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This study was designed to empirically evaluate the classification accuracy of various definitions of invalid performance in two forced‐choice recognition performance validity tests (PVTs; FCRCVLT‐II and Test of Memory Malingering [TOMM‐2]). The proportion of at and below chance level responding defined by the binomial theory and making any errors was computed across two mixed clinical samples from the United States and Canada (N = 470) and two sets of criterion PVTs. There was virtually no overlap between the binomial and empirical distributions. Over 95% of patients who passed all PVTs obtained a perfect score. At chance level responding was limited to patients who failed ≥2 PVTs (91% of them failed 3 PVTs). No one scored below chance level on FCRCVLT‐II or TOMM‐2. All 40 patients with dementia scored above chance. Although at or below chance level performance provides very strong evidence of non‐credible responding, scores above chance level have no negative predictive value. Even at chance level scores on PVTs provide compelling evidence for non‐credible presentation. A single error on the FCRCVLT‐II or TOMM‐2 is highly specific (0.95) to psychometrically defined invalid performance. Defining non‐credible responding as below chance level scores is an unnecessarily restrictive threshold that gives most examinees with invalid profiles a Pass. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Southeast University (English Edition) is the property of Journal of Southeast University Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Evaluating written texts is believed to be a time-consuming process that can lack consistency and objectivity. Automated essay scoring (AES) can provide solutions to some of the limitations of human scoring. This research aimed to evaluate the performance of one AES system, Grammarly, in comparison to human raters. Both approaches' performances were analyzed quantitatively using Corder's (1974) error analysis approach to categorize the writing errors in a corpus of 197 essays written by English as a foreign language (EFL) learners. Pearson correlation coefficient and paired sample t-tests were conducted to analyze and compare errors detected by both approaches. According to the study's results, a moderate correlation between human raters and AES in terms of the total scores and the number of errors detected. Results also indicated that the total number of errors detected by AES is significantly higher than human raters and that the latter tend to give students higher scores. The findings encourage a more open attitude towards AES systems to support EFL writing teachers in assessing students' work. [ABSTRACT FROM AUTHOR]

We discuss and implement a spectral method approach to computing stationary and axisymmetric black hole solutions and their properties in modified theories of gravity. The resulting code is written in the Julia language and is transparent and easily adapted to new settings. We test the code on both general relativity and on Einstein-scalar-Gauss–Bonnet gravity. It is accurate and fast, converging on a spinning solution in these theories with tiny errors ( in most cases) in a matter of seconds. [ABSTRACT FROM AUTHOR]

Traditional transform optical devices are designed from anisotropic magnetic materials which are difficult to fabricate. In this paper, we design and simulate a conformal carpet invisible cloak and bending waveguide device with isotropic material. According to the existing conformal coordinate transformation, we deduce the perfect parameters required by the conformal device. And the finite element method and error analysis of the model equation and the basic process of adaptive algorithm are given. We first simulated a carpet cloak and bending waveguide device with perfect parameters; then we used the idea of parameter segmentation to design a carpet cloak that requires 35 isotropic materials and use the idea of layering to design the conformal bending waveguide device, and relevant numerical results are presented; finally, we designed the adaptive finite element algorithm to realize the numerical simulation of Maxwell's equations in isotropic material. [ABSTRACT FROM AUTHOR]

The forecast error growth as a function of lead time of atmospheric phenomena is caused by initial and model errors. When studying the initial error growth, it turns out that small scale phenomena, which contribute little to the forecast product, significantly affect the ability to predict this. The question under investigation is whether omitting these atmospheric phenomena will improve the predictability of the resulting value. The topic is studied in the extended Lorenz (2005) system. This system shows that omitting small spatiotemporal scales will reduce predictability more than modeling it. Generally, a system with model error (omitting phenomena) will not improve predictability. A theory explaining and describing this behavior is developed, with the difference between systems (model error) produced at each time step seen as the error of the initial conditions. The resulting model error is then defined as the sum of the increments of the time evolution of the initial conditions so defined. The theory is compared to the fit parameters that define the model error in certain approximations of the average forecast error growth. Parameters are interpreted in this context, and the hypotheses are used to estimate the errors described in the theory. It is proposed how to distinguish increments to prediction error growth from small spatiotemporal-scales phenomena and model error. Results are presented for the error growth of the ECMWF system, where a 40 % reduction in model error between 1987 and 2011 is calculated based on the developed theory, while over the same time, the instability of the system with respect to initial condition errors has grown. [ABSTRACT FROM AUTHOR]

An adaptive hybrid neural control scheme is presented for uncertain non-linear discrete-time Systems (UNLDTS) with non-symmetric dead-zone input and unknown disturbances. This work aims to design an efficient control scheme for the proposed systems in the case of non-symmetric dead-zone as the input due to the presence of which the control of such systems becomes very complex and difficult. The system is converted into an n-step ahead predictor and an adaptive compensative term is introduced to overcome the non-symmetric dead-zone present in the system. A hybrid neural network controller is constructed for the control of the proposed class of systems. The designed controller is proved to be semi-globally uniformly ultimately bounded with the assistance of Lyapunov theory and the error is proved to approach very close to zero. The effectiveness of the proposed scheme is validated through two simulation examples and one example has been inspired from a real word system named continuous stirred tank reactor taken in discrete-time form which ensures the applicability of this controller in real-world applications. [ABSTRACT FROM AUTHOR]

The error analysis of the robot has a very practical significance for improving its accuracy. Therefore, this paper conducts an error analysis for a new five-degree-of-freedom hybrid robot designed to conduct responsible surface machining. Initially, the error sources of the hybrid robot were sorted out to determine the number of error sources. Then, the error mapping model of the hybrid robot is established by the closed-loop vector method and the first-order perturbation method. Based on the mapping property of the 6th-order velocity Jacobi matrix, the compensable and non-compensable error sources affecting the posture error at the end of the hybrid robot are separated. Finally, the error analysis of the separated error sources is carried out to study the effect of single error sources and multiple error sources coupled with the posture error at the end of the robot. The results show that among the individual error sources, the dynamic and fixed platform hinge position error has the most significant effect on the end of the robot; among the integrated posture errors after coupling multiple error sources, the position of the dynamic and fixed platform hinge position error and the translational joint initial position dominate; the analysis of the different trajectories also yields that the error introduced by each error source increases gradually with the increase of the end trajectory. When designing this hybrid robot, attention should be paid to the manufacturing and installation accuracy of the dynamic and fixed platform hinge point positions and the translational joint initial position. [ABSTRACT FROM AUTHOR]

This paper considers the problem of optimizing the average tracking error for an elliptic partial differential equation with an uncertain lognormal diffusion coefficient. In particular, the application of the multilevel quasi-Monte Carlo (MLQMC) method to the estimation of the gradient is investigated, with a circulant embedding method used to sample the stochastic field. A novel regularity analysis of the adjoint variable is essential for the MLQMC estimation of the gradient in combination with the samples generated using the circulant embedding method. A rigorous cost and error analysis shows that a randomly shifted quasi-Monte Carlo method leads to a faster rate of decay in the root mean square error of the gradient than the ordinary Monte Carlo method, while considering multiple levels substantially reduces the computational effort. Numerical experiments confirm the improved rate of convergence and show that the MLQMC method outperforms the multilevel Monte Carlo method and single level quasi-Monte Carlo method. [ABSTRACT FROM AUTHOR]

Theories of free will are often measured against how well they capture everyday intuitions about free will. But what are these everyday intuitions, and what theoretical commitments do they express? Empirical methods have delivered mixed messages. In response, some free will theorists have developed error theories to undermine the credentials of countervailing intuitions. These efforts are predicated on the idea that people might misunderstand determinism in any of several ways. This paper sheds light on the comprehension problem. We first discuss recent efforts to explain systematic errors in how people interpret determinism. Then, we present the alarming results of two new preregistered studies exploring three types of comprehension failure: (a) epiphenomenal bypassing, (b) fatalistic bypassing, and (c) indeterministic intrusion. Our findings suggest that misunderstanding runs deeper than others have supposed. This casts doubt on existing models of commonsense thinking about free will. Unless and until researchers properly control for the kinds of misunderstandings we identify, research on free will intuitions cannot shed light on whether ordinary thinking reflects commitments to compatibilism or incompatibilism. [ABSTRACT FROM AUTHOR]

Knowledge defeat occurs when a subject knows that p, gains a defeater for her belief, and thereby loses her knowledge without necessarily losing her belief. It's far from obvious that externalists can accommodate putative cases of knowledge defeat since a belief that satisfies the externalist conditions for knowledge can satisfy those conditions even if the subject later gains a defeater for her belief. I'll argue that virtue reliabilists can accommodate defeat intuitions via a new kind of error theory. I argue that in cases where the subject holds dogmatically onto her belief in the face of an apparent defeater, her belief never qualified as knowledge, since the belief was not gained via an exercise of her epistemic virtues. In cases where the subject suspends her judgment upon receiving the putative defeater her original belief might have qualified as knowledge, but crucially, in such cases knowledge is lost due to loss of belief, rather than due to the epistemic force of the defeater. Therefore, knowledge defeat isn't a genuine phenomenon even though there are no cases where a subject knows what she originally believed after receiving the putative defeater. [ABSTRACT FROM AUTHOR]

Copyright of China Sciencepaper is the property of China Sciencepaper and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Random fields are widely used to characterize the inherent spatial uncertainty in engineering applications. However, for widely existing manifolds, few studies focus on the simulation of Gaussian/non‐Gaussian fields over manifolds due to the geometry complexity. Recently, we proposed a two‐stage method to simulate Gaussian fields over manifolds. In this study, we extend it to a three‐stage method for non‐Gaussian fields. In the first stage, the original manifold is dimensional reduced to a Euclidean domain by the isometric feature mapping. By this step, the geodesic distance is preserved to guarantee the correlation structure unchanged. In the second stage, conventional representations can be used to simulate the underlying Gaussian field over the Euclidean domain. In the third stage, an enhanced translation procedure is proposed to translate the underlying Gaussian field to the target non‐Gaussian field over the manifold. To explain the applicability and accuracy of the three‐stage method, two kinds of non‐Gaussian fields over three different manifolds are simulated. Then, a global error is proposed to evaluate the performance of the method, and the error analysis demonstrates the method is accurate enough. Finally, two engineering structures, that is, a compressed half‐cylinder and a Canopy shell with complex geometry, are investigated to illustrate the potential applications of the method. [ABSTRACT FROM AUTHOR]

In this paper, we develop a novel discontinuous Galerkin (DG) finite element method for solving the Poisson's equation u x x + u y y = f (x , y) on Cartesian grids. The proposed method consists of first applying the standard DG method in the x -spatial variable leading to a system of ordinary differential equations (ODEs) in the y -variable. Then, using the method of line, the DG method is directly applied to discretize the resulting system of ODEs. In fact, we propose a fully DG scheme that uses p -th and q -th degree DG methods in the x and y variables, respectively. We show that, under proper choices of numerical fluxes, the method achieves optimal convergence rate in the L 2 -norm of O (h p + 1) + O (k q + 1) for the DG solution, where h and k denote, respectively, the mesh step sizes for the x and y variables. Our theoretical results are validated through several numerical experiments. [ABSTRACT FROM AUTHOR]

In this work we study an inverse problem of recovering a space-time-dependent diffusion coefficient in the subdiffusion model from the distributed observation, where the mathematical model involves a Djrbashian–Caputo fractional derivative of order |$\alpha \in (0,1)$| in time. The main technical challenges of both theoretical and numerical analyses lie in the limited smoothing properties due to the fractional differential operator and high degree of nonlinearity of the forward map from the unknown diffusion coefficient to the distributed observation. We establish two conditional stability results using a novel test function, which leads to a stability bound in |$L^2(0,T;L^2(\varOmega))$| under a suitable positivity condition. The positivity condition is verified for a large class of problem data. Numerically, we develop a rigorous procedure for recovering the diffusion coefficient based on a regularized least-squares formulation, which is then discretized by the standard Galerkin method with continuous piecewise linear elements in space and backward Euler convolution quadrature in time. We provide a complete error analysis of the fully discrete formulation, by combining several new error estimates for the direct problem (optimal in terms of data regularity), a discrete version of fractional maximal |$L^p$| regularity and a nonstandard energy argument. Under the positivity condition, we obtain a standard |$\ell ^2(L^2(\varOmega))$| error estimate consistent with the conditional stability. Further, we illustrate the analysis with some numerical examples. [ABSTRACT FROM AUTHOR]

We present the first a priori error analysis of a class of space-discretizations by Hybridizable Discontinuous Galerkin (HDG) methods for the time-dependent Maxwell's equations introduced in Sánchez et al. [Comput. Methods Appl. Mech. Eng. 396 (2022) 114969]. The distinctive feature of these discretizations is that they display a discrete version of the Hamiltonian structure of the original Maxwell's equations. This is why they are called ''Hamiltonian" HDG methods. Because of this, when combined with symplectic time-marching methods, the resulting methods display an energy that does not drift in time. We provide a single analysis for several of these methods by exploiting the fact that they only differ by the choice of the approximation spaces and the stabilization functions. We also introduce a new way of discretizing the static Maxwell's equations in order to define the initial condition in a manner consistent with our technique of analysis. Finally, we present numerical tests to validate our theoretical orders of convergence and to explore the convergence properties of the method in situations not covered by our analysis. [ABSTRACT FROM AUTHOR]

This paper considers the strong error analysis of the Euler and fast Euler methods for nonlinear overdamped generalized Langevin equations driven by the fractional noise. The main difficulty lies in handling the interaction between the fractional Brownian motion and the singular kernel, which is overcome by means of the Malliavin calculus and fine estimates of several multiple singular integrals. Consequently, these two methods are proved to be strongly convergent with order nearly min{2(H + α − 1), α}, where H ∈ (1/2, 1) and α ∈ (1 − H, 1) respectively characterize the singularity levels of fractional noises and singular kernels in the underlying equation. This result improves the existing convergence order H + α − 1 of Euler methods for the nonlinear case, and gives a positive answer to the open problem raised in Fang and Li [ESAIM Math. Model. Numer. Anal.54 (2020) 431–463]. As an application of the theoretical findings, we further investigate the complexity of the multilevel Monte Carlo simulation based on the fast Euler method, which turns out to behave better performance than the standard Monte Carlo simulation when computing the expectation of functionals of the considered equation. Finally, numerical experiments are carried out to support the theoretical results. [ABSTRACT FROM AUTHOR]

Different types of anemometers and direction determining devices are used in measuring wind speed and direction. Especially, low-cost and accurate measuring devices are required for the production and estimates of electricity generated from wind energy. Therefore, a design for an anemometer has been carried out using appropriate lowcost laser distance sensors, microcontrollers, and integrated electronic circuit equipment. The resulting anemometer from the design works based on the distance from the measurement center that changes according to wind speed and direction. The wind speed and direction data are obtained by digitally calculating this distance. By following a different approach than the existing techniques in measuring wind speed and direction, the data obtained in this method was compared with a real anemometer and an error analysis was performed. The relative error value was found to be 0.01685 as a result of the error analysis. [ABSTRACT FROM AUTHOR]

In this paper, a thermomechanical problem involving a viscoelastic Timoshenko beam is analyzed from a numerical point of view. The so-called thermodiffusion effects are also included in the model. The problem is written as a linear system composed of two second-order-in-time partial differential equations for the transverse displacement and the rotational movement, and two first-order-in-time partial differential equations for the temperature and the chemical potential. The corresponding variational formulation leads to a coupled system of first-order linear variational equations written in terms of the transverse velocity, the rotation speed, the temperature and the chemical potential. The existence and uniqueness of solutions, as well as the energy decay property, are stated. Then, we focus on the numerical approximation of this weak problem by using the implicit Euler scheme to discretize the time derivatives and the classical finite element method to approximate the spatial variable. A discrete stability property and some a priori error estimates are shown, from which we can conclude the linear convergence of the approximations under suitable additional regularity conditions. Finally, some numerical simulations are performed to demonstrate the accuracy of the scheme, the behavior of the discrete energy decay and the dependence of the solution with respect to some parameters. [ABSTRACT FROM AUTHOR]

Error Analysis was developed by early Second Language Acquisition (SLA) researchers as a way to investigate interlanguage and better understand the second-language learning processes. While it is no longer an active branch of research in SLA, it remains a useful tool for those concerned with accuracy in language use. Given the elevated importance of accuracy in English for Research and Publication Purposes (ERPP), this may be one area where Error Analysis may continue to inform research and praxis. The high degree of language precision demanded in ERPP contexts can be a source of frustration for many engaged in scholarly publication, especially those for whom English is an additional language, such as the Japanese scientists studied in this paper. For Japanese scientists and possibly others, an empirical profile of their most frequent error patterns may help them to better deal with accuracy in research writing. With this motivation, this study applies a corpus-assisted error analysis framework to quantify sentence-level grammar errors and identify the most frequent error patterns in the research article manuscripts of Japanese scientists. A corpus of 53 research article manuscripts with 4,495 errors comprises the primary data. Additionally, two raters and a comparison of errors from scientists from six different L1 backgrounds are employed to triangulate the data and investigate the reliability and generalizability of the findings. Findings reveal that the top ten most frequent errors comprise 52.9%, or half of all errors in the corpus, and are dominated by errors with determiners and prepositions. [ABSTRACT FROM AUTHOR]

In this paper, we describe a spectral Tau approach for approximating the solutions of a system of multi-order fractional differential equations which resulted from coronavirus disease mathematical modeling (COVID-19). The non-singular fractional derivative with a Mittag-Leffler kernel serves as the foundation for the fractional derivatives. Also the operational matrix of fractional differentiation on the domain [0, a] is presented. Then, the convergence analysis of the proposed approximate approach is established and the error bounds are determined in a weighted L² norm. Finally, by applying the Tau method, some of the important parameters in the model's impact on the dynamics of the disease are graphically displayed for various values of the non-integer order of the ABC-derivative. [ABSTRACT FROM AUTHOR]

The trapezium and Simpson's methods are widely used for numerical integration. In most circumstances, Simpson's method is more accurate than the trapezium method but only applicable to cases with equal intervals of even numbers. This technical note reports the formulation of two modified Simpson's methods, the trapezium-corrected Simpson's method (TCSM) and cubic-corrected Simpson's method (CCSM), as general-purpose symmetric formulas to solve numerical integrations with equal intervals of odd numbers (n = 5) with the same level of accuracy as that of Simpson's method applied to the even number near n. Error analysis in terms of the order of error bound and case studies in this note demonstrate and validate the usefulness of the proposed formulas for solving different types of theoretical problems and real-world applications. In terms of accuracy of approximation for cases with equal intervals of odd numbers, CCSM performs better than TCSM by at least one order in error bound whereas TCSM performs better than the trapezium method by at least one order in error bound. [ABSTRACT FROM AUTHOR]

A nonconforming finite element method (FEM) is proposed and analyzed for the clamped thin elastic Kirchhoff plate unilaterally constrained by an elastic obstacle. The discrete scheme is constructed by using the strongly discontinuous Bergan's energy-orthogonal plate element, which has simple degrees of freedom and about 25 percent fewer global dimension than that of the famous triangular Morley element. A novel error analysis is presented to overcome the difficulties caused by the strong discontinuity and derive the optimal estimate. Numerical experiments are carried out to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, based on the Wachspress generalized barycentric coordinates, we propose and analyze a polygonal finite volume element method (PFVEM) for solving the anisotropic diffusion equation on convex polygonal meshes. In particular, the PFVEM reduces to the classical P 1 -FVEM on triangular meshes and it is not identical to the classical Q 1 -FVEM on quadrilateral meshes. A new proof is given to Proposition 8 in [19] , a result that is crucial to the derivation of the interpolation error estimates in both H 1 and H 2 norms. The original proof is based on a certain geometric assumption, which is shown not always true by a counterexample given in this paper. Moreover, for the error analysis of the PFVEM, we prove the H 2 error estimate of the Wachspress interpolation. Under the coercivity assumption, the optimal H 1 error estimate for the finite volume element solution is obtained. Several numerical examples are presented to show the efficiency and robustness of the proposed method for the heterogeneous and anisotropic diffusion problems on polygonal meshes. [ABSTRACT FROM AUTHOR]

In unit-level small area estimation (SAE), the commonly used nested error regression (NER) model assumes normality which is not always the case. To handle non-normal data, researchers in statistics have developed a novel approach using exchangeable and extendible copula called the multivariate exchangeable copula (MEC) model. This study compares the performance of parametric MEC and NER models in estimating the sub-district average of per capita expenditure (PCE) in Pidie Regency, Aceh Province. This study presents PCE, which has a skewed distribution of the three-parameter skew-normal. The parametric MEC model uses a Gaussian copula from the Elliptical family and an empirical best unbiased prediction (EBUP) estimator. Meanwhile, the NER model uses an empirical best linear unbiased prediction (EBLUP) estimator. The results reveal that at a 95% confidence level, the parametric MEC model outperforms the NER model with a smaller root of mean squared error (RMSE) and provides a more precise estimate of the sub-district average of PCE. This study highlights the importance of considering the parametric MEC model as an alternative method for skewed data in unit-level SAE. The results of this study have the potential to support the achievement of Goal 1 (to end poverty) and Goal 10 (to reduce inequality) of the sustainable development goals (SDGs) by providing average PCE estimates at the sub-district level. [ABSTRACT FROM AUTHOR]

Due to its electronic properties, Zinc Oxide (ZnO) is one of the important materials used in new generation solar cells. However, it is necessary to increase the working efficiency of pure ZnO with the rays coming from the sun. Doping with foreign atoms is one of the important techniques in this sense. In this study, the doping of ZnO crystal with Se atom was investigated theoretically. Density functional theory (DFT) was used in the calculations. However, DFT+U correction was made in the calculations to correct the known errors of the theory. With this method, the band gap of pure ZnO was calculated at 3.27 eV. This value is close to the experimental value of 3.44 eV. The Se atom causes local distortions in the crystal structure. However, these deteriorations do not significantly change the characteristic properties of the ZnO crystal. Doping with Se mainly leads to a change in the electronic structure. When the Se and Zn atoms, which have more valence electrons, are replaced, two occupied energy levels are formed in the band gap, above the valence band maximum, due to impurity. These energy levels increase the light absorption activity of ZnO in the visible region. Another important data obtained is that the lack of oxygen in the Se-doped ZnO crystal positively affects the absorption activity in the visible region. [ABSTRACT FROM AUTHOR]

Recently, the drive level capacitance profiling (DLCP) technique has been proven to be effective in resolving the spatial and energetic distributions of defects through feasible measurements. However, the discussion on its ranges and resolutions is still missing, which is urgent in evaluating the validity of the calculated defect profiles. In this work, we propose a method to analyze the ranges and resolutions of DLCP. Assuming that the test instrument has more influence on the experimental results than the experimental environment, this method can be used to evaluate the resolution of DLCP for different test instruments. Through revisiting the equations involved in DLCP, we learned that the sources of the limits and resolutions are (1) the instrument system error and inherent resolution and (2) the device impedance. Consequently, from the study of device impedance and the measuring instrument system error, the resolutions of DLCP could be calculated according to the error propagation theory. We provide the spatial distribution of the minimum selection range of AC signal δV used by DLCP and the spatial resolution of DLCP technology. This method can be used to evaluate the resolution of DLCP for different test instruments. [ABSTRACT FROM AUTHOR]

Copyright of Formación Universitaria is the property of Centro de Informacion Tecnologica (CIT) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this study, firstly, the residual method, which was developed for initial value problems, is improved to find unknown coefficients without requiring for any system solution. Later, the adaptation of improved residual method is given to find approximate solutions of boundary value problems. Finally, the method improved and adapted for boundary value problems is used to find both critical eigenvalue and eigenfunctions of the one-dimensional Bratu problem. The most significant advantage of the method is finding approximate solutions of nonlinear problems without any linearization or solving any system of equations. Error analysis of the adapted method is given and an upper bound on the approximation error is derived for the eigenfunctions. The numerical results obtained are compared with the theoretical findings. Comparisons and theoretical observations show that the improved and adapted method is very convenient and successful in solving boundary value problems and eigenvalue problems approximately with high accuracy. [ABSTRACT FROM AUTHOR]

Enhanced sampling methods, such as forward flux sampling (FFS), have great capacity for accelerating stochastic simulations of nonequilibrium biochemical systems involving rare events. However, the description of the tradeoffs between simulation efficiency and error in FFS remains incomplete. We present a novel and mathematically rigorous analysis of the errors in FFS that, for the first time, covers the contribution of every phase of the simulation. We derive a closed form expression for the optimally efficient count of samples to take in each FFS phase in terms of a fixed constraint on sampling error. We introduce a new method, forward flux pilot sampling (FFPilot), that is designed to take full advantage of our optimizing equation without prior information or assumptions about the phase weights and costs along the transition path. In simulations of both single and multidimensional gene regulatory networks, FFPilot is able to completely control sampling error. We then discuss how memory effects can introduce additional error when relaxation along the transition path is slow. This extra error can be traced to correlations between the FFS phases and can be controlled by monitoring the covariance between them. Finally, we show that, in sets of simulations with matched error, FFPilot is on the order of tens-to-hundreds of times faster than direct sampling and noticeably more efficient than previous FFS methods. [ABSTRACT FROM AUTHOR]

Kinetic energy equipartition is a premise for many deterministic and stochastic molecular dynamics methods that aim at sampling a canonical ensemble. While this is expected for real systems, discretization errors introduced by the numerical integration may lead to deviations from equipartition. Fortunately, backward error analysis allows us to obtain a higher-order estimate of the quantity that is actually subject to equipartition. This is related to a shadow Hamiltonian, which converges to the specified Hamiltonian only when the time-step size approaches zero. This paper deals with discretization effects in a straightforward way. With a small computational overhead, we obtain refined versions of the kinetic and potential energies, whose sum is a suitable estimator of the shadow Hamiltonian. Then, we tune the thermostatting procedure by employing the refined kinetic energy instead of the conventional one. This procedure is shown to reproduce a canonical ensemble compatible with the refined system, as opposed to the original one, but canonical averages regarding the latter can easily be recovered by reweighting. Water, modeled as a rigid body, is an excellent test case for our proposal because its numerical stability extends up to time steps large enough to yield pronounced discretization errors in Verlet-type integrators. By applying our new approach, we were able to mitigate discretization effects in equilibrium properties of liquid water for time-step sizes up to 5 fs. [ABSTRACT FROM AUTHOR]

This paper considers a theoretical substantiation of the influence of a perturbation of a moving singular point on the analytical approximate solution to the Van der Pol equation obtained earlier by the author. A priori estimates of the error of the analytical approximate solution are obtained, which allows the solving of the inverse problem of the theory of error: what should the structure of the analytical approximate solution be in order to obtain a result with a given accuracy? Thanks to a new approach for obtaining a priori evaluations of errors, based on elements of differential calculus, the domain, used to obtain an analytical approximate solution, was substantially expanded. A variant of optimizing a priori estimates using a posteriori estimates is illustrated. The results of a numerical experiment are also presented. [ABSTRACT FROM AUTHOR]

Moral error theorists think that moral judgments such as 'stealing is morally wrong' express truth-apt beliefs that ascribe moral properties to objects and actions. They also think that moral properties are not instantiated. Since moral error theorists think that moral judgments can only be true if they correctly describe moral properties, they think that no moral judgment is true. The belief problem for moral error theory is that this theory is inconsistent with every plausible theory of belief. I argue that moral error theorists can solve the belief problem. My argument is twofold. First, the belief problem rests on a false presupposition about how moral error theorists reason over time. Once we get clear on how would-be error theorists in fact reason towards the error theory and how, once they are error theorists, they subsequently reason about what they should do with their erroneous moral thought and talk, the belief problem evaporates. Second, even if my first argument fails and error theorists do face the belief problem, then we can still identify a plausible theory of belief that is consistent with moral error theory. [ABSTRACT FROM AUTHOR]

The accuracy of the end-effector motion trajectory is a critical performance indicator for cable-driven parallel mechanisms. This study aims to address the problem of trajectory error during the end-effector motion in a cable-driven parallel mechanism. It proposes a comprehensive compensation method based on the simultaneous application of the improved sparrow search algorithm and the cable length space error compensation algorithm, leveraging kinematic analysis. To compensate for the motion trajectory error of the end-effector caused by the geometric parameter error, the study establishes the kinematic model of the cable-driven parallel mechanism using the vector method. It creates the end-effector position error model and motion trajectory error model using the differential kinematic theory, analyzes the impact of the geometric parameter error on the motion trajectory error, constructs the kinematic parameter identification matrix, and uses an improved sparrow search algorithm to compensate for the position error of the motion trajectory interpolation point. For the motion trajectory error of the end-effector caused by non-geometric parameter error, the study analyzes the intrinsic correlation between the adjacent position error of the end-effector and the variation of the cable length using the error similarity theory. It then compensates for the position error of the interpolation point of the trajectory using a cable length space interpolation compensation method to enhance the motion trajectory accuracy of the end-effector. The study experimentally verifies the proposed comprehensive compensation method for end-effector motion trajectory error on a 4-cable-driven 2-DOF parallel mechanism, which reduces the motion trajectory error of the end-effector by 75%. [ABSTRACT FROM AUTHOR]

This paper demonstrates how qualitative analysis can be a novel means of investigating theories of error and causation in natural gas pipeline incidents. Qualitative analysis offers unique opportunities to understand process, interactions, and the role of context in identifying active error and latent conditions in incident causation. Through the coding of text from 24 onshore natural gas pipeline incident reports on leaks and explosions in the United States and Canada, our findings reveal a proportion of active and latent errors consistent with other hazardous infrastructure contexts (roughly 3:1 latent‐active ratio across 817 coded errors). These findings underscore the robustness of extant error theory and support the argument for documenting multiple, connected causes of disaster in aggregate. Conclusions highlight the utility of in‐depth case analyses and critique present pipeline incident database aggregation. Our interpretation provides a means to convey complex causation in aggregate form thus enabling more nuanced future qualitative and qualitative analyses. [ABSTRACT FROM AUTHOR]

In this paper, the unconditional superconvergence error analysis of the semi-implicit Euler scheme with low-order conforming mixed finite element discretization is investigated for time-dependent Navier–Stokes equations. In terms of the high-accuracy error estimates of the low-order finite element pair on the rectangular mesh and the unconditional boundedness of the numerical solution in L ∞ -norm, the superclose error estimates for velocity in H 1 -norm and pressure in L 2 -norm are derived firstly by dealing with the trilinear term carefully and skillfully. Then, the global superconvergence results are obtained with the aid of the interpolation post-processing technique. Finally, some numerical experiments are carried out to support the theoretical findings. [ABSTRACT FROM AUTHOR]

Using polarization-maintaining fiber (PMF) in dual-frequency heterodyne interferometry has the advantages of reducing the laser's own drift, obtaining high-quality light spots, and improving thermal stability. Using only one single-mode PMF to achieve the transmission of dual-frequency orthogonal, linearly polarized beam requires angular alignment only once to realize the transmission of dual-frequency orthogonal, linearly polarized light, avoiding coupling inconsistency errors, so that it has the advantages of high efficiency and low cost. However, there are still many nonlinear influencing factors in this method, such as the ellipticity and non-orthogonality of the dual-frequency laser, the angular misalignment error of the PMF, and the influence of temperature on the output beam of the PMF. This paper uses the Jones matrix to innovatively construct an error analysis model for the heterodyne interferometry using one single-mode PMF, to realize the quantitative analysis of various nonlinear error influencing factors, and clarify that the main error source is the angular misalignment error of the PMF. For the first time, the simulation provides a goal for the optimization of the alignment scheme of the PMF and the improvement of the accuracy to the sub-nanometer level. In actual measurement, the angular misalignment error of the PMF needs to be smaller than 2.87° to achieve sub-nanometer interference accuracy, and smaller than 0.25° to make the influence smaller than ten picometers. It provides theoretical guidance and an effective means for improving the design of heterodyne interferometry instruments based on PMF and further reducing measurement errors. [ABSTRACT FROM AUTHOR]

We present a new numerical approach to solving the fractional differential Riccati equations numerically. The approach—called the Mittag-Leffler–Galerkin method—comprises the finite Mittag-Leffler function and the Galerkin method. The error analysis of the method was studied. As a result, we present two theorems by which the error can be bounded. In addition to error analysis, the residual correction method, which allows us to estimate the error and obtain new approximate solutions, is also presented. To show how the method is applied, and the efficiency of the proposed method, some test examples were considered. When the numerical results obtained were examined, it was found that while the method achieves better results than some of the known methods in the literature, it also achieves results that are similar to those of others of the known methods. [ABSTRACT FROM AUTHOR]

We explore the effect of neutron lifetime and its uncertainty on standard big bang nucleosynthesis (BBN). BBN describes the cosmic production of the light nuclides, 1 H , D, 3 H + 3 He , 4 He , and 7 Li + 7 Be , in the first minutes of cosmic time. The neutron mean life τ n has two roles in modern BBN calculations: (1) it normalizes the matrix element for weak n ↔ p interconversions, and (2) it sets the rate of free neutron decay after the weak interactions freeze-out. We review the history of the interplay between τ n measurements and BBN, and present a study of the sensitivity of the light element abundances to the modern neutron lifetime measurements. We find that τ n uncertainties dominate the predicted 4 He error budget, but these theory errors remain smaller than the uncertainties in 4 He observations, even with the dispersion in recent neutron lifetime measurements. For the other light element predictions, τ n contributes negligibly to their error budget. Turning the problem around, we combine present BBN and cosmic microwave background (CMB) determinations of the cosmic baryon density to predict a "cosmologically preferred" mean life of τ n (BBN + CMB) = 870 ± 16 s , which is consistent with experimental mean life determinations. We show that if future astronomical and cosmological helium observations can reach an uncertainty of σ obs (Y p) = 0.001 in the 4 He mass fraction Y p , this could begin to discriminate between the mean life determinations. [ABSTRACT FROM AUTHOR]

The feature extraction of Gaofen-2 Remote Sensing Image (RSI) has problems such as poor extraction accuracy and large noise reduction error. Therefore, this paper designs an RSI feature extraction method based on high score 2 wavelet transform (WT). The RSI is collected with the help of Gaofen-2 satellite and high-resolution remote sensing technology, the key points of the image are determined through the Gaussian difference scale space, and the key points of the edge are judged by the peak curvature value of the difference function at the edge junction, so as to complete the RSI acquisition. Specific filtering and spatial domain transformations are used to remove image noise and improve the quality of RSI. The mean shift (MS) algorithm is used to iteratively find the area with the most dense sample points in the RSI space, complete the image analysis, and realize the preprocessing of the high score 2 RSI. The linear features of the RSI are determined by the WT algorithm, and the image threshold is set for feature extraction of the high score 2 RSI. The experimental results show that in the RSI noise reduction error analysis of different methods, the noise reduction error curve of the sample RSI of the method proposed in this paper has the lowest trend, which is always lower than 2%. Compared with the two methods proposed before, the error is higher. At the same time, in the accuracy analysis of key point feature extraction, the proposed scheme has better accuracy. Therefore, it can be seen that this method has better comprehensive performance, and the proposed method can effectively improve the feature extraction accuracy of RSI and reduce the noise in RSI. [ABSTRACT FROM AUTHOR]

In this paper, the regularity of the solution for a multi-term time-fractional fourth-order equation is analyzed, and the derived result shows that the solution behaves a weak singularity at initial time t = 0. By introducing an intermediate variable p = − Δ u , we obtain a system of two second-order differential equations, which is discretised by using the L1 scheme on graded meshes in time and the mixed finite element method (MFEM) in space. It is shown that the optimal pointwise-in-time error estimate is derived for the proposed scheme. Moreover, the fast L1-MFEM is constructed to improve the computational efficiency. Finally, numerical experiments are provided to further verify our theoretical convergent result and the computational efficiency of the proposed two schemes. [ABSTRACT FROM AUTHOR]

This paper deals with the generalization of the fractional operational matrix of Jacobi wavelets. The fractional population growth model was solved by using this operational matrix and compared with other existing methods to illustrate the applicability of the method. Then, convergence and error analysis of this procedure were studied. [ABSTRACT FROM AUTHOR]

In this work, the Fourier-cosine series (COS) method has been combined with the Boundary Element Method (BEM) for a fast evaluation of barrier option prices. After a description of its use in the Black and Scholes (BS) model, the focus of the paper is on the application of the proposed methodology to the barrier option evaluation in the Heston model, where its contribution is fundamental to improve computational efficiency and to make BEM appealing among finance practitioners as a valid alternative to Monte Carlo (MC) or other more traditional approaches. An error analysis is provided on the number of terms used in the Fourier-cosine series expansion, where the error bound estimation is based on the characteristic function of the log-asset price process. A Matlab code implementing this technique is attached at the end of the paper. [ABSTRACT FROM AUTHOR]

According to Streumer and Wodak, a particular type of formal objection to normative error theory fails because it rests on a questionable assumption about the logical duality of the normative concepts of permissibility and impermissibility. In this discussion, we argue that there is an error in their indictment; as such, the formal objection to normative error theory might still prevail. [ABSTRACT FROM AUTHOR]

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In this research article, a discontinuous Galerkin method with a weighted parameter θ and a penalty parameter γ is proposed for solving the first order hyperbolic equation. The key aim of this method is to design an error estimation for both a priori and a posteriori error analysis on general finite element meshes. It is also exposed to the reliability and effectiveness of both parameters in the order of convergence of the solutions. For a posteriori error estimation, residual adaptive mesh- refining algorithm is employed. A series of numerical experiments are illustrated that demonstrate the efficiency of the method. [ABSTRACT FROM AUTHOR]