Approximate Invariance Research Articles

Education and Attitudes Toward Migration in a Cross Country Perspective.

The paper examines the dynamics of native populations’ opposition to migration and the role of education in shaping such opposition in European countries using data from the last four editions of the European Social Survey between years 2010 and 2016. We examine both the direct association between education and opposition to migration as well as the mediated association that occurs through feelings of threat. We test for measurement equivalence across countries and years of the two latent constructs in our analyses (opposition to migration and feelings of threat) by applying sequential methods used in alignment optimization to identify partial equivalence and check the level of approximate measurement invariance using BSEM modeling. Our results indicate that the opposition to migration and the feelings of threat scales achieve metric invariance but not scalar invariance in cross-country comparisons. At the substantive level, our findings suggest that better educated individuals express lower opposition to migration than the poorly educated and that as much as 60% of education differentials in opposition to migration are due to the mediated effect through feelings of threat. The high degree of heterogeneity in associations both across countries and over time are, in part, explained by the presence of foreign-born populations and living standards in a country and time point.

An illustration of Bayesian approximate measurement invariance with longitudinal data and a small sample size

This article illustrates the Bayesian approximate measurement invariance (MI) approach in Mplus with longitudinal data and small sample size. Approximate MI incorporates zero-mean small variance prior distributions on the differences between parameter estimates over time. Contrary to traditional invariance testing methods, where exact invariance is tested, this method allows for some “wiggle room” in the parameter estimates over time. The procedure is illustrated using longitudinal data on college students’ academic stress as it changes in the period leading up to and right after an important midterm. Results show that traditional invariance testing methods come to a standstill due to the small sample size. Bayesian approximate MI testing was able to identify non-invariant parameters, after which a partially invariant model could be estimated.

PAC: A novel self-adaptive neuro-fuzzy controller for micro aerial vehicles

There exists an increasing demand for a flexible and computationally efficient controller for micro aerial vehicles (MAVs) due to a high degree of environmental perturbations. In this work, an evolving neuro-fuzzy controller, namely Parsimonious Controller (PAC) is proposed. It features fewer network parameters than conventional approaches due to the absence of rule premise parameters. PAC is built upon a recently developed evolving neuro-fuzzy system known as parsimonious learning machine (PALM) and adopts new rule growing and pruning modules derived from the approximation of bias and variance. These rule adaptation methods have no reliance on user-defined thresholds, thereby increasing the PAC’s autonomy for real-time deployment. PAC adapts the consequent parameters with the sliding mode control (SMC) theory in the single-pass fashion. The boundedness and convergence of the closed-loop control system’s tracking error and the controller’s consequent parameters are confirmed by utilizing the LaSalle–Yoshizawa theorem. Lastly, the controller’s efficacy is evaluated by observing various trajectory tracking performance from a bio-inspired flapping wing micro aerial vehicle (BI-FWMAV) and a rotary wing micro aerial vehicle called hexacopter. Furthermore, it is compared to three distinctive controllers. Our PAC outperforms the linear PID controller and feed-forward neural network (FFNN) based nonlinear adaptive controller. Compared to its predecessor, G-controller, the tracking accuracy is comparable, but the PAC incurs significantly fewer parameters to attain similar or better performance than the G-controller.

K-PHD Tek-Ton Frekans Kestiricisinin Bir Kesin Değişinti İfadesi: Rasgele Faz Durumu

The k-PHD method, a generalization of the well-known Pisarenko harmonic decomposition (PHD) method, is considered for frequency estimation of a single real random-phased sinusoid in noise. With the use of a simple variance analysis technique, an exact expression of the k-PHD frequency variance is derived. An approximate k-PHD variance formula for sufficiently large data lengths and signal-to-noise ratios is also given. Computer simulations are included to validate the theoretical development.

Remaining Useful Life Prediction with Similarity Fusion of Multi-Parameter and Multi-Sample Based on the Vibration Signals of Diesel Generator Gearbox

The prediction of electrical machines’ Remaining Useful Life (RUL) can facilitate making electrical machine maintenance policies, which is important for improving their security and extending their life span. This paper proposes an RUL prediction model with similarity fusion of multi-parameter and multi-sample. Firstly, based on the time domain and frequency domain extraction of vibration signals, the performance damage indicator system of a gearbox is established to select the optimal damage indicators for RUL prediction. Low-pass filtering based on approximate entropy variance (Aev) is introduced in this process because of its stability. Secondly, this paper constructs Dynamic Time Warping Distance (DTWD) as a similarity measurement function, which belongs to the nonlinear dynamic programming algorithm. It performed better than the traditional Euclidean distance. Thirdly, based on DTWD, similarity fusion of multi-parameter and multi-sample methods is proposed here to achieve RUL prediction. Next, the performance evaluation indicator Q is adopted to evaluate the RUL prediction accuracy of different methods. Finally, the proposed method is verified by experiments, and the Multivariable Support Vector Machine (MSVM) and Principal Component Analysis (PCA) are introduced for comparative studies. The results show that the Mean Absolute Percentage Error (MAPE) of the similarity fusion of multi-parameter and multi-sample methods proposed here is below 14%, which is lower than MSVM’s and PCA’s. Additionally, the RUL prediction based on the DTWD function in multi-sample similarity fusion exhibits the best accuracy.

Constraints imposed by zero-crossing invariance on cochlear models with two mechanical degrees of freedom.

The zero crossings of basilar-membrane (BM) responses to clicks are nearly independent of stimulus intensity. This work explores the constraints that this invariance imposes on one-dimensional nonlinear cochlear models with two degrees of freedom (2DoF). The locations of the poles and zeros of the BM admittance, calculated for a set of linear models in which the strength of the active force is progressively decreased, provides a playground for evaluating the behavior of a corresponding nonlinear model at increasing stimulus levels. Mathematical constraints on the model parameters are derived by requiring that the poles of the admittance move horizontally in the s-plane as the active force is varied. These constraints ensure approximate zero-crossing invariance over a wide stimulus level range in a nonlinear model in which the active force varies as a function of the local instantaneous BM displacement and velocity. Two different 2DoF models are explored, each capable of reproducing the main qualitative characteristics of the BM response to tones (i.e., the tall and broad activity pattern at low stimulus levels, the large gain dynamics, and the partial decoupling between gain and phase). In each model, the motions of the two masses are compared with response data from animal experiments.

International Comparisons of Emotionally Reactive Problems in Preschoolers: CBCL/1½–5 Findings from 21 Societies

Our goal was to conduct international comparisons of emotion regulation using the 9-item Emotionally Reactive (ER) syndrome of the Child Behavior Checklist for Ages 1½–5. We analyzed parent ratings for 17,964 preschoolers from 21 societies, which were grouped into 8 GLOBE study culture clusters (e.g., Nordic, Confucian Asian). Omnicultural broad base rates for ER items ranged from 8.0% to 38.8%. Rank ordering for mean item ratings varied widely across societies (omnicultural Q = .50) but less so across culture clusters (M Q = .66). Societal similarity in mean item rank ordering varied by culture cluster, with large within-cluster similarity for Anglo (Q = .96), Latin Europe (Q = .74), Germanic (Q = .77), and Latin American (Q = .76) clusters, but smaller within-cluster similarity for Nordic, Eastern Europe, and Confucian Asian clusters (Qs = .52, .23, and .44, respectively). Confirmatory factor analyses of the ER syndrome supported configural invariance for all 21 societies. All 9 items showed full to approximate metric invariance, but only 3 items showed approximate scalar invariance. The ER syndrome correlated . 65 with the Anxious/Depressed (A/D) syndrome and .63 with the Aggressive Behavior syndrome. ER items varied in base rates and factor loadings, and societies varied in rank ordering of items as low, medium, or high in mean ratings. Item rank order similarity among societies in the same culture cluster varied widely across culture clusters, suggesting the importance of cultural factors in the assessment of emotion regulation in preschoolers.

KINETICS QUASIINVARIANTS OF CHEMICAL REACTIONS IN OPEN SYSTEMS

The methods of nonequilibrium multi-experiments are one of the new approaches to solving inverse problems of chemical kinetics and optimization of chemical reactors. Currently, these methods are developed only for closed isothermal systems. In this paper, a generalization of the dual-experiment method and its extended version of the multi-experiment method for open systems is obtained, which allows to determine the approximate kinetic invariants (quasiinvariants) of chemical reactions in open continuous stirred tank reactor. The multi-experiment method for open systems is based on conducting two or more special nonequilibrium (unsteady) experiments under certain conditions. For nonlinear reactions of arbitrary complexity (multi-step, multi-equilibria), simple relations are obtained that allow to calculate the conditions for nonequilibrium experiments necessary for the identification of the reaction mechanism under study. The method allows to use any permissible values, except equilibrium ones, as initial values of reagent concentrations. The technique of carrying out multi-experiments and performing the necessary numerical calculations based on the multiple integration of systems of ordinary differential equations under different initial conditions is developed. The examples of using the developed method for one-stage linear and two-stage nonlinear reactions with two and three reagents are given. Found with the help of this method, the kinetic curves of the nonequilibrium quasiinvariants compared with the nonequilibrium curves of change of concentrations during the whole reaction. It is shown that quasiinvariant curves change within narrower limits than concentrations in different experiments, i.e. remain practically constant in time. The obtained results are also applicable for open nonisothermal systems.

Bias and variance of asymmetric double‐sided two‐way ranging

Asymmetric double-sided two-way ranging (ADS-TWR) is a method of range estimation through precisely time-stamped messages sent between two transceivers. In contrast to symmetric double-sided two-way ranging (SDS-TWR), ADS-TWR suppresses the errors induced by transceiver clock drifts even when the message reply delays are unequal. However, due to the nonlinearity of the ADS-TWR estimator, its mean and variance cannot be evaluated in a straightforward or exact way. This article presents an analytical approach of evaluating an approximation of bias and variance of the range estimators and applies it on an exemplary set of parameters, typical for ultra-wide band (UWB) localization systems. Moreover, the obtained results are verified by a Monte Carlo simulation. It will be proven that ADS-TWR is safe to be used in most of the present applications, and its precision is rather similar to SDS-TWR.

Assessing the inter-patient variability in the area under the concentration curve

In this paper, we check the accuracy of an approximate variance for the area under the concentration curve (AUC). Based on the model function of a random effects model, an analytic expression for the AUC can be obtained. Then an approximate variance for the AUC can be derived after the linearisation of it using the Taylor series expansion. This variance is used in the construction of confidence interval to check the accuracy of the approximation made. We assume that the data on concentration are collected with the advancement of a dose-finding study. Following the allocation of the lowest dose to a cohort of patients, the concentration of drug in the blood samples is measured at the locally D-optimum time points. The successive doses for the cohorts are determined by the popular continual reassessment method. Four PK proles, along with three plausible dose-response scenarios, are investigated through a simulation study. The numerical findings assure the quality of the approximated variance.

KINETICS QUASIINVARIANTS OF CHEMICAL REACTIONS IN CLOSED SYSTEMS

The limitations of the dual-method and its extended version of the multi-experiment method in determining the exact time kinetic (thermodynamic) invariants and approximate invariants (quasiinvariants) of chemical reactions in closed isothermal systems are discussed. It is shown that for reactions, which allow except for internal equilibria, also boundary equilibria (multiple equilibria, multiequilibrium), for example, autocatalytic ones, there are always some "inconvenient" boundary values of reagent concentrations. These "uncomfortable" values cannot be used as the initial concentrations (conditions) for non-equilibrium multi-experiments (forward, reverse or intermediate), because for these values of non-equilibrium solutions cease to exist and, consequently, the reaction can proceed only in the equilibrium regime. As a result, the "usual " method of multi-experiments, using only the boundary values of the equilibrium concentrations of reagents, is not applicable. In this paper, a generalization of this method is proposed and a technique for conducting multi-experiments is developed, which is applicable for wider classes of reactions, including those with boundary equilibria, as well as autocatalytic reactions. This generalized method of multi-experiments (MME) allows one to bypass the limitations of the conventional multi-experiment method (dual-method) and to determine the exact time thermodynamic (kinetic) invariants of linear and some nonlinear chemical reactions, as well as approximate time invariants of any nonlinear chemical reactions in closed isothermal systems. The conditions of multi-experiments which are necessary for the correct operation of this method are determined. Examples of using the generalized method of multi-experiments for one-step and two-step nonlinear reactions with one and two independent reagents, respectively, are given. The kinetic time invariants and quasinvariants found with this method are compared with the exact solutions for the cases where they exist.

A note on the empirical Bayes heterogeneity variance estimator in meta-analysis.

This paper focuses on the empirical Bayes (EB) or Mandel-Paule estimator of the heterogeneity variance in meta-analysis, which was discussed by Morris and proposed in earlier publications by Mandel and Paule in an inter-laboratory context. The relationship of the EB estimator to other heterogeneity variance estimators typically used in meta-analysis is explored, and approximate variance estimators for the EB estimate of the heterogeneity variance are proposed based on the M-estimation method. Statistical inference for the overall treatment effect using the EB estimator and the proposed standard errors is discussed using two example data sets from meta-analysis applications.

Dilaton-assisted generation of the Fermi scale from the Planck scale

In scale-invariant theories of gravity the Planck mass $M_P$, which appears due to spontaneous symmetry breaking, can be the only scale at the classical level. It was argued that the second scale can be generated by a quantum non-perturbative gravitational effect. The new scale, associated with the Higgs vacuum expectation value, can be orders of magnitude below $M_P$, leading to the hierarchy between the Fermi and the Planck scales. We study a theory in which the non-perturbative effect is sensitive both to the physics at energy scales as high as $M_P$ and to the low-energy, Standard Model physics. This makes it possible to constrain the mechanism from experiment. We find that the crucial ingredients of the mechanism are non-minimal coupling of the scalar fields to gravity, the approximate Weyl invariance at high energies, and the metastability of the low-energy vacuum.

An approximate probabilistic solution of a random SIR-type epidemiological model using RVT technique

This paper adapts a multi-dimensional Random Variable Transformation technique to derive a comprehensive stochastic description of the Susceptible-Infected-Recovered epidemiological model. An approximate solution of a system of nonlinear differential equations, that characterizes this model, is deterministically obtained and, from this approximation, we derive the first probability density functions for the solution processes of susceptible, infected and recovered percentages. These probability density functions are used to find the approximate mean and variance functions, as well as the confidence intervals. Taking a general situation, the infection contact rate, the recovery rate and the initial conditions are taken to be random variables with arbitrary distributions. To test the validity of the theoretical findings associated to the proposed random epidemiological model, some numerical results are tabulated and graphically presented through an illustrative example.

Efficient estimate of residual stress variance using complex variable finite element methods

The incorporation of residual stress states into structural components is often used to improve fatigue performance. However there is frequently significant uncertainty regarding the magnitude of the induced residual stresses due to variation in material properties, loading, geometry, the thermo/mechanical processes, and measurement uncertainty. This variation should be quantified to have confidence that desired residual stress state has been induced and that the probability of failure over the operating life of the structural component has been reduced. This research demonstrates an approximate but efficient method whereby the variance in the residual stress state is estimated using a first order Taylor series approximation. The key component of the method consists of evaluating the sensitivities of the residual stresses with respect to random variables by performing a few complex-variable finite element analyses. The method was verified by approximating the residual stress variance of a sphere subjected to an autofrettage process and having random input parameters. The analysis was performed for two material models, elastic-perfectly plastic and bilinear isotropic hardening. The variance approximations provided by the proposed method were compared against Monte Carlo sampling estimates. For the elastic-perfectly plastic case, the Monte Carlo sampling was conducted on the analytical solution of the residual stress field. This numerical example required the derivation of analytical expressions of the residual stresses and their sensitivities to the random variables for the cases of full or partial yielding during loading and reverse yielding during unloading. For the bilinear isotropic hardening material model, the Monte Carlo sampling was conducted on a finite element model of the sphere. The proposed method provided good accuracy and required less than 2% of the computational time required for the Monte Carlo sampling approach. In addition, this new approach provides sensitivity information regarding the contribution of each random variable to the overall variance of the residual stress state.

Some calibration estimators for finite population mean in two-stage stratified random sampling

In the present article, an effort has been made to develop calibration estimators of the population mean under two-stage stratified random sampling design when auxiliary information is available at primary stage unit (psu) level. The properties of the developed estimators are derived in-terms of design based approximate variance and approximate consistent design based estimator of the variance. Some simulation studies have been conducted to investigate the relative performance of calibration estimator over the usual estimator of the population mean without using auxiliary information in two-stage stratified random sampling. Proposed calibration estimators have outperformed the usual estimator without using auxiliary information.

On variance of sample matrix eigenvalue

The variance of a matrix eigenvalue estimator is considered. This estimator is a function of simple random sample variances and covariances of a multidimensional random variable whose distribution is not necessarily normal. The variance of the eigenvalue estimator is approximated based on the Taylor expansion for a function of simple random sample moments. A method for approximating the variance of the canonical correlation estimator is also proposed. A simulation analysis of the accuracy of variance estimation is presented. The considered approximation of variance can be applied to assessing the variance of a statistic which is the solution of any implicit interdependence functions of sample moments.

One-pass person re-identification by sketch online discriminant analysis

Person re-identification (re-id) is to match people across disjoint camera views in a multi-camera system, and re-id has been an important technology applied in smart city in recent years. However, the majority of existing person re-id methods assumes all data samples are available in advance for training. However, in a real-world scenario person images detected from multi-camera system are coming sequentially, and thus these methods are not designed for processing sequential data in an online way. While there is a few work on discussing online re-id, most of them require considerable storage of all passed labelled data samples that have been ever observed. In this work, we present an one-pass person re-id model that adapts the re-id model based on each newly observed data and no passed data are required for each update. More specifically, we develop a Sketch online Discriminant Analysis (SoDA) by embedding sketch processing into Fisher discriminant analysis (FDA). SoDA can efficiently keep the main data variations of all passed samples in a low rank matrix when processing sequential data samples, and estimate the approximate within-class variance (i.e. within-class covariance matrix) from the sketch data information. We provide theoretical analysis on the effect of the estimated approximate within-class covariance matrix. In particular, we derive upper and lower bounds on the Fisher discriminant score (i.e. the quotient between between-class variation and within-class variation after feature transformation) in order to investigate how the optimal feature transformation learned by SoDA sequentially approximates the offline FDA that is learned on all observed data. Extensive experimental results have shown the effectiveness of our SoDA and empirically support our theoretical analysis.

Self-organized Higgs criticality

The critical point for a Higgs sector can be a point of interest in the potential for a modulus field such as the radion of an extra dimensional construction, or the dilaton of spontaneously broken approximate conformal invariance. In part motivated by conjectures about the self-organized critical state in statistical physics, we construct a 5D model in which there is an infrared emergent Higgs instability due to violation of the Breitenlohner-Freedman bound deep in the interior of a near AdS geometry. This is holographically dual to a “running” scaling dimension transitioning from real to complex with decreasing scale. The complex scaling indicates an instability to be resolved by condensates which modify the interior geometry and backreact on the 5D radion potential. Studying the model at small gravitational backreaction, we find a rich possible vacuum structure and uncover evidence that resolution of the instability requires a non-trivial cosmology.

Quasi-Invariants of Chemical Reactions with Nonideal Kinetics

A method is developed to determine approximate dynamic kinetic invariants (quasi-invariants) of complex chemical reactions with nonideal general-form kinetic laws. The quasi-invariants are expressions relating nonequilibrium reactant concentrations and temperatures, measured in two or more experiments under different initial conditions (multiexperiments) that remain almost constant throughout the reaction. The number of quasi-invariants is determined by the number of independent reactants. The application of the method was illustrated by the example of a two-step reaction in an open system with the Marcelin- de Donder kinetics. The quasi-invariant curves obtained for this reaction were compared with the concentration curves for the entire reaction time. It was shown that the quasi-invariants vary over a narrower range than their corresponding concentrations and temperature in various temperatures; i.e., the quasi-invariants remain nearly constant over time. The method expands the range of tools for the solution of inverse problems of unsteady-state kinetics of chemical reactions in nonideal systems.