Approximate Invariance Research Articles

Iterative Ratio Method: a method to map the depth to the Moho from gravity anomalies using linear approximate invariance

Interfaces characterized by a density contrast are common models to interpret gravity data. Two key parameters of the interface inversion are the density contrast and constant offset, which are free parameters. We propose to iteratively estimate the two free parameters by a new method: the iterative-ratio (ITRAT) method. The method is based on the linear approximate invariance of depth and free parameters and on the availability of several depth constraints. The free parameters are estimated iteratively to update the interface depth. By processing the synthetic Moho model, we find that the ITRAT method generally converges after two iterations with good accuracy for the free-parameter estimates and Moho depth. Random tests for the constant density model show that the accuracy of ITRAT method is slightly affected by the noise of gravity data and by the number of constraints, but it is sensitive to the uncertainty of constraints. For the variable density model, the ITRAT method will estimate a group of constant density contrast and constant offset to obtain a better Moho model, which has the lower depth error than the model with a mean density contrast. The new method is finally demonstrated by mapping the Moho of the Santos basin (Brazil) according to the depth constraints and regional gravity anomalies.

Approximate confidence interval for the reciprocal of a normal mean with a known coefficient of variation

An approximate confidence interval for the reciprocal of a normal population mean with a known coefficient of variation is proposed. This has applications in the area of nuclear physics, agriculture and economic when the researcher knows the coefficient of variation. The proposed confidence interval is based on the approximate expectation and variance of the estimator by Taylor series expansion. A Monte Carlo simulation study was conducted to compare the performance of the proposed confidence interval with the existing confidence interval. Simulation results show that the proposed confidence interval performs as well as the existing one in terms of coverage probability. However, the approximate confidence interval is very easy to calculate compared with the exact confidence interval.

Moment-based approximation for variance of semi-Markovian random walk with gamma distributed interference of chance

Moment-based approximation for variance of semi-Markovian random walk with gamma distributed interference of chance

Universal rapidity scaling of entanglement entropy inside hadrons from conformal invariance

When a hadron is probed at high energy, a nontrivial quantum entanglement entropy inside the hadron emerges due to the lack of complete information about the hadron wave function extracted from this measurement. In the high-energy limit, the hadron becomes a maximally entangled state, with a linear dependence of entanglement entropy on rapidity, as has been found in a recent analysis based on parton description. In this paper, we use an effective conformal field theoretic description of hadrons on the light cone to show that the linear dependence of the entanglement entropy on rapidity found in parton description is a general consequence of approximate conformal invariance and does not depend on the assumption of weak coupling. Our result also provides further evidence for a duality between the parton and string descriptions of hadrons. Published by the American Physical Society 2024

A non-iterative compensation method for machining errors of thin-walled parts considering coupling effect of tool-workpiece deformation

Thin-walled parts have significant application value in the aerospace industry due to their high strength-to-weight ratio. However, their low rigidity makes them susceptible to cutting force-induced error, which may seriously affect their machining accuracy. Error compensation is an effective method for addressing this issue. However, the commonly used mirror compensation method can cause residual errors due to the coupling effect of the tool-workpiece deformation. The influence mechanism of this coupling effect on error compensation is analyzed through an iterative compensation method. This method efficiently reduces residual errors. However, its computation efficiency is insufficient to meet the requirements of real-time compensation. Therefore, a non-iterative compensation method is proposed to directly calculate the compensation values considering the coupling effect of the tool-workpiece deformation. Through the approximate invariance of the overall cutting coefficient matrix and the pre-given system parameter, the proposed method avoids the repeated calculation of cutting forces and improves the computation efficiency. Experiment results of milling thin-walled blades show that after compensation using the proposed method, the machining accuracy of the thin-walled blade has seen a further increase of 18.1% in comparison to the mirror compensation method. Moreover, the proposed method achieves comparable compensation accuracy to the iterative method with a 66% reduction in computation time. The proposed method has significant potential for real-time compensation in the machining of complex 5-axis thin-walled parts.

Short Versions of the Penn State Worry Questionnaire: Psychometric Performance in a Sample of People Seeking Help

Worry is a cognitive transdiagnostic variable that is relevant for psychopathology research. The Penn State Worry Questionnaire (PSWQ) was developed to measure it. We aimed to examine the psychometric properties of three short versions of the PSWQ (11, 8, and 7 items) in a sample of Mexicans seeking help. A sample of 1391 individuals (82.2% women) seeking online psychological help completed the 11-item PSWQ, as well as measures of depression and anxiety. Single and multi-group confirmatory factor analyses were conducted. Good fit was achieved in the three versions only after adding correlated residuals to the models. Internal consistency reliability was excellent for the PSWQ-11 (ω = .93) and the PSWQ-A (ω = .90); it was acceptable for the PSWQ-5 (ω = .81). Furthermore, evidence of approximate invariance between sexes and age groups was found. Finally, the three versions were similarly associated with depression and anxiety.

Are "Global Measures" of Psychological Intimate Partner Violence Against Women Really Comparable? A Measurement Invariance Analysis of Controlling Behaviors in 19 Low- and Middle- Income Countries.

Background One third of adult women report lifetime psychological intimate partner violence (IPV). Controlling behavior is a common dimension of psychological IPV; however, evidence is mixed on its cross-national and cross-time measurement invariance, limiting its use to monitor Sustainable Development Goal (SDG) 5.2.1, to eliminate all forms of violence against women. We explored easier-to-modify survey-design features and harder-to-modify individual-level and national-level characteristics that may account for non-invariance of these controlling-behavior items. Methods We analyzed data on five controlling behaviors administered to 373,167 ever-partnered women 15-49 years in 19 low- or middle-income countries in which at least two national Demographic and Health Surveys were administered during 2005-2019. We performed multiple-group confirmatory factor analysis (MGCFA) to test for exact forms of invariance and alignment optimization (AO) to test for approximate invariance across 7-9 survey-design groups, defined by the number of preceding questionnaire modules (to proxy respondent burden) and weeks of interviewer training (to proxy interviewer skills). Adjustment for covariates in the MGCFA assessed whether individual- and national-level characteristics could account for any observed non-invariance across survey-design groups. Results In MGCFA without covariates, configural invariance of the controlling-behavior items was observed across survey-design groups. Exact invariance, partial invariance (with 20% of parameter estimates freed), and approximate invariance were not observed across groups. In adjusted MGCFA, neither woman-level covariates (schooling, attitudes about IPV against women) nor national-level covariates (women's mean schooling, mean attitudes about IPV against women, gender-related legal environment) alone or combined accounted for the non-invariance of controlling-behavior items across survey-design groups. Conclusions Comparing estimates for controlling behavior across country, time, and survey design variations warrants caution. Standardizing questionnaire length and interviewer training may improve the invariance of these items. Other characteristics, like ethnicity and language, may account for the non-invariance of controlling-behavior items across survey-design groups and should be tested. Current controlling-behavior items should be refined to enhance their comparability, and new controlling-behavior items should be identified and tested to improve the item set's content validity. Given current evidence of the high prevalence and health impacts of psychological IPV against women, advancing this research agenda is needed to monitor SDG 5.2.1.

COVID-19-infected cases in Thailand during the Omicron wave using the capture-recapture method

Thailand is among many countries, severely affected by the COVID-19 pandemic. In December 2021, the Thai Ministry of Public Health announced the discovery of the first imported case of the Omicron variant, and the local transmission of the Omicron variant was confirmed. The Omicron variant spread rapidly but was less dangerous than the Delta. Some patients experienced mild or no symptoms and self-treated without requiring medical assistance. Lower fatality rates during the Omicron outbreak were reported compared with previous variants. Information concerning hidden COVID-19-infected patients is beneficial and will lead to a better understanding of the disease outbreak mechanism. This study proposed the lower bound estimator under the capture-recapture (CR) method to estimate the true value of COVID-19 infections in Thailand during the Omicron wave. The Chao lower bound estimator for the Poisson mixture model was created to take into account the fact that populations can be different based on how cases and deaths have been spread out over time. The approximate variance of the estimator was constructed for a confidence interval of 95%, focusing on the ratio of total estimated infected cases to observed cases in March 2022. The average ratio was 2.99 (95% CI: 2.96 to 3.01), suggesting that for every 100 observed patients, at least 199 infected patients were underreported.

Dilaton forbidden dark matter

Dilaton effective field theory (dEFT) describes the long distance behavior of certain confining, near-conformal gauge theories that have been studied via lattice computation. Pseudo-Nambu- Goldstone bosons (pNGBs), emerging from the breaking of approximate, continuous, internal symmetries, are coupled to an additional scalar particle, the dilaton, arising from the spontaneous breaking of approximate scale invariance. This effective theory has been employed to study possible extensions of the standard model. In this paper, we propose a complementary role for dEFT, as a description of the dark matter of the Universe, with the pNGBs identified as the dark matter particles. We show that this theory provides a natural implementation of the “forbidden” dark matter mechanism, and we identify regions of parameter space for which the thermal history of dEFT yields the measured dark matter relic density. Published by the American Physical Society 2024

Sociability across Eastern-Western cultures: Is it the same underlying construct?

In this study, we examined cross-cultural differences in sociability, a core personality facet of the higher order extraversion trait, which has been reported at lower levels in Eastern versus Western cultures several decades ago. Up until now, however, East-West cultural comparisons on the Western-defined construct of sociability have been limited, despite the extensive research published on extraversion indicating that this personality dimension is globally relevant across cultures. Following current practices, we first assessed for measurement invariance (MI) on the Cheek and Buss sociability scale between Chinese (n = 816, 47.2% male, M = 18.51 years, SD = 1.26 years) and Canadian (n = 995, 30.8% male, M = 19.62 years, SD = 1.25 years) young adult samples to ensure any comparisons would be valid and meaningful. Results from a multigroup confirmatory factor analysis (exact invariance) showed that there was measurement non-invariance at the scalar level in the sociability construct across country and country by sex, and the newer alignment method (approximate invariance) confirmed these results, suggesting that mean level comparisons of sociability were biased and noninformative. Our findings indicated that although a few of the higher-level personality dimensions such as extraversion are considered universal, the facets underlying their meaning, like sociability, are not as clearly delineated between cultures. Alongside the present-day pursuit of understanding personality across cultures through an indigenous measurement lens in tandem with the notion of universality, researchers should also consider narrowing their focus onto lower-level facets, each of which is likely to be uniquely embedded into a cultural context.

Geographically weighted regression model-calibration for finite population parameter estimation under two stage sampling design

In many agricultural, forestry, environmental, and ecological surveys, data are often spatial in nature and exhibit spatial nonstationarity. A well-known method for addressing spatial nonstationarity and capturing the spatially varying relationships between different variables is Geographic Weighted Regression (GWR). The calibration approach is one of the most widely used techniques in sample surveys for incorporating the known population characteristics of auxiliary variables by changing the original sampling design weights. The model-calibration approach is an improvement on the conventional calibration approach that can handle a variety of assisting working models. Two-stage sampling is one of the most frequently used sampling strategies in large-scale sample surveys. In the present study, a couple of GWR model-calibration estimators were proposed under two-stage sampling, assuming the availability of population-level complete auxiliary information. Under a set of regularity assumptions, the asymptotic properties of the developed estimators have been evaluated such as design unbiasedness, model unbiasedness, approximate variance, and estimators of variances. The performance of the developed estimators has been compared with the existing estimators through a spatial simulation study and a design-based simulation based on real data. The performance of the proposed estimator was found to be more precise than the existing estimators under two-stage sampling.

Calibration Estimation of Population Total in Two-Stage Sampling Design under unavailability of Population Level Auxiliary Information for the selected PSUs

Calibration approach is a popular technique in sample surveys which incorporates auxiliary information in the estimation process assuming that population aggregates of auxiliary variable are available. Many often under two-stage sampling design, such population aggregates of auxiliary variable, i.e., population mean or total are unavailable and under such situations, estimation of population total has been limited to the use of two phase sampling. Therefore, in the present study, efficient estimator of population total is developed under two-stage sampling design when population aggregates of auxiliary variable are unavailable for the selected psu’s. The calibrated estimator is developed using the information on known population aggregates of additional auxiliary variable which is less linearly related to the study variable through two step calibration approach. The approximate variance and variance estimator of the proposed calibrated estimator has also been developed. Empirical evaluations using both real and simulated data shows the superior performance of the developed calibrated estimator in comparison to the existing estimators.

Assessing Modeled Mesoscale Stirring Using Microscale Observations

Abstract We assess the representation of mesoscale stirring in a suite of models against an estimate derived from microstructure data collected during the North Atlantic Tracer Release Experiment (NATRE). We draw heavily from the approximate temperature variance budget framework of Ferrari and Polzin. This framework assumes two sources of temperature variance away from boundaries: first, the vertical stirring of the large-scale mean vertical gradient by small-scale turbulence; and second, the lateral stirring of large-scale mean along-isopycnal gradients by mesoscale eddies. Temperature variance so produced is transformed and on average transferred down scales for ultimate dissipation at the microscale at a rate χ estimated using microstructure observations. Ocean models represent these pathways by a vertical mixing parameterization, and an along-isopycnal lateral mixing parameterization (if needed). We assess the rate of variance production by the latter as a residual from the NATRE dataset and compare against the parameterized representations in a suite of model simulations. We find that variance production due to lateral stirring in a Parallel Ocean Program version 2 (POP2) 1/10° simulation agrees well, to within the estimated error bars, with that inferred from the NATRE estimate. A POP2 1° simulation and the Estimating the Circulation and Climate of the Ocean Version 4 release 4 (ECCOV4r4) simulation appear to dissipate an order of magnitude too much variance by applying a lateral diffusivity, when compared to the NATRE estimate, particularly below 1250 m. The ECCOV4r4-adjusted lateral diffusivities are elevated where the microstructure suggests elevated χ sourced from mesoscale stirring. Such elevated values are absent in other diffusivity estimates suggesting the possibility of compensating errors and caution in interpreting ECCOV4r4’s adjusted lateral diffusivities. Significance Statement We look at whether microstructure turbulence observations can provide a useful metric for judging the fidelity of representation of mesoscale stirring in a suite of models. We focus on the region of the North Atlantic Tracer Release Experiment (NATRE), the site of a major ocean turbulence observation campaign, and use an approximate variance budget framework for the region with observational estimates from Ferrari and Polzin (2005). The approach provides a novel framework to evaluate the approximate representation of mesoscale stirring in a variety of models.

On the Use of Inverse Exponentiation to Improve the Efficiency of Calibration Estimators in Stratified Double Sampling

This study introduces the concept of inverse exponentiation in formulating calibration weights in stratified double sampling and proposes a more improved calibration estimator based on Koyuncu and Kadilar (2014) calibration estimator. The variance of the proposed logarithmic calibration estimator has been derived under large sample approximation. Calibration asymptotic optimum estimator and its approximate variance estimator are derived for the proposed logarithmic calibration estimator. Results of empirical study showed that the proposed logarithmic calibration estimator performs better than the Koyuncu and Kadilar (2014) calibration estimator with appreciable gains in efficiency. Also, simulation study for the comparison of the proposed logarithmic estimator with a Global estimator [Generalized Regression (GREG) estimator ] proved the robustness of the proposed logarithmic calibration estimator and by extension the efficacy of inverse exponentiation in calibration weightings. Analysis and evaluation are presented. International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 91-102

Analytical analysis of the generation of a rotating driving magnetic field on the outer surface of a magnetic pinch load with a helical return current post

A recently emerging approach adopts a directionally time-varying (rotating) magnetic field to drive a pinch load, aiming to mitigate the inherent magneto-Rayleigh-Taylor instability in dynamic Z pinches. A helical return current post (RCP) serves as a functional structural element capable of generating the requisite driving magnetic field for this purpose in the load region. This paper first calculates the current azimuthally induced on the outer surface of a magnetically pinched load within this type of RCP using a zero-dimensional lumped-parameter circuit model. The results show that the induced current deviates significantly from the presumed “perfect” induced current (100% amplitude) as reported in the literature [S. A. Sorokin, ); P. F. Schmit , ); G. A. Shipley , ); and P. C. Campbell , ], with an effective coefficient of current induction considerably less than 1. However, even when the load is fully compressed to the axis, the effective coefficient does not approach zero but rather converges to a finite value that solely depends on the aspect ratio of the RCP. This is quite favorable for the suppression of magneto-Rayleigh-Taylor instability in the Z pinch. As for the pointlike X pinch, the axial magnetic field does not tend to zero but a finite value, though the effective coefficient tends to zero, and this result may be used to suppress the instability in X pinch and improve the time stability and spatiotemporal unity of hot spots. In addition, the anode and cathode plates have the potential to enhance the current induced in the load. This paper then analyzes the axial distribution and time behavior of the induced current adopting an approximate analytical method and numerical integration and finds an approximate invariance that can be well characterized by δt, the product of the normalized skin depth and time. Similar values of δt indicate similar axial distribution characteristics. When δt is lower than, at, or higher than the critical region (∼0.1–0.3), the axial distribution appears dumbbell shaped, nearly flat, and arched, respectively. These distributively induced currents can be exploited to achieve quasispherical, near flat, and dumbbell-shaped implosions, respectively. Published by the American Physical Society 2024

Bayesian active learning line sampling with log-normal process for rare-event probability estimation

Line sampling (LS) stands as a powerful stochastic simulation method for structural reliability analysis, especially for assessing small failure probabilities. To further improve the performance of traditional LS, a Bayesian active learning idea has recently been pursued. This work presents another Bayesian active learning alternative, called ‘Bayesian active learning line sampling with log-normal process’ (BAL-LS-LP), to traditional LS. In this method, we assign an LP prior instead of a Gaussian process prior over the distance function so as to account for its non-negativity constraint. Besides, the approximation error between the logarithmic approximate distance function and the logarithmic true distance function is assumed to follow a zero-mean normal distribution. The approximate posterior mean and variance of the failure probability are derived accordingly. Based on the posterior statistics of the failure probability, a learning function and a stopping criterion are developed to enable Bayesian active learning. In the numerical implementation of the proposed BAL-LS-LP method, the important direction can be updated on the fly without re-evaluating the distance function. Four numerical examples are studied to demonstrate the proposed method. Numerical results show that the proposed method can estimate extremely small failure probabilities with desired efficiency and accuracy.

Bayesian approximation for parameterized KALMAN filter for investigation and simulation of unknown noise variance trajectory following in state space models with different noise distributions

Bayesian approach can be used for parameter identification and extraction in state space models and its ability for analyzing sequence of data in dynamical system is proved in different literatures. In this paper, Bayesian approach for approximation of variances in measurement noise with KALMAN filter is applied for estimation of the dynamical state and measurement data in discrete dynamical system. Detection of uncertainty and estimation of those can be done simultaneously with adaptive KALMAN filter. This algorithm at each step time estimates noise variance and state of system with KALMAN filter. Then, approximation is formed at each step separately and at each step sufficient statistics of the state and noise variances are computed with a fixed-point iteration of a KALMAN filter. For showing influence of variance in measurement data on algorithm different simulations is applied. First, effect of variance and its distribution on detection performance is simulated in KALMAN filter without Bayesian formulation. Then simulation is applied to KALMAN filter with ability of variance tracking of measurement data.in these simulations, influence of distribution of measurement data in each step is estimated and true variance of data is obtained by algorithm and is compared in different scenarios. Afterwards, one typical modeling of nonlinear state space model with inducing noise measurement is simulated by this approach. Finally, the performance and the important limitations of this algorithm in these simulations are explained.

Review of sample size determination methods for the intraclass correlation coefficient in the one-way analysis of variance model.

Reliability of measurement instruments providing quantitative outcomes is usually assessed by an intraclass correlation coefficient. When participants are repeatedly measured by a single rater or device, or, are each rated by a different group of raters, the intraclass correlation coefficient is based on a one-way analysis of variance model. When planning a reliability study, it is essential to determine the number of participants and measurements per participant (i.e. number of raters or number of repeated measurements). Three different sample size determination approaches under the one-way analysis of variance model were identified in the literature, all based on a confidence interval for the intraclass correlation coefficient. Although eight different confidence interval methods can be identified, Wald confidence interval with Fisher's large sample variance approximation remains most commonly used despite its well-known poor statistical properties. Therefore, a first objective of this work is comparing the statistical properties of all identified confidence interval methods-including those overlooked in previous studies. A second objective is developing a general procedure to determine the sample size using all approaches since a closed-form formula is not always available. This procedure is implemented in an R Shiny app. Finally, we provide advice for choosing an appropriate sample size determination method when planning a reliability study.

Cross-National Measurement of Mathematics Intrinsic Motivation: An Investigate of Measurement Invariance with MG-CFA and Aligment Method Across Fourteen Countries

One of the main objectives of international large-scale assessments is to make comparisons between different countries, education policies, education systems, or subgroups. One of the main criteria for making comparisons between different groups is to ensure measurement invariance. The purpose of this study was to test the measurement invariance of the mathematics intrinsic motivation scale across 14 countries. For this purpose, the "students like learning mathematics" scale, which measures intrinsic motivation for mathematics, was included in the TIMSS 2019 cycle. The study sample consisted of a total of 152992 students, 70192 4th grade and 82800 8th grade students from 14 different countries participating in the TIMSS 2019 cycle. Measurement invariance was tested with Multi-Group Confirmatory Factor Analysis (MG-CFA) and Alignment Method. The mathematics intrinsic motivation scale provides only configural invariance according to MG-CFA at the 4th grade level, whereas the scale provides approximate invariance according to the alignment method. At the 8th grade level, the scale provides configural and metric invariance according to MG-CFA, whereas the scale provides approximate invariance according to the alignment method. The results indicate that the mathematics intrinsic motivation scale provides approximate measurement invariance at both grade levels and that comparisons can be made between the scores of the identified countries.

Transporting randomized trial results to estimate counterfactual survival functions in target populations.

When the distributions of treatment effect modifiers differ between a randomized trial and an external target population, the sample average treatment effect in the trial may be substantially different from the target population average treatment, and accurate estimation of the latter requires adjusting for the differential distribution of effect modifiers. Despite the increasingly rich literature on transportability, little attention has been devoted to methods for transporting trial results to estimate counterfactual survival functions in target populations, when the primary outcome is time to event and subject to right censoring. In this article, we study inverse probability weighting and doubly robust estimators to estimate counterfactual survival functions and the target average survival treatment effect in the target population, and provide their respective approximate variance estimators. We focus on a common scenario where the target population information is observed only through a complex survey, and elucidate how the survey weights can be incorporated into each estimator we considered. Simulation studies are conducted to examine the finite-sample performances of the proposed estimators in terms of bias, efficiency and coverage, under both correct and incorrect model specifications. Finally, we apply the proposed method to assess transportability of the results in the Action to Control Cardiovascular Risk in Diabetes-Blood Pressure (ACCORD-BP) trial to all adults with Diabetes in the United States.