Density convergence in the Breuer-Major theorem for Gaussian stationary sequences

Consider a Gaussian stationary sequence with unit variance $X=\{X_k;k\in {\mathbb{N}}\cup\{0\}\}$. Assume that the central limit theorem holds for a weighted sum of the form $V_n=n^{-1/2}\sum^{n-1}_{k=0}f(X_k)$, where $f$ designates a finite sum of Hermite polynomials. Then we prove that the uniform convergence of the density of $V_n$ towards the standard Gaussian density also holds true, under a mild additional assumption involving the causal representation of $X$.Comment: Published at http://dx.doi.org/10.3150/14-BEJ646 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Central limit theorem for an additive functional of the fractional Brownian motion

We prove a central limit theorem for an additive functional of the $d$-dimensional fractional Brownian motion with Hurst index $H\in(\frac{1}{1+d},\frac{1}{d})$, using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion.Comment: Published in at http://dx.doi.org/10.1214/12-AOP825 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

2-(4-Bromo­phen­yl)-3,4-dihydro­isoquinolin-2-ium thio­cyanate hemihydrate

In the title hemihydrated salt, C15H13BrN+·NCS−·0.5H2O, the two benzene rings are aligned at a dihedral angle of 46.9 (1)°. The six-membered heterocycle of the dihydro­isoquinoline unit adopts a half-chair conformation. The water mol­ecule and thio­cyanate ion are linked by O—H⋯N hydrogen bonds, generating a four-membered ring motif. In addition, C—H⋯O and C—H⋯S inter­actions link the components into a chain along the c axis. π–π inter­actions [centroid–centroid distance = 3.974 (2) Å] link the chains into sheets and further π—π [centroid–centroid distance = 3.746 (2) Å] and C—H⋯π inter­actions give rise to a three-dimensional nework

Online Estimation of ARW Coefficient of Fiber Optic Gyro

As a standard method for noise analysis of fiber optic gyro (FOG), Allan variance has too large offline computational burden and data storages to be applied to online estimation. To overcome the barriers, the state space model is firstly established for FOG. Then the Sage-husa adaptive Kalman filter (SHAKF) is introduced in this field. Through recursive calculation of measurement noise covariance matrix, SHAKF can avoid the storage of large amounts of history data. However, the precision and stability of this method are still the primary matters that needed to be addressed. Based on this point, a new online method for estimation of the coefficient of angular random walk is proposed. In the method, estimator of measurement noise is constructed by the recursive form of Allan variance at the shortest sampling time. Then the estimator is embedded into the SHAKF framework resulting in a new adaptive filter. The estimations of measurement noise variance and Kalman filter are independent of each other in this method. Therefore, it can address the problem of filtering divergence and precision degrading effectively. Test results of both digital simulation and experimental data of FOG verify the validity and feasibility of the proposed method

Quantifying the Expressive Capacity of Quantum Systems: Fundamental Limits and Eigentasks

The expressive capacity of quantum systems for machine learning is limited by quantum sampling noise incurred during measurement. Although it is generally believed that noise limits the resolvable capacity of quantum systems, the precise impact of noise on learning is not yet fully understood. We present a mathematical framework for evaluating the available expressive capacity of general quantum systems from a finite number of measurements, and provide a methodology for extracting the extrema of this capacity, its eigentasks. Eigentasks are a native set of functions that a given quantum system can approximate with minimal error. We show that extracting low-noise eigentasks leads to improved performance for machine learning tasks such as classification, displaying robustness to overfitting. We obtain a tight bound on the expressive capacity, and present analyses suggesting that correlations in the measured quantum system enhance learning capacity by reducing noise in eigentasks. These results are supported by experiments on superconducting quantum processors. Our findings have broad implications for quantum machine learning and sensing applications.Comment: 7 + 21 pages, 4 + 12 figures, 1 tabl

Corneal Surface Ablation Laser Refractive Surgery for the Correction of Myopia: A Network Meta-analysis

PURPOSE: To systematically compare the efficacy, predictability, safety, postoperative haze, pain scores, and epithelial healing time of four corneal surface ablation procedures. METHODS: PubMed, Embase, Cochrane Library, and the U.S. trial registry were searched up to June 2018. Randomized controlled trials were selected. Efficacy (uncorrected distance visual acuity of 20/20 or better), predictability (refractive spherical equivalent within ±0.50 diopters [D] of the target), and safety (loss of two or more lines of spectacle corrected distance visual acuity) were set as primary outcome measures. Haze, pain scores, and epithelial healing time were set as secondary outcome measures. RESULTS: Eighteen studies involving 1,423 eyes were included. According to the Grading of Recommendations Assessment, Development, and Evaluation, the quality of outcomes were moderate to high (70.6%). There were no differences in efficacy, predictability, safety, haze, day 1 pain, and epithelial healing time between treatments. Epithelial laser in situ keratomileusis (epi-LASIK) had statistically significantly higher pain scores on day 3 compared to photorefractive keratectomy (PRK) (weighted mean differences [WMD] = 2.2, 95% credible intervals [CrI] = 0.19 to 4.01) and transepithelial PRK (T-PRK) (WMD = 2.7, 95% CrI = 0.51 to 4.84). The surface under the cumulative ranking curve ranking results (best to worst) showed laser epithelial keratomileusis (LASEK) ranked highest for efficacy, predictability, safety, and day 1 pain scores. Epi-LASIK ranked best for grade 1 haze scores. T-PRK ranked best for haze of 0.5 or higher, haze scores day 3 pain scores, and epithelial healing time. CONCLUSIONS: Surface laser refractive surgeries are comparable in terms of efficacy, predictability, safety, and postoperative haze except for day 3 pain scores, with epi-LASIK being more painful compared to PRK and T-PRK. [J Refract Surg. 2018;34(11):726-735.]