Uniform Deviation Research Articles

Blind Carrier Frequency Offset Estimation Based on Eighth-Order Statistics for Coherent Optical QAM Systems

We propose a carrier frequency offset estimation (FOE) algorithm based on eighth-order statistics for optical quadrature amplitude modulation (QAM) signals. The FOE algorithm does not involve fast Fourier transformation and can be implemented by hardware with little memory and computation resources. Simulation results show that in a 10.709-GBaud/s optical 16-QAM system, carrier frequency offset ranging between ± 1.25 GHz can be estimated with a uniform standard deviation of 2 MHz when the optical signal-to-noise ratio is 17 dB and 410 symbols are utilized.

Better Moisture Control in Coke Manufacturing- a Case Study

The purpose of coke quenching is to quench the incandescent coke in the hot car using intense water sprays covering entire cross-section of the red hot coke bed and preventing it from burning, at the same time to obtain coke of uniform and minimum deviations in coke moisture. This case study presents a simple approach of developing a Standard Operating Procedure (SOP) to reduce the variation in moisture in Coke by analyzing past data and using Cause and Effect diagram and critically analyzing the contribution of different factors in introducing variation in moisture. The pre and post SOP implementation results are analyzed statistically to ensure that the difference in variance of moisture content is statistically significant. After implementing the action plan for one quarter, overwhelming results were noticed. The standard deviation of moisture on day to day basis has reduced from 2.5% to 1.0%.

Better moisture control in coke manufacturing- a case study

The purpose of coke quenching is to quench the incandescent coke in the hot car using intense water sprays covering entire cross-section of the red hot coke bed and preventing it from burning, at the same time to obtain coke of uniform and minimum deviations in coke moisture. This case study presents a simple approach of developing a Standard Operating Procedure (SOP) to reduce the variation in moisture in Coke by analyzing past data and using Cause and Effect diagram and critically analyzing the contribution of different factors in introducing variation in moisture. The pre and post SOP implementation results are analyzed statistically to ensure that the difference in variance of moisture content is statistically significant. After implementing the action plan for one quarter, overwhelming results were noticed. The standard deviation of moisture on day to day basis has reduced from 2.5% to 1.0%. Keywords: Quenching, Metallurgical coke, Blast furnace, non-recovery oven, Drain time.

A note on uniform exponential convergence of sample average approximation of random functions

Shapiro and Xu (2008) [17] investigated uniform large deviation of a class of Hölder continuous random functions. It is shown under some standard moment conditions that with probability approaching one at exponential rate with the increase of sample size, the sample average approximation of the random function converges to its expected value uniformly over a compact set. This note extends the result to a class of discontinuous functions whose expected values are continuous and the Hölder continuity may be violated for some negligible random realizations. The extension entails the application of the exponential convergence result to a substantially larger class of practically interesting functions in stochastic optimization.

Large deviations theorems in nonparametric regression on functional data

In this Note we prove large deviations principles for the Nadaraya–Watson estimator of the regression of a real-valued variable with a functional covariate. Under suitable conditions, we show pointwise and uniform large deviations theorems.

Some Limit Theorems of Survival Function Estimator for m-Dependent Processes

Let {X n , n ≥ 1} be a stationary sequence of m-dependent random variables with survival function . The empirical survival function based on X 1,…, X n is proposed as an estimator for . In this article, we obtain some asymptotic results of the survival function estimator, which include uniform moderate deviations, Berry-Esséen bound, Cramér type large deviation, and so on.

Moderate deviations for a test of symmetry based on deconvolution kernel density estimators

Suppose that Y1,Y2,…Yn are independent and identically distributed n observations from convolution model Y=X+ɛ, where X is an unobserved random variable with unknown density, Xf and ɛ is the measurement error with a known density function. Set \(\hat fn\left( x \right)\) to be a nonparametric kernel density estimator of fX, and the pointwise and uniform moderate deviations of statistic \(\sup _{x \in R} \left| {\hat f} \right._n \left( x \right) - \left| {\hat f} \right._n \left( { - x} \right)\) are given by Gine and Guillou’s exponential inequality.

Concentration inequalities and confidence bands for needlet density estimators on compact homogeneous manifolds

Let X 1, . . . , X n be a random sample from some unknown probability density f defined on a compact homogeneous manifold M of dimension d ≥ 1. Consider a ‘needlet frame’ \({\{\phi_{j\eta}\}}\) describing a localised projection onto the space of eigenfunctions of the Laplace operator on M with corresponding eigenvalues less than 22j, as constructed in Geller and Pesenson (J Geom Anal 2011). We prove non-asymptotic concentration inequalities for the uniform deviations of the linear needlet density estimator f n (j) obtained from an empirical estimate of the needlet projection \({\sum_\eta \phi_{j \eta}\int f \phi_{j \eta}}\) of f. We apply these results to construct risk-adaptive estimators and nonasymptotic confidence bands for the unknown density f. The confidence bands are adaptive over classes of differentiable and Hölder-continuous functions on M that attain their Hölder exponents.

Uniform large deviations for multivalued stochastic differential equations with Poisson jumps

Based on a variational representation for functionals of a general Poisson random measure plus an independent infinite-dimensional Brownian motion developed by Budhiraja, Dupuis, and Maroulas, the Freidlin-Wentzell large deviation principle is established for multivalued stochastic differential equations with Poisson jumps in this paper.

LARGE DEVIATIONS FOR INFINITE‐DIMENSIONAL STOCHASTIC SYSTEMS WITH JUMPS

Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational representation formula which for an infinite sequence of i.i.d real Brownian motions and a Poisson random measure was shown in [5].

Trigonometric polynomials of least deviation from zero in measure and related problems

We give a solution of the problem on trigonometric polynomials f n with the given leading harmonic y cos n t that deviate the least from zero in measure, more precisely, with respect to the functional μ ( f n ) = mes { t ∈ [ 0 , 2 π ] : | f n ( t ) | ≥ 1 } . For trigonometric polynomials with a fixed leading harmonic, we consider the least uniform deviation from zero on a compact set and find the minimal value of the deviation over compact subsets of the torus that have a given measure. We give a solution of a similar problem on the unit circle for algebraic polynomials with zeros on the circle.

Numerical simulation of microstructure formation of suspended particles in magnetorheologicalfluids

Microstructure formation of magnetic particles and nonmagnetic particles inmagnetorheological (MR) fluids is investigated using the particle method simulation basedon simplified Stokesian dynamics. Spherical nonmagnetic particles are rearranged in thefield direction due to the formation of magnetic particles in chain-like clusters. Clusterformation of spherocylindrical magnetic particles forces spherical nonmagnetic particles toarrange in the direction of the field. In contrast, the spherocylindrical nonmagneticparticles, with an aspect ratio of two or three, are not sufficiently rearranged in the fielddirection by cluster formation of spherical magnetic particles. Even after clusterformation in the presence of a magnetic field, the uniformity of distribution ofparticles on the plane perpendicular to the field direction shows very little change.However, the deviation of uniformity in particle distribution is reduced whenthe volume fraction of magnetic particles is the same as that of nonmagneticparticles.

Uniform large deviation for pinned hyperbolic Brownian motion

We shall establish uniform large deviations for the pinned Brownian motions on a class of two dimensional hyperbolic Riemannian manifolds. It will be shown that the corresponding rate function is given via the infinitesimal generator of a new diffusion process obtained by a harmonic transform of the Brownian motion based on a ground state for the Laplacian.

Force Transmission Error Analysis for a High-Pressure Single-Sinker Magnetic Suspension Densimeter

The magnetic suspension densimeter (MSD) is a sophisticated, state-of-the-art device that provides extremely accurate results for density measurements. The MSD uses a magnetic technique to couple a mass inside a measurement cell with an external mass balance for mass measurement. This article presents a force transmission error (FTE) analysis for a high-pressure, single-sinker MSD. Due to the magnetic working principle of the apparatus, magnetic properties of the high-pressure cell and external magnetic fields affect the measurements slightly. For the analysis, McLinden et al. suggest making measurements using two different sinkers, a titanium sinker and a copper sinker, having the same mass. The measurements cover densities for methane, ethane, carbon dioxide and nitrogen over the temperature range from 265 K to 450 K (±5 mK stability) up to 180 MPa (uncertainty of 0.01 % full scale: 200 MPa). Comparing and manipulating the measurements permit determination of apparatus and fluid specific effects that contribute to the FTE. For this MSD, the apparatus effect is about 200 ppm, which effectively masks any fluid specific effect. A comprehensive analysis of the FTE produces a uniform deviation for density values of about 0.05 % at 2σ across the full range of pressure.

Effect of Grading of Chromite Ores on the Quality of Briquettes

In this paper, the concept of grading of the feed ores has been used for the purpose of evaluation of the compactness of the briquettes. Fuller curve, the most popular ideal grading curve, has been considered. Ideal grading curves can lead to the maximum extent of compaction in the briquettes, ensuring highest strengths of the briquettes. The strength of the briquettes from a given fine ore mix has been assessed in relation to the extent of shift of the grading curve for the feed mix, from its ideal Fuller curve. Two parameters, namely, root mean square deviation (RMSD) and coefficient of uniformity (CU) have been used as the measure of the shifts from the corresponding Fuller curves. Mathematical equations have been derived to establish the correlations between the shatter strengths and hot compressive strengths with RMSD and CU. It is observed from the current work that closeness of a feed mix to its Fuller curve can provide satisfactory strength of the briquettes, but the incremental benefit in strength of the briquettes is reduced progressively with closeness to Fuller curve. This approach can be used to produce briquettes of significantly high strength through selective and optimised grading of the feed mixes.

Moderate deviations for deconvolution kernel density estimators with ordinary smooth measurement errors

In this paper, we establish the pointwise and uniform moderate deviations limit results for the deconvolution kernel density estimator in the errors-in-variables model, when the measurement error possesses an ordinary smooth distribution. The results are similar to the moderate deviations theorems for the classical kernel density estimators, but a factor related to the ordinary smooth order is needed to account for the measurement errors.

On the estimate of the uniform deviation from the class of functions with bounded third derivative

The problem of the uniform approximation of a continuous function on a closed interval by a class of functions with a uniformly bounded third derivative is considered. It is shown that the value of best approximation of a function by this class cannot be estimated linearly in terms of its third-order modulus of continuity. At the same time, such estimates exist for classes with bounded first or second derivatives.

On Uniform Deviations of General Empirical Risks with Unboundedness, Dependence, and High Dimensionality

The statistical learning theory of risk minimization depends heavily on probability bounds for uniform deviations of the empirical risks. Classical probability bounds using Hoeffding's inequality c...

Sheet resistance uniformity in drive-in step for different multi-crystalline silicon wafer dispositions

In this work, we present a study of emitters realized using different configurations of the silicon wafers in the quartz boat. The phosphorous liquid source is sprayed onto p-type multi-crystalline silicon substrates and the drive-in is made at high temperature in a muffle furnace. Three different configurations of the wafers in the boat are tested: separated, back to back and compact block of wafers. A fourth configuration is also used in source–receptor mode. The emitter phosphorous concentration profile is obtained by SIMS analysis. The resulting emitters are characterized by sheet resistance measurements and a comparison is made between the wafers within the same batch and from one batch to another. The uniformity and the standard deviation of the sheet resistance are calculated in each case. The emitter sheet resistance mapping of the wafer set in the middle of the boat for a given process gives a mean R sq 14.66 Ω/sq with a standard deviation of 1.76% and uniformity of 18.7%. Standard deviations of 2.116% and 1.559% are obtained for wafers in the batch when using the spaced and compact configurations, respectively. The standard deviation is reduced to 0.68% when the wafers are used in source/receptor mode. A comparison is also made between wafers with different dilution of phosphorous source in ethanol. From these results we can conclude that the compact configuration offers better uniformity and lower standard deviation. Furthermore, when combined with the source-receptor configuration these parameters are significantly improved. This study allows the experimenter to identify the technological parameters of the solar cell emitter manufacturing and target precisely the desired values of the sheet resistance while limiting the number of rejected wafers.

A Robust Steady-State Model for Flowing-Fluid Temperature in Complex Wells

Summary This paper presents an analytic model for computing the wellbore-fluid-temperature profile for steady fluid flow. Although wells with a constant-deviation angle can be handled with existing analytic models, complex well architectures demand rigorous treat-ment. For example, changing geothermal-temperature-gradient and deepwater wells present significant challenges. Additionally, available analytic models rarely provide calculation methods for various required thermal parameters, such as the Joule-Thompson (J-T) coefficient and fluid expansivity. The approach taken in this study entails dividing the wellbore into many sections of uniform thermal properties and deviation angle. The governing differential equation is solved for each section, with fluid temperature from the prior section as the boundary condition. This piecewise approach makes the model versatile, allowing step-by-step calculation of fluid temperature for the entire wellbore. We present simple, thermodynamically sound approaches for estimating thermal parameters. Success is indicated when performance of the proposed model is compared with data from three wells, producing two-phase gas/oil mixture, single-phase oil, and single-phase gas. Sensitivity of the estimated fluid temperatures to various thermal properties is also examined with our model. Overall, the effects of the J-T coefficient and liquid expansivity are found to be significant.