Reducing variance in univariate smoothing

A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias remains unchanged. The nearby points are chosen to maximize the variance reduction. We study in detail the case of univariate local linear regression. While the new estimator retains many advantages of the local linear estimator, it has appealing asymptotic relative efficiencies. Bandwidth selection rules are available by a simple constant factor adjustment of those for local linear estimation. A simulation study indicates that the finite sample relative efficiency often matches the asymptotic relative efficiency for moderate sample sizes. This technique is very general and has a wide range of applications.Comment: Published at http://dx.doi.org/10.1214/009053606000001398 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Evidence for Dirac Fermions in a honeycomb lattice based on silicon

Silicene, a sheet of silicon atoms in a honeycomb lattice, was proposed to be a new Dirac-type electron system similar as graphene. We performed scanning tunneling microscopy and spectroscopy studies on the atomic and electronic properties of silicene on Ag(111). An unexpected $\sqrt{3}\times \sqrt{3}$ reconstruction was found, which is explained by an extra-buckling model. Pronounced quasi-particle interferences (QPI) patterns, originating from both the intervalley and intravalley scattering, were observed. From the QPI patterns we derived a linear energy-momentum dispersion and a large Fermi velocity, which prove the existence of Dirac Fermions in silicene.Comment: 6 pages, 4 figure

A new time-frequency method to reveal quantum dynamics of atomic hydrogen in intense laser pulses: Synchrosqueezing Transform

This study introduces a new adaptive time-frequency (TF) analysis technique, synchrosqueezing transform (SST), to explore the dynamics of a laser-driven hydrogen atom at an {\it ab initio} level, upon which we have demonstrated its versatility as a new viable venue for further exploring quantum dynamics. For a signal composed of oscillatory components which can be characterized by instantaneous frequency, the SST enables rendering the decomposed signal based on the phase information inherited in the linear TF representation with mathematical support. Compared with the classical type TF methods, the SST clearly depicts several intrinsic quantum dynamical processes such as selection rules, AC Stark effects, and high harmonic generation

Observation of clinical efficacy of pattern scan laser photocoagulation on diabetic retinopathy

AIM: To evaluate the clinical efficacy of pattern scan laser photocoagulation(Pascal)on proliferative diabetic retinopathy(PDR).<p>METHODS: A total of 93 patients with retinopathy(186 eyes)were randomly divided into treatment group(96 eyes of 48 patients)who treated with panretinal photocoagulation(PRP)using Pascal at one time and control group(90 eyes of 45 patients)who treated with PRP using multi-wavelength krypton laser in 4-5 times. The visual acuity, FFA, OCT, visual field will be evaluated of each patient before and after the treatment.<p>RESULTS: The visual acuity findings were stated as below: the overall effective rate of visual acuity in treatment group is 85.4% while it is 82.2% in control group. The overall effective rate in two groups has no significant difference. The retinal sensitivity has no significant decrease in the treatment group while which decreased significantly in the control group.<p>CONCLUSION: The clinical efficacy of Pascal on treating the PDR is better than which of the regular argon laser. The field of vision has no significant narrowed after the Pascal treatment which can efficiently shorten the length of treatment and reduce the pain sensation