A Theoretical Analysis of NDCG Type Ranking Measures

A central problem in ranking is to design a ranking measure for evaluation of ranking functions. In this paper we study, from a theoretical perspective, the widely used Normalized Discounted Cumulative Gain (NDCG)-type ranking measures. Although there are extensive empirical studies of NDCG, little is known about its theoretical properties. We first show that, whatever the ranking function is, the standard NDCG which adopts a logarithmic discount, converges to 1 as the number of items to rank goes to infinity. On the first sight, this result is very surprising. It seems to imply that NDCG cannot differentiate good and bad ranking functions, contradicting to the empirical success of NDCG in many applications. In order to have a deeper understanding of ranking measures in general, we propose a notion referred to as consistent distinguishability. This notion captures the intuition that a ranking measure should have such a property: For every pair of substantially different ranking functions, the ranking measure can decide which one is better in a consistent manner on almost all datasets. We show that NDCG with logarithmic discount has consistent distinguishability although it converges to the same limit for all ranking functions. We next characterize the set of all feasible discount functions for NDCG according to the concept of consistent distinguishability. Specifically we show that whether NDCG has consistent distinguishability depends on how fast the discount decays, and 1/r is a critical point. We then turn to the cut-off version of NDCG, i.e., NDCG@k. We analyze the distinguishability of NDCG@k for various choices of k and the discount functions. Experimental results on real Web search datasets agree well with the theory.Comment: COLT 201

Two-dimensional modeling of the tearing-mode-governed magnetic reconnection in the large-scale current sheet above the two-ribbon flare

We attempt to model magnetic reconnection during the two-ribbon flare in the gravitationally stratified solar atmosphere with the Lundquist number of $S=10^6$ using 2D simulations. We found that the tearing mode instability leads to the inhomogeneous turbulence inside the reconnecting current sheet (CS) and invokes the fast phase of reconnection. Fast reconnection brings an extra dissipation of magnetic field which enhances the reconnection rate in an apparent way. The energy spectrum in the CS shows the power-law pattern and the dynamics of plasmoids governs the associated spectral index. We noticed that the energy dissipation occurs at a scale $l_{ko}$ of 100-200~km, and the associated CS thickness ranges from 1500 to 2500~km, which follows the Taylor scale $l_T=l_{ko} S^{1/6}$. The termination shock(TS) appears in the turbulent region above flare loops, which is an important contributor to heating flare loops. Substantial magnetic energy is converted into both kinetic and thermal energies via TS, and the cumulative heating rate is greater than the rate of the kinetic energy transfer. In addition, the turbulence is somehow amplified by TS, of which the amplitude is related to the local geometry of the TS.Comment: 22 pages, 10 figures; Accepted for publication in Research in Astronomy and Astrophysic

Maximizing spin-orbit torque efficiency of Ta(O)/Py via modulating oxygen-induced interface orbital hybridization

Spin-orbit torques due to interfacial Rashba and spin Hall effects have been widely considered as a potentially more efficient approach than the conventional spin-transfer torque to control the magnetization of ferromagnets. We report a comprehensive study of spin-orbit torque efficiency in Ta(O)/Ni81Fe19 bilayers by tuning low-oxidation of \b{eta}-phase tantalum, and find that the spin Hall angle {\theta}DL increases from ~ -0.18 of the pure Ta/Py to the maximum value ~ -0.30 of Ta(O)/Py with 7.8% oxidation. Furthermore, we distinguish the efficiency of the spin-orbit torque generated by the bulk spin Hall effect and by interfacial Rashba effect, respectively, via a series of Py/Cu(0-2 nm)/Ta(O) control experiments. The latter has more than twofold enhancement, and even more significant than that of the former at the optimum oxidation level. Our results indicate that 65% enhancement of the efficiency should be related to the modulation of the interfacial Rashba-like spin-orbit torque due to oxygen-induced orbital hybridization cross the interface. Our results suggest that the modulation of interfacial coupling via oxygen-induced orbital hybridization can be an alternative method to boost the change-spin conversion rate.Comment: 15 pages, 4 figure

Variations and Determinants of Hospital Costs for Acute Stroke in China

BACKGROUND: The burden of stroke is high and increasing in China. We modelled variations in, and predictors of, the costs of hospital care for patients with acute stroke in China. METHODS AND FINDINGS: Baseline characteristics and hospital costs for 5,255 patients were collected using the prospective register-based ChinaQUEST study, conducted in 48 Level 3 and 14 Level 2 hospitals in China during 2006-2007. Ordinary least squares estimation was used to determine factors associated with hospital costs. Overall mean cost of hospitalisation was 11,216 Chinese Yuan Renminbi (CNY) (≈US$1,602) per patient, which equates to more than half the average annual wage in China. Variations in cost were largely attributable to stroke severity and length of hospital stay (LOS). Model forecasts showed that reducing LOS from the mean of 20 days for Level 3 and 18 days for Level 2 hospitals to a duration of 1 week, which is common among Western countries, afforded cost reductions of 49% and 19%, respectively. Other lesser determinants varied by hospital level: in Level 3 hospitals, health insurance and the occurrence of in-hospital complications were each associated with 10% and 18% increases in cost, respectively, whilst treatment in a teaching hospital was associated with approximately 39% decrease in cost on average. For Level 2 hospitals, stroke due to intracerebral haemorrhage was associated with a 19% greater cost than for ischaemic stroke. CONCLUSIONS: Changes to hospital policies to standardise resource use and reduce the variation in LOS could attenuate costs and improve efficiencies for acute stroke management in China. The success of these strategies will be enhanced by broader policy initiatives currently underway to reform hospital reimbursement systems

Folic acid therapy reduces the first stroke risk associated with hypercholesterolemia among hypertensive patients

Background and Purpose - We sought to determine whether folic acid supplementation can independently reduce the risk of first stroke associated with elevated total cholesterol levels in a subanalysis using data from the CSPPT (China Stroke Primary Prevention Trial), a double-blind, randomized controlled trial. Methods - A total of 20 702 hypertensive adults without a history of major cardiovascular disease were randomly assigned to a double-blind daily treatment of an enalapril 10-mg and a folic acid 0.8-mg tablet or an enalapril 10-mg tablet alone. The primary outcome was first stroke. Results - The median treatment duration was 4.5 years. For participants not receiving folic acid treatment (enalapril-only group), high total cholesterol (≥ 200 mg/dL) was an independent predictor of first stroke when compared with low total cholesterol (\u3c200 mg/dL; 4.0% versus 2.6%; hazard ratio, 1.52; 95% confidence interval, 1.18-1.97; P=0.001). Folic acid supplementation significantly reduced the risk of first s roke among participants with high total cholesterol (4.0% in the enalapril-only group versus 2.7% in the enalapril-folic acid group; hazard ratio, 0.69; 95% confidence interval, 0.56-0.84 P\u3c0.001; number needed to treat, 78; 95% confidence interval, 52-158), independent of baseline folate levels and other important covariates. By contrast, among participants with low total cholesterol, the risk of stroke was 2.6% in the enalapril-only group versus 2.5% in the enalapril-folic acid group (hazard ratio, 1.00; 95% confidence interval, 0.75-1.30; P=0.982). The effect was greater among participants with elevated total cholesterol (P for interaction=0.024). Conclusions - Elevated total cholesterol levels may modify the benefits of folic acid therapy on first stroke. Folic acid supplementation reduced the risk of first stroke associated with elevated total cholesterol by 31% among hypertensive adults without a history of major cardiovascular diseases

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data