Computational Errors Research Articles

Enhancing Equation Solving: Extending the Applicability of Steffensen-Type Methods

Local convergence analysis is mostly carried out using the Taylor series expansion approach, which requires the utilization of high-order derivatives, not iterative methods. There are other limitations to this approach, such as the following: the analysis is limited to finite-dimensional Euclidean spaces; no a priori computable error bounds on the distance or uniqueness of the solution results are provided. The local convergence analysis in this paper positively addresses these concerns in the more general setting of a Banach space. The convergence conditions involve only the operators in the methods. The more important semi-local convergence analysis not studied before is developed by using majorizing sequences. Both types of convergence analyses are based on the concept of generalized continuity. Although we study a certain class of methods, the same approach applies to extend the applicability of other schemes along the same lines.

Examining the college English classroom teaching quality using the fuzzy evaluation model

English teaching at college levels is more sophisticated and advanced compared to high schools and professionals. The teaching must have high-quality meetings, real-world interactions, and professional applications. Therefore teaching quality evaluation periodically is performed internally and externally through skill validation and joint training. This article introduces a Regressive Fuzzy Evaluation Model (RFEM) for analyzing the quality of college classroom English teaching quality. This evaluation model operates over the teaching quality metrics such as performance, student understandability, and application. The understandability and English application to the real world is modeled by referring to the performance as the regressive factor. The regressive factor is analyzed for two fuzzification outputs: high and low, by analyzing the individual factors over cumulative teaching grades. The regression for low fuzzy outputs is analyzed using mean understandability and application score from the previous assessment instance. This is required for training the fuzzification from the mean score rather than the low level. Therefore the quality improvements from the lagging features are addressed by providing a new teaching method. Further fuzzy regression is initiated from the mean to the high level reducing the computation time and errors.

Integrating Non-Positional Numbering Systems into E-Commerce Platforms: A Novel Approach to Enhance System Fault Tolerance

In the dynamic landscape of electronic commerce, the robustness of platforms is a critical determinant of operational continuity and trustworthiness, necessitating innovative approaches to fault tolerance. This study pioneers an advanced strategy for enhancing fault tolerance in e-commerce systems, utilizing non-positional numbering systems (NPNS) inspired by the mathematical robustness of the Chinese Remainder Theorem (CRT). Traditional systems rely heavily on positional numbering, which, despite its ubiquity, harbors limitations in flexibility and resilience against computational errors and system faults. In contrast, NPNS, characterized by their independence, equitability, and residue independence, introduce a transformative potential for system architecture, significantly increasing resistance to disruptions and computational inaccuracies. Our discourse extends beyond theoretical implications, delving into practical applications within contemporary e-commerce platforms. We introduce and elaborate on new terminologies, concepts, and a sophisticated classification system for fault-tolerance mechanisms within the framework of NPNS. This nuanced approach not only consolidates understanding but also identifies underexplored pathways for resilience in digital commerce infrastructure. Furthermore, this research highlights the empirical significance of adopting NPNS, offering a methodologically sound and innovative avenue to safeguard against system vulnerabilities. By integrating NPNS, platforms can achieve enhanced levels of redundancy and fault tolerance, essential for maintaining operational integrity in the face of unforeseen system failures. This integration signals a paradigm shift, emphasizing proactive fault mitigation strategies over reactive measures. Conclusively, this study serves as a seminal reference point for subsequent scholarly endeavors, advocating for a shift towards NPNS in e-commerce platforms. The practical adaptations suggested herein are poised to redefine stakeholders’ approach to system reliability, instigating a new era of confidence in e-commerce engagements.

Service Quality of Electronic Identity Cards, Solokan Jeruk District, Bandung Regency

Public service is an important duty that cannot be ignored by the government, including local governments, including the service of electronic identity cards (E-KTP) issuance in Solokan Jeruk District, Bandung Regency and it was the issue in this study. The aim of the study was to figure out and analyze deeply about the quality of service in making electronic identity cards (E-KTP) and the factors that support and inhibit the issuance of electronic identity cards (E-KTP) in Solokan Jeruk District, Bandung Regency. The results showed that the service of making electronic identity cards (E-KTP) in Solokan District, Bandung Regency, in its implementation there were still obstacles in the service process, such as the internet network was often disrupted, computer errors, E-KTP forms were not available, and limited budgets. Efforts applied by Solokan Jeruk to overcome the inhibiting factors in electronic identity cards (E-KTP) services were as like improving coordination with Disdukcapil, Bandung Regency, coordination with the Bandung Regency communication and information service, and consistency in maintaining internet network devices and updating data regularly.

Retracted articles use less free and open-source software and cite it worse

Abstract As an essential mechanism of scientific self-correction, articles are retracted for many reasons, including errors in processing data and computation of results. In today’s data-driven science, the validity of research data and results significantly depends on the software employed. We investigate the relationship between software usage and research validity, eventually leading to article retraction, by analyzing software mentioned across 1,924 retraction notices and 3,271 retracted articles. We systematically compare software mentions and related information with control articles sampled by coarsened exact matching by recognizing publication year, scientific domain, and journal rank. We identify article retractions caused by software errors or misuse and find that retracted articles use less free and open-source software, hampering reproducible research and quality control. Moreover, such differences are also present concerning software citation, where retracted articles less frequently follow software citation guidelines regarding free and open-source software.

A Method for Calculating the Success Probability of Spare Parts Support Tasks for Series Mechanical Components

In response to the potential computational errors caused by neglecting the number of spare parts and the maintenance time for calculating the success probability of repairable products, a calculation method for mechanical series components is proposed in this paper, which is considered the factors such as the quantity of spare parts and the maintenance time required for using spare parts, and the calculation model and steps for the mission success probability of repairable products are provided. Due to the comprehensive impact of maintenance time and the quantity of spare parts, the accuracy of the calculation is improved. The effectiveness of this method has been verified through example simulation calculations, and it is expected to have certain application value for product reliability and supportability evaluation.

Two Convergence Results for Inexact Orbits of Nonexpansive Operators in Metric Spaces with Graphs

In this work we show that if iterates of a nonexpansive self-mapping of a complete metric with a graph converge uniformly on a subset of the space, then this convergence is stable under the presence of small computational errors.

Panic-Pressure Conversion Model From Microscopic Pedestrian Movement to Macroscopic Crowd Flow

Abstract Understanding the effects of panic on crowd dynamics in emergency situations has long been considered necessary for pedestrian evacuation control. In the case of disasters, stampedes caused by panic behaviors occur with high possibility, and pedestrians are crushed or trampled, leading to enormous casualties. To eliminate the computational errors accumulated in the traditional macromodel, a macro-microconversion model based on the SF (social force) model and the AR (Aw-Rascle) model is proposed in this paper. The purpose is to use the crowd parameters of the microscopic model as the input part of the macroscopic model and to combine the advantages of the two models to ensure accuracy and improve calculation performance. The concept of the “pressure term” is defined to measure the panic level of the crowd. In addition, a flowchart of the numerical simulation is designed based on the road network conditions at the trampling site. To validate the conversion model, a numerical simulation is conducted in a case study of the Mecca Hajj stampede in 2015. The simulation results display the whole process of crowd marching and meeting with the dynamic variations of the “pressure term.” The simulation results are compared with the traditional simulation results based on a Gaussian distribution, which verifies that the simulation results obtained by the proposed method are closer to the real situation. Moreover, in this study, a new micromacro transformation method for crowd evaluation dynamics, which can enhance computing speed and execution efficiency, is provided.

Inexact Iterates of Nonexpansive Mappings with Summable Errors in Metric Spaces with Graphs

In our joint work with Dan Butnariu (2006) we established the stability of the convergence of iterates of a nonexpansive mapping on a complete metric space in the presence of summable computational errors. In a recent paper of ours, we extended this result to inexact iterates of nonexpansive mappings on complete metric spaces with graphs under a certain assumption on the iterates. In the present paper we obtain an analogous result by removing that assumption on the iterates and replacing it with an additional assumption on the graph.

Accelerating Polyhedral Discrete Element Method with CUDA

This paper presents an efficient CUDA-based implementation of a nonspherical discrete element method where irregular particles are described by using polyhedrons. Two strategies are employed to exploit the parallelism of the numerical method. One is to perform contact detection based on the contact pair level instead of the traditional particle level. The second is to reduce the computational burden of each kernel function by allocating thread blocks reasonably. Contact detection between potential contact pairs is the most complicated, time-consuming, and essential process for the polyhedral discrete element method. The linear bounding volume hierarchies are introduced to fix this issue. The hierarchies of the bounding volume tree are organized in a spatially coherent way. Such a structure can minimize branch divergence and is very suitable for parallel implementation with GPU. Two numerical examples are presented to show the performance of the code. It is found from the scenario of two sphere collision that improving the mesh resolution of polyhedral particles can reduce the computational error while slowing down the computational speed correspondingly. A trade-off must be made between accuracy and efficiency. The other example of self-gravitating aggregation demonstrates the code is convergent, stable, and highly efficient. Particularly, with a mainstream GPU, the proposed method easily performs hundreds of times faster than the serial CPU code that does the same function.

Hybrid approaches based on Singular Spectrum Analysis and [formula omitted]- Nearest Neighbors for clearness index forecasting

With the increase in solar energy penetration in electric power systems, it is necessary to predict future solar radiation. With this, the solar power generation capacity can be predicted, allowing accurate scheduling for other sources. The solar radiation or the clearness index (CI) prediction was already presented using artificial intelligence, hybrid algorithms, among other approaches. In this paper, two hybrid approaches for clearness index forecasting are proposed. The first one combines batch singular spectral analysis and k-nearest neighbors (k-NN), and is called SSA-B + k-NN, whereas the second associates recursive singular spectral analysis and k-NN, and is named SSA-R + k-NN. The first one performs the SSA-B algorithm for the time series decomposition using a more usual approach, in which the eigenvalues and eigenvectors are calculated in batch. The second one performs the SSA-R algorithm for the time series decomposition, in which the eigenvalues and eigenvectors are updated recursively . The computational costs and mean square errors (MSE) were compared. The results were also compared to the ones obtained with other methods based on k-NN published in the literature. The results illustrate that the hybrid approaches proposed in this paper obtained a lower MSE compared to the results previously presented.

Positioning system design of closed-loop magnetically driven laser steering manipulator for endoscopic microsurgery

This study presents a closed-loop magnetically driven laser steering manipulator positioning system for endoscopic microsurgery. A multimagnetic field strength sensor circuit is embedded in a 16−mm diameter analog laser steering manipulator. The magnetic field distribution of a cylindrical permanent magnet in three-dimensional space is first modeled using an integral model to overcome the large error induced by the magnetic dipole model when the sensor and permanent magnet are close. The integral in the model is then decomposed using the Gauss–Legendre quadrature to improve the computational efficiency of the formulation. Moreover, five commonly used global search optimization methods are compared. Then, the algorithm with the fastest computational rate among these five algorithms, the tree-seed algorithm, is fused with the Levenberg–Marquardt algorithm, which performs well in local search, to obtain a hybrid optimization algorithm. Finally, it is demonstrated through static and dynamic experiments that the system based on the hybrid algorithm can obtain satisfactory computational errors while maintaining a high computational rate.

Exploiting Deep Learning Techniques for the Verification of Handwritten Signatures

Biometric featuresare common measures of identity verification where signaturesarethe most used type. The digital technology has given birth to new ways of biometric identification, such as fingerprints, iris and face recognition,while dealing with handwritten signatures is still a challenging task, because handwritten signatures are more prone to forgery than other means of verification due to issues like computer error, insufficient datasets, and loss of information. This work aims to develop a system that takes a signature image as its input and determines whether the signature is genuine written by its author or forged by another individual. The system is based on a neural network algorithm called Convolutional Siamese Neural Networks, which is used for deep learning and computer vision as well as other machine learning tasks such as natural language processing and digital signal processing.A Contrastive Loss function which compares the Euclidean distance of the output feature vectors is used, and a writer-independent model is used for training and image classification. This work’s objective is toenhance the precision of signature verification and take it as a base for future work on signature verification and use it in user identification, fraud detection and prevention, and forensic investigation applications. The system can be applied in banking, government and private organizations, and forensic investigation for identity and document verification, impersonation and fraud detection and prevention, crime and judicial investigation, and passport verification

Resultant Normal Contact Force-Based Contact Friction Model for the Combined Finite-Discrete Element Method and Its Validation

In the conventional FDEM (Combined Finite and Discrete Element Method), each contact pair might have multiple contact points where friction forces are applied, leading to non-unique friction force assignments and potentially introducing computational errors. This study introduces a new contact friction algorithm for FDEM based on the resultant normal contact force. This method necessitates determining the friction force at a unique equivalent contact point, thereby significantly simplifying the computational flow and reducing memory usage. A series of numerical tests are performed to validate the effectiveness of the proposed contact model. Using collision and block sliding tests, the proposed contact friction model is verified to be able to accurately capture the frictional effect between discrete bodies and circumvent the problematic kinetic energy dissipation issue associated with the original contact friction algorithm. For the Brazilian splitting and uniaxial compression tests, the simulated results closely align with those generated using the original contact friction algorithm and match the experimental measurements well, demonstrating the applicability of the proposed algorithm in fracturing analysis. Furthermore, by using the proposed contact friction algorithm, a computational efficiency enhancement of 8% in contact force evaluation can be achieved.

Evaluation on technical status of concrete cable-stayed bridge based on improved FAHP

Because of the large number of components and complex evaluation indexes of long-span bridges, it is necessary to adopt the evaluation method suitable for complex structures. Since the hypothetical membership degree of fuzzy theory and the layer weight of traditional analytic hierarchy process (AHP) may have subjective bias, the evaluation precision may be influenced if it is applied independently in bridge evaluation and thus the fuzzy analytic hierarchy process (FAHP) is more applicable to large-span concrete cable-stayed bridge. The traditional analytic hierarchy process using triangular fuzzy number (FAHP) has the shortcomings of computational errors and limited range, so the improved FAHP is adopted. The improved FAHP method introduces the reliability into the judgment matrix, which can not only solve the existing problems, but also reflect the influence of the fuzziness of the man-made subjective judgment on the result. Based on the detection results for a concrete cable-stayed bridge in Jilin Province, the corresponding hierarchy of index system is established, the trapezoidal function is used to calculate membership degree, and the weight of each index relative to target layer is calculated. Improved FAHP is finally applied to assess the security levels of various parts of this bridge and make comprehensive evaluation on the whole bridge.

3-D Millimeter Wave Fast Imaging Technique Based on 2-D SISO/MIMO Array

In this article, a novel three-dimensional (3-D) imaging method based on the range decomposing algorithm (RDA) is proposed for millimeter wave imaging. We combined it with binomial theory and we derive the theoretical formulation of RDA applied to single-input–single-output (SISO)/multiple-input–multiple-output (MIMO) array; meanwhile, its computational complexity and computational error are analyzed. Compared to the classical Fourier algorithm, such as the range migration algorithm (RMA) and the phase shift migration (PSM), the proposed algorithm can replace the time-consuming interpolation and accumulation operations with reasonable approximations and transformations offering a more efficient approach, while maintaining the image quality. In addition, a method based on RDA which is applicable to the transformation between MIMO and SISO, is proposed to further enhance the processing efficiency. Proof-of-principle simulation using echo data collected from a large number of antennas, verifies that the proposed algorithm has higher efficiency. In order to better verify the feasibility of the proposed algorithm, a scanning prototype located in the millimeter wave band is designed. The experimental results of different targets demonstrate that the proposed algorithm achieves significantly higher reconstruction efficiency when compared to the traditional algorithms.

Attitude measurement of permanent magnet spherical motors based on adaptive mahony complementary filtering

An adaptive attitude measurement algorithm called adaptive mahony complementary filter(AMCF) is proposed to address the issues of drift and noise in gyroscope measurements, as well as the high computational complexity, error accumulation, and sensitivity to noise in the quaternion extended kalman filter(QEKF) within the permanent magnet spherical motor(PMSM) inertial measurement unit. Firstly, this method corrects the gyroscope’s angular velocity bias by utilizing the error between theoretical and actual accelerations. Subsequently, the covariance is adjusted by comparing dynamic accelerations to mitigate disturbances. The fourth-order Runge-Kutta method is employed to continuously update the quaternion, thereby achieving higher accuracy in attitude measurement. Finally, static and dynamic experimental investigations are conducted on the PMSM. The experimental results demonstrate that the AMCF offers faster computation speed compared to the QEKF and higher accuracy than the fast complementary filtering(FCF). This indicates that utilizing the AMCF enables better real-time attitude measurement for three-degree-of-freedom mechanical structures.

Multi-Slot Over-the-Air Computation in Fading Channels

IoT systems typically involve separate data collection and processing, and face the scalability issue when the number of nodes increases. For some tasks, only the result of data fusion is needed. Then, the whole process can be realized in an efficient way, integrating the data collection and fusion in one step by over-the-air computation (AirComp). Its shortcoming, however, is signal distortion when channel gains of nodes are different, which cannot be well solved by transmission power control alone in times of deep fading. To address this issue, in this paper, we propose a multi-slot over-the-air computation (MS-AirComp) framework for the sum estimation in fading channels. Compared with conventional data collection (one slot for each node) and AirComp (one slot for all nodes), MS-AirComp is an alternative policy that lies between them, exploiting multiple slots to improve channel gains so as to facilitate power control. Avoiding to obtain instantaneous channel gains of all nodes at the sink is a key point. Specifically, the transmissions are distributed over multiple slots and a threshold of channel gain is set for distributed transmission scheduling. Each node transmits its signal only once, in the slot when its channel gain first gets above the threshold, or in the last slot when its channel gain remains below the threshold. Theoretical analysis gives the closed-form of the computation error in fading channels, based on which the optimal parameters are found. Noticing that computation error tends to be reduced at the cost of more transmission power, a method is suggested to control the increase of transmission power. Simulations confirm that the proposed method can effectively reduce computation error, compared with state-of-the-art methods.

An Energy-Efficient Bayesian Neural Network Accelerator With CiM and a Time-Interleaved Hadamard Digital GRNG Using 22-nm FinFET

Bayesian neural networks (BNNs) have been proposed to address the problems of overfitting and overconfident decision making, common in conventional neural networks (NNs), due to their ability to model and express uncertainty in their predictions. However, BNNs require multiple inference passes to produce the necessary posterior distributions used to generate these highly desirable uncertainty estimates. As such, BNNs require not only an efficient, high-performance multiply-accumulation (MAC) operation but also an efficient Gaussian random number generator (GRNG) with high-quality statistics. In this article, an NN accelerator chip, leveraging a multi-bit analog compute-in-memory (CiM) static random-access memory (SRAM) macro, with a tightly coupled and highly efficient GRNG scheme, is presented in the Intel 22FFL process. The CiM macro achieves a peak energy efficiency of 32.2 TOP/sW, with 8-bit precision, while ensuring accurate on-chip matrix-vector multiplications (MVMs) with a computation error less than 0.5%. The variable precision GRNG achieves a peak throughput of 7.31 GSamp/s for an energy efficiency of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim$</tex-math> </inline-formula> 1 TSamp/J. Overall, our proposed system achieves a peak energy efficiency of 1170 GOP/s/W, a 35–133 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula> improvement over the state-of-the-art BNN accelerators, with 98.14% accuracy for the MNIST dataset.

Numerical Study of Indoor Oil Mist Particle Concentration Distribution in an Industrial Factory Using the Eulerian–Eulerian and Eulerian–Lagrangian Methods

The transport and prediction of the concentration of particles in confined spaces are crucial for human well-being; this has become particularly evident during the current worldwide pandemic. Computational fluid dynamics (CFD) has been widely used for such predictions, relying on Eulerian–Eulerian (EE) and Eulerian–Lagrangian (EL) models to study particle flow. However, there is a lack of research on industrial factories. In this study, a scaled laboratory in an industrial factory was established for oil mist particles in a machining factory, and oil mist dispersion experiments were conducted under roof exhaust and mixed ventilation conditions. After that, the oil mist concentration distribution in the factory under the same working conditions was calculated by Eulerian and Lagrangian methods, and the corresponding calculation errors and resource consumption were compared. It was found that the simulation results of both methods are acceptable for mixed ventilation and roof exhaust ventilation systems. When there are more vortices in the factory, the Lagrangian method increases the computation time by more than 53% to satisfy the computational accuracy, and the computational error between the Eulerian and Lagrangian methods becomes about 10% larger. For oil mist particles with an aerodynamic diameter of 0.5 μm, both Eulerian and Lagrangian methods have reliable accuracy. Based on the same flow field, the Lagrangian method consumes more than 400 times more computational resources than the Eulerian method. This study can provide a reference for the simulation of indoor particulate transport in industrial factories.