelisms between our monotonicity and the positive mass theorem of Schoen–Yau and Witten.National Science Foundation (U.S.) (Grant DMS-11040934)National Science Foundation (U.S.). Focused Research Group (Grant DMS 0854774)National Science Foundation (U.S.) (Grant 0932078

Numerical Hermitian Yang-Mills Connections and Kahler Cone Substructure

We further develop the numerical algorithm for computing the gauge connection of slope-stable holomorphic vector bundles on Calabi-Yau manifolds. In particular, recent work on the generalized Donaldson algorithm is extended to bundles with Kahler cone substructure on manifolds with h^{1,1}>1. Since the computation depends only on a one-dimensional ray in the Kahler moduli space, it can probe slope-stability regardless of the size of h^{1,1}. Suitably normalized error measures are introduced to quantitatively compare results for different directions in Kahler moduli space. A significantly improved numerical integration procedure based on adaptive refinements is described and implemented. Finally, an efficient numerical check is proposed for determining whether or not a vector bundle is slope-stable without computing its full connection.Comment: 38 pages, 10 figure