Super Smooth Research Articles

Policy Optimization Using Semiparametric Models for Dynamic Pricing

ABSTRACT In this article, we study the contextual dynamic pricing problem where the market value of a product is linear in its observed features plus some market noise. Products are sold one at a time, and only a binary response indicating success or failure of a sale is observed. Our model setting is similar to the work by? except that we expand the demand curve to a semiparametric model and learn dynamically both parametric and nonparametric components. We propose a dynamic statistical learning and decision making policy that minimizes regret (maximizes revenue) by combining semiparametric estimation for a generalized linear model with unknown link and online decision making. Under mild conditions, for a market noise cdf F ( · ) with mth order derivative ( m ≥ 2 ), our policy achieves a regret upper bound of O ˜ d ( T 2 m + 1 4 m − 1 ) , where T is the time horizon and O ˜ d is the order hiding logarithmic terms and the feature dimension d. The upper bound is further reduced to O ˜ d ( T ) if F is super smooth. These upper bounds are close to Ω ( T ) , the lower bound where F belongs to a parametric class. We further generalize these results to the case with dynamic dependent product features under the strong mixing condition. Supplementary materials for this article are available online.

Inference on distribution functions under measurement error

This paper is concerned with inference on the cumulative distribution function (cdf) FX∗ in the classical measurement error model X=X∗+ϵ. We consider the case where the density of the measurement error ϵ is unknown and estimated by repeated measurements, and show validity of a bootstrap approximation for the distribution of the deviation in the sup-norm between the deconvolution cdf estimator and FX∗. We allow the density of ϵ to be ordinary or super smooth. We also provide several theoretical results on the bootstrap and asymptotic Gumbel approximations of the sup-norm deviation for the case where the density of ϵ is known. Our approximation results are applicable to various contexts, such as confidence bands for FX∗ and its quantiles, and for performing various cdf-based tests such as goodness-of-fit tests for parametric models of X∗, two sample homogeneity tests, and tests for stochastic dominance. Simulation and real data examples illustrate satisfactory performance of the proposed methods.

Multivariate partially linear regression in the presence of measurement error

In this paper, multivariate partially linear model with error in the explanatory variable of nonparametric part, where the response variable is m dimensional, is considered. By modification of local-likelihood method, an estimator of parametric part is driven. Moreover, the asymptotic normality of the generalized least square estimator of the parametric component is investigated when the error distribution function is either ordinarily smooth or super smooth. Applications in the Engel curves are discussed and through Monte Carlo experiments performances of $$\hat{\beta }_{n}$$ are investigated.

An investigation on the tribological properties of multilayer graphene and MoS2 nanosheets as additives used in hydraulic applications

Recently, we have proposed an Electro-hydrostatic-actuator (EHA) based on a novel linear oscillating motor, which permits nanoparticle additives, such as layered graphene and MoS2, using in hydraulic oil. Especially under a super smooth (Ra~5nm) surface unlike past studies, the tribological properties of these additives is sent more highlight. In addition, oil temperature is introduced into the friction process. We show that the friction coefficient can be decreased to as low as 0.04 when adding MoS2 nanaosheets for the chemical absorption and forming “available solid lubricant” under smooth surface and high temperature while multilayer graphene performs relatively unstable tribological properties because of agglomerates and crystal defects. It can be concluded that MoS2 nanosheets possess better potential value for the application.

Generation of Super Smooth Surface in Compression Test

To investigate the possibility of nanoprocessing by metal forming, the generation of super smooth surface by a simple compression test was attempted. To obtain fundamental information about the generation of a super-smooth surface during metal forming, we investigated a simple compression test of aluminum strips (A1100, 0.8mm thick). In the present study, to examine the effect of materials, compression tests of copper strips were conducted. The tool and specimen surfaces were observed using a conventional stylus surface profilometer and an atomic force microscope. The tool and specimen surfaces were examined by the power spectrum method and the zeroset method of fractal analysis.

Study on Optimal Methodology of RMS Roughness in Super Smooth Surfaces by CCI

Roughness parameters such as the root-mean-square (RMS) roughness in super smooth surfaces are heavily influenced by evaluation ways and measuring method. With the help of CCI6000, relationships were investigated respectively between the RMS roughness with the instrument parameter set and cutoff wavelength. The study revealed that there was an optimal set of measurement parameters and a dynamic cutoff wavelength that would identify different wavelength regimes when measuring super smooth surfaces. It was found that the proposed scheme greatly reduced the influences of CCI instrument parameters and cutoff length on RMS roughness in the measurement of hard disk surfaces. RMS roughness exhibited a steady-state trend and the processed surface morphology conformed to the arrangement of atoms and the polishing feature of CMP technique.

Study on Fullerene Wheel and Diamond Wheel with Super Fine Grain for Creating Super Smooth Surface(Superabrasive/new wheel grinding process)

Fullerene has some special structural, physical, and mechanical properties. The precise and efficient machining by this material to the required quality has not yet been well established. In this paper, a comparative study was conducted to investigate the special aspects in the polishing of silicon wafer using the fullerene wheel, and the diamond wheel of super fine grains. The stability of surface roughness, effects of material grains sizes on the grinding results, and microscopic analysis of grinding phenomena by both materials were also analyzed in detail. The sintering temperature of near 700℃ is suitable for manufacturing diamond wheel. The carbon beads fit to fabricate the small pores in the vitrified-bonded wheel in comparison with the polyethylene beads. The surface roughness of hardened steel is rather larger when ground by 0〜1/8μm than when ground by 0〜1/4μm of diamond grain. This is because the abrasive grains were covered with the bond. It was clarified that we can obtain the surface roughness of 5nm Ra when using fullerene in polishing of silicon wafer.

Wavelet deconvolution

This paper studies the issue of optimal deconvolution density estimation using wavelets. The approach taken here can be considered as orthogonal series estimation in the more general context of the density estimation. We explore the asymptotic properties of estimators based on thresholding of estimated wavelet coefficients. Minimax rates of convergence under the integrated square loss are studied over Besov classes B/sub /spl sigma/pq/ of functions for both ordinary smooth and supersmooth convolution kernels. The minimax rates of convergence depend on the smoothness of functions to be deconvolved and the decay rate of the characteristic function of convolution kernels. It is shown that no linear deconvolution estimators can achieve the optimal rates of convergence in the Besov spaces with p<2 when the convolution kernel is ordinary smooth and super smooth. If the convolution kernel is ordinary smooth, then linear estimators can be improved by using thresholding wavelet deconvolution estimators which are asymptotically minimax within logarithmic terms. Adaptive minimax properties of thresholding wavelet deconvolution estimators are also discussed.

Estimating the Distribution Function of a Stationary Process Involving Measurement Errors

A nonparametric estimation of a distribution function is considered when observations contain measurement errors. A method is developed to establish asymptotic normality results for a deconvoluting kernel-type estimator for ρ-mixing stochastic processes corrupted by some noise process. It is shown that the asymptotic distribution depends on the smoothness of the noise distributions, which are characterized as either ordinary smooth or super smooth. Also, the kind of dependence of the noise process is crucial to the form of the asymptotic variance.

Ultraprecision Machining. Ultraprecision Polishing for Super Smooth Surface and Newly Proposed P-MAC Polishing.

Ultraprecision Machining. Ultraprecision Polishing for Super Smooth Surface and Newly Proposed P-MAC Polishing.

Estimating the conditional mode of a stationary stochastic process from noisy observations

Let {(X i, Y i,)}, i≥1, be a strictly stationary process from noisy observations. We examine the effect of the noise in the response Y and the covariates X on the nonparametric estimation of the conditional mode function. To estimate this function we are using deconvoluting kernel estimators. The asymptotic behavior of these estimators depends on the smoothness of the noise distribution, which is classified as either ordinary smooth or super smooth. Uniform convergence with almost sure convergence rates is established for strongly mixing stochastic processes, when the noise distribution is ordinary smooth.

Nonparametric Regression with Errors in Variables

The effect of errors in variables in nonparametric regression estimation is examined. To account for errors in covariates, deconvolution is involved in the construction of a new class of kernel estimators. It is shown that optimal local and global rates of convergence of these kernel estimators can be characterized by the tail behavior of the characteristic function of the error distribution. In fact, there are two types of rates of convergence according to whether the error is ordinary smooth or super smooth. It is also shown that these results hold uniformly over a class of joint distributions of the response and the covariate, which is rich enough for many practical applications. Furthermore, to achieve optimality, we show that the convergence rates of all possible estimators have a lower bound possessed by the kernel estimators.

Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processes

Errors-in-variables regression is the study of the association between covariates and responses where covariates are observed with errors. In this paper, we consider the estimation of multivariate regression functions for dependent data with errors in covariates. Nonparametric deconvolution technique is used to account for errors-in-variables. The asymptotic behavior of regression estimators depends on the smoothness of the error distributions, which are characterized as either ordinarily smooth or super smooth. Asymptotic normality is established for both strongly mixing and ϱ-mixing processes, when the error distribution function is either ordinarily smooth or super smooth.

Improvement of Conventional Polishing Conditions for Obtaining Super Smooth Surfaces of Glass and Metal Works

Summary In order to ensure the super smooth surface on specific optical devices used in short wavelength optics, a conventional optical polishing method has been improved. taking account of mechanical actions of abrasives, dusts and polisher surface structure. Soft tools as polisher. for instance pitches, waxes and new plastics, were applied to finish of fused quartz, stainless steel, etc. In pitch polishing, worked surfaces with fine abrasive powders and these mixed with coarse hers as a dust model were compared. By using the harder pitch polisher, surface roughness becomes the larger and its tendency is remarkable under dust conditions. Fused quartz works was polished with smooth fluorocarbon foam polisher instead of pitch polisher. Surface roughness value reachs less than 1 nm Rmax with CeO2 powders. Under careful condition for dust, its value results in less than 0.5 nm Rmax with good success in using fluorocarbon foam polisher and fine SiO2 powders.