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In the case of strong coupling, analyzing a complex system by finite element method costs so much due to the degrees of freedom. Although introducing modal superposition technique is able to reduce the sum of coupling system's freedoms, it is still based on the assumption of neglecting the coupling influence between the high-order modes and low-order modes belonging to different subsystems. And it may result in non-convergence when uncoupling modes are used. Based on the undamped acoustic and vibration coupling equation, this paper presents a new coupling method called patch transfer function method (PTFM), by which the coupling face is tackled as a series of independent patches. The patch transfer functions of each patch are calculated by the average value of the nodal value, then the coupling system PTFs can be obtained by the continuity equation. It is faster to predict the coupling system response, as the inversion of coupling equation is substituted for the transfer function from source to receiver. At last, with the model of plate and air-cavity coupling system, this paper reveals the accuracy of PTFM by comparing the result of direct coupling method (DCM). And the theory and calculation error of the method are discussed. [ABSTRACT FROM AUTHOR]

Paper chip is an efficient and inexpensive device for pesticide residues detection. However, the reasons of detection error are not clear, which is the main problem to hinder the development of pesticide residues detection. This paper focuses on error analysis for pesticide detection performed on paper-based microfluidic chip devices, which test every possible factor to build the mathematical models for detection error. In the result, double-channel structure is selected as the optimal chip structure to reduce detection error effectively. The wavelength of 599.753 nm is chosen since it is the most sensitive detection wavelength to the variation of pesticide concentration. At last, the mathematical models of detection error for detection temperature and prepared time are concluded. This research lays a theory foundation on accurate pesticide residues detection based on paper-based microfluidic chip devices. [ABSTRACT FROM AUTHOR]

The XY model is a simplified insulation model for transformers that aims to connect the frequency spectrum of major insulation, insulation paper, and oil. It enables the calculation of the paper's frequency spectrum, facilitating a quantitative evaluation of the transformer's insulation status. Given the scarcity of research addressing the accuracy of the XY model and its corresponding equivalent circuit, this paper investigates the accuracy of the XY model and conducts an in‐depth analysis of the error associated with its equivalent circuit. Firstly, the frequency spectrum of oil‐paper insulations based on the XY model with varying moisture content and structure configurations were measured, followed by the simulation of both the corresponding 2D‐coaxial and XY models. By comparing the results obtained from these simulations with experimental data on oil‐paper insulation, the accuracy of XY model is verified. Subsequently, two variants of the equivalent circuit of the XY model are derived by combining the oil, spacer, and paper differently, which denoted as Type I and II circuits. Finally, we analyzed and explained the errors present in these equivalent circuits compared with the XY model. Our findings show that the width‐thickness ratio of oil‐paper insulation is the most critical influencing factor, while moisture content and insulation structure have a less decisive impact. Notably, for general transformers, as the width‐thickness ratio is between 30 and 70, the relative error of the Type I circuit remains consistently below 0.3% across different frequencies. Consequently, the Type I circuit proves to be a more suitable representation of the equivalent circuit for the XY model in the context of general transformers. © 2024 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

This article deals with the error analysis of a Galerkin‐mixed finite element methods for the advection–reaction–diffusion Brinkman flow in porous media. Numerical methods for incompressible miscible flow in porous media have been studied extensively in the last several decades. In practical applications, the lowest‐order Galerkin‐mixed method is the most popular one, where the linear Lagrange element is used for the concentration and the lowest‐order Raviart–Thomas element, the lowest‐order Nédélec edge element and piece‐wise constant discontinuous Galerkin element are used for the velocity, vorticity and pressure, respectively. The existing error estimate of this lowest‐order finite element method is only O(h)$$ O(h) $$ for all variables in spatial direction, which is not optimal for the concentration variable. This paper focuses on a new and optimal error estimate of a linearized backward Euler Galerkin‐mixed FEMs, where the second‐order accuracy for the concentration in spatial directions is established unconditionally. The key to our optimal error analysis is a new negative norm estimate for Nédélec edge element. Moreover, based on the computed numerical concentration, we propose a simple one‐step recovery technique to obtain a new numerical velocity, vorticity and pressure with second‐order accuracy. Numerical experiments are provided to confirm our theoretical analysis. [ABSTRACT FROM AUTHOR]

Low-altitude airspace is developing rapidly, but the utilization rate of airspace resources is low. Therefore, in order to solve the problem of the safe operation of the fusion of large UAVs and manned aircraft in the same airspace, this paper analyzes the theoretical calculation of the collision risk of the fusion operation of manned aircraft and UAVs at Feng Ming Airport in Zigong, verifying that while assessing the safety spacing of 10 km in the lateral direction, it further simulates the possibility of calculating the theoretical smaller safety spacing. The study will propose a new theory of error spacing safety margin and improve it according to the traditional Event collision risk model, combining the error spacing safety margin to establish an improved collision model more suitable for the fusion operation of manned and unmanned aircraft and reduce the redundancy of calculation. The error factors affecting manned and unmanned aircraft at Zigong Airport are analyzed, and theoretical calculations are analyzed by combining the actual data of Zigong Airport. Finally, the Monte Carlo simulation method is used to solve the error, substitute the calculation results, and simulate a section of the trajectory of the fusion operation for the reverse argument. The theoretical calculation results show that the collision risk from 10 km to 8 km satisfies the lateral target safety level (TSL) specified by ICAO under both traditional and improved models. The collision risk calculated by the improved model incorporating the error spacing safety margin is smaller, which enhances the safety of the model calculations. The results of the study can provide theoretical references for the fusion operation of manned and unmanned aircraft. [ABSTRACT FROM AUTHOR]

Heterodox ideas face an uphill battle. This is not least the case for heterodox conspiracy theories. As an empirical observation, this is hardly controversial. What is controversial is whether and to what extent this should be the case. Some authors have gone so far as to argue that heterodox conspiracy theories should be generally dismissed, and that it is precisely their heterodox status that justifies such dismissal. Most particularists are likely to object strongly to such an assessment, arguing that conspiracy theories – whether heterodox or orthodox – should not be dismissed before careful examination of the relevant evidence. But even particularists will probably concede that proponents of heterodox conspiracy theories have to bear a special epistemic burden. The main aim of this paper is to take a closer look at this particular epistemic burden. Drawing on the literature about peer disagreement, genealogical debunking arguments, and related philosophical debates, I focus in particular on the question of whether and under what conditions it can be rational to defend heterodox conspiracy theories, and argue that what I will call theories of error play a crucial role in this context. [ABSTRACT FROM AUTHOR]

Presentists hold that only present things exist. But we all, presentists included, utter sentences that appear to involve quantification over non-present objects, and so we all, presentists included, seem to commit ourselves to such objects. Equally, we all, presentists included, take utterances of many past-tensed (and some future-tensed) sentences to be true. But if no past or future things exist, it's hard to see how there can be anything that those utterances are about, which makes them true. This paper presents a hitherto unexplored response to both problems: pretence fictionalism about the non-present. This view combines semantic factualism with psychological non-cognitivism. Sentences that appear to quantify over the non-present have propositional content and (almost all of) those propositions are false because the thing they are about – the non-present – does not exist. Nevertheless, when we utter such sentences we don't thereby utter something false. Our utterances do not report the belief that the propositional content of the sentence uttered is true; rather, they express a non-cognitive attitude towards that content: namely an attitude of pretence. Hence by thinking various thoughts, and uttering various sentences we are, collectively, pretending as though things were (or will be) thus and so. [ABSTRACT FROM AUTHOR]

Abstract: Costa''s dirty paper coding (DPC) offers a good framework for precoding for transmission over additive Gaussian channels with additive states non-causally known at the transmitter but not at the receiver. In this paper, rate calculation, error probability analysis and code design for DPC are investigated from a practical point-of-view. Based on Monte-Carlo numerical integration and simulations, we first show that the gap to the full AWGN capacity can be partially bridged using some finite-dimensional lattices with good packing and quantizing properties. Then the difficult problem of codebook selection is addressed through some illustrative examples. Analysis sheds light on the dual roles of “packing” and “shaping” as well as on their inter-connection at finite-dimensional coding, by opposition to the asymptotic case (i.e., infinite dimension) where the two coding components are decoupled. [Copyright &y& Elsevier]

Wavelet neural networks (WNNs) were used to investigate the influence of operational variables in the soda-ethanol pulping of oil palm fronds (viz. NaOH concentration (10-30%), ethanol concentration (15-75%), cooking temperature (150-190 ºC), and time (60-180 min)) on the resulting pulp and paper properties (viz. screened yield, kappa number, tensile index, and tear index). Performance assessments demonstrated the predictive capability of WNNs, in that the experimental results of the dependent variables with error less than 6% were reproduced, while satisfactory R-squared values were obtained. It thus corroborated the good fit of the WNNs model for simulating the soda-ethanol pulping process for oil palm fronds. [ABSTRACT FROM AUTHOR]

In this paper, the flower‐shaped microstrip antenna (FSMA) is investigated theoretically and experimentally for the first time. A theoretical model is proposed to investigate the radiation characteristic of an FSMA using conformal mapping technique. The flower shape is mapped to a circular shape with the help of an appropriate mapping relation. The wave equation is solved in the transformed domain using Galerkin technique to obtain the approximate solution of eigenfunction and eigenvalue. Resonant frequency, internal field patterns, input impedance, and far‐field radiation patterns of the FSMA are investigated. Three antenna prototypes are fabricated for experimental verification. The acceptable agreement is found among the calculated, simulated, and measured data. Our theory shows an error of less than 1.45% in predicting the resonance frequency. Quality factor and bandwidth are also described. This theoretical approach not only quickly evaluates the performance of an FSMA but also provides the instruction to design an FSMA. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new scheme for the integration of the periodic nonlinear Schrödinger equation and rigorously prove convergence rates at low regularity. The new integrator has decisive advantages over standard schemes at low regularity. In particular, it is able to handle initial data in Hs for 0 < s ≤ 1. The key feature of the integrator is its ability to distinguish between low and medium frequencies in the solution and to treat them differently in the discretization. This new approach requires a well-balanced filtering procedure which is carried out in Fourier space. The convergence analysis of the proposed scheme is based on discrete (in time) Bourgain space estimates which we introduce in this paper. A numerical experiment illustrates the superiority of the new integrator over standard schemes for rough initial data. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper we studied the Voronovskaya type theorem for modified Gamma operators presented by A. İzgi in the paper “Voronovskaya type asymptotic approximation by modified Gamma operators” [Applied Mathematics and Computation 217 (2011) 8061–8067]. We show that this theorem is not true. We present a correct form of this theorem and its proof. Furthermore, we obtain an error estimate for modified Gamma operators. [Copyright &y& Elsevier]

In 1935, Erdös proved that all natural numbers can be written as a sum of a square of a prime and a square-free number. In 1939, Pillai derived an asymptotic formula for the number of such representations. The mathematical review of Pillai's paper stated that the proof of the above result contained inaccuracies, thus casting a doubt on the correctness of the paper. In this paper, we re-examine Pillai's paper and show that his argument was essentially correct. Afterwards, we improve the error term in Pillai's theorem using the Bombieri-Vinogradov theorem. [ABSTRACT FROM AUTHOR]

In 1999 Amodio and Mazzia presented a new backward error analysis for LU factorization and introduced a new growth factor ρ n. Their very interesting approach allowed them to obtain sharp error bounds. In particular, they derive nice results assuming that partial pivoting is used. However, the forward error bound for the solution of a linear system whose coefficient matrix A is an M-matrix given in Theorem 4.1 of that paper is not correct. They first obtain a bound for the condition number κ (U) assuming that one has the LU factorization of an M-matrix and then they apply the bounds obtained when partial pivoting is used. But if P is the permutation associated with partial pivoting then PA = LU can fail to be an M-matrix and the bound for κ (U) can be false, as shown in our Example 1.1. We also prove that, for a pivoting strategy presented in the paper, the growth factor of an M-matrix A is ρn ( A) = 1 and κ (U) ≤ κ (A), where U is the upper triangular matrix obtained after applying such a pivoting strategy. [ABSTRACT FROM AUTHOR]

The article focuses on the number theory of Gaussian integers. Within the complex numbers, the analogues of the integers are the Gaussian integers, those complex numbers whose real and imaginary parts are both integers. There is a theory of divisibility, including greatest common divisors, and the purpose of this article is to present a new gcd algorithm for Gaussian integers. The standard algorithm is a straightforward extension of the Euclidean algorithm for ordinary integers. The gcd algorithm is better suited to paper-and-pencil computation, and it is less error-susceptible than the standard one. Another attractive feature is that it is based on a simple parity argument. The basic divisibility definitions for Gaussian integers are simply restatements of those for ordinary integers. There are many interesting results which can be proved using parity arguments. The gcd algorithm establishes that any two Gaussian integers have a greatest common divisor, and it is interesting to see that this result has an odd-even proof.

The dual five-axis machining machine is state-of-the-art equipment designed for producing thin-walled aerospace parts like skins and panels. It comprises two five-axis machine tools with mirrored synchronous motions: one bi-rotary machine for milling and the other machine for follow-up support. The high absolute accuracy of the five-axis machine tools themselves and the high synchronous motion accuracy between the two machines are both crucial to ensure machining accuracy. This paper proposes an efficient method to measure and identify geometric and dynamic errors of dual five-axis machine tools. Using the R-test combined with three measurement trajectories to measure the absolute motion error of two five-axis machine tools and the synchronous motion error between the two machines. The designed trajectories include the main rotary axis linkage conditions and can fully reflect the primary motion forms of the dual five-axis machine tool. The main position-independent geometric errors and rotational axis linkage dynamic errors are identified by converting quasi-static and dynamic measurement data from three different trajectories into a unified reference coordinate system. The entire process requires only one instrument installation, effectively avoiding time-consuming repetitive installations and calibration processes while reducing the impact of installation errors on results. The effectiveness of the proposed method for measuring and identifying the geometric and dynamic errors is analyzed combined with Monte Carlo simulation. Experiments were carried out on a dual five-axis mirror milling system (MMS) with a 5000 mm X-stroke. Both simulations and experiments confirmed that the proposed method is efficient in quickly identifying key error sources of the MMS. [Display omitted] • An efficient method to measure and identify geometric and dynamic errors during synchronous motion of the MMS is proposed. • A geometric and dynamic error model is introduced for identifying key errors using error sensitivity theory. • A 3-step measurement strategy that enables rapid separation of linkage errors of the MMS is introduced. • Both simulation and experiment show the proposed method could obtain key error sources of the MMS with high efficiency. [ABSTRACT FROM AUTHOR]

This paper argues that the allure of conspiracy theories lies in their evolutionary origins, specifically in our capacity to communicate unrepresented threats. Drawing on threat-detection psychology and error management theory, it posits that these theories serve as adaptive responses to perceived threats and social coalition-building, rather than as flaws in reasoning. [ABSTRACT FROM AUTHOR]

In this paper, we present a new error analysis of a class of charge-conservative finite element methods for stationary inductionless magnetohydrodynamics (MHD) equations. The methods use the standard inf-sup stable Mini/Taylor–Hood pairs to discretize the velocity and pressure, and the Raviart–Thomas face element for solving the current density. Due to the strong coupling of the system and the pollution of the lower-order Raviart–Thomas face approximation in analysis, the existing analysis is not optimal. In terms of a mixed Poisson projection and the corresponding estimate in negative norms, we establish new and optimal error estimates. In particular, we prove that the method with the lowest-order Raviart–Thomas face element and Mini element provides the optimal accuracy for the velocity in L 2 -norm, and the method with the lowest-order Raviart–Thomas face element and P 2 − P 1 Taylor-Hood element supplies the optimal accuracy for the velocity in H 1 -norm and the pressure in L 2 -norm. Furthermore, we propose a simple recovery technique to obtain a new numerical current density of one order higher accuracy by re-solving a mixed Poisson equation. Numerical results are provided to verify the theoretical analysis. • New and optimal error analysis of charge-conservative finite element methods are established. • A simple recovery technique is proposed to obtain a new current density with higher accuracy. • Numerical examples are provided to verify the theoretical findings. [ABSTRACT FROM AUTHOR]

The primary objective of this paper is to investigate the error analysis for the damped Boussinesq equation with the Ciarlet-Raviart mixed finite element method, focusing on achieving superconvergence. By employing a skillful mean technique and a high precision estimate of the bilinear element, as well as combining with projection and interpolation technique, we first obtain a superclose error estimate between interpolation of the exact solution and numerical solution. Subsequently, by applying an interpolation post-processing approach, we efficiently derive a global superconvergence result. Finally, several numerical results are presented to support our theoretical analysis. [ABSTRACT FROM AUTHOR]

Partially linear additive models (PLAMs) have attracted much attention in the statistical machine learning community due to their interpretability and flexibility in data-driven prediction and inference. Since the performance of PLAMs is closely related to the structure information of linear and nonlinear components, several approaches have been proposed for regression estimation and data-driven structure discovery. However, the existing automatic discovery strategy is limited to the mean regression framework and is usually sensitive to non-Gaussian noises, e.g. skewed noise and heavy-tailed noise. To further improve the robustness of PLAMs, this paper proposes a Robust Partially Linear Trend Filtering (RPLTF) for regression estimation and structure discovery by integrating the mode-induced error metric and the trend filtering-based nonlinear approximation into regularized PLAMs. Besides the computing algorithm of RPLTF, we establish its upper bound on generalization error in theory. Empirical examples are provided to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The interaction between laser beams and backscattering object surfaces lies at the fundamental working principle of any Terrestrial Laser Scanning (TLS) system. Optical properties of surfaces such as concrete, metals, wood, etc., which are commonly encountered in structural health monitoring of buildings and structures, constitute an important category of systematic and random TLS errors. This paper presents an approach for considering the random errors caused by object surfaces. Two surface properties are considered: roughness and reflectance. The effects on TLS measurements are modeled stepwise in form of a so-called synthetic variance-covariance matrix (SVCM) based on the elementary error theory. A line of work is continued for the TLS stochastic model by introducing a new approach for determining variances and covariances in the SVCM. Real measurements of cast stone façade elements of a tall building are used to validate this approach and show that the quality of the estimation can be improved with the appropriate SVCM. [ABSTRACT FROM AUTHOR]

Using deep neural networks to solve partial differential equations (PDEs) has attracted a lot of attention recently. However, why the deep learning method works is falling far behind its empirical success. In this paper, we provide a rigorous numerical analysis on the deep Ritz method (DRM) for second-order elliptic equations with Dirichlet, Neumann and Robin boundary conditions, respectively. We establish the first nonasymptotic convergence rate in H 1 norm for DRM using deep neural networks with smooth activation functions including logistic and hyperbolic tangent functions. Our results show how to set the hyper-parameter of depth and width to achieve the desired convergence rate in terms of the number of training samples. [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]

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 we propose a variant of enriched Galerkin methods for second order elliptic equations with over-penalization of interior jump terms. The bilinear form with interior over-penalization gives a non-standard norm which is different from the discrete energy norm in the classical discontinuous Galerkin methods. Nonetheless we prove that optimal a priori error estimates with the standard discrete energy norm can be obtained by combining a priori and a posteriori error analysis techniques. We also show that the interior over-penalization is advantageous for constructing preconditioners robust to mesh refinement by analyzing spectral equivalence of bilinear forms. Numerical results are included to illustrate the convergence and preconditioning results. • A new locally mass conservative finite element method with interior over-penalized enriched Galerkin methods (IOP-EG). • A priori error analysis of IOP-EG independent of over-penalization. • A robust preconditioner construction and analysis by operator preconditioning approach. [ABSTRACT FROM AUTHOR]

A second‐order accurate, linear numerical method is analyzed for the Landau–Lifshitz equation with large damping parameters. This equation describes the dynamics of magnetization, with a non‐convexity constraint of unit length of the magnetization. The numerical method is based on the second‐order backward differentiation formula in time, combined with an implicit treatment for the linear diffusion term from the harmonic mapping part and explicit extrapolation for the nonlinear terms. Afterward, a projection step is applied to normalize the numerical solution at a point‐wise level. This numerical scheme has shown extensive advantages in the practical computations for the physical model with large damping parameters, which comes from the fact that only a linear system with constant coefficients (independent of both time and the updated magnetization) needs to be solved at each time step, and has greatly improved the numerical efficiency. Meanwhile, a theoretical analysis for this linear numerical scheme has not been available. In this paper, we provide a rigorous error estimate of the numerical scheme, in the discrete ℓ∞(0,T;ℓ2)∩ℓ2(0,T;Hh1)$$ {\ell}&amp;#x0005E;{\infty}\left(0,T;{\ell}&amp;#x0005E;2\right)\cap {\ell}&amp;#x0005E;2\left(0,T;{H}_h&amp;#x0005E;1\right) $$ norm, under suitable regularity assumptions and reasonable ratio between the time step size and the spatial mesh size. In particular, the projection operation is nonlinear, and a stability estimate for the projection step turns out to be highly challenging. Such a stability estimate is derived in details, which will play an essential role in the convergence analysis for the numerical scheme, if the damping parameter is greater than 3. [ABSTRACT FROM AUTHOR]

In this paper, we study the learning performance of regularized large-margin unified machines (LUMs) for classification problem. The hypothesis space is taken to be a reproducing kernel Hilbert space $ {\mathcal H}_K $, and the penalty term is denoted by the norm of the function in $ {\mathcal H}_K $. Since the LUM loss functions are differentiable and convex, so the data piling phenomena can be avoided when dealing with the high-dimension low-sample size data. The error analysis of this classification learning machine mainly lies upon the comparison theorem [3] which ensures that the excess classification error can be bounded by the excess generalization error. Under a mild source condition which shows that the minimizer $ f_V $ of the generalization error can be approximated by the hypothesis space $ {\mathcal H}_K $, and by a leave one out variant technique proposed in [13], satisfying error bound and learning rate about the mean of excess classification error are deduced. [ABSTRACT FROM AUTHOR]

Approximate adders are some of the fundamental arithmetic operators that are being employed in error-resilient applications, to achieve performance/energy/area gains. This improvement usually comes at the cost of some accuracy and, therefore, requires prior error analysis, to select an approximate adder variant that provides acceptable accuracy. Most of the state-of-the-art error analysis techniques for approximate adders assume input bits and operands to be independent of one another, while some also assume the operands to be uniformly distributed. In this paper, we analyze the impact of these assumptions on the accuracy of error estimation techniques, and we highlight the need to address these assumptions, to achieve better and more realistic quality estimates. Based on our analysis, we propose DAEM, a data- and application-aware error analysis methodology for approximate adders. Unlike existing error analysis models, we neither assume the adder operands to be uniformly distributed nor assume them to be independent. Specifically, we use 2D joint input probability mass functions (PMFs), populated using sample data, in order to incorporate the data and application knowledge in the analysis. These 2D joint input PMFs, along with 2D error maps of approximate adders, are used to estimate the error PMF of an adder network. The error PMF is then utilized to compute different error measures, such as the mean squared error (MSE) and mean error distance (MED). We evaluate the proposed error analysis methodology on audio and video processing applications, and we demonstrate that our methodology provides error estimates having a better correlation with the simulation results, as compared to the state-of-the-art techniques. [ABSTRACT FROM AUTHOR]

In this paper, we present an immersed finite element (IFE) method for solving the elastodynamics interface problems on interface-unfitted meshes. For spatial discretization, we use vector-valued P 1 and Q 1 IFE spaces. We establish some important properties of these IFE spaces, such as inverse inequalities, which will be crucial in the error analysis. For temporal discretization, both the semi-discrete and the fully discrete schemes are derived. The proposed schemes are proved to be unconditionally stable and enjoy optimal rates of convergence in the energy, L 2 and semi- H 1 norms. Numerical examples are designed to verify our theoretical analysis and to demonstrate the stability and robustness of our schemes. [ABSTRACT FROM AUTHOR]

In this paper, we utilized a hybrid method for the unsteady flow of the non-Newtonian third-grade fluid that combines the finite difference with the asymptotic interpolation method. This hybrid method is used to satisfy the semiunbound domain condition of the fluid flow's length approaching infinity. The primary issue with this research is how much of the hybrid approach's error may be accepted to guarantee that the method is significant. This paper discussed theoretical error analysis for numerical solutions, including the range and norm of error. The perturbation method's concept is used to assess the hybrid method's error. It is discovered that the hybrid approach's relative error norm is lower than that of the finite difference method. In terms of the error standard, the hybrid approach is more consistent. Error analysis is performed to check for the accuracy as well as the platform for variable mesh size finite difference method in the future research. [ABSTRACT FROM AUTHOR]

This paper is concerned with new error analysis of a lowest-order backward Euler Galerkin-mixed finite element method for the time-dependent Ginzburg-Landau equations. The method is based on a commonly-used nonuniform approximation, in which a linear Lagrange element, the lowest-order Nédélec edge element, and the Raviart-Thomas face element are used for the order parameter ψ, the magnetic field curlA, and the magnetic potential A, respectively. This mixed method has been widely used in practical simulations due to its low cost and ease of implementation. In the Ginzburg-Landau model, the order parameter ψ is the most important variable, which indicates the state of the superconductor. An important feature of the method is the inconsistency of the approximation orders. A crucial question is how the first-order approximation of (curlA, A) influences the accuracy of ψh. The main purpose of this paper is to establish the second-order accuracy for the order parameter in a spatial direction, although the accuracy for (curlA, A) is first order only. Previous analysis only gave the first-order convergence for all three variables due to certain artificial pollution involved in the analysis. Our analysis is based on a nonstandard quasi-projection for ψ and the corresponding more precise estimates, including the H-1 -norm. With the quasi-projection, we prove that the lower-order approximation to (curlA, A) does not pollute the accuracy of ψh. Our numerical experiments confirm the optimal convergence of ψh. The approach can be extended to many other multiphysics models.. [ABSTRACT FROM AUTHOR]

In this paper, motivated by the competitive performance of the proximal stochastic variance reduction gradient (Prox-SVRG) method, a novel general inertial Prox-SVRG (GIProx-SVRG) algorithm is proposed for solving a class of nonconvex finite sum problems. More precisely, Nesterov's momentum trick-based extrapolation accelerated step is incorporated into the framework of Prox-SVRG method. The GIProx-SVRG algorithm possesses more general accelerated expression and thus can potentially achieve accelerated convergence speed. Moreover, based on the supermartingale convergence theory and the error bound condition, we establish a linear convergence rate for the iterate sequence generated by the GIProx-SVRG algorithm. We observe that there is no theory in which the general extrapolation technique is incorporated into the Prox-SVRG method, whereas we establish such a theory in this paper. Experimental results demonstrate the superiority of our method over state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Abstract: In this short note we point to an error in the proof of a theorem stated in [L. Balková, E. Pelantová, Š. Starosta, On Brlek-Reutenauer conjecture, Theoret. Comput. Sci. 412 (2011) 5649–5655]. By constructing a counterexample, we show that the assertion of the theorem is actually incorrect. Although this theorem is of a technical character, it was used in an argument leading to a corollary of a general interest to the Brlek-Reutenauer conjecture, and thus as a consequence of this note we have that the proof of the mentioned corollary is also flawed. [Copyright &y& Elsevier]

In this paper, we establish the error analysis for distributed pairwise learning with multi-penalty regularization, based on a divide-and-conquer strategy. We demonstrate with L 2 -error bound that the learning performance of this distributed learning scheme is as good as that of a single machine which could process the whole data. With semi-supervised data, we can relax the restriction of the number of local machines and enlarge the range of the target function to guarantee the optimal learning rate. As a concrete example, we show that the work in this paper can apply to the distributed pairwise learning algorithm with manifold regularization. [ABSTRACT FROM AUTHOR]

Purpose: Deep learning is an emerging reconstruction method for positron emission tomography (PET), which can tackle complex PET corrections in an integrated procedure. This paper optimizes the direct PET reconstruction from sinogram on a long axial field of view (LAFOV) PET. Methods: This paper proposes a novel deep learning architecture to reduce the biases during direct reconstruction from sinograms to images. This architecture is based on an encoder-decoder network, where the perceptual loss is used with pre-trained convolutional layers. It is trained and tested on data of 80 patients acquired from recent Siemens Biograph Vision Quadra long axial FOV (LAFOV) PET/CT. The patients are randomly split into a training dataset of 60 patients, a validation dataset of 10 patients, and a test dataset of 10 patients. The 3D sinograms are converted into 2D sinogram slices and used as input to the network. In addition, the vendor reconstructed images are considered as ground truths. Finally, the proposed method is compared with DeepPET, a benchmark deep learning method for PET reconstruction. Results: Compared with DeepPET, the proposed network significantly reduces the root-mean-squared error (NRMSE) from 0.63 to 0.6 (p < 0.01) and increases the structural similarity index (SSIM) and peak signal-to-noise ratio (PSNR) from 0.93 to 0.95 (p < 0.01) and from 82.02 to 82.36 (p < 0.01), respectively. The reconstruction time is approximately 10 s per patient, which is shortened by 23 times compared with the conventional method. The errors of mean standardized uptake values (SUVmean) for lesions between ground truth and the predicted result are reduced from 33.5 to 18.7% (p = 0.03). In addition, the error of max SUV is reduced from 32.7 to 21.8% (p = 0.02). Conclusion: The results demonstrate the feasibility of using deep learning to reconstruct images with acceptable image quality and short reconstruction time. It is shown that the proposed method can improve the quality of deep learning-based reconstructed images without additional CT images for attenuation and scattering corrections. This study demonstrated the feasibility of deep learning to rapidly reconstruct images without additional CT images for complex corrections from actual clinical measurements on LAFOV PET. Despite improving the current development, AI-based reconstruction does not work appropriately for untrained scenarios due to limited extrapolation capability and cannot completely replace conventional reconstruction currently. [ABSTRACT FROM AUTHOR]

Bart Streumer thinks that we cannot believe the global normative error theory. Streumer's argument presupposes a Cartesian theory of belief fixation. The Cartesian theory entails that we can understand a proposition without believing it. But the Cartesian theory of belief fixation is false, and the Spinozan theory is true. The Spinozan theory of belief fixation entails that we cannot understand a proposition without believing it. The present paper argues that Streumer's claim is false, and we can believe the global normative error theory because the Spinozan theory is correct. The paper then applies the Spinozan theory of belief fixation to the "Now what?" problem for global normative error theory and responds to objections. [ABSTRACT FROM AUTHOR]

In this paper we construct a quadrature scheme to numerically solve the nonlocal diffusion equation (Aα + bI)u = f with Aα the αth power of the regularly accretive operator A. Rigorous error analysis is carried out and sharp error bounds (up to some negligible constants) are obtained. The error estimates include a wide range of cases in which the regularity index and spectral angle of A, the smoothness of f, and the size of b and α are all involved. The quadrature scheme is exponentially convergent with respect to the step size and is root-exponentially convergent with respect to the number of solves. Some numerical tests are presented in the last section to verify the sharpness of our estimates. Furthermore, both the scheme and the error bounds can be utilized directly to solve and analyze time-dependent problems. [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]

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]

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 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]

Abstract: This editorial is an annex, essentially an amplification of earlier Animal Feed Science and Technology (AFST) editorials which focused on analytical and statistical issues of papers submitted for publication in AFST. This amplification is needed because, since publication of those editorials, there has been a sharp increase in papers submitted to AFST (particularly in vitro gas, ruminal in sacco, continuous culture fermenter and mini-silo studies), in which there have been substantive disagreements among authors, reviewers and editors as to what, exactly, constitutes acceptable statistical replicates as opposed to pseudo replicates. In this editorial, the Co-Editors in Chief of AFST provide clarification of their view relative to use of analytical observations in statistical analyses in papers submitted for consideration for publication in AFST. If the objective is to compare feeds and from the results, make inferences to populations, only multiple samples of each feed represent an acceptable feed base. This suggests that means comparisons based on repeated assays of the same sample, whether by chemical, physical or microbiological methods, will almost certainly be rejected by the CEIC. [Copyright &y& Elsevier]

The paper focuses on the analysis of the Euler projection Galerkin finite element method (FEM) for the dynamics of magnetization in ferromagnetic materials, described by the Landau–Lifshitz equation with the point-wise constraint |$|{\textbf{m}}|=1$|⁠. The method is based on a simple sphere projection that projects the numerical solution onto a unit sphere at each time step, and the method has been used in many areas in the past several decades. However, error analysis for the commonly used method has not been done since the classical energy approach cannot be applied directly. In this paper we present an optimal |$\textbf{L}^2$| error analysis of the backward Euler sphere projection method by using quadratic or higher order finite elements under a time step condition |$\tau =O(\epsilon _0 h)$| with some small |$\epsilon _0>0$|⁠. The analysis is based on more precise estimates of the extra error caused by the sphere projection in both |$\textbf{L}^2$| and |$\textbf{H}^1$| norms, and the classical estimate of dual norm. Numerical experiment is provided to confirm our theoretical analysis. [ABSTRACT FROM AUTHOR]

Analysis of multisource errors accompanying process execution and study of the propagation effects of the corresponding multiprocess manufacturing process are the basic prerequisites for optimizing the generation process and improving the quality of the product. This paper proposes an analytical framework for error propagation effects in multiprocess manufacturing, which completely covers error source analysis, mathematical calculation of error propagation accumulation, and description of error propagation effects, which can provide better support for error traceability, error propagation monitoring, and error dissipation in manufacturing production. First of all, establish the process state model into the features of the manufacturing level, analyze the type of multisource error, and its mode of action when executing the process operation; second, establish the mathematical calculation model of error propagation accumulation based on state space equation is established, so as to realize calculation and analysis of error propagation; and finally, establish the link graph and link matrix of error propagation influence in multiprocess manufacturing process are established to further reveal the scope and path of error propagation influence. In this section of the case study, a plate cover part had been taken as an example, the multisource error in its manufacturing was analyzed, and the propagation and accumulation of these error values are obtained by state space and state transition theory. On this basis, the link graph and its corresponding link matrix were used to explicitly describe the error propagation effects during the multiprocess manufacturing of the example part. The example analysis illustrated the proposed error analysis framework could analyze and calculate the multisource error of multiprocess manufacturing and visually describe the error propagation effects, which showed the effectiveness and feasibility of the proposed method framework. [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]

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]