Statistical and systematic errors in Monte Carlo sampling

We have studied the statistical and systematic errors which arise in Monte Carlo simulations and how the magnitude of these errors depends on the size of the system being examined when a fixed amount of computer time is used. We find that, depending on the degree of self-averaging exhibited by the quantities measured, the statistical errors can increase, decrease, or stay the same as the system size is increased. The systematic underestimation of response functions due to the finite number of measurements made is also studied. We develop a scaling formalism to describe the size dependence of these errors, as well as their dependence on the bin length (size of the statistical sample), both at and away from a phase transition. The formalism is tested using simulations of thed=3 Ising model at the infinite-lattice transition temperature. We show that for a 96×96×96 system noticeable systematic errors (systematic underestimation of response functions) are still present for total run lengths of 10⁶ Monte Carlo steps/site (MCS) with measurements taken at regular intervals of 10 MCS.This paper is dedicated to Jerry Percus on the occasion of his 65th birthday.     

Some systematic errors of magnetic induced anisotropy measurements

The paper presents an estimate of the magnitude of additional torsion of magnetostatic origin, and sets forth the conditions determining its periodicity in a homogeneous and an inhomogeneous magnetic field.It further deals with the eifect of inaccurate specimen orientation on the determination of coefficientsF andG and finds the following: If is the error of orientation of the plane of measurement, the error ofF measurement is [2F+G] sin² and the error of (1/2)G measurement is [F}+(1/2)G] sin² at most. If is the error of the setting of the direction of measurement or annealing, the maximum error ofF measurement is [–F±(1/2)G] sin² 2, and that of (1/2)G measurement is [–(1/2)G±F] sin² 2].In conclusion, the author wishes to express his thanks to Dr. J. ternberk CSc. for his valuable discussion and comments on this paper.     

MUB tomography performance under influence of systematic errors

We propose a method for accounting the simplest type of systematic errors in the mutually unbiased bases (MUB) tomography, emerging due to an imperfect (non-orthogonal) preparation of measurement bases. The present approach allows to analyze analytically the performance of MUB tomography in finite systems of an arbitrary (prime) dimension. We compare the estimation error appearing in such an imperfect MUB-based tomography with those intrinsically present in the framework of the symmetric informationally complete positive operator value measure (SIC-POVM) reconstruction scheme and find that MUB tomography outperforms the perfect SIC-POVM tomography including the case of strong errors.     

复式螺旋测微器螺距误差补偿与示值误差综合

本文简要介绍了复式螺旋测微器的设计原理,在复式螺旋运动误差分析的基础上,提出了一种螺距误差自动补偿方法。通过样机的螺距误差实测曲线和测微器示值误差检定结果,验证了它的可行性和示值误差综合的正确性。     

Quality assessment of speckle patterns for DIC by consideration of both systematic errors and random errors

The performance of digital image correlation (DIC) is influenced by the quality of speckle patterns significantly. Thus, it is crucial to present a valid and practical method to assess the quality of speckle patterns. However, existing assessment methods either lack a solid theoretical foundation or fail to consider the errors due to interpolation. In this work, it is proposed to assess the quality of speckle patterns by estimating the root mean square error (RMSE) of DIC, which is the square root of the sum of square of systematic error and random error. Two performance evaluation parameters, respectively the maximum and the quadratic mean of RMSE, are proposed to characterize the total error. An efficient algorithm is developed to estimate these parameters, and the correctness of this algorithm is verified by numerical experiments for both 1 dimensional signal and actual speckle images. The influences of correlation criterion, shape function order, and sub-pixel registration algorithm are briefly discussed. Compared to existing methods, method presented by this paper is more valid due to the consideration of both measurement accuracy and precision.     

An evaluation of precision and systematic errors in vibrational CARS thermometry

The extraction of temperatures from experimental CARS spectra is discussed and demonstrated in an electrically heated over and a low-pressure flame. The present work is focused, in particular, on how the precision of CARS thermometry is limited by the accuracy with which the experimental parameters are known, on characteristics of the diode-array detector, on saturation effects due to stimulated Raman scattering and on the influence of spectral resolution on precision and accuracy.     

Elimination of systematic errors in applied accurate lattice parameter measurements

The method of accurate lattice parameters evaluation of polycrystalline materials is described which does not require direct quantitative data expressing the magnitude of systematic errors. Positions of a series of lines in back reflection region are used as input data for the computer evaluation, which are a linear function of the Bragg angle (or its complement) so that in the case of film measurement the diameter of the camera, and in the case of diffractometer measurement, the zero setting of the goniometer need not be determined independently. The method is illustrated in detail for back reflection film measurements in a cylinder camera. The method is aimed at making easy the applied accurate lattice parameter measurements.The author is deeply indebted to the late Professor M. E.Straumanis for valuable discussions in 1970 about the experimental problems of accurate lattice parameters measurements by film method and for making possible to use the original instruments in his laboratory. The author expresses his thanks to Mrs. V.Gregorová and Mr. M.Jelínek for taking part in the experiments.     

Study of systematic errors of bound-state parameters in SVZ sum rules

We study systematic errors of the ground-state parameters obtained from Shifman—Vainshtein—Zakharov sum rules, making use of the harmonic-oscillator potential model as an example. In this case, one knows the exact solution for the polarization operator, which allows one to obtain both the OPE to any order and the parameters (masses and decay constants) of the bound states. We determine the parameters of the ground state making use of the standard procedures of the method of sum rules and compare the obtained results with the known exact values. We show that, in the situation when the continuum contribution to the polarization operator is not known and is modeled by an effective continuum, the method of sum rules does not allow one to control the systematic uncertainties of the extracted ground-state parameters. The text was submitted by the authors in English.     

Correction of systematic errors in the fabrication of fiber Bragg gratings

We suggest a novel method for significant improvement of fiber Bragg grating (FBG) spectral characteristics based on compensation of repeatable errors during the grating writing process. The method is based on an open loop scheme in which a test grating is written first and then a corrected design is obtained and implemented by writing another (compensated) grating. The results are presented for a FBG dispersion compensator.     

On systematic errors in spectral line parameters retrieved with the Voigt line profile

Systematic errors inherent in the Voigt line profile are analyzed. Molecular spectrum processing with the Voigt profile is shown to underestimate line intensities by 1–4%, with the errors in line positions being 0.0005 cm^?1 and the decrease in pressure broadening coefficients varying from 5% to 55%.     

实验误差及减小测量误差的几种方法

在高中物理实验教学过程中，我们不仅要让学生动手实验，探索物理规律，同时还要渗透物理实验思想与物理实验方法以及实验误差分析的教育．在设计实验方案、安排实验、进行实验测量时，都要采取适当的方法或措施来减小测量中的误差．本文就谈谈在物理实验中所涉及的误差问题以及减小测量误差的几种常用方法．     

Analysis of systematic errors of lidar gas analysis in the atmosphere by the differential absorption lidar method

In the present work, systematic errors of lidar gas analysis in the atmosphere by the differential absorption lidar method in the near-and middle-IR ranges of the spectrum are analyzed. It is demonstrated that the systematic errors depend on many factors, including the meteorological parameters and concentrations of the examined gases along the sensing path, instability of the spectral parameters of laser radiation lines, shift of the absorption line centers caused by the air pressure, Doppler broadening of backscattered signals, and other sources of errors. Methods of error minimization in reconstructing lidar profiles of the examined atmospheric gas concentrations are suggested. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 68–73, June, 2008.     

A novel determination method of thin film optical parameters with least dependence on photometric measurement systematic errors

We present a novel determination method of thin film optical parameters based on partial derivatives selection, which is with least impact of photometric measurement systematic errors on the characterization accuracy of thin film optical parameters. The spectral measurement data used in our numerical simulations are the single wavelength photometric data of P-polarization light measured at different incident angles. It is shown that, under the same level of systematic errors in the measurement data, the deviations of the fitted optical parameters values from real ones in spectral bands with opposite signs of partial derivatives for most incident angles at which measurement data are collected are much smaller than other spectral regions. The theoretical explanations are discussed. It is advisable to select spectrophotometric data from the recommended spectral bands and to remove the dangerous spectral bands according to derivatives information for optical characterization of thin films with best accuracy.     

Optimal filtering of states of discrete linear stochastic system by using multichannel measurement complexes with Markovian observation errors

We consider the problem of state filtering of a discrete linear stochastic system by data of multichannel measurement complexes, characterized by internal Markovian phase transformations affecting the observation process. A reduced filtering algorithm, with substantially less computational complexity than the general algorithm, is obtained in the case of identical measurement complexes.Anzhero-Sudzhenskii Branch of the Tomsk Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 93–98, December, 1993.     

Double focus interferometers and errors the influence of their sample setting errors

Double Focus interferometers are attractive for reducing the influence of ambient conditions due to their common-path configuration. This paper describes the influence of sample setting errors in these interferometers. They have been divided into two types, i.e. the normal illumination type and the oblique illumination type. For each type, an equation of the measurement error due to sample setting error has been derived with Gaussian optics. The measurement error of the normal illumination type becomes a parabolic function of the position on the sample surface. The derived error equations have been verified by ray tracing and by experiment. The error of the oblique type is smaller than that of the normal type.     

Extraction of parton distributions and \alpha_{\mathrm{s}} from DIS data within a Bayesian treatment of systematic errors

We have performed a NLO QCD global fit of BCDMS, NMC, H1 and ZEUS data with full account of point-to-point correlations using the Bayesian approach to the treatment of systematic errors. Parton distributions in the proton with their experimental uncertainties, including both statistical and systematic, are obtained. The gluon distribution in a wide region of x is found to be softer than the gluon distribution extracted in standard global analyses which include prompt photon data. We obtain a robust estimate of C.L.) based on Chebyshev's inequality, which is compatible with an earlier determination of from the DIS data, but is less dependent on high-twist effects. Received: 5 May 1997 / Revised version: 12 October 1998 / Published online: 8 September 1999