Approximate Invariance Research Articles

Isomorph Invariance of Higher-Order Structural Measures in Four Lennard-Jones Systems.

In the condensed liquid phase, both single- and multicomponent Lennard–Jones (LJ) systems obey the “hidden-scale-invariance” symmetry to a good approximation. Defining an isomorph as a line of constant excess entropy in the thermodynamic phase diagram, the consequent approximate isomorph invariance of structure and dynamics in appropriate units is well documented. However, although all measures of the structure are predicted to be isomorph invariant, with few exceptions only the radial distribution function (RDF) has been investigated. This paper studies the variation along isomorphs of the nearest-neighbor geometry quantified by the occurrence of Voronoi structures, Frank–Kasper bonds, icosahedral local order, and bond-orientational order. Data are presented for the standard LJ system and for three binary LJ mixtures (Kob–Andersen, Wahnström, ). We find that, while the nearest-neighbor geometry generally varies significantly throughout the phase diagram, good invariance is observed along the isomorphs. We conclude that higher-order structural correlations are no less isomorph invariant than is the RDF.

Distributed stochastic principal component analysis using stabilized Barzilai-Borwein step-size for data compression with WSN

The popularity of diverse IoT-based applications and services continuously generating tremendous amount of data has revealed the significance of data compression (DC). Principal component analysis (PCA) is one of the most commonly employed algorithms for DC. However, when dealing with large-scale matrices, the standard PCA takes a very long time and requires a lot of memory. Therefore, this paper presents a novel distributed stochastic PCA algorithm (DSPCA) for hierarchical sensor network based on gradient-based adaptive PCA (GA-PCA), where the standard PCA is reformulated as a single-pass stochastic setting to find the direction of approximate maximal variance. The step-size in each iteration is obtained by incorporating the stabilized Barzilai-Borwein method with the gradient optimization. This enables DSPCA to be processed with low computational complexity while maintaining a high convergence speed. Computer simulation with two types of datasets displays that the proposed scheme consistently outperforms the representative DC schemes in terms of reconstruction accuracy of original data and explained variance.

On linear and nonlinear acoustics in stratified variable-area ducts and atmospheres and Lighthill's proposition

Abstract

Bivariate Generalized Burr and Related Distributions: Properties and Estimation

Compound distributions gained their importance from the fact that natural factors have compound effects, as in the medical, social and logical experiments. Dubey (1968) introduced the compound Weibull by compounding Weibull distribution with gamma distribution. The main aim of this paper is to define a bivariate generalized Burr (compound Weibull) distribution so that the marginals have univariate generalized Burr distributions. Several properties of this distribution such as marginals, conditional distributions and product moments have been discussed. The maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance- covariance matrix have been obtained. Some simulations have been performed to see the performances of the MLEs. One data analysis has been performed for illustrative purpose.

Profile optimum planning for degradation analysis

AbstractDegradation tests are widely used to assess the lifetime information of highly reliable products. Before conducting a degradation test, the fundamental issues in regard to decision variables are to determine how many sample sizes are needed, how long samples need to be tested, and how many measurements are taken, particularly in early experiments with limited budgets. By minimizing the approximate variance of the estimated qth quantile of the product's lifetime distribution with a cost constraint, profile optimum planning (POP) is proposed to provide a systematic solution to these decision variables under mild conditions. Based on the derived theoretical results, the use of flow charts efficiently simplifies complex optimization problems in practical applications. In addition, sensitivity analysis is studied to elucidate the effect of how the uncertainty in POP can be divided and allocated to the experimental costs and model parameters. Technical derivations, flow charts, and analysis results are available online as Supporting Information.

Comparing Depressive Symptoms, Emotional Exhaustion, and Sleep Disturbances in Self-Employed and Employed Workers: Application of Approximate Bayesian Measurement Invariance.

Studies investigating differences in mental health problems between self-employed and employed workers have provided contradictory results. Many of the studies utilized scales validated for employed workers, without collecting validity evidence for making comparisons with self-employed. The aim of this study was (1) to collect validity evidence for three different scales assessing depressive symptoms, emotional exhaustion, and sleep disturbances for employed workers, and combinators; and (2) to test if these groups differed. We first conducted approximate measurement invariance analysis and found that all scales were invariant at the scalar level. Self-employed workers had least mental health problems and employed workers had most, but differences were small. Though we found the scales invariant, we do not find them optimal for comparison of means. To be more precise in describing differences between groups, we recommend using clinical cut-offs or scales developed with the specific purpose of assessing mental health problems at work.

Wave-driven Shocks in Stellar Outbursts: Dynamics, Envelope Heating, and Nascent Blast Waves

Abstract We address the shocks from acoustic pulses and wave trains in general one-dimensional flows, with an emphasis on the application to super-Eddington outbursts in massive stars. Using approximate adiabatic invariants, we generalize the classical equal-area technique in its integral and differential forms. We predict shock evolution for the case of an initially sinusoidal but finite wave train, with separate solutions for internal shocks and head or tail shocks, and demonstrate detailed agreement with numerical simulations. Our internal shock solution motivates improved expressions for the shock-heating rate. Our solution for head and tail shocks demonstrates that these preserve dramatically more wave energy to large radii and have a greater potential for the direct ejection of matter. This difference highlights the importance of the waveform for shock dynamics. Our weak-shock analysis predicts when shocks will become strong and provides a basis from which this transition can be addressed. We use it to estimate the mass ejected by sudden sound pulses and weak central explosions.

Determining the dimensionality and gender invariance of the MACE work-to-family enrichment scale using bifactor and approximate invariance tests

larification. Research purpose: The main aim of our study was to get clarity on the dimensionality of the MACE-W2FE. The secondary aim was to test for approximate invariance of the measure for gender groups. Motivation for the study: Variations in the reported measurement models for the MACE-W2FE between studies are not conducive for theory development and called for clarification. Previous models reported were a multidimensional model and a second-order model. Approximate measurement invariance is a prerequisite for study differences between gender groups. Research approach/design and method: We did seek to resolve the problem by using bifactor model analysis, factor strength indices and local indicator misspecification analyses using a sample of 786 South African employees. Invariance was tested using the alignment optimisation method. Main findings: In this study, we solved a substantive research problem by determining that the data from the study best supported a single breadth factor or first-order factor model that was essentially unidimensional. The invariance tests across gender groups confirmed approximate configural, measurement and scalar invariances for the unidimensional model. Practical/managerial implications: Researchers and practitioners may include the MACE-W2FE in studies as a single-aggregated score without negligible loss in measurement precision. Contribution/value-add: The extended confirmatory factor analyses we conducted proved valuable in resolving the MACE-W2FE’s dimensionality vacillations, thereby enhancing the validity of inferences made from scale scores.

Accurate Statistical Model of Radiation Patterns in Analog Beamforming Including Random Error, Quantization Error, and Mutual Coupling

Analog beamforming technology is being used to overcome various technical drawbacks of mm-wave wireless communications systems. However, the errors caused by circuit implementations, quantized control, and imperfect isolation between antenna elements result in radiation pattern (RP) distortion and performance deterioration. In particular, the quantization error and mutual coupling cause the active reflection coefficient (ARC) of each antenna element to vary with respect to the main beam direction, resulting in statistical behavior changes depending on steering angles. In this article, we derive the statistical behavior of RPs with all those dominant errors taken into account. The analysis reveals that Beckmann distribution offers the exact solution for the cumulative distribution of the sidelobe level (SLL), which is very consistent with a Monte Carlo simulation including the ARC. In addition, the Rician distribution reflecting the three errors exhibits overall good accuracy, with inherent deviation from the Monte Carlo simulation results at certain steering angles due to the approximation of uncorrelated RPs and identical variances that are not valid in real antenna arrays. Our analysis also indicates that, to define the maximum probability of exceeding a certain SLL, the variance and correlation should be considered along with the mean of the RPs.

Ratio-product estimator in stratified double sampling based on coefficient of skewness of the auxiliary variable

In this paper, a ratio-product estimator for estimating the population mean of the study variable based on the population coefficient of skewness of the auxiliary variable is suggested in stratified double sampling. Asymptotic optimum estimator and its approximate bias and variance expressions are derived. Properties of the suggested estimator are studied with some known existing estimators identified as special members of this class of estimators. Analytical and numerical investigations showed that the suggested estimator is more efficient than the conventional regression estimator of mean in stratified double sampling and existing estimators of its class in stratified double sampling. Analysis and evaluation are presented.

Twelve-month clinical and imaging outcomes of the uncaging coronary DynamX bioadaptor system.

We aimed to assess the safety and efficacy of the DynamX Novolimus-Eluting Coronary Bioadaptor System, a novel device that initially acts as a second-generation drug-eluting stent, but after six months frees the vessel through uncaging elements. This multicentre study enrolled 50 patients with single de novo lesions. In-device acute lumen gain was 1.61±0.34 mm, and device and procedure success was 100%. Up to 12 months, two target lesion failures occurred: both were cardiac deaths (day 255 and day 267 post procedure). No definite or probable device thrombosis was observed. Mean late lumen loss was 0.12±0.18 mm in-device and 0.11±0.16 mm in-segment. Per intravascular ultrasound, the mean device area and mean vessel area increased significantly by 5% and 3%, respectively, while the mean lumen area was maintained. Stationary optical coherence tomography in seven patients demonstrated restoration of cyclic pulsatility, with an approximate lumen area variance of 11% between systole and diastole. The DynamX bioadaptor showed drug-eluting stent-like acute performance and safety and efficacy up to one year. Positive remodelling with an increase of vessel and device area while maintaining the mean lumen area was demonstrated. Long-term follow-up and randomised trials are required to assess the benefit of this device on events beyond one year.

OPTIMAL LIQUIDATION TRAJECTORIES FOR THE ALMGREN–CHRISS MODEL

We consider an optimal liquidation problem with infinite horizon in the Almgren–Chriss framework, where the unaffected asset price follows a Lévy process. The temporary price impact is described by a general function that satisfies some reasonable conditions. We consider a market agent with constant absolute risk aversion, who wants to maximize the expected utility of the cash received from the sale of the agent’s assets, and show that this problem can be reduced to a deterministic optimization problem that we are able to solve explicitly. In order to compare our results with exponential Lévy models, which provide a very good statistical fit with observed asset price data for short time horizons, we derive the (linear) Lévy process approximation of such models. In particular we derive expressions for the Lévy process approximation of the exponential variance–gamma Lévy process, and study properties of the corresponding optimal liquidation strategy. We then provide a comparison of the liquidation trajectories for reasonable parameters between the Lévy process model and the classical Almgren–Chriss model. In particular, we obtain an explicit expression for the connection between the temporary impact function for the Lévy model and the temporary impact function for the Brownian motion model (the classical Almgren–Chriss model), for which the optimal liquidation trajectories for the two models coincide.

Dual-Transform Source Separation Using Sparse Nonnegative Matrix Factorization

In this article, we propose a new source separation method in which the dual-tree complex wavelet transform (DTCWT) and short-time Fourier transform (STFT) algorithms are used sequentially as dual transforms and sparse nonnegative matrix factorization (SNMF) is used to factorize the magnitude spectrum. STFT-based source separation faces issues related to time and frequency resolution because it cannot exactly determine which frequencies exist at what time. Discrete wavelet transform (DWT)-based source separation faces a time-variation-related problem (i.e., a small shift in the time-domain signal causes significant variation in the energy of the wavelet coefficients). To address these issues, we utilize the DTCWT, which comprises two-level trees with different sets of filters and provides additional information for analysis and approximate shift invariance; these properties enable the perfect reconstruction of the time-domain signal. Thus, the time-domain signal is transformed into a set of subband signals in which low- and high-frequency components are isolated. Next, each subband is passed through the STFT and a complex spectrogram is constructed. Then, SNMF is applied to decompose the magnitude part into a weighted linear combination of the trained basis vectors for both sources. Finally, the estimated signals can be obtained through a subband binary ratio mask by applying the inverse STFT (ISTFT) and the inverse DTCWT (IDTCWT). The proposed method is examined on speech separation tasks utilizing the GRID audiovisual and TIMIT corpora. The experimental findings indicate that the proposed approach outperforms the existing methods.

Consequences of multiple imputation of missing standard deviations and sample sizes in meta-analysis.

Meta‐analyses often encounter studies with incompletely reported variance measures (e.g., standard deviation values) or sample sizes, both needed to conduct weighted meta‐analyses. Here, we first present a systematic literature survey on the frequency and treatment of missing data in published ecological meta‐analyses showing that the majority of meta‐analyses encountered incompletely reported studies. We then simulated meta‐analysis data sets to investigate the performance of 14 options to treat or impute missing SDs and/or SSs. Performance was thereby assessed using results from fully informed weighted analyses on (hypothetically) complete data sets. We show that the omission of incompletely reported studies is not a viable solution. Unweighted and sample size‐based variance approximation can yield unbiased grand means if effect sizes are independent of their corresponding SDs and SSs. The performance of different imputation methods depends on the structure of the meta‐analysis data set, especially in the case of correlated effect sizes and standard deviations or sample sizes. In a best‐case scenario, which assumes that SDs and/or SSs are both missing at random and are unrelated to effect sizes, our simulations show that the imputation of up to 90% of missing data still yields grand means and confidence intervals that are similar to those obtained with fully informed weighted analyses. We conclude that multiple imputation of missing variance measures and sample sizes could help overcome the problem of incompletely reported primary studies, not only in the field of ecological meta‐analyses. Still, caution must be exercised in consideration of potential correlations and pattern of missingness.

A flexible analytic model of cosmic variance in the first billion years

ABSTRACT Cosmic variance is the intrinsic scatter in the number density of galaxies due to fluctuations in the large-scale dark matter density field. In this work, we present a simple analytic model of cosmic variance in the high-redshift Universe (z ∼ 5–15). We assume that galaxies grow according to the evolution of the halo mass function, which we allow to vary with large-scale environment. Our model produces a reasonable match to the observed ultraviolet (UV) luminosity functions in this era by regulating star formation through stellar feedback and assuming that the UV luminosity function is dominated by recent star formation. We find that cosmic variance in the UV luminosity function is dominated by the variance in the underlying dark matter halo population, and not by differences in halo accretion or the specifics of our stellar feedback model. We also find that cosmic variance dominates over Poisson noise for future high-z surveys except for the brightest sources or at very high redshifts (z ≳ 12). We provide a linear approximation of cosmic variance for a variety of redshifts, magnitudes, and survey areas through the public python package galcv. Finally, we introduce a new method for incorporating priors on cosmic variance into estimates of the galaxy luminosity function and demonstrate that it significantly improves constraints on that important observable.

Severity Analysis of Mitral Regurgitation Using Discrete Wavelet Transform

This paper exhibits a computer-aided diagnosis system for the severity analysis of mitral regurgitation (MR) and assesses the discriminatory capability of Daubechies wavelet-based texture modeling. The Daubechies wavelet family has been utilized for the image decomposition because of its approximate shift invariance property. Seven statistical texture features have been utilized after the decomposition of the image up to four levels and after that concatenated. A supervised classifier, support vector machine (SVM) has been utilized with 10-fold cross-validation approach. The highest classification accuracies are 99.12 ± 0.44 utilizing db2, 99.70 ± 0.29 utilizing db4, and 97.68 ± 1.04 utilizing db4 wavelet in A2C, A4C, and PLAX respectively. The exploratory outcomes show that the proposed algorithm is effective and db4 beat among the Daubechies wavelet family considered amid this audit for precise severity investigation of the MR images.

Quasi-Invariants of Chemical Reactions in the Ideal Displacement Reactor

Mathematical models of nonequilibrium processes in distributed systems are described by partial differential equations with given boundary conditions and, as a rule, cannot be solved analytically. The absence of exact solutions of such models does not allow one to find exact invariants; i.e., functions are strictly constant on these solutions. This article has developed a method for determining the approximate spatiotemporal kinetic invariants (quasi-invariants) of chemical reactions that do not take into account diffusion in an ideal displacement reactor. Spacetime quasi-invariants are explicit algebraic expressions that relate the nonequilibrium values of the concentrations of the reagents and/or temperatures measured in two or more experiments with various specially selected initial and input conditions (multiexperiments). The selection of suitable initial conditions makes it possible to find such functions of solutions that weakly depend on the time and length of the reactor, i.e., remain almost constant throughout the reaction in the entire reactor volume. It is shown that the number of quasi-invariants is determined by the number of independent model variables (reagent concentrations and temperature). The application of the method is illustrated by the example of a one-stage reaction occurring in a reactor of ideal displacement. The quasi-invariant 3D surfaces found for this reaction are compared with 3D plots of concentration and temperature changes during the reaction. It is shown that quasi-invariants vary in a smaller range (along the ordinate axis) than the corresponding concentrations and temperatures in different experiments, i.e., are spacetime approximate invariants. Quasi-invariants of this kind can be observed on the dependences of the model variables (concentrations and temperatures) on the time and length of the reactor in the form of various flattened three-dimensional structures (“lying” waves). The method expands the tools for analyzing the unsteady kinetics of chemical reactions in distributed systems of ideal displacement.

The O(N ) model with \u03d56 potential in \u211d2\xd7 \u211d+

We study the large N limit of O(N ) scalar field theory with classically marginal ϕ6 interaction in three dimensions in the presence of a planar boundary. This theory has an approximate conformal invariance at large N . We find different phases of the theory corresponding to different boundary conditions for the scalar field. Computing a one loop effective potential, we examine the stability of these different phases. The potential also allows us to determine a boundary anomaly coefficient in the trace of the stress tensor. We further compute the current and stress-tensor two point functions for the Dirichlet case and decompose them into boundary and bulk conformal blocks. The boundary limit of the stress tensor two point function allows us to compute the other boundary anomaly coefficient. Both anomaly coefficients depend on the approximately marginal ϕ6 coupling.

Modeling Diffusivity Tests in Heterogeneous Aquifers: A Stochastic First‐Order Approach

AbstractThe diffusivity test considered here consists of injecting (or pumping) a volume of water through short segments of a well for a short time and measuring the travel time of the peak of the head signal at different points in the surrounding aquifer volume. The specific storage is assumed to be constant, while the hydraulic conductivity of the heterogeneous aquifer is modeled as a random lognormal field. The axi‐symmetric anisotropic structure is characterized by a few parameters (logconductivity mean and variance and horizontal and vertical integral scales). The paper determines the mean and variance of the peak travel time as function of distance from an instantaneous source by solving the flow equation using a first‐order approximation in the logconductivity variance. The mean travel time is recast in terms of the equivalent conductivity, which decreases from the harmonic mean near the source to the effective conductivity in uniform flow for a sufficiently large distance. Similarly, the variance drops from its maximum near the source to a small value. Application to field test is discussed and topics of future investigations are suggested.

Differencing versus nondifferencing in factor‐based forecasting

SummaryThis paper studies performance of factor‐based forecasts using differenced and nondifferenced data. Approximate variances of forecasting errors from the two forecasts are derived and compared. It is reported that the forecast using nondifferenced data tends to be more accurate than that using differenced data. This paper conducts simulations to compare root mean squared forecasting errors of the two competing forecasts. Simulation results indicate that forecasting using nondifferenced data performs better. The advantage of using nondifferenced data is more pronounced when a forecasting horizon is long and the number of factors is large. This paper applies the two competing forecasting methods to 68 I(1) monthly US macroeconomic variables across a range of forecasting horizons and sampling periods. We also provide detailed forecasting analysis on US inflation and industrial production. We find that forecasts using nondifferenced data tend to outperform those using differenced data.