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Recently, a number of efficient iteration methods for the solution of a special class of block 3 × 3 saddle point systems have been proposed by some authors. In order to easily evaluate the strong stability of these numerical algorithms and provide a practical and reliable termination criterion, in this paper, we perform the structured backward error analysis for this type of block 3 × 3 saddle point system and present an explicit and computable formula of the normwise structured backward error. Some numerical experiments are performed to demonstrate that our results can be used to easily test the stability of running algorithms, and the new stopping criterion based on the derived structured backward error is more suitable and efficient than the commonly used residue-based one. [ABSTRACT FROM AUTHOR]

A reproducing kernel Hilbert space (RKHS) approximation problem arising from learning theory is investigated. Some K-functionals and moduli of smoothness with respect to RKHSs are defined with Fourier–Bessel series and Fourier–Bessel transforms, respectively. Their equivalent relation is shown, with which the upper bound estimate for the best RKHS approximation is provided. The convergence rate is bounded with the defined modulus of smoothness, which shows that the RKHS approximation can attain the same approximation ability as that of the Fourier–Bessel series and Fourier–Bessel transform. In particular, it is shown that for a RKHS produced by the Bessel operator, the convergence rate sums up to the bound of a corresponding convolution operator approximation. The investigations show some new applications of Bessel functions. The results obtained can be used to bound the approximation error in learning theory. [ABSTRACT FROM AUTHOR]

Determining the threshold separating poor from non-poor populations is one of the most influential choices when measuring poverty. Commonly used selection criteria leave considerable room for discretion or are not appropriate as academic standards. This vacuum in academic guidance leads to arbitrary and/or ideologically driven choices. This can greatly influence the measurement of a societal phenomenon, and thus research and public policy decisions over a period that extends well beyond the mandate of those making that threshold decision. This paper sets out an empirical validation method that contributes to reducing the range of thresholds and thereby aids decision-makers in making that normative decision. Our method uses an absolute concept of empirical validity and requires that the microdata for measuring poverty hold additional information closely associated with poverty. The method builds on insights from theory on measurement error that, for any given threshold, some persons are wrongly identified as poor (false positives) and others are wrongly identified as not poor (false negatives), and that the reduction of one error can only be attained by increasing the other. Our method uses the additional microdata to disaggregate the population into (likely) false positives and (likely) false negatives and analyzes marginal changes in this composition as the poverty threshold becomes stricter. Using Canadian data, we show that this approach substantially narrows the range of thresholds for two unidimensional poverty indicators, namely a material deprivation and an income poverty indicator. The underlying principle of the method extends to other (unidimensional) social indicators. The analysis itself can also serve other purposes, such as deepening our understanding of poverty and the cost-effectiveness of policies to reduce it. [ABSTRACT FROM AUTHOR]

This paper analyzes the usefulness of approximate addition for digital image compression. Discrete Cosine Transform (DCT) is an important operation in digital image compression. We used accurate addition and approximate addition individually while calculating the DCT to perform image compression. Accurate addition was performed using the accurate adder and approximate addition was performed using different approximate adders individually. The accurate adder and approximate adders were implemented in an application specific integrated circuit (ASIC)-type design environment using a 32–28 nm complementary metal oxide semiconductor (CMOS) standard cell library and in a field programmable gate array (FPGA)-based design environment using a Xilinx Artix-7 device. Error analysis was performed to calculate the error parameters of various approximate adders by applying one million random input vectors. It is observed that the approximate adders help to better reduce the file size of compressed images than the accurate adder. Simultaneously, the approximate adders enable reductions in design parameters compared to the accurate adder. For an ASIC-type implementation using standard cells, an optimum approximate adder achieved 27.1% reduction in delay, 46.4% reduction in area, and 50.3% reduction in power compared to a high-speed accurate carry look-ahead adder. With respect to an FPGA-based implementation, an optimum approximate adder achieved 8% reduction in delay and 19.7% reduction in power while requiring 47.6% fewer look-up tables (LUTs) and 42.2% fewer flip-flops compared to the native accurate FPGA adder. [ABSTRACT FROM AUTHOR]

In order to quickly and accurately predict the spatial geometric error field of the five-axis machine tool processing, a method for predicting the comprehensive error field of the five-axis machine tool processing space based on the "S"-shaped specimen family is studied. Firstly, for the five-axis CNC machine tool in the form of A-C dual turntable, the geometric error model of the rotating axis is established based on the multi-body dynamics theory; the error mapping relationship between the processing technology system and the workpiece is analyzed based on the "S"-shaped specimen family, and the identification of 12 geometric errors of the two rotating shafts. Then, the error value of the sampling point is measured based on the "S"-shaped test piece in machine contact, and the double-circle center coordinate value is determined according to the curvature of the measured wire of the test piece, in order to identify the geometric errors of the two rotation axes of the five-axis machine tool. Finally, based on the prediction method, the comprehensive error field of the five-axis CNC machine tool processing space is analyzed. Compared with other geometric error identification methods, the measurement accuracy of this method meets the processing requirements and can further evaluate the comprehensive performance of the machine tool. [ABSTRACT FROM AUTHOR]

A space solar power station (SSPS) has become a huge potential candidate to provide abundant and clean electrical energy for terrestrial users by collecting and converting solar power in space. In this paper, an innovative two-layer ring truss-based SSPS is proposed. It consists of the top layer concentrator-based spherical one-time reflection region, the bottom layer space radiator using symmetric or asymmetric cable networks, a ring truss for a supporting structure, a photoelectric conversion system, and transmitting antennas. The construction strategies including the triangular facets modularity of top layer concentrator, area requirement of bottom layer space radiator, two-segment optimization design of generatrix of photoelectric conversion system, and aperture derivation of transmitting antenna are carried out. Then, the performance analysis mainly including the modularization theory error calculation, energy collection and distribution, and thermal characteristics in orbit of this proposed SSPS is presented. Finally, the system parameters are estimated and summarized for a better sense of the proposed SSPS. The results indicate that 100% energy collection can be achieved for an ideal concentrator, and 80% with a modular division layer of 6 and tracking error of no more than 2°. The results demonstrate the feasibility of the proposed SSPS concept and can provide a reference for future space energy harvesting and space exploration projects. [ABSTRACT FROM AUTHOR]

Purpose: To study in simulation and in theory the accuracy and precision of dynamic T1 measurements obtained using the previously published single‐reference variable flip angle (SR‐VFA) technique, with a focus on the effects of dynamic changes in T2* on the calculation. Methods: Monte Carlo simulations were performed over 1000 noisy iterations for the VFA method, the SR‐VFA method, and a proposed method, SR‐VFA with a T2* correction (SR‐VFA‐T2*). Dynamic T1 estimates were calculated analytically for each method, with signals modeled by the steady‐state spoiled gradient echo equation. The mean and standard deviation of these estimates were calculated and compared to truth, while varying repetition time (TR), baseline and dynamic T1, echo time (TE), baseline and dynamic T2*, flip angles, and the number of averages on baseline scans. Additionally, the variance of T1 in the SR‐VFA and SR‐VFA‐T2* methods was derived analytically based on the theory of propagation of errors. This equation was used to produce an inverse‐variance weighted linear combination to improve T1 mapping precision in the SR‐VFA‐T2* method. Flip angle sensitivity of dynamic T1 precision in the SR‐VFA and SR‐VFA‐T2* methods was also performed. Results: Substantial bias can be produced by the SR‐VFA method when the ratio of the T2* decay of the dynamic signal versus that of the baseline signals deviates from 1, with a 0.01 deviation leading to approximately a 1% bias in cases of high SNR and TR ≫ T1. This bias can be corrected by estimating the baseline and dynamic T2* values in this ratio via multiecho measurements. The bias and precision of the SR‐VFA‐T2* method, when normalized to scan time, is found to rival and sometimes improve upon the two flip angle VFA method when an inverse variance weighted linear combination is applied across its multiecho T1 maps. The analytic variance equation presented is found to be accurate within 1% relative to the Monte Carlo simulations over a broad parameter space. Flip angle ranges that maximize SR‐VFA and SR‐VFA‐T2*T1 precision over a broad parameter space are given, and each is defined relative to TR and T1. Conclusions: Multiecho SR‐VFA‐T2* T1 mapping is found in simulation and theory to be a promising alternative to the VFA method that maintains speed of the SR‐VFA method with accuracy and precision similar to the VFA method. [ABSTRACT FROM AUTHOR]

As an extension of the finite element method, the virtual element method (VEM) can handle very general polygonal meshes, making it very suitable for non-matching meshes. In (Wriggers et al. in Comput. Mech. 58:1039–1050, 2016), the lowest-order virtual element method was applied to solve the contact problem of two elastic bodies on non-matching meshes. The numerical experiments showed the robustness and accuracy of the virtual element scheme. In this paper, we establish a priori error estimate of the virtual element method for the contact problem and prove that the lowest-order VEM achieves linear convergence order, which is optimal. [ABSTRACT FROM AUTHOR]

This article presents a novel method for validating compass devices. To this end, the post-processing method was used, i.e., the previously recorded vessel's heading from three compass devices was applied. A spectral analysis of the recorded heading in the frequency domain was conducted by applying the fast Fourier transform method. Based on a synthetic summary of the results of spectral analysis in the heading error frequency domain, the factors causing errors of low-frequency compass device indications, manifested by the vessel's yawing due to the vessel steering errors on the pre-determined course and the external factors causing total drift of the vessel, were eliminated. To this end, the convolution functions in the form of the sum of input signals with an impulse response, i.e., the filter with a finite impulse response (FIR) and with an infinite impulse response (IIR), were used to compare the effectiveness of the methods estimating the vessel's heading. The final stage of the research process in the methodology applied was the use of state- and time-discrete Markov processes whose task is to determine the matrices of the intensity of transitions between the states of individual compass systems. [ABSTRACT FROM AUTHOR]

In this paper, we compute the approximate numerical solution for the Volterra-Fredholm integral equation (VFIE) by using the shifted Jacobi collocation (SJC) method which depends on the operational matrices. Some properties of the shifted Jacobi polynomials are introduced. These properties allow us to transform the Volterra- Fredholm integral equation into a system of algebraic equations in a nice form with the expansion coefficients of the solution. Also, the convergence and error analysis are studied extensively. Finally, some examples which verify the efficiency of the given method are supplied and compared with other methods. [ABSTRACT FROM AUTHOR]

In this work, a time-fractional biharmonic equation with a Caputo derivative of fractional order α ∈ (0 , 1) is considered, whose solutions exhibit a weak singularity at initial time t = 0. For this problem, a system of two second-order differential equations is derived by introducing a intermediate variable p = − Δ u , then discretised the system using the standard finite element method in space together with the L1 discretisation of Caputo derivative on graded mesh in time. The H 1 -norm stability result of the method is established, and then a sharp H 1 -norm local convergent result is presented. Finally, numerical experiments are provided to further verify our theoretical analysis for each fixed value of α. [ABSTRACT FROM AUTHOR]

This study aims to use structural equation modeling (SEM) to investigate the role of error processing in behavioral adaptation in children by testing relationships between error‐related and stimulus‐related event‐related potentials (ERPs) obtained from two sessions of a speeded Eriksen flanker task. First, path models of averaged ERP components and mean response times (N1 → P2 → N2 → P3 → RTs) while controlling for trait effects, age, and sex, on each was examined separately for correct and incorrect trials from each session. While the model demonstrated acceptable fit statistics, the four models yielded diverse results. Next, path models for correct and incorrect trials were tested using latent variables defined by factoring together respective measures of ERP component amplitudes from each session. Comparison of correct and incorrect models revealed significant differences in the relationships between the successive measures of neural processing after controlling for trait effects. Moreover, latent variable models controlling for both trait and session‐specific state variables yielded excellent model fit while models without session‐specific state variables did not. In the final model, the error‐related neural activity (i.e., the ERN and Pe) from incorrect trials was found to significantly relate to the stream of neural processes contributing to trials with the correct behavior. Importantly, the relationship between RT and error detection in the final model signifies a brain‐and‐behavior feedback loop. These findings provided empirical evidence that supports the adaptive orienting theory of error processing by demonstrating how the neural signals of error processing influence behavioral adaptations that facilitate correct behavioral performance. Our research builds on Wessel's adaptive orienting theory where post‐error psychological processes of automatic inhibition and attentional orientation lead to improved performance accuracy. Novel use of structural equation modeling of correct trials demonstrates that phases of brain activity predict response time. Additionally, response time predicts performance monitoring (ERN/PE amplitudes) which in turn predicts attention‐based components (N1/N2 amplitudes) in the brain processing of correct trials supporting the adaptive orienting theory. [ABSTRACT FROM AUTHOR]

The single-degree-of-freedom and three-degree-of-freedom viscous damping systems are simulated based on the Morlet wavelet function transformation in an effort to study the wavelet transform and further promote the optimization of nonlinear system modal identification. In the meantime, the modal animation display technology is studied using the Visual Basic (VB) 6.0 software and Open GL three-dimensional graphics library. The research object is a thin plate member with five degrees of freedom. The research results are as follows. In the single-degree-of-freedom viscous damping system, the identification frequency is 11.545 rad/s, and the damping ratio is 2.87%. The simulation result has a small gap with the set damping ratio, and the identification in the system is accurate and reliable. In the three-degree-of-freedom damping system, the recognition accuracy of the first-order wavelet coefficient model is higher. Besides, the recognition accuracy of the natural frequency in the second-order is better, and the damping ratio error value is 11.08%. In the third-order, the natural frequency and the damping ratio have a large error from the theory; the error values are 24.53% and 32.11%, respectively. In the meantime, VB 6.0 software and Open GL software can effectively identify the actual shape of the research object, showing a good application effect. The above results can provide scientific and effective reference materials for subsequent research on nonlinear system modal identification. [ABSTRACT FROM AUTHOR]

In incompressible flow problems, the finite element discretization of pressure and velocity can be done through either stable spaces or stabilized pairs. For equal-order stabilized methods with piecewise linear discretization, the classical theory guarantees only linear convergence for the pressure approximation. However, a higher order is often observed, yet seldom discussed, in numerical practice. Such experimental observations may, in the absence of a sound a priori error analysis, mislead the selection of finite element spaces in practical applications. Therefore, we present here a numerical analysis demonstrating that an initial higher-order pressure convergence may in fact occur under certain conditions, for equal-order elements of any degree. Moreover, our numerical experiments clearly indicate that whether and for how long this behavior holds is a problem-dependent matter. These findings confirm that an optimal pressure convergence can in general not be expected when using unbalanced velocity-pressure pairs. [ABSTRACT FROM AUTHOR]

People must make inferences about a potential mate's desirability based on incomplete information. Under such uncertainty, there are two possible errors: people could overperceive a mate's desirability, which might lead to regrettable mating behavior, or they could underperceive the mate's desirability, which might lead to missing a valuable opportunity. How do people balance the risks of these errors, and do men and women respond differently? Based on an analysis of the relative costs of these two types of error, we generated two new hypotheses about biases in initial person perception: the Male Overperception of Attractiveness Bias (MOAB) and the Female Underperception of Attractive Bias (FUAB). Participants (N = 398), who were recruited via social media, an email distribution list, and snowball sampling, rated the attractiveness of unfamiliar opposite-sex targets twice: once from a blurred image, and once from a clear image. By randomizing order of presentation (blurred first vs. clear first), we isolated the unique effects of uncertainty —which was only present when the participant saw the blurred image first. As predicted, men over perceived women's attractiveness, on average. By contrast, as predicted, women under perceived men's attractiveness, on average. Because multiple possible decision rules could produce these effects, the effects do not reveal the algorithm responsible for them. We explicitly addressed this level of analysis by identifying multiple candidate algorithms and testing the divergent predictions they yield. This suggested the existence of more nuanced biases: men overperceived the attractiveness of unattractive (but not attractive) women, whereas women underperceived the attractiveness of attractive (but not unattractive) men. These findings highlight the importance of incorporating algorithm in analyses of cognitive biases. [ABSTRACT FROM AUTHOR]

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The profile of the globoidal indexing cam is a spatially undevelopable surface. It needs a special computer numerical control (CNC) machine tool to finish batch production, and its machining quality will be affected by the motion error of each part of the machine tool and the clamped positioning error of the workpiece. Firstly, the mathematical model of the error of the machine tool for machining the globoidal cam surface is derived, and the influence of the error of the machine tool for machining the globoidal cam surface is given. Secondly, an error tracking method for globoidal cam profile machining error based on error sensitivity coefficient grouping is proposed, which improves the data processing speed and the accuracy of the tracking results. Finally, the error analysis and traceability method of the globoidal cam is verified by experiments, and the error traceability results are fed back to the processing link. The machining quality of globoidal cam is improved by the error compensation, which provides the key technology for the integration of the design, manufacture, and measurement of the globoidal cam. [ABSTRACT FROM AUTHOR]

In this paper, we present a method for performance evaluation of autonomous vehicle storage and retrieval systems (AVS/RSs) with tier-captive single-aisle vehicles. A discrete-time open queueing network approach is applied. The data obtained from the evaluation of the lift and vehicle movements can be used directly as input for the general discrete service time distributions of the queueing network. Furthermore, the approach allows for the computation of the retrieval transaction time distribution as well as of the distribution of the number of transactions waiting to be stored. Consequently, not only expected values and variances but also quantiles of the performance measures can be obtained. Comparison to discrete-event simulation quantifies approximation errors resulting from the decomposition approach in the discrete-time domain. Moreover, the errors obtained by the discrete-time approach are compared to the errors obtained using a continuous-time open queueing network approach. Finally, it will be outlined how the model can be used for designing AVS/RSs according to given system requirements, such as storage capacity, throughput, height and length of the system as well as the 95% quantile of the retrieval transaction time. [ABSTRACT FROM AUTHOR]

Grounded theory is a well-established methodology within the social sciences and more recently within the field of advertising. This article looks at how it has been used in advertising research and in particular two key areas: the consumption of advertising and the world of advertising creatives. The article concentrates on common mistakes found in grounded theory papers submitted for publication in leading journals. It offers 10 important points for consideration that should help authors improve the quality of their research by avoiding such errors. The article concludes by suggesting potential areas of advertising where grounded theory may be applied in future research. [ABSTRACT FROM PUBLISHER]

In this paper, we present a combination of three forecast models, ARIMA, exponential smoothing and dynamic regression, in order to predict the West Texas Intermediate (WTI) crude oil spot price and the Brent North Sea (Brent) crude oil spot price. Using samples from the period between January 1994 and June 2012 (in-sample), we identify the parameters and estimate the models. The validated models are combined to perform a forecast out-of-sample between July 2012 and June 2013. The results demonstrate that among the three models tested in-sample with Brent Prices, based on the MAPE measurement error, the ARIMA (2,1,8) model produced the best result, and the dynamic regression model was the best in-sample model for the WTI price. In the validation phase, the dynamic regression models did not prove to be valid, and therefore the combinations are performed only with the ARIMA and exponential smoothing models. For both proxies of oil prices, the combination of forecasts using ARIMA and exponential smoothing (out-of-sample) performed better than individual ARIMA and exponential models and also better than our benchmark models (naive forecast and Neural Network model). Based on the results, it can be inferred that using to a combination of forecasts to predict WTI and Brent spot prices is promising. We also point out that the selected model is easily replicable in spreadsheets and forecasting software and is based only on the past or lagged WTI or Brent values for future predictions. [ABSTRACT FROM PUBLISHER]

This paper examines the exponentially weighted moving average (EWMA)chart with estimated process parameters. As the run length distribution is skewed when the process is in-control or slightly out-of-control, the average run length (ARL) provides less meaningful interpretation of a chart’s performance. Therefore, in this paper, the median run length (MRL) and expected MRL (EMRL) are used as alternative performance criteria. Additionally, the methodology for computing the EMRL of the EWMAchart with known process parameters is presented. Since the performance of the EWMAchart is affected by estimation error, a study on the minimum number of Phase-I samples required so that the chart with estimated parameters has a desired performance is conducted. As this study reveals that a large number of Phase-I samples are needed, optimal design procedures for minimising the out-of-control MRL and EMRL of the EWMAchart with estimated process parameters are suggested. By using these proposed procedures, the EWMAchart with estimated parameters will have a closer performance to its known parameters counterpart, even with a reasonable number of Phase-I samples. The construction of the MRL based EWMAchart with estimated parameters is illustrated using real data and compared with the corresponding chart based on ARL. [ABSTRACT FROM PUBLISHER]

Umbrella sampling efficiently yields equilibrium averages that depend on exploring rare states of a model by biasing simulations to windows of coordinate values and then combining the resulting data with physical weighting. Here, we introduce a mathematical framework that casts the step of combining the data as an eigenproblem. The advantage to this approach is that it facilitates error analysis. We discuss how the error scales with the number of windows. Then, we derive a central limit theorem for averages that are obtained from umbrella sampling. The central limit theorem suggests an estimator of the error contributions from individual windows, and we develop a simple and computationally inexpensive procedure for implementing it. We demonstrate this estimator for simulations of the alanine dipeptide and show that it emphasizes low free energy pathways between stable states in comparison to existing approaches for assessing error contributions. Our work suggests the possibility of using the estimator and, more generally, the eigenvector method for umbrella sampling to guide adaptation of the simulation parameters to accelerate convergence. [ABSTRACT FROM AUTHOR]

The hierarchical structure of production planning has the advantage of assigning different decision variables to their respective time horizons and therefore ensures their manageability. However, the restrictive structure of this top-down approach implying that upper level decisions are the constraints for lower level decisions also has its shortcomings. One problem that occurs is that deterministic mixed integer decision problems are often used for long-term planning, but the real production system faces a set of stochastic influences. Therefore, a planned utilisation factor has to be included into this deterministic aggregate planning problem. In practice, this decision is often based on past data and not consciously taken. In this paper, the effect of long-term forecast error on the optimal planned utilisation factor is evaluated for a production system facing stochastic demand and the benefit of exploiting this decision’s potential is discussed. Overall costs including capacity, backorder and inventory costs, are determined with simulation for different multi-stage and multi-item production system structures. The results show that the planned utilisation factor used in the aggregate planning problem has a high influence on optimal costs. Additionally, the negative effect of forecast errors is evaluated and discussed in detail for different production system environments. [ABSTRACT FROM AUTHOR]

Expanding recent observations by Hammond & Meng (J. Fluid Mech., vol. 921, 2021, A16), we present a range of detailed experimental data of the radial distribution function (r.d.f.) of inertial particles in isotropic turbulence for different Stokes number, St, showing that the r.d.f. grows explosively with decreasing separation r, exhibiting r-6 scaling as the collision radius is approached, regardless of St or particle radius a. To understand such explosive clustering, we correct a number of errors in the theory by Yavuz et al. (Phys. Rev. Lett., vol. 120, 2018, 244504) based on hydrodynamic interactions between pairs of small, weakly inertial particles. A comparison between the corrected theory and the experiment shows that the theory by Yavuz et al. underpredicts the r.d.f. by orders of magnitude. To explain this discrepancy, we explore several alternative mechanisms for this discrepancy that were not included in the theory and show that none of them are likely the explanation. This suggests new, yet-to-be-identified physical mechanisms are at play, requiring further investigation and new theories. [ABSTRACT FROM AUTHOR]

In response to the continuous increase in the country's demand for LNG, improving the measurement accuracy of arrival trade at LNG receiving stations has become a top priority. Methods The causes of errors are analyzed with the basic standards, basic charact eristics, and receiving process of LNG international trade transfer, and at the same time the calculation formula of measurement errors is derived by using error propagation theory. Results By reducing the calorific value measurement error and improving the accuracy of liquid level measurement and gas chromatography measurement, the influencing factors in the calculation of the LNG example were reduced. Conclusions. A more accurate measurement error rate is obtained so as to improve the measurement accuracy of arrival trade, which can provide a basis for the measurement error calculation and management of domestic LNG receiving stations. [ABSTRACT FROM AUTHOR]

When reasoning about science studies, people often make causal theory errors by inferring or accepting a causal claim based on correlational evidence. While humans naturally think in terms of causal relationships, reasoning about science findings requires understanding how evidence supports—or fails to support—a causal claim. This study investigated college students' thinking about causal claims presented in brief media reports describing behavioral science findings. How do science students reason about causal claims from correlational evidence? And can their reasoning be improved through instruction clarifying the nature of causal theory error? We examined these questions through a series of written reasoning exercises given to advanced college students over three weeks within a psychology methods course. In a pretest session, students critiqued study quality and support for a causal claim from a brief media report suggesting an association between two variables. Then, they created diagrams depicting possible alternative causal theories. At the beginning of the second session, an instructional intervention introduced students to an extended example of a causal theory error through guided questions about possible alternative causes. Then, they completed the same two tasks with new science reports immediately and again 1 week later. The results show students' reasoning included fewer causal theory errors after the intervention, and this improvement was maintained a week later. Our findings suggest that interventions aimed at addressing reasoning about causal claims in correlational studies are needed even for advanced science students, and that training on considering alternative causal theories may be successful in reducing casual theory error. [ABSTRACT FROM AUTHOR]

We consider a numerical scheme for the approximation of a system that couples the evolution of a two-dimensional hypersurface to a reaction--diffusion equation on the surface. The surfaces are assumed to be graphs and evolve according to forced mean curvature flow. The method uses continuous, piecewise linear finite elements in space and a backward Euler scheme in time. Assuming the existence of a smooth solution, we prove optimal error bounds both in L∞(L²) and in L²(H¹). We present several numerical experiments that confirm our theoretical findings and apply the method in order to simulate diffusion induced grain boundary motion. [ABSTRACT FROM AUTHOR]

Minimum error entropy (MEE) is an information theoretic learning approach that minimizes the information contained in the prediction error, which is measured by entropy. It has been successfully used in various machine learning tasks for its robustness to heavy-tailed distributions and outliers. In this paper, we consider its use in nonparametric regression and analyze its generalization performance from a learning theory perspective by imposing a (1 +) th order moment condition on the noise variable. To this end, we establish a comparison theorem to characterize the relation between the excess generalization error and the prediction error. A relaxed Bernstein condition and concentration inequalities are used to derive error bounds and learning rates. Note that the (1 +) th moment condition is rather weak particularly when < 1 because the noise variable does not even admit a finite variance in this case. Therefore, our analysis explains the robustness of MEE in the presence of heavy-tailed distributions. [ABSTRACT FROM AUTHOR]

To simultaneously measure topographies of both surfaces of a transparent plate through wavelength-tuning interferometry at arbitrary cavity lengths, a flexible phase shift matching algorithm (FPSMA) is proposed. The FPSMA includes two parts: 1) taking the four-term third-order Nuttall window as an example, a phase demodulation approach is designed and analyzed for extracting the harmonic phases of the front surface, rear surface, and thickness variation of the measured plate and 2) based on the residual error analysis of the developed $5N$ -Nuttall algorithm for different cavity length coefficients $M$ and the phase-shifting parameters $N$ , a parameter-change technique that allows the developed phase demodulation approach is applied to arbitrary cavity lengths by adaptively changing the phase shifts and frames of the captured interferograms. By this technique, the algorithm failures due to the spectral aliasing of harmonics can be avoided effectively and conveniently, and then the correct phase demodulation can be ensured. Besides, using the developed method, when the values of $N$ or $M$ are chosen in advance, the corresponding available measurement ranges can be given. Besides, the relationship between the window length and the measurement limitation of the measurable thinnest optical thickness is investigated. Considering the common linear and nonlinear errors in the wavelength-shifting process, the error analysis of FPSMA is performed and discussed for situations close to reality. The comparative studies and the experimental results of two transparent parallel plates also support the performance of the developed FPSMA. [ABSTRACT FROM AUTHOR]

Animation refers to the process of giving motion to inanimate objects. Animations have been used to facilitate learning both in the classroom and in the individual study. Several softwares have allowed the creation of increasingly sophisticated animations. In particular, Manim is a Python library that gives motion to mathematical formulas, geometric shapes, texts, and plots. In this work, I present the process used to create animations with Manim of concepts of the theory of errors, generally seen by Physics, Mathematics and Engineering students in the introductory Experimental Physics classes. Through animations, concepts originally shown statically in books can be dynamically presented. The animations I present here can be used to produce interactive teaching materials and as complementary material in Physics lab classes. [ABSTRACT FROM AUTHOR]

We consider an adaptive multiresolution-based lattice Boltzmann scheme, which we have recently introduced and studied from the perspective of the error control and the theory of the equivalent equations. This numerical strategy leads to high compression rates, error control and its high accuracy has been explained on uniform and dynamically adaptive grids. However, one key issue with non-uniform meshes within the framework of lattice Boltzmann schemes is to properly handle acoustic waves passing through a level jump of the grid. It usually yields spurious effects, in particular reflected waves. In this paper, we propose a simple mono-dimensional test-case for the linear wave equation with a fixed adapted mesh characterized by a potentially large level jump. We investigate this configuration with our original strategy and prove that we can handle and control the amplitude of the reflected wave, which is of fourth order in the space step of the finest mesh. Numerical illustrations show that the proposed strategy outperforms the existing methods in the literature and allow to assess the ability of the method to handle the mesh jump properly [ABSTRACT FROM AUTHOR]

The article focuses on an error analysis of the truncated Taylor series expansion method for computing matrix exponential by taking into account both the truncation error and the rounding error. Topics include considered the derived error bound will be useful to determine the order of expansion or computing precision required to attain the prespecified error level.

We propose a numerical method for computing the solutions of high-dimensional Markovian backward stochastic difference equations (BSΔEs), in which we apply a sparse grid quadrature/interpolation formula. This allows us to calculate the approximated solution accurately and efficiently, which we justify through a rigorous error analysis. Finally, we use a simple numerical experiment to demonstrate the performance of our method. [ABSTRACT FROM AUTHOR]

In the present work, first of all, a new numerical fractional differentiation formula (called the CF2 formula) to approximate the Caputo-Fabrizio fractional derivative of order a; (0 <α < 1) is developed. It is established by means of the quadratic interpolation approximation using three points (t j-2;y(t j-2)); (t j-1;y(t j-1)), and (t j; y(t j)) on each interval [t j-1; t j] for (j ≥ 2), while the linear interpolation approximation are applied on the first interval [t0; t1]. As a result, the new formula can be formally viewed as a modification of the classical CF1 formula, which is obtained by the piecewise linear approximation for y(t). Both the computational efficiency and numerical accuracy of the new formula is superior to that of the CF1 formula. The coefficients and truncation errors of this formula are discussed in detail. Two test examples show the numerical accuracy of the CF2 formula. The CF1 formula demonstrates that the new CF2 is much more effective and more accurate than the CF1 when solving fractional differential equations. Detailed stability analysis and region stability of the CF2 are also carefully investigated. [ABSTRACT FROM AUTHOR]

Several applications of computational science and engineering, including population dynamics, optimal control, and physics, reduce to the study of a system of second-order boundary value problems. To achieve the improved solution of these problems, an efficient numerical method is developed by using spline functions. A non-polynomial cubic spline-based method is proposed for the first time to solve a linear system of second-order differential equations. Convergence and stability of the proposed method are also investigated. A mathematical procedure is described in detail, and several examples are solved with numerical and graphical illustrations. It is shown that our method yields improved results when compared to the results available in the literature. [ABSTRACT FROM AUTHOR]

This article proposes a follow up of Fazzo's contributions on the stemma codicum of aristotle's Metaphysics -- including her Chôra 2015 paper, its completion in the 2017 Revue d'Histoire des Textes and, most recently, a contribution on the text of Zeta 17 in Aristotelica 1 2022. all of these are summarized and framed here in the context of today's lively debate. We then introduce the data of Marco ghione's collation and comparison of the readings of the two oldest manuscripts J and E : J, the Vind. phil. gr. 100, early 9th century -- the so-called "aristotle of Vienna" -- is thus extensively compared with E, Paris. gr. 1853, early 10th century, with selected reference to the earliest hands at work (J, J2, E1). Based on Paul Maas' theory of errors, we are now in condition to face the crucial issue : does the latter depend on the former ? This helps resolving the one residual opacity or incertitude concerning the upper part of the Metaphysics' stemma. [ABSTRACT FROM AUTHOR]

In this paper, we prove some regularity results for a noncoercive nonlinear Dirichlet problem in an unbounded domain. The main result is obtained in the hypothesis that suitable coefficients of the operator associated to the problem belong to a class of functional spaces strictly containing Lebesgue ones. This can be done by approximation via coercive nonlinear Dirichlet problems. Under additional assumptions, we also get the boundedness of a solution. [ABSTRACT FROM AUTHOR]

In this paper, we describe a computational model for the simulation of fluidstructure interaction problems based on a fictitious domain approach. We summarize the results presented over the last years when our research evolved from the finite element immersed boundary method (FE-IBM) to the actual finite element distributed Lagrange multiplier (FEDLM) method. We recall the well-posedness of our formulation at the continuous level in a simplified setting. We describe various time semi-discretizations that provide unconditionally stable schemes. Finally, we report the stability analysis for the finite element space discretization, where some improvements and generalizations of the previous results are obtained. [ABSTRACT FROM AUTHOR]

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I defend the intention-dependence of artifacts (IDA), which says that something is an artifact of kind K only if it is the successful product of an intention to make an artifact of kind K. I consider objections from two directions. First, that artifacts are often mind- and intention-dependent, but that this isn't necessary, as shown by swamp cases. I offer various error theories for why someone would have artifact intuitions in such cases. Second, that while artifacts are necessarily mind-dependent, they aren't necessarily intention-dependent. I consider and reject three kinds of cases which purport to show this: accidental creation, automated production, and mass production. I argue that intentions are present in all of these cases, but not where we would normally expect. [ABSTRACT FROM AUTHOR]

This paper presents a study of the performance of the Tau method using Chebyshev basis functions for solving fourth-order differential equation with boundary conditions. Existence and uniqueness of the solution of this equation are investigated transforming it into the Volterra–Fredholm integral equation. We use the operational Tau matrix representation with Chebyshev basis functions for constructing the algebraic equivalent representation of the problem.This representation is an special semi lower triangular system whose solution gives the components of the vector solution. Applying Gronwall's and the generalized Hardy's inequality, convergence analysis and error estimation of the Tau method are discussed. The error analysis indicates that the numerical errors decay exponentially when the source function are sufficiently smooth. Illustrative examples are given to represent the efficiency and the accuracy of the proposed method. Also, some comparisons are made with existing results such that the results obtained by Tau method are more accurate than the proposed methods in this case. [ABSTRACT FROM AUTHOR]

We construct high-order semidiscrete-in-time, and fully discrete (with Fourier-- Galerkin in space) schemes for the incompressible Navier-Stokes equations with periodic boundary conditions and carry out corresponding error analysis. The schemes are of implicit-explicit type based on a scalar auxiliary variable approach. It is shown that numerical solutions of these schemes are uniformly bounded without any restriction on time step size. These uniform bounds enable us to carry out a rigorous error analysis for the schemes up to fifth-order in a unified form and derive global error estimates in l∞ (0, T;H¹)∩l2(0, T;H²) in the two-dimensional case as well as local error estimates in l∞ (0, T;H¹)∩l2(0, T;H²) in the three-dimensional case. We also present numerical results confirming our theoretical convergence rates and demonstrating advantages of higher-order schemes for flows with complex structures in the double shear layer problem. [ABSTRACT FROM AUTHOR]

When unexpected events occur during goal‐directed behavior, they automatically trigger an orienting‐related cascade of psychological and neural processes through which they influence behavior and cognition. If the unexpected event was caused by an action error, additional error‐specific, strategic‐related processes have been proposed to follow the initial orienting period. Little is known about the neural interactions between action errors and unexpected perceptual events, two instantiations of unexpected events, in these two putative stages of post‐error processing. Here, we aimed to address this by investigating the electrophysiological dynamics associated with action errors and unexpected perceptual events using scalp EEG with a focus on the frontal midline (FM) delta‐to‐theta oscillations (1–8 Hz) indicative of the performance‐monitoring system. Specifically, we examined how the timing of unexpected sounds would influence behavior and neural oscillations after action errors, depending on the length of the intertrial interval (ITI). Our data showed that unexpected sounds aggravated post‐error decreases in accuracy when they occurred (1) immediately after errors (i.e., post‐error orienting period), regardless of ITI and (2) immediately after the post‐error stimulus (i.e., post‐error strategic period), at short ITIs. Meanwhile, action errors and unexpected sounds independently produced increased FM delta‐to‐theta power during the post‐error orienting period, regardless of ITIs. However, when unexpected sounds occurred during the post‐error strategic period, action errors produced lower FM delta‐to‐theta power than correct responses, at short ITIs. These differential effects of unexpected events on behavior and FM delta‐to‐theta dynamics support the notion of the two post‐error periods during which different processes are implemented. We provide evidence from behavior and frontal midline delta‐to‐theta oscillations in support of the notion of the two post‐error periods (immediately following an error or following the subsequent stimulus). Error processing is differentially affected by the occurrence of other unexpected events during the two post‐error periods. These findings are in line with the adaptive orienting theory of error processing. [ABSTRACT FROM AUTHOR]

In this paper, a numerical method based on modified hat functions (MHFs) is investigated to find an approximate solution for a fractional-order system of stochastic integro-differential equations. The fractional and stochastic operational matrices of integration of these functions are employed to present the numerical approach. By using these operational matrices and properties of MHFs, the considered problem is transformed into a system of algebraic equations which can be easily solved by an iterative method. Also, error analysis of the proposed method is discussed. At the end, the accuracy and effectiveness of this approach are studied by some numerical examples. [ABSTRACT FROM AUTHOR]

A number of non-standard finite element methods have been proposed in recent years, each of which derives from a specific class of PDE-constrained norm minimization problems. The most notable examples are L L ⁎ methods. In this work, we argue that all high-order methods in this class should be expected to deliver substandard uniform h -refinement convergence rates. In fact, one may not even see rates proportional to the polynomial order p > 1 when the exact solution is a constant function. We show that the convergence rate is limited by the regularity of an extraneous Lagrange multiplier variable which naturally appears via a saddle-point analysis. In turn, limited convergence rates appear because the regularity of this Lagrange multiplier is determined, in part, by the geometry of the domain. Numerical experiments support our conclusions. [ABSTRACT FROM AUTHOR]

According to moral error theory, there are no ethical facts. Error theorists often defend this view with the metaphysical argument from queerness. This argument purports to show that it is most reasonable to believe that ethical facts do not exist, because such facts are metaphysically queer and explanatorily redundant. This paper argues that even if we assume that ethical facts are metaphysically queer and explanatorily redundant, the argument from queerness does not warrant the rejection of ethical facts. It only shows that it is most reasonable to refrain from believing that ethical facts exist. The argument from queerness therefore merely supports metaethical scepticism: that is, it merely supports agnosticism about the existence of ethical facts. This is cause for optimism, because metaethical scepticism is less of a threat to our moral practice than moral error theory. [ABSTRACT FROM AUTHOR]

We explore an empirical puzzle regarding error management theory. While previous research has stressed the role of self-efficacy in explaining who adopts an error management orientation (EMO), our findings from three empirical studies in an auditing context indicate another powerful yet neglected individual difference: humility. In Study 1, we draw on qualitative data collected through 18 months of participant observations and 38 interviews to reveal the role of humility in adopting an EMO. In Study 2, we refine our findings by quantitatively exploring and testing the relationships of both humility and self-efficacy with various facets of an EMO. We find positive relations of humility with all examined facets, and find that humility predicts these facets over and above selfefficacy. In Study 3, we replicate and extend our findings by drawing on an additional sample and by exploring the role of past performance for these relationships. Again, we find that humility is a robust predictor of key EMO facets over and above self-efficacy as well as past performance. The discovery of the role of humility challenges the predominant consideration of self-efficacy, and has implications for studying error orientation, error management training, and error management culture. [ABSTRACT FROM AUTHOR]