Classical Error Research Articles

Cardiac MRI segmentation using shifted-window multilayer perceptron mixer networks.

In this work, we proposed a deep-learning segmentation algorithm for cardiac magnetic resonance imaging (MRI) to aid in contouring of the left ventricle (LV), right ventricle (RV), and Myocardium (Myo). 
Methods: We proposed a shifted window multilayer perceptron (Swin-MLP) mixer network which is built upon a 3D U-shaped symmetric encoder-decoder structure. We evaluated our proposed network using public data from 100 individuals. The network performance was quantitatively evaluated using 3D volume similarity between the ground truth contours and the predictions using Dice score coefficient, sensitivity, and precision as well as 2D surface similarity using Hausdorff distance (HD), mean surface distance (MSD) and residual mean square distance (RMSD). We benchmarked the performance against two other current leading edge networks known as Dynamic UNet and Swin-UNetr on the same public dataset. 
Results: The proposed network achieved the following volume similarity metrics when averaged over three cardiac segments: Dice = 0.952±0.017, precision = 0.948±0.016, sensitivity = 0.956±0.022. The average surface similarities were HD = 1.521±0.121 mm, MSD = 0.266±0.075 mm, and RMSD = 0.668±0.288 mm. The network shows statistically significant improvement in comparison to the Dynamic UNet and Swin-UNetr algorithms for most volumetric and surface metrics with p-value less than 0.05. Overall, the proposed Swin-MLP mixer network demonstrates better or comparable performance than competing methods. 
Conclusions: The proposed Swin-MLP mixer network demonstrates more accurate segmentation performance compared to current leading edge methods. This robust method demonstrates the potential to streamline clinical workflows for multiple applications.

Fluvial bedload transport modelling: advanced ensemble tree-based models or optimized deep learning algorithms?

The potential of advanced tree-based models and optimized deep learning algorithms to predict fluvial bedload transport was explored, identifying the most flexible and accurate algorithm, and the optimum set of readily available and reliable inputs. Using 926 datasets for 20 rivers, the performance of three groups of models was tested: (1) standalone tree-based models Alternating Model Tree (AMT) and Dual Perturb and Combine Tree (DPCT); (2) ensemble tree-based models Iterative Absolute Error Regression (IAER), ensembled with AMT and DPCT; and (3) optimized deep learning models Long Short-Term Memory (LSTM) and Recurrent Neural Network (RNN) ensembled with Grey Wolf Optimizer. Comparison of the predictive performance of the models with that of commonly used empirical equations and sensitivity analysis of the driving variables revealed that: (i) the coarse grain-size percentile D 90 was the most effective variable in bedload transport prediction (where D x is the xth percentile of the bed surface grain size distribution), followed by D 84, D 50, flow discharge, D 16, and channel slope and width; (ii) all tree-based models and optimized deep learning algorithms displayed ‘very good’ or ‘good’ performance, outperforming empirical equations; and (iii) all algorithms performed best when all input parameters were used. Thus, a range of different input variable combinations must be considered in the optimization of these models. Overall, ensemble algorithms provided more accurate predictions of bedload transport than their standalone counterpart. In particular, the ensemble tree-based model IAER-AMT performed most strongly, displaying great potential to produce robust predictions of bedload transport in coarse-grained rivers based on a few readily available flow and channel variables.

Total Least Squares Estimation in Hedonic House Price Models

In real estate valuation using the Hedonic Price Model (HPM) estimated via Ordinary Least Squares (OLS) regression, subjectivity and measurement errors in the independent variables violate the Gauss–Markov theorem assumption of a non-random coefficient matrix, leading to biased parameter estimates and incorrect precision assessments. In this contribution, the Errors-in-Variables model equipped with Total Least Squares (TLS) estimation is proposed to address these issues. It fully considers random errors in both dependent and independent variables. An iterative algorithm is provided, and posterior accuracy estimates are provided to validate its effectiveness. Monte Carlo simulations demonstrate that TLS provides more accurate solutions than OLS, significantly improving the root mean square error by over 70%. Empirical experiments on datasets from Boston and Wuhan further confirm the superior performance of TLS, which consistently yields a higher coefficient of determination and a lower posterior variance factor, which shows its more substantial explanatory power for the data. Moreover, TLS shows comparable or slightly superior performance in terms of prediction accuracy. These results make it a compelling and practical method to enhance the HPM.

Does energy transition reduce carbon inequality? A global analysis.

Energy transition from fossil fuels to renewables is instrumental in mitigating climate change. Low-income countries have a higher share of renewable energy in their total energy consumption than rich countries (WDI, 2023). Thus, it is imperative to examine the role of energy transition in affecting relative CO2 emissions between rich and poor sections of the societies across income groups of the countries. In this context, our study contributes by constructing the carbon inequality models with renewable and non-renewable energy consumption as prime explanatory variables separately for 114 countries over a data period 1990-2019. The models are estimated individually for high-middle-low-income countries by controlling for foreign direct investment (FDI), economic growth, and innovations. Starting with preliminary econometric operations, we employ the dynamic simulated panel autoregressive distributed lag approach and Driscoll-Kraay standard error regression for empirical investigation. We find that energy transition reduces carbon inequality globally. Innovation has a negative impact, economic growth has a positive impact on carbon inequality, and FDI has an asymmetric impact based on the income level of the countries. The crucial global policy implications are discussed.

Multilevel Monte Carlo Methods for Stochastic Convection–Diffusion Eigenvalue Problems

We develop new multilevel Monte Carlo (MLMC) methods to estimate the expectation of the smallest eigenvalue of a stochastic convection–diffusion operator with random coefficients. The MLMC method is based on a sequence of finite element (FE) discretizations of the eigenvalue problem on a hierarchy of increasingly finer meshes. For the discretized, algebraic eigenproblems we use both the Rayleigh quotient (RQ) iteration and implicitly restarted Arnoldi (IRA), providing an analysis of the cost in each case. By studying the variance on each level and adapting classical FE error bounds to the stochastic setting, we are able to bound the total error of our MLMC estimator and provide a complexity analysis. As expected, the complexity bound for our MLMC estimator is superior to plain Monte Carlo. To improve the efficiency of the MLMC further, we exploit the hierarchy of meshes and use coarser approximations as starting values for the eigensolvers on finer ones. To improve the stability of the MLMC method for convection-dominated problems, we employ two additional strategies. First, we consider the streamline upwind Petrov–Galerkin formulation of the discrete eigenvalue problem, which allows us to start the MLMC method on coarser meshes than is possible with standard FEs. Second, we apply a homotopy method to add stability to the eigensolver for each sample. Finally, we present a multilevel quasi-Monte Carlo method that replaces Monte Carlo with a quasi-Monte Carlo (QMC) rule on each level. Due to the faster convergence of QMC, this improves the overall complexity. We provide detailed numerical results comparing our different strategies to demonstrate the practical feasibility of the MLMC method in different use cases. The results support our complexity analysis and further demonstrate the superiority over plain Monte Carlo in all cases.

Reprint of: Robust inference on correlation under general heterogeneity

Considerable evidence in past research shows size distortion in standard tests for zero autocorrelation or zero cross-correlation when time series are not independent identically distributed random variables, pointing to the need for more robust procedures. Recent tests for serial correlation and cross-correlation in Dalla, Giraitis, and Phillips (2022) provide a more robust approach, allowing for heteroskedasticity and dependence in uncorrelated data under restrictions that require a smooth, slowly-evolving deterministic heteroskedasticity process. The present work removes those restrictions and validates the robust testing methodology for a wider class of innovations and regression residuals allowing for heteroscedastic uncorrelated and non-stationary data settings. The updated analysis given here enables more extensive use of the methodology in practical applications. Monte Carlo experiments confirm excellent finite sample performance of the robust test procedures even for extremely complex white noise processes. The empirical examples show that use of robust testing methods can materially reduce spurious evidence of correlations found by standard testing procedures.

A formal model accounting for measurement reliability shows attenuated effect of higher education on intelligence in longitudinal data.

The effect of higher education on intelligence has been examined using longitudinal data. Typically, these studies reveal a positive effect, approximately 1 IQ point per year of higher education, particularly when pre-education intelligence is considered as a covariate in the analyses. However, such covariate adjustment is known to yield positively biased results if the covariate has measurement errors and is correlated with the predictor. Simultaneously, a negative bias may emerge if the intelligence measure after higher education has non-classical measurement errors as in data from the 1970 British Cohort Study that were used in a previous study of the effect of higher education. In response, we have devised an estimation method that used iterated simulations to account for both classical measurement errors in the covariate and non-classical errors in the dependent variable. Upon applying this method in a reanalysis of the data from the 1970 British Cohort Study, we find that the estimated effect of higher education diminishes to 0.4 IQ points per year. Additionally, our findings suggest that the impact of higher education is somewhat more pronounced in the initial 2 years of higher education, aligning with the notion of diminishing marginal cognitive benefits.

Self-error learning framework-based algorithm for parameter recovery of extended Wiener–Hammerstein systems subject to quantised measurements

In this study, a novel estimation scheme is proposed for identifying extended Wiener–Hammerstein systems with hysteresis nonlinearity subject to quantised measurements. The proposed scheme is established in a self-error learning framework to achieve high-performance parameter estimation compared with classic error feedback learning estimation algorithms. Initially, the useful identification data can be extracted from contaminated system data by introducing an adaptive filter. Then, with the help of the filtered data, the identification error expression used to establish the estimator is derived. Subsequently, an online compensation estimation error variable is proposed to eliminate the effect of the regression vector on the convergence performance. A new adaptive law is designed with adaptive recursive gain, considering the compensation estimation error data and parameter initial error data. Under general persistent excitation (PE) condition, the PE condition of the regressor information is verified online, and the estimator convergence is strictly proven. Finally, the statistical results of two illustrated examples and a real-word example are provided to validate the positive features and effectiveness of the proposed estimation scheme.

LordNet: An efficient neural network for learning to solve parametric partial differential equations without simulated data

Neural operators, as a powerful approximation to the non-linear operators between infinite-dimensional function spaces, have proved to be promising in accelerating the solution of partial differential equations (PDE). However, it requires a large amount of simulated data, which can be costly to collect. This can be avoided by learning physics from the physics-constrained loss, which we refer to it as mean squared residual (MSR) loss constructed by the discretized PDE. We investigate the physical information in the MSR loss, which we called long-range entanglements, and identify the challenge that the neural network requires the capacity to model the long-range entanglements in the spatial domain of the PDE, whose patterns vary in different PDEs. To tackle the challenge, we propose LordNet, a tunable and efficient neural network for modeling various entanglements. Inspired by the traditional solvers, LordNet models the long-range entanglements with a series of matrix multiplications, which can be seen as the low-rank approximation to the general fully-connected layers and extracts the dominant pattern with reduced computational cost. The experiments on solving Poisson’s equation and (2D and 3D) Navier–Stokes equation demonstrate that the long-range entanglements from the MSR loss can be well modeled by the LordNet, yielding better accuracy and generalization ability than other neural networks. The results show that the Lordnet can be 40× faster than traditional PDE solvers. In addition, LordNet outperforms other modern neural network architectures in accuracy and efficiency with the smallest parameter size.

Examining the Influence of Macroeconomic Factors and Corporate Governance on Firm Performance in the ACE Market

This study focused on investigating the impact of macroeconomic factors and corporate governance on the financial performance of firms listed on the ACE Market of Bursa Malaysia. The ACE Market serves as a platform for smaller, emerging companies, providing them with an opportunity to raise capital with less stringent requirements compared to the Main Market. Using a panel data set of 72 companies over the period 2018-2022, the research employed panel-corrected standard errors (PCSE) regression. PCSE is a panel regression model that accounts for contemporaneous correlations, corrects for deviations from spherical errors, and enhances inference from linear models. The analysis revealed that ACE market companies, on average, show a negative return on equity (ROE) but positive numbers of women (NOW) and board meetings (NOM). The PCSE regression results, however, failed to show a statistically significant relationship between NOW and ROE, suggesting that the presence of women on the board of directors does not significantly impact the firm performance. The findings provide valuable insights for the firms in the ACE market companies regarding the consideration of important factors in improving firm performance. The research's broader goal is to inform the development of strategies fostering enhanced overall performance and sustainability in the ACE market. The study also suggests several recommendations such as broadening the scope and inclusion of international trade dynamics variables.

Parallel observations process of Tianwen-1 orbit determination

Abstract To meet various requirements of the future deep space missions of China, State Key Laboratory of Astronautic Dynamics constructs a new orbit determinatin software with parallel observations process. By using 32 threads, the computational efficiency per iteration (including spacecraft’s integration) could be promoted to 10 times as that of single-threaded orbit determination. Suppose the number of observations is p p , the number of estimated parameters (including spacecraft’s state) is q q , the amount of computation of one observation is x x , the amount of computation of one Givens transformation is y y and the best number of threads is proved to be [ p ⋅ ( x + y ) / ( q ⋅ y ) ] 1 / 2 {\left[p\cdot \left(x+y)\text{/}\left(q\cdot y)]}^{1\text{/}2} for one-step threads combination. The root mean square of the postfit residuals of China’s deep space monitoring network (CDSMN) and China’s Very Long Baseline Interferometry (VLBI) network (CVN) observations in the Earth-Mars transfer phase and the Mars-orbiting phase are almost the same: about 0.3 m for Ranging, about 0.3 mm/s for Doppler, about 3 cm for VLBI delay and about 0.5 mm/s for VLBI delay rate. It is also found that all the four types of observations of CDSMN and CVN are needed in orbit determination for deep space maneuver and braking at periareion calculation. In the Mars-orbiting phase, the position accuracy after orbit determination under CDSMN-only tracking mode can reach about 1 km.

Adaptive Weighted Error-Correction Method Based on the Error Distribution Characteristics of Multi-Channel Alignment.

As process nodes of advanced integrated circuits continue to decrease below 10 nm, the requirement for overlay accuracy is becoming stricter. The alignment sensor measures the position of the alignment mark relative to the wafer; thus, sub-nanometer alignment position accuracy is vital. The Phase Grating Alignment (PGA) method is widely used due to its high precision and stability. However, the alignment error caused by the mark asymmetry is the key obstacle preventing PGA technology from achieving sub-nanometer alignment accuracy. This error can be corrected using many methods, such as process verification and multi-channel weighted methods based on multi-diffraction, multi-wavelength and multi-polarization state alignment sensors. However, the mark asymmetry is unpredictable, complex and difficult to obtain in advance. In this case, the fixed-weight method cannot effectively reduce the alignment error. Therefore, an adaptive weighted method based on the error distribution characteristic of a multi-channel is proposed. Firstly, the simulation result proves that the error distribution characteristic of the multi-alignment result has a strong correlation with the mark asymmetry. Secondly, a concrete method of constructing weight values based on error distribution is described. We assume that the relationship between the weight value of each channel and the deviations of all channels' results is second-order linear. Finally, without other prior process correction in the simulation experiment, the residual error's Root Mean Square (RMS) of fixed weighted method is 14.0 nm, while the RMS of the adaptive weighted method is 0.01 nm, when dealing with five typical types of mark asymmetry. The adaptive weighted method exhibits a more stable error correction effect under unpredictable and complicated mark asymmetry.

The effect of geopolitical risk and green technology on load capacity factors in BRICS

This study explores the interaction between geopolitics, natural resources, and load capacity factors (LCF) within BRICS countries. Using fixed effects, random effects, quantile regression, and Driscoll Kraay Standard Error approaches, we found that for every 1% increase in green technology adoption, LCF decreased by 0.14%–0.54%. This effect suggests that green technologies may reduce LCF. Geopolitical risk positively influences LCF, with a 1% increase resulting in a 0.14%–0.48% rise across quantiles, thus enhancing reliability and sustainability. Furthermore, economic growth, renewable energy, and natural resources rents enhance the ratio of biocapacity to ecological footprint.

Evaluating energy transmission characteristics of Non-Newtonian fluid flow in stratified and non-stratified regimes: A comparative study

Considering the natural and industrial importance of flow characterization in stratified media, the current study is articulated. This work highlights the influence of linear stratification as well as convective surfaces in both thermal and solutal fields on the rheological attributes of Williamson fluid flow through an inclined surface. Novel physical aspects of a uniformly provided magnetic field of strength B and chemically reactive species are also included. The concerned transport equations are derived from the associated conservation laws in dimensional forms. Modification in the developed couple system is achieved by using a set of similar variables. Levenberg-Marquardt Scheme (LMS) and Bayesian Regularization Scheme (BRS) are utilized in comparative manner to analyze initial data accessed for quantities of interest. The data used in the generation of MLP was 80 percent for model training and 20 percent for testing and validation. Error histograms, performance plots, fitness curves, and regression plots for training, testing, and validation are presented. Data in the form of tables and graphs are presented, which express an excellent match between the ANN-predicted and targeted values. It is revealed that an artificial neural network approach can provide highly efficient forecasting for such problems by providing accurate data for quantities of interest. It is noticed that Nusselt number and Sherwood number enhances up to 33 % and 29 % versus respective stratification parameters. Velocity profile declines against magnetic field parameter (M) whereas, skin friction coefficient increments up to 25 %. Appliance of convective boundary constraints at the surface of inclined sheet tends to enhance the temperature and concentration fields.

Liquid‐Metal‐Based Soft Pressure Sensor and Multidirectional Detection by Machine Learning

AbstractElectronic skin (e‐skin) is an emerging technology with promising applications in various fields, including human–machine interfaces, prosthetics, and robotics. Soft and flexible sensors are vital components for the e‐skin that can mimic human skin's sensing capabilities. Among soft sensors, liquid‐metal‐based sensors have gained attention owing to their unique properties, such as high electrical conductivity, stretchability, and elasticity. Herein, a novel approach is presented that enables multidirectional pressure sensing with a machine‐learning approach from the transient response of the liquid‐metal‐based soft pressure sensor for the e‐skins. In this study, a soft sensor is developed that utilizes liquid metal and has an array of microchannels on a dome‐shaped structure to detect pressures from multiple directions. The transient response from six microchannels of the sensor is used as the input for a convolutional neural network (CNN) to predict the direction (classification accuracy of 99.1%) and magnitude (regression error of 20.13%) of the applied pressures in real time. Finally, a potential application of the developed liquid‐metal‐based soft sensor as a human–machine interface device is demonstrated by using it to control an RC model car through multidirectional predictions (pressure direction and magnitude) through machine learning in real time.

A form-grinding wheel optimization method for helical gears based on a PSO-SVM model

A gear form-grinding optimization method is proposed to obtain an optimal profile of a form-grinding wheel by solving a transcendental equation of the contact line between a form-grinding wheel and a helical gear workpiece. Since the equation of the contact line is transcendental, the relationship between the installation angle of the form-grinding wheel and the shape of the contact line cannot be represented by explicit functions, which makes it difficult to obtain the optimal profile of the form-grinding wheel. An optimization method of the contact line between the form-grinding wheel and the gear is proposed using three evaluation parameters that are the overrun, the shift, and the offset. Some gear form-grinding performances, such as machining stroke, tooth deviation, and grinding chatter, can be quantitatively described using those evaluation parameters. Further, a method for optimizing evaluation parameters is proposed, which uses a particle swarm optimization-support vector machine (PSO-SVM) model with the advantage of small-sample robustness to solve evaluation parameters. The PSO-SVM model is trained under the condition of different installation angles of the form-grinding wheel as the input and the evaluation function as the output. The R-squared value of the overrun is 0.986 that vilidate the high accuracy of the PSO-SVM model. Gear form-grinding test results show the proposed method can effectively improve grinding accuracy.

Global Precipitation Nowcasting of Integrated Multi-satellitE Retrievals for GPM: A U-Net Convolutional LSTM Architecture

Abstract This paper presents a deep supervised learning architecture for 30 min global precipitation nowcasts with a 4-hour lead time. The architecture follows a U-Net structure with convolutional long short-term memory (ConvLSTM) cells empowered by ConvLSTM-based skip connections to reduce information loss due to the pooling operation. The training uses data from the Integrated MultisatellitE Retrievals for GPM (IMERG) and a few key drivers of precipitation from the Global Forecast System (GFS). The impacts of different training loss functions, including the mean-squared error (regression) and the focal-loss (classification), on the quality of precipitation nowcasts are studied. The results indicate that the regression network performs well in capturing light precipitation (<1.6 mm hr−1) while the classification network can outperform the regression counterpart for nowcasting of high-intensity precipitation (>8 mm hr−1), in terms of the critical success index (CSI). It is uncovered that including the forecast variables can improve precipitation nowcasting, especially at longer lead times in both networks. Taking IMERG as a relative reference, a multi-scale analysis, in terms of fractions skill score (FSS), shows that the nowcasting machine remains skillful for precipitation rate above 1 mm hr−1 at the resolution of 10 km compared to 50 km for GFS. For precipitation rates greater than 4 mm hr−1, only the classification network remains FSS-skillful on scales greater than 50 km within a 2-hour lead time.

International managerial skill and big Colombian big exporting firms' performance, 2006–2014

AbstractThis paper uses a sample of the biggest private Colombian exporting firms to propose and estimate a two‐step methodology for measuring international managerial skill and calculating its impact on international firm performance. The first step quantifies the managerial team's organisational capital contribution to rise firms' export proficiency through the average of a regression residuals group conformed by export unit value residuals for differentiated products (multiplying by −1 the price competition products' residuals) and export quantity residuals for homogeneous products. The second step results indicate that: (i) international managerial quality has a significant and robust positive effect on export value, (ii) better managers in the international market do not increase the number of products exported but upgrade export basket's quality and (iii) export value elasticity relative to international managerial quality is around 5 times larger than export value elasticity relative to exogenous global demand shocks.

Improved uniform error bounds on an exponential wave integrator method for the nonlinear Schrödinger equation with wave operator and weak nonlinearity

In this paper, we establish the improved uniform error bounds for the Lawson-type exponential wave integrator Fourier pseudo-spectral (LEWIFP) method for the nonlinear Schrödinger equation with wave operator (NLSW) and weak nonlinearity characterized by a small constant ε∈(0,1]. We first convert the NLSW to a coupled system and then consider the LEWIFP method for the coupled system. The LEWIFP method is proved to be time symmetric and mass-conservative which is very important from the point of view of numerical geometric integration. Through careful and rigorous convergence analysis, we establish improved uniform error bounds for the full-discretization at O(hm+ε2pτ2) in the long-time domain up to O(1/ε2p) where m is determined by the regularity conditions. These error bounds are much better than the classical error bounds O(hm+τ2) provided by the traditional error analysis. In error analysis, in addition to the classical tools such as mathematical induction and energy method, we adopt the regularity compensation oscillation (RCO) technique to analyze the accumulation of errors carefully. The numerical experiments support our error estimates and demonstrate the discrete mass-conservation. In addition, the numerical results show that the discrete energy is stable in the time domain up to O(1/ε2p).

Comparing Two Smoothing Approaches in Estimating Kinematic Parameters.

We compare two signal smoothing and differentiation approaches: a frequently used approach in the speech community of digital filtering with approximation of derivatives by finite differences and a spline smoothing approach widely used in other fields of human movement science. In particular, we compare the values of a classic set of kinematic parameters estimated by the two smoothing approaches and assess, via regressions, how well these reconstructed values conform to known laws about relations between the parameters. Substantially smaller regression errors were observed for the spline smoothing than for the filtering approach. This result is in broad agreement with reports from other fields of movement science and underpins the superiority of splines also in the domain of speech.