During the evaluation of the continuous measurement signal of analytical instruments by a digital computer, the signal is sampled periodically, and the analytical information [1] is computed from this sequence of discrete values representing the signal by the procedure called data reduction [2]. For example, retention data, peak heights and/or peak areas are produced from the raw discretized si...

We investigate function estimation in nonparametric regression models with random design and heteroscedastic correlated noise. Adaptive properties of warped wavelet nonlinear approximations are studied over a wide range of Besov scales, f ∈ B π,r, and for a variety of L error measures. We consider error distributions with Long-RangeDependence parameter α,0 < α ≤ 1; heteroscedasticity is modeled...

The paper presents lower and upper bounds on the number of parity check digits required for a linear code that detects solid bursts of length b or less and simultaneously any e or less random errors. An example of such a code is also provided. Further, codes capable of detecting and simultaneously correcting such errors have also been dealt with.

A statistically consistent and physically realistic approach for validating vector magnitude measurements is developed, based on a model for random measurement noise that explicitly satisfies a nonnegativity constraint for all ‘‘noisy’’ vector magnitude measurements. Numerical and analytic approximations are used to quantify the nonlinear functional dependence of sample conditional means on tru...

We show that quantum expander codes, a constant-rate family of quantum LDPC codes, with the quasi-linear time decoding algorithm of Leverrier, Tillich and Zémor can correct a constant fraction of random errors with very high probability. This is the first construction of a constant-rate quantum LDPC code with an efficient decoding algorithm that can correct a linear number of random errors with...

Errors and error sources occurring in rotating-analyzer ellipsometry are discussed. From general considerations it is shown that a rotating-analyzer ellipsometer is inaccurate if applied at P = 00 and in cases when 0 = 0' or where A is near 00 or 1800. Window errors, component imperfections, azimuth errors and all other errors may, to first order, be treated independently and can subsequently b...

While the impact of measurement errors inherent in network data has been widely recognized, relatively little work has been done to solve the problem mainly due to the complex dependence nature of network data. In this paper, we propose a Bayesian inference framework for summary statistics of the true underlying network, based on the network observed with measurement errors. To the best of our ...

This paper presents lower and upper bounds on the number of parity-check digits required for a linear code that corrects random errors and errors which are in the form of low-density bursts.

[1] In order to validate the reported precision of space‐based atmospheric composition measurements, validation studies often focus on measurements in the tropical stratosphere, where natural variability is weak. The scatter in tropical measurements can then be used as an upper limit on single‐profile measurement precision. Here we introduce a method of quantifying the scatter of tropical measu...