Independent Measurement Errors Research Articles

Single-shot quantum error correction with the three-dimensional subsystem toric code

Fault-tolerant protocols and quantum error correction (QEC) are essential to building reliable quantum computers from imperfect components that are vulnerable to errors. Optimizing the resource and time overheads needed to implement QEC is one of the most pressing challenges. Here, we introduce a new topological quantum error-correcting code, the three-dimensional subsystem toric code (3D STC). The 3D STC can be realized with geometrically-local parity checks of weight at most three on the cubic lattice with open boundary conditions. We prove that one round of parity-check measurements suffices to perform reliable QEC with the 3D STC even in the presence of measurement errors. We also propose an efficient single-shot QEC decoding strategy for the 3D STC and numerically estimate the resulting storage threshold against independent bit-flip, phase-flip and measurement errors to be pSTC ≈ 1.045%. Such a high threshold together with local parity-check measurements make the 3D STC particularly appealing for realizing fault-tolerant quantum computing.

Biomarker-Based Methods and Study Designs to Calibrate Dietary Intake for Assessing Diet–Disease Associations

BackgroundDietary biomarkers measured in biospecimens can play an important role in correcting for random and systematic measurement error in self-reported nutrient intake when assessing diet–disease associations. To date, high-quality biomarkers for calibrating self-reported dietary intake have only been developed for a few nutrients. ObjectivesTo investigate new study designs and regression calibration approaches for calibrating self-reported nutrient intake for use in disease association analyses. MethodsWe studied 3 regression calibration approaches: 1) an existing approach built on a calibration cohort assuming the existence of an objective biomarker (i.e., biomarker with random independent measurement error), 2) a proposed approach using a biomarker development cohort, and 3) a proposed 2-stage approach using both cohorts. We conducted simulation studies to compare the performance of different study designs/methods for estimating diet–disease associations and applied suitable methods to examine the association of sodium and potassium intake with cardiovascular disease (CVD) risk in Women's Health Initiative cohorts. ResultsSimulation studies showed that the first approach can lead to biased association estimation when the objective biomarker assumption is violated; the second and third proposed approaches obviate the need for such an objective biomarker. Precision for estimating the association depends critically on sample size of the biomarker development cohort and the strength of the self-reported nutrient intake. Analyses based on the second and third approaches support previously reported significant findings using the first approach about associations of the ratio of sodium to potassium intake with CVD risk while providing efficiency gain for some outcomes. ConclusionsSelf-reported dietary intake needs to be calibrated for measurement error correction in diet–disease association analyses. When there are no existing objective biomarkers that can be used for calibration purpose, controlled feeding studies can be used to develop new biomarkers for use in calibration or can be used to calibrate self-reported dietary intake directly.

Vapor-liquid equilibrium in the tin–lead system in primary vacuum

The boiling point method (isothermal version) was used to determine the partial pressure of saturated lead vapor over lead-tin solutions with the following lead content (the rest is tin), wt.%: 96.43, 93.02, 89.55, 80.73, 64.18, and 43.80 (93.93, 88.42, 83.08, 70.59, 50.65, and 30.87 at.%, respectively). The partial pressures of tin were calculated by the numerical integration of the Duhem–Margules equation using the auxiliary function proposed by Darken. The tin and lead partial pressure values over their melts were approximated by temperatureconcentration dependences. The total determination error was calculated as a sum of independent measurement errors: temperature, mass, pressure, approximation of experimental data, equal to 7.78 %. Based on the values of saturated lead and tin vapor partial pressures, the boundaries of liquid and vapor coexistence fields in the tin-lead system in a primary vacuum of 100 and 1 Pa were calculated and specified: boiling temperature – as a temperature at which the sum of metal partial pressures is equal to 100 and 1 Pa, vapor composition – as the ratio of metal vapor partial pressures at this temperature. It was found that the reason for the increased content of tin in lead condensate during the distillation of alloys with a lead content of less than 5 at.% (8.41 wt.%) and tin accumulation in the distillation residue is partial pressure values of tin vapor comparable to that of lead. Tin accumulation in the distillation residue should not exceed a concentration of ~ 50 wt.% during the distillation separation of lead-tin melts by lead evaporation in a real process under non-equilibrium conditions. If the specified concentration is exceeded, the condensate obtained will require repeating the evaporation-condensation process.

Model-Based Clustering with Measurement or Estimation Errors.

Model-based clustering with finite mixture models has become a widely used clustering method. One of the recent implementations is MCLUST. When objects to be clustered are summary statistics, such as regression coefficient estimates, they are naturally associated with estimation errors, whose covariance matrices can often be calculated exactly or approximated using asymptotic theory. This article proposes an extension to Gaussian finite mixture modeling—called MCLUST-ME—that properly accounts for the estimation errors. More specifically, we assume that the distribution of each observation consists of an underlying true component distribution and an independent measurement error distribution. Under this assumption, each unique value of estimation error covariance corresponds to its own classification boundary, which consequently results in a different grouping from MCLUST. Through simulation and application to an RNA-Seq data set, we discovered that under certain circumstances, explicitly, modeling estimation errors, improves clustering performance or provides new insights into the data, compared with when errors are simply ignored, whereas the degree of improvement depends on factors such as the distribution of error covariance matrices.

A cautionary note on the finite sample behavior of maximal reliability.

Several calls have been made for replacing coefficient α with more contemporary model-based reliability coefficients in psychological research. Under the assumption of unidimensional measurement scales and independent measurement errors, two leading alternatives are composite reliability and maximal reliability. Of these two, the maximal reliability statistic, or equivalently Hancock's H, has received a significant amount of attention in recent years. The difference between composite reliability and maximal reliability is that the former is a reliability index for a scale mean (or unweighted sum), whereas the latter estimates the reliability of a scale score where indicators are weighted differently based on their estimated reliabilities. The formula for the maximal reliability weights has been derived using population quantities; however, their finite-sample behavior has not been extensively examined. Particularly, there are two types of bias when the maximal reliability statistic is calculated from sample data: (a) the sample maximal reliability estimator is a positively biased estimator of population maximal reliability, and (b) the true reliability of composites formed with maximal reliability weights calculated from sample data is on average less than the population reliability. Both effects are more pronounced in small-sample scenarios (e.g., <100). We also demonstrate that the composite reliability estimator for equally weighted composite exhibits substantially less bias, which makes it a more appropriate choice for the small-sample case. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Demographic-specific Validity of the Cancer Prevention Study-3 Sedentary Time Survey.

This study examined the 1-yr test-retest reliability and criterion validity of sedentary time survey items in a subset of participants from a large, nationwide prospective cohort. Participants included 423 women and 290 men age 31 to 72 yr in the Cancer Prevention Study-3. Reliability was assessed by computing Spearman correlation coefficients between responses from prestudy and poststudy surveys. Validity was assessed by comparing survey-estimated sedentary time with a latent variable representing true sedentary time estimated from the 7-d diaries, accelerometry, and surveys through the method of triads. Sensitivity analyses were restricted to 566 participants with an average of 14+ h of diary and accelerometer data per day for 7 d per quarter. Reliability estimates for total sitting time were moderate or strong across all demographic strata (Spearman ρ ≥ 0.6), with significant differences by race (P = 0.01). Reliability estimates were strongest for the TV-related sedentary time item (Spearman ρ, 0.74; 95% confidence interval, 0.70-0.77). The overall validity coefficient (VC) for survey-assessed total sedentary time was 0.62 (95% confidence interval, 0.55-0.69), although VC varied by age group and activity level (P < 0.05). However, VC were similar across groups (P < 0.05) when restricting to highly compliant participants in a sensitivity analysis. The Cancer Prevention Study-3 sedentary behavior questionnaire has acceptable reliability and validity for ranking or categorizing participants according to sedentary time. Acceptable reliability and validity estimates persist across various demographic subgroups.

Experimental evaluation of the nonclassical relation between measurement errors using entangled photon pairs as a probe

We have experimentally evaluated the non-classical relation between measurement errors in a joint measurement of two non-commuting polarizations by using entangled photon pairs as a probe. The joint measurement was realized by filtering polarization directions that are sensitive to both of the two target polarizations and the same filtering procedures were applied independently to the two photons of an entangled pair. Since the statistically independent measurement errors of two identical measurements performed on entangled pairs will reduce an overall visibility of the correlation by the square of the local visibilities, the squared visibilities of the local measurements can be obtained directly from the measurement data. We apply this method to determine the visibility of the correlation between the products of the two non-commuting polarizations, a characteristic of the measurement errors that can not be obtained locally since there is no self-adjoint operator that describes this product of measurement outcomes as a single photon observable. The experimental results clearly show that the square of the product visibility is negative, indicating the non-classical nature of the statistical relation between the measurement errors of non-commuting polarizations.

Decentralised estimation with correlation limited by optimal processing of independent data

Decentralised estimation aims at providing the best combination of multiple estimates. Since the exact solutions are expensive in terms of computation and communication requirements, the mean square error optimality is traded for the bound optimality. Fusion under unknown correlations has been inspected for two decades and the research now focuses on a partial knowledge of the correlations. This paper focuses on the assumption that the estimates to be fused were obtained by the optimal processing of local data with independent measurement errors. A generalisation of a recent solution to such a problem is proposed. In particular, non-uniqueness of the optimal fusion weights is discovered. The relation of the generalised and existing solutions is discussed and illustrative examples are given.

Implications of measurement error structure on the visualization of multivariate chemical data: hazards and alternatives

The analysis of multivariate chemical data is commonplace in fields ranging from metabolomics to forensic classification. Many of these studies rely on exploratory visualization methods that represent the multidimensional data in spaces of lower dimensionality, such as hierarchical cluster analysis (HCA) or principal components analysis (PCA). However, such methods rely on assumptions of independent measurement errors with uniform variance and can fail to reveal important information when these assumptions are violated, as they often are for chemical data. This work demonstrates how two alternative methods, maximum likelihood principal components analysis (MLPCA) and projection pursuit analysis (PPA), can reveal chemical information hidden from more traditional techniques. Experimental data to compare different methods consists of near-infrared (NIR) reflectance spectra from 108 samples of wood that are derived from four different species of Brazilian trees. The measurement error characteristics of the spectra are examined and it is shown that, by incorporating measurement error information into the data analysis (through MLPCA) or using alternative projection criteria (i.e., PPA), samples can be separated by species. These techniques are proposed as powerful tools for multivariate data analysis in chemistry.

Causes of blood methylomic variation for middle-aged women measured by the HumanMethylation450 array

ABSTRACTTo address the limitations in current classic twin/family research on the genetic and/or environmental causes of human methylomic variation, we measured blood DNA methylation for 479 women (mean age 56 years) including 66 monozygotic (MZ), 66 dizygotic (DZ) twin pairs and 215 sisters of twins, and 11 random technical duplicates using the HumanMethylation450 array. For each methylation site, we estimated the correlation for pairs of duplicates, MZ twins, DZ twins, and siblings, fitted variance component models by assuming the variation is explained by genetic factors, by shared and individual environmental factors, and by independent measurement error, and assessed the best fitting model. We found that the average (standard deviation) correlations for duplicate, MZ, DZ, and sibling pairs were 0.10 (0.35), 0.07 (0.21), -0.01 (0.14) and -0.04 (0.07). At the genome-wide significance level of 10−7, 93.3% of sites had no familial correlation, and 5.6%, 0.1%, and 0.2% of sites were correlated for MZ, DZ, and sibling pairs. For 86.4%, 6.9%, and 7.1% of sites, the best fitting model included measurement error only, a genetic component, and at least one environmental component. For the 13.6% of sites influenced by genetic and/or environmental factors, the average proportion of variance explained by environmental factors was greater than that explained by genetic factors (0.41 vs. 0.37, P value <10−15). Our results are consistent with, for middle-aged woman, blood methylomic variation measured by the HumanMethylation450 array being largely explained by measurement error, and more influenced by environmental factors than by genetic factors.

Correction of confidence intervals in excess relative risk models using Monte Carlo dosimetry systems with shared errors.

In epidemiological studies, exposures of interest are often measured with uncertainties, which may be independent or correlated. Independent errors can often be characterized relatively easily while correlated measurement errors have shared and hierarchical components that complicate the description of their structure. For some important studies, Monte Carlo dosimetry systems that provide multiple realizations of exposure estimates have been used to represent such complex error structures. While the effects of independent measurement errors on parameter estimation and methods to correct these effects have been studied comprehensively in the epidemiological literature, the literature on the effects of correlated errors, and associated correction methods is much more sparse. In this paper, we implement a novel method that calculates corrected confidence intervals based on the approximate asymptotic distribution of parameter estimates in linear excess relative risk (ERR) models. These models are widely used in survival analysis, particularly in radiation epidemiology. Specifically, for the dose effect estimate of interest (increase in relative risk per unit dose), a mixture distribution consisting of a normal and a lognormal component is applied. This choice of asymptotic approximation guarantees that corrected confidence intervals will always be bounded, a result which does not hold under a normal approximation. A simulation study was conducted to evaluate the proposed method in survival analysis using a realistic ERR model. We used both simulated Monte Carlo dosimetry systems (MCDS) and actual dose histories from the Mayak Worker Dosimetry System 2013, a MCDS for plutonium exposures in the Mayak Worker Cohort. Results show our proposed methods provide much improved coverage probabilities for the dose effect parameter, and noticeable improvements for other model parameters.

A Joint Model for Possibly Multivariate Longitudinal End Point in Clinical Cohort Study

This paper is motivated in modeling a joint mixed effect model incorporating random effects with independent measurement error for both end points. Both the association in the evolution (AOE) for two or possibly multiple outcomes and evolution in the association (EOA) are expected to be assessed by joint mixed effect model. The proposed model is further trustful of grasping the problem of nonlinearity and absence of normality assumption and in turn is to predict the effect of associated covariates in the progressive evolution of longitudinal outcomes throughout the given time interval. As case study the two outcomes Systolic Blood Pressure (SBP) and Diastolic Blood Pleasure (DBP) of hypertensive patients are considered. The summary statistics of the two end points are included in this context. Thus, the average follow-up is 4.21(0.088) months, the average SBP and DBP of hypertensive patients are 136.12(0.367) and 85.13(0.273) respectively and the standard deviation of SBP and DBP are 16.21 and 12.06 respectively. Moreover, the average age of the hypertensive patients is 50.63(0.315) years old. The values inside the brackets refer the standard errors. Finally, the straight lines on the two plots indicate the normality of the two outcomes. This study suggests for the further work to the extended non-linear mixed effect model for correlated multivariate repeated measure data usually called longitudinal data. Moreover, the study can incorporate the joint model of multivariate longitudinal outcome with time to event outcomes. In order to come up with flexible and robust models, the authors can further extend these models to non-parametric smoothing models of longitudinal endpoints and survival times.

Error tolerance of topological codes with independent bit-flip and measurement errors

Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be calculated by mapping the underlying quantum problem to a related classical statistical-mechanical spin system with quenched disorder. Here, we present results for the general fault-tolerant regime, where we consider both qubit and measurement errors. However, unlike in previous studies, here we vary the strength of the different error sources independently. Our results highlight peculiar differences between toric and color codes. This study complements previous results published in New J. Phys. 13, 083006 (2011).

Linear Increments with Non-monotone Missing Data and Measurement Error.

Linear increments (LI) are used to analyse repeated outcome data with missing values. Previously, two LI methods have been proposed, one allowing non‐monotone missingness but not independent measurement error and one allowing independent measurement error but only monotone missingness. In both, it was suggested that the expected increment could depend on current outcome. We show that LI can allow non‐monotone missingness and either independent measurement error of unknown variance or dependence of expected increment on current outcome but not both. A popular alternative to LI is a multivariate normal model ignoring the missingness pattern. This gives consistent estimation when data are normally distributed and missing at random (MAR). We clarify the relation between MAR and the assumptions of LI and show that for continuous outcomes multivariate normal estimators are also consistent under (non‐MAR and non‐normal) assumptions not much stronger than those of LI. Moreover, when missingness is non‐monotone, they are typically more efficient.

TOA-Based Source Localization: A Linearization Approach Adopting Coordinate System Translation

This paper addresses the localization of a timing signal source based on the time of arrival (TOA) measurements that are collected from nearby sensors that are position known and synchronized to each other. Generally speaking, for such TOA-based source localization, the corresponding observation equations contain nonlinear relationship between measurements and unknown parameters, which normally results in the nonexistence of any efficient unbiased estimator that attains the Cramer-Rao lower bound (CRLB). In this paper, we devise a new approach that utilizes linearization and adopts suitable coordinate system translation to eliminate nonlinearity from the converted observation equations. The performance analysis and simulation study conducted show that our proposed algorithm can achieve the CRLB when the zero-mean Gaussian and independent measurement errors are sufficiently small.

The relationship between mean square differences and standard error of measurement: Comment on Barchard (2012).

In the discussion of mean square difference (MSD) and standard error of measurement (SEM), Barchard (2012) concluded that the MSD between 2 sets of test scores is greater than 2(SEM)² and SEM underestimates the score difference between 2 tests when the 2 tests are not parallel. This conclusion has limitations for 2 reasons. First, strictly speaking, MSD should not be compared to SEM because they measure different things, have different assumptions, and capture different sources of errors. Second, the related proof and conclusions in Barchard hold only under the assumptions of equal reliabilities, homogeneous variances, and independent measurement errors. To address the limitations, we propose that MSD should be compared to the standard error of measurement of difference scores (SEMx-y) so that the comparison can be extended to the conditions when 2 tests have unequal reliabilities and score variances.

O3-1.5 Using data linkage to explore use of GP services by smokers

Introduction It is understood how confounding of mediator-outcome associations resulting in collider biases may cause error when estimating direct and indirect effects. Here we assess the impact of non-differential and independent measurement error of the exposure and mediator. Methods We used as a motivating example the association of childhood socioeconomic position (exposure) with adult psychological distress (outcome), and possible mediation by adult socioeconomic position (mediator). We use quantitative bias analysis methods to quantify the impact of misclassification of exposure and mediator on three target parameters: the total effect of exposure on outcome; the direct effect (by conditioning on the mediator); and the indirect effect (identified by the percentage reduction in the excess OR upon adjusting for the mediator). Results ORs before and after adjustment for mediators are both biased to the null by non-differential misclassification of the exposure, but the percentage reduction in the excess OR is not affected by measurement error of the exposure. Conversely, measurement error of the mediator rapidly biases the percentage reduction the excess OR downwards. Conclusions If the research objective is to quantify the proportion of the total association that is due to mediation (ie, indirect effect), then minimising (or adjusting for) non-differential misclassification bias of the mediator is much more important than that for the exposure (or outcome). Considering the relative importance of collider bias and measurement error when estimating direct and indirect effects, measurement error (of mediators in particular) will often be a (much) greater source of systematic error.

Determining if the Relative Shear Modulus or the Inverse of the Relative Shear Modulus Should be Imaged Using Axial Strain Ratios on Agar Phantoms

An axial strain image is considered to be an image of a relative shear modulus. However, through simulations of focal lesions, it was previously confirmed that reconstruction imaging of the 1-D relative shear modulus or its inverse obtained from the ratio of the axial strain in the axial direction ( i.e., the axial strain ratio), with respect to a reference strain, produces larger contrast-to-noise ratios (CNRs) than that of the axial strain, although both of the reconstructions have smaller relative contrasts than that of the original shear modulus. The reference strain is appropriately chosen in the area of a homogeneous neighborhood in front of or behind the target by viewing in the B-mode and strain images. It has also been confirmed that the evaluations of CNRs of reconstructions immediately after strain measurement permit a prediction of which reconstructions should be imaged, i.e., a decision can be made without obtaining the reconstruction images, but by using the statistical evaluations of the measured strains in the focal lesion and in the surrounding region. In this study, the feasibility of using this prediction is verified through agar phantom experiments using actual measured axial strains obtained with the 2-D cross-spectrum phase-gradient method. The resulting successful prediction revealed that the assumptions of independent stationary and random axial-strain measurement errors in the focal lesion and in the surrounding region are appropriate. (E-mail: c-sumi@sophia.ac.jp)

Analysis of multi‐arm tumor growth trials in xenograft animals using phase change adaptive piecewise quadratic models

Xenograft trials allow tumor growth in human cell lines to be monitored over time in a mouse model. We consider the problem of inferring the effect of treatment combinations on tumor growth. A piecewise quadratic model with flexible phase change locations is proposed to model the effect of change in therapy over time. Each piece represents a growth phase, with phase changes in response to change in treatment. Piecewise slopes represent phase-specific (log) linear growth rates and curvature parameters represent departure from linear growth. Trial data are analyzed in two stages: (i) subject-specific curve fitting (ii) analysis of slope and curvature estimates across subjects. A least-squares approach with penalty for phase change point location is proposed for curve fitting. In simulation studies, the method is shown to give consistent estimates of slope and curvature parameters under independent and AR (1) measurement error. The piecewise quadratic model is shown to give excellent fit (median R(2)=0.98) to growth data from a six armed xenograft trial on a lung carcinoma cell line.

Adjusting for measurement error in the value added model: evidence from Portugal

The multilevel value added approach to measuring school effectiveness is now widely used. We propose a method to adjust for measurement error to investigate the extent to which this changes school effect estimates. It is applied to longitudinal data collected in the region of Cova da Beira (NUT III) for 1st, 3rd, 5th, 7th and 8th grades. Three different variance component models are considered, depending on the predictor variables included. Assuming measurement error occurs in explanatory and/or response variables, corrections are made for different values of the coefficient of reliability. Moreover, models are fitted under the assumption of either independent or correlated measurement errors.