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Encapsulation of the fine powder of ammonium molybdophosphate (AMP) was carried out to produce AMP-Ca-alginate composite beads for removal of Cs+, U6+, Co2+ and Sr2+ ions from multicomponent media using a fixed-bed column. The results denote that the initial concentration (50, 100 and 200 mg/L from each ion), bed length (3, 6 and 8 cm) and flow rates (0.5, 1.5 and 2 mL/min) affect the sorption operation. The column performance was 40, 37.5, 32.34 and 31.7% for Cs+, U6+, Co2+ and Sr2+, respectively. Thomas and Yoon-Nelson models were utilised to forecast the breakthrough curves for adsorption. The two models are found as well-fitted models for investigated ions adsorption system except for the adsorption of Cs+ is more fitted for the Thomas model at a high flow rate. Marquardt's percent standard deviation error function was used and confirmed these results. Good separation of strontium and caesium with a purity of 100% from this multi-component solution is accomplished by elution using 4 M of NaNO3 and HNO3 solution. The desorption percent of the loaded ions was 98, 91, 76 and 37.5% for Cs+, Sr2+, U6+ and Co2+, respectively. Overall, AMP-Ca-alginate composite beads are an environmentally friendly potential sorbent for hazardous ions from multicomponent media. [ABSTRACT FROM AUTHOR]

In this article, we propose a Poisson-Lindley distribution as a stochastic abundance model in which the sample is according to the independent Poisson process. Jeffery's and Bernardo's reference priors have been obtaining and proposed the Bayes estimators of the number of species for this model. The proposed Bayes estimators have been compared with the corresponding profile and conditional maximum likelihood estimators for their square root of the risks under squared error loss function (SELF). Jeffery's and Bernardo's reference priors have been considered and compared with the Bayesian approach based on biological data. [ABSTRACT FROM AUTHOR]

Unblinded interim analyses in clinical trials with adaptive designs are gaining increasing popularity. Here, the type I error rate is controlled by defining an appropriate conditional error function. Since various approaches to the selection of the conditional error function exist, the question of an optimal choice arises. In this article, we extend existing work on optimal conditional error functions by two results. Firstly, we prove that techniques from variational calculus can be applied to derive existing optimal conditional error functions. Secondly, we answer the question of optimizing the conditional error function of an optimal promising zone design and investigate the efficiency gain. [ABSTRACT FROM AUTHOR]

This paper proposes a nonlinear optimization method for designing a high-order recursive allpass digital phase system that comprises several cascade-connected second-order (SO) allpass sections. This method first splits a given phase design specification (approximation target) into a set of equal sub-specifications, and then the equal sub-specification acts as the ideal phase for each of the SO sections. Since an SO section can be designed via employing a linear programming to minimize a linear fractional error function, this splitting process generates an excellent starting point (good initial values for the coefficients of the cascaded SO sections) for further minimizing the overall approximation error. This paper first derives a wide variety of fractional polynomial error functions for designing cascade-connected allpass phase systems of different high orders, and then shows that a high-order cascade-connected allpass phase system can be designed by utilizing a nonlinear solver to minimize the peak deviation of such a fractional polynomial error. Using the derived fractional polynomial error functions in the system design enables the system designer to find an excellent starting point for further minimizing the approximation error and thus reach a convergent design solution. This paper first derives a set of fractional polynomial errors, and then adopts the eighth-order cascade-connected phase system design to exemplify the effectiveness of the fractional-polynomial-error-based design tactic. Furthermore, the stability of the cascade-connected high-order allpass system can be readily checked via confirming that all of the cascaded SO sections have their poles inside the unit circle in the complex plane. [ABSTRACT FROM AUTHOR]

In this paper, an intelligence approach based on radial basis function neural networks (RBFNNs) is used for solving fuzzy optimal control problems, utilizing the generalized Hukuhara derivatives. At the first step, we consider the fuzzy Euler–Lagrange conditions for both fuzzy unconstrained and constrained variational problems and Pontryagin maximum principle (PMP) for fuzzy optimal control problems, both of them depending on the generalized Hukuhara derivatives. The necessary optimality conditions for these problems are examined in the form of two-point boundary value problems (TPBVPs). A fuzzy neural network approach that utilizes of radial basis functions (RBFs) as its activation functions for one of the hidden layers is described to approximate the solution of the related TPBVP. This neural network uses the center points of RBFs as the training dataset, and the Levenberg–Marquardt algorithm is selected as the optimizer. By relying on the ability of RBFNN as function approximator, the fuzzy solutions of variables (state, co-state and control) are substituted in the associated TPBVP. The obtained algebraic nonlinear equations system is then converted into an error function minimization problem. A learning scheme based on the Levenberg–Marquardt algorithm is employed as the optimizer to derive the adjustable parameters of fuzzy solutions. In order to clarify the effectiveness of the studied RBFNN, some numerical results are supplied. [ABSTRACT FROM AUTHOR]

ABSTRACT This article investigates the distributed adaptive multi‐lane fusion control for two‐dimensional (2‐D) plane vehicle platoons with variable distance constraints, input hysteresis, and angle sensor faults. Variable distance constraints occur within a limited time interval (VDCOLT), which limits vehicle spacing within a variable range during preset time intervals while keeping the vehicle spacing unconstrained at other times. Combined with a transformed error function, a new shifting function is introduced to convert the constrained spacing error variables into the unconstrained variables while keeping the unconstrained variable unchanged. Designing the position controller ensures that the distance satisfies VDCOLT and reduces the adverse effects caused by unknown signs of input hysteresis by using a Nussbaum function. Moreover, a new angle controller based on the hyperbolic tangent function is designed to solve the problem of angle sensor faults. Furthermore, the stability of the vehicle platoon is achieved through the backstepping control and sliding‐mode control methods. Finally, a numerical simulation is provided to verify the proposed techniques. [ABSTRACT FROM AUTHOR]

Electrohydrodynamic (EHD) printing is an additive manufacturing technique capable of microscale and nanoscale structures for biomedical, aerospace, and electronic applications. To realize stable printing at its full resolution, the monitoring of jetting behavior while printing and optimization of the printing process are necessary. Various machine vision control schemes have been developed for EHD printing. However, in-line machine vision systems are currently limited because only limited information can be captured in situ toward quality assurance and process optimization. In this article, we presented a machine learning-embedded machine vision control scheme that is able to characterize jetting and recognize the printing quality by using only low-resolution observations of the Taylor Cone. An innovative approach was introduced to identify and measure cone-jet behavior using low-fidelity image data at various applied voltage levels, stand-off distances, and printing speeds. The scaling law between voltages and the line widths enables quality prediction of final printed patterns. A voting ensemble composed of k-nearest neighbor (KNN), classification and regression tree (CART), random forest, logistic regression, gradient boost classifier, and bagging models was employed with optimized hyperparameters to classify the jets to their corresponding applied voltages, achieving an 88.43% accuracy on new experimental data. These findings demonstrate that it is possible to analyze jetting status and predict high-resolution pattern dimensions by using low-fidelity data. The voltage analysis based on the in situ data will provide additional insights for system stability, and it can be used to establish the error functions for future advanced control schemes. [ABSTRACT FROM AUTHOR]

Dynamic LR and QR factorization are fundamental problems that exist widely in the control field. However, the existing solutions under noises are lack of convergence speed and anti-noise ability. To this end, this paper incorporates the advantages of Dynamic-Coefficient Type (DCT) and Integration-Enhance Type (IET) Zeroing Neural Dynamic (ZND), and proposes an Adaptive and Robust-Enhanced Neural Dynamic (AREND). On this basis, a Strategy of Integration-Coupling (SIC) is proposed to address multiple error function problems, improving model stability and application scenarios. This strategy is experimentally proven to be effective and has potential expansion capability. After that, the convergence and robustness of our AREND is theoretically analyzed. Furthermore, the proposed AREND is verified by numerical experiments of low-to-high dimensional factorization in comparison with existing solutions. Finally, the real-time 3-D Angle of Arrival (AoA) localization in multiple high-noise conditions, is validated to the accuracy of the proposed model. Code is available at https://github.com/Alana2a3/AREND-Code-Implementation. [ABSTRACT FROM AUTHOR]

Synchronization plays a pivotal role in understanding various natural events. Understanding this concept with reference to a biologically inspired dynamical model of a neuron is also essential. It is basically a rhythm adjustment phenomenon and a consequence of the coupling between the individual units. In the present work, we aim to derive sufficient conditions for the synchronization of coupled Fitzhugh Nagumo Dynamics using Lyapunov stability analysis. In particular, a non-smooth Lyapunov function based upon the geodesic distance between respective states of coupled systems has been chosen as the Lyapunov function, and the concept of upper Dini-derivative has been utilized to calculate the derivative of the Lyapunov function along the error dynamics. The negative definiteness of the derivative of the Lyapunov function gives sufficient coupling gain for synchronization. The findings are verified on the Matlab simulation platform. The results should help to enhance the knowledge of neural dynamics. [ABSTRACT FROM AUTHOR]

Wastewater treatment is of utmost importance in providing all equitable and safe drinking water. In the present study, a chitosan impregnated sugarcane bagasse biochar SCNC biocomposite has been synthesized for the removal of Congo red (CR) dye from an aqueous solution. The SCNC biocomposite was thoroughly characterized through Brunauer, Emmett and Teller (BET) and N2 adsorption isotherm, point of zero charge (pHPZC), elemental analysis, Scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR) and Thermogravimetric analysis (TGA) analysis. Moreover, SCNC biocomposite was further employed to remove CR dye from the aqueous solution in batch mode. The SCNC biocomposite could remove more than 95.0% of CR at an initial concentration of (100mgL− 1), adsorbent dosage (0.05 g), time (200 min), pH ~ 3. The SCNC biocomposite achieved maximum adsorption capacity of 170mgg− 1. The equilibrium adsorption data for CR dye were best fitted to the Langmuir isotherm model with R2, 0.999. The kinetic and isotherm were statistically investigated using the chi-square statistic (χ2), mean square error (MSE), and the sum of squares error (SSE) Because of the higher correlation coefficient (R2 ≥ 0.999) and lower error functions, the equilibrium CR adsorption isotherms for a single-dye system fit Langmuir and the PSO kinetic model. The thermodynamic studies revealed the spontaneous and endothermic nature of adsorption of CR dye onto SCNC biocomposite. The SCNC biocomposite can be regenerated up to the 5th cycle successfully. The mechanism of CR adsorption onto SCNC was elucidated. [ABSTRACT FROM AUTHOR]

ABSTRACT In order to improve the penetration ability of missiles in the end guidance stage, and considering the delay problem when designing the guidance control loop separately, this article mainly studies the design problem of an integrated guidance control law under input saturation and attitude angle constraints. For the lower triangular structure model of the integrated guidance and control system, this article mainly uses an improved backstepping method to design the controller, and introduces an error compensation term in the design of the virtual controller to improve system stability. Introducing auxiliary variables and barrier Lyapunov functions to handle saturation and state constraint problems; in the face of the main problems of atmospheric disturbances, unmodeled dynamic errors of the system, and unknown acceleration of the target, this article mainly adopts a finite time observer for processing. The final simulation results demonstrate the effectiveness and superiority of the controller designed in this article. [ABSTRACT FROM AUTHOR]

In this paper, we propose an improved adaptive frequency sweep strategy based on the asymptotic waveform evaluation (AWE) technique for simulating broadband antennas across a wide frequency range. Our approach maintains high accuracy compared to traditional frequency sweep methods, as demonstrated through simulation results of several commonly used broadband antennas. A novel error function is introduced specifically designed for broadband antenna simulation, which effectively improves the adaptive frequency sweep process. By analyzing the relationship between target error and computational time, we determine the optimal balance zone between efficiency and accuracy. Our findings provide valuable insights for efficient and accurate simulation of broadband antennas. [ABSTRACT FROM AUTHOR]

Objective. Pulse pressure waves contain information about human physiology. There is a need for a simple, accurate way to know cardiovascular health in the clinic, so as to realize the implementation of convenient and effective early health monitoring for patients with arteriosclerosis. Approach. This study proposes an arteriosclerosis assessment method based on fitting a lognormal function, along with improving a conventional electronic sphygmomanometer. During the deflation phase of blood pressure measurement, the cuff pressure was kept constant (40 mmHg) and an additional 10 s of pulse signal was acquired. To derive the pulse pressure waveforms for a single cycle, the acquired pulse data of 101 cases were preprocessed in this study, including filtering for noise removal, onset point identification, removal of baseline drift, and normalization. In this study, an improved pulse resolution algorithm is proposed for the multimodal problem of the pulse wave, combining waveform matching and threshold setting, and finally obtaining the resolution parameters of the lognormal function with an average error less than 1.5%. Main results. According to the correlation analysis, the resolved parameters A 1, W 2, C 2, W 3, and C 3 were significantly correlated with brachial-ankle Pulse Wave Velocity, and the absolute correlation range in 0.17–0.53, which can be used as a reference index for arteriosclerosis. An arteriosclerosis assessment model was constructed based on the support vector mechanism, and the prediction accuracy was 91.1%. Significance. This study provides a new solution idea for the arteriosclerosis assessment method as well as the pulse resolution algorithm, which has a greater reference value. [ABSTRACT FROM AUTHOR]

In this study, statistical inference for competing risks model with latent failure times following the Kumaraswamy‐G (Kw‐G) family of distributions under a unified progressive hybrid censoring (UPHC) scheme is developed. Maximum likelihood estimates (MLEs) of the unknown model parameters are obtained, and their existence and uniqueness properties are discussed. Using the asymptotic properties of MLEs, the approximate confidence intervals for the model parameters are constructed. Further, Bayes estimates with associated highest posterior density credible intervals for the model parameters are developed under squared error loss function with informative and noninformative priors. These estimates are obtained under both restricted and nonrestricted parameter spaces. Moreover, frequentist and Bayesian approaches are developed to test the equality of shape parameters of the two competing failure causes. The comparison of censoring schemes based on different criteria is also discussed. Monte Carlo simulation studies are used to evaluate the performance of the proposed statistical inference procedures. An electrical appliances data set is analyzed to illustrate the applicability of the proposed methodologies. [ABSTRACT FROM AUTHOR]

Under "dual-carbon" goals and rapid renewable energy growth, increasing start-stop frequency poses new challenges to safe operations of pumped-storage power plant equipment. Ensuring equipment safety and predictive maintenance under complex conditions urgently requires vibration warnings and trend forecasting for pumped-storage units. In this study, the measured vibration-signal characteristics of pumped-storage units in a strong background-noise environment are obtained using a noise-reduction method that integrates BA-VMD and wavelet thresholding. We monitored the vibration-signal data of hydroelectric units over a long period of time, and the measured vibration-signal characteristics of pumped-storage units in a strong background-noise environment are accurately obtained using a noise-reduction method that integrates BA-VMD and wavelet thresholding. In this paper, a BP neural network prediction model, a support vector machine (SVM) prediction model, a convolutional neural network (CNN) prediction model, and a long short-term memory network (LSTM) prediction model are used to predict the trend of vibration signals of the pumped-storage unit under different operating conditions. The model prediction effect is analyzed by using the different error evaluation functions, and the prediction results are compared with the predicted results of the four different methods. By comparing the prediction effects of the four different methods, it is concluded that LSTM has higher prediction accuracy and can predict the vibration trends of hydropower units more accurately. [ABSTRACT FROM AUTHOR]

High-precision tracking control is very important in high-speed train (HST) operation. This study proposes an adaptive global terminal sliding mode control scheme based on limited error (AEG-SMC) for trajectory tracking of HST. AEG-SMC is firstly proposed for the nonlinear dynamic system to improve the accuracy of tracking error and solve the problem of parameter uncertainty in the model. Then, AEG-SMC uses an adaptive method to approximate the uncertain parameters in the model to obtain real-time parameter estimation, and an error index function is given to realise fast and high-precision tracking of the system by global terminal sliding mode control (GSMC). AEG-SMC is able to design the required error indicators before conducting control, thereby ensuring the high-quality response and stability of the system. Finally, the simulation results show that the speed tracking error and control input of HST with AEG-SMC are also the smallest among the mentioned methods. [ABSTRACT FROM AUTHOR]

Over the past decades, surface wave methods have been routinely employed to retrieve the physical characteristics of the first tens of meters of the subsurface, particularly the shear wave velocity profiles. Traditional methods rely on the application of the multichannel analysis of surface waves to invert the fundamental and higher modes of Rayleigh waves. However, the limitations affecting this approach, such as the 1D model assumption and the high degree of subjectivity when extracting the dispersion curve, motivate us to apply the elastic full‐waveform inversion, which, despite its higher computational cost, enables leveraging the complete information embedded in the recorded seismograms. Standard approaches solve the full‐waveform inversion using gradient‐based algorithms minimizing an error function, commonly measuring the misfit between observed and predicted waveforms. However, these deterministic approaches lack proper uncertainty quantification and are susceptible to get trapped in some local minima of the error function. An alternative lies in a probabilistic framework, but, in this case, we need to deal with the huge computational effort characterizing the Bayesian approach when applied to non‐linear problems associated with expensive forward modelling and large model spaces. In this work, we present a gradient‐based Markov chain Monte Carlo full‐waveform inversion where we accelerate the sampling of the posterior distribution by compressing data and model spaces through the discrete cosine transform. Additionally, a proposal is defined as a local, Gaussian approximation of the target density, constructed using the local Hessian and gradient information of the log posterior. We first validate our method through a synthetic test where the velocity model features lateral and vertical velocity variations. Then we invert a real dataset from the InterPACIFIC project. The obtained results prove the efficiency of our proposed algorithm, which demonstrates to be robust against cycle‐skipping issues and able to provide reasonable uncertainty evaluations with an affordable computational cost. [ABSTRACT FROM AUTHOR]

As an essential tool for processing fuzzy or chaotic information, the main feature of the first-order Takagi–Sugeno (T–S) neuro-fuzzy model is utilizing a set of IF-THEN fuzzy rules to represent non-linear systems, showcasing commendable non-linear approximation ability and significant interpretability. However, the coexistence of linear rules and the affiliation function of fuzzy sets makes the integer-order gradient descent method (IOGDM), commonly used in training the first-order T–S neuro-fuzzy model, fail to accurately capture the intricate relationships among weights, resulting in the error function struggling to converge rapidly to low values. To enhance the convergence speed and training accuracy of the first-order T–S neuro-fuzzy model during the training process, a fractional-order gradient descent method (FOGDM) is proposed to update the fuzzy rule parameters and neural network weights of the model in this paper. By subdividing the gradient into fractional orders, FOGDM exhibits heightened flexibility in gradient adjustments, thus better capturing the complex non-linear relationships among parameters during the optimization process. The weak and strong convergence of the proposed approach is meticulously demonstrated in this paper, ensuring that the weight of error functions converges to a constant value and that the gradient of the error functions tends toward zero, respectively. Simulation results analysis indicates that, compared to IOGDM, FOGDM exhibits faster convergence speed and more significant generalization capabilities. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel approach to enhance the accuracy and convergence behavior of Self-Organizing Maps (SOM) by incorporating a reweighted zero-attracting term into the loss function. We evaluated two SOM versions: conventional SOM and robust adaptive SOM (RASOM). The enhanced versions, reweighted zero-attracting SOM (RZA-SOM) and reweighted zero-attracting RASOM (RZA-RASOM), include an l 1 norm in the error function to add a zero-attractor term, which improves weight coefficient adjustments while preserving topology. The models were assessed for convergence speed and misadjustment under sparsity assumptions of the true coefficient matrix, and their robustness was tested under conditions of increased non-zero taps. Using six different datasets, we compared the performance of RZA-SOM and RZA-RASOM against conventional SOM and RA-SOM in terms of accuracy, quantization error, and topology preservation. Experimental results consistently demonstrated that RZA-SOM and RZA-RASOM surpassed the performance of conventional SOM and RA-SOM. • Introduction of novel reweighted zero-attractor term in loss function for heightened SOM algorithmic precision. • Heightened convergence rates and improved behavior, marked by earlier error steady-state attainment during training. • Enhanced robustness against outliers and superior handling of imbalanced data in multiclass clustering scenarios. • Rigorous experimental evaluations across six distinct datasets effectively underpin proposed algorithmic enhancements. [ABSTRACT FROM AUTHOR]

In this work, we introduce an alternative model for the design and analysis of strategyproof mechanisms that is motivated by the recent surge of work in "learning-augmented algorithms." Aiming to complement the traditional worst-case analysis approach in computer science, this line of work has focused on the design and analysis of algorithms that are enhanced with machine-learned predictions. The algorithms can use the predictions as a guide to inform their decisions, aiming to achieve much stronger performance guarantees when these predictions are accurate (consistency), while also maintaining near-optimal worst-case guarantees, even if these predictions are inaccurate (robustness). We initiate the design and analysis of strategyproof mechanisms that are augmented with predictions regarding the private information of the participating agents. To exhibit the important benefits of this approach, we revisit the canonical problem of facility location with strategic agents in the two-dimensional Euclidean space. We study both the egalitarian and utilitarian social cost functions, and we propose new strategyproof mechanisms that leverage predictions to guarantee an optimal trade-off between consistency and robustness. Furthermore, we also prove parameterized approximation results as a function of the prediction error, showing that our mechanisms perform well, even when the predictions are not fully accurate. Funding: The work of E. Balkanski was supported in part by the National Science Foundation [Grants CCF-2210501 and IIS-2147361]. The work of V. Gkatzelis and X. Tan was supported in part by the National Science Foundation [Grant CCF-2210502] and [CAREER Award CCF-2047907]. [ABSTRACT FROM AUTHOR]

Association rule mining is a highly effective approach to data analysis for datasets of varying sizes, accommodating diverse feature values. Nevertheless, deriving practical rules from datasets with numerical variables presents a challenge, as these variables must be discretized beforehand. Quantitative association rule mining addresses this issue, allowing the extraction of valuable rules. This paper introduces an extension to quantitative association rules, incorporating a two-variable function in their consequent part. The use of correlation functions, statistical test functions, and error functions is also introduced. We illustrate the utility of this extension through three case studies employing software engineering datasets. In case study 1, we successfully pinpointed the conditions that result in either a high or low correlation between effort and software size, offering valuable insights for software project managers. In case study 2, we effectively identified the conditions that lead to a high or low correlation between the number of bugs and source lines of code, aiding in the formulation of software test planning strategies. In case study 3, we applied our approach to the two-step software effort estimation process, uncovering the conditions most likely to yield low effort estimation errors. [ABSTRACT FROM AUTHOR]

We develop a framework for measuring under- and overreaction in expectation formation. The basic insight is that under- and overreaction to new information is identified (up to sign) by the impulse response function of forecast errors. Our measurement procedure yields estimates of under- and overreaction to different shocks at various horizons. In an application to inflation expectations, we find that forecasters underreact to aggregate shocks but overreact to idiosyncratic shocks. We illustrate how our approach can be used to (i) quantify the importance of different biases, (ii) estimate theoretical models, and (iii) shed light on existing empirical approaches and puzzles. [ABSTRACT FROM AUTHOR]

To achieve the broadband applicability of standard voltage transformers in "dual high" power systems, an equivalent circuit model of the standard voltage transformer is first established. Using the complex magnetic permeability method and utilizing existing core parameters, the excitation impedance values are obtained. Next, based on the equivalent circuit model, the no-load error function of the standard voltage transformer is analyzed, and through simulation, the no-load error response curve of the standard voltage transformer in the frequency range of 20 Hz to 3000 Hz is derived. The simulation results indicate that within the 20 Hz to 700 Hz range, both the no-load ratio error and the no-load angular error meet the accuracy requirements, with the ratio error within ±0.05% and the angular error within 2′. Additionally, the derivation of the error transfer function demonstrates the correlation between the no-load error values and the number of turns and cross-sectional area of the standard voltage transformer. Simulation results, obtained by increasing and decreasing the number of turns and cross-sectional area by 10%, provide valuable insights for the error compensation and structural design of standard voltage transformers. [ABSTRACT FROM AUTHOR]

This paper explores an application of the sigmoidal function—the complementary integral Gaussian error function (erfc(.))—in two-dimensional (2D) uniform and nonuniform filter bank synthesis. The complementary integral Gaussian error function graph represents a smooth low-pass filter magnitude response. A parameter changes the function slope and increases the magnitude response selectivity. The theory is applied to 2D band-pass filter banks. Exact expressions for the magnitude response parameters are determined. As a result, 2D uniform and nonuniform filter banks with very high selectivity and exact shapes are obtained. Three synthesis examples of 2D filter banks with circular and fan-shaped magnitude responses are provided. The theoretical exposition is supplemented with two examples of image analysis using 2D uniform and nonuniform filter banks. A procedure to reduce the computations in image analysis is proposed. A comparison of filter synthesis between Parks–McLellan's 2D filters and the erfc(.) demonstrates the significantly shorter calculation time of the proposed method. [ABSTRACT FROM AUTHOR]

In order to improve the damage prediction effect of concrete structural column and beam structure, this paper uses multimedia technology to improve the damage prediction effect of reinforced concrete structural column and beam structure. Moreover, this paper presents the intelligent transformation model and the corresponding solution of the general damage problem, and deduces the error relationship between the result estimator and the importance function according to the error of the importance function. In addition, by analyzing the relationship between the importance function and the dual transport calculation, this paper proposes a complementary dual calculation process that can provide the importance function to each other, and builds an intelligent prediction model. Through the experimental research, it can be seen that the multimedia technology algorithm proposed in this paper can play an important role in the damage prediction of concrete structural columns and beams. [ABSTRACT FROM AUTHOR]

Structural noise and outliers are widely present in real‐world state estimate scenarios, and they significantly degrade the performance of most filtering algorithms based on minimum mean square error (MMSE) criterion. To address this problem, this paper first models structural noise and outliers as independent and piecewise identical distribution (IPID). Then, a minimum error weighted entropy‐based Kalman filter (MEWE‐KF) is proposed, where a new cost function is constructed by introducing a weight function related to error location distances in an original information space into the minimum error entropy (MEE) criterion. Further, the iterative formulations of the proposed filter are derived, and the computational complexity and the convergence are also analyzed. Simulation results show that the proposed filter with adaptive weights has the superior performance for suppressing structural noise and outliers. [ABSTRACT FROM AUTHOR]

ABSTRACT The Kalman filter provides an optimal estimation for a linear system with Gaussian noise. However, when the noises are non‐Gaussian in nature, its performance deteriorates rapidly. For non‐Gaussian noises, maximum correntropy Kalman filter (MCKF) is developed which provides a more accurate result. In a scenario, where the actual system model differs from nominal consideration, the performance of the MCKF degrades. For such cases, in this article, we have proposed a new robust filtering technique for a linear system which maximizes a cost function defined by exponential of weighted past and present errors weighted with the kernel bandwidth. During filtering, at each time step, the kernel bandwidth is selected by maximizing the correntropy function of error. Further, a convergence condition of the proposed algorithm is derived. Numerical examples are presented to show the usefulness of the proposed filtering technique. [ABSTRACT FROM AUTHOR]

Process capability indices (PCIs), are widely used to gauge how well a process performs within its requirements. While greater PCIs are indicative of improved process “quality,” they do not necessarily translate into lower rejection rates. Therefore, using a loss‐based PCI to gauge process capability makes more sense. In this paper, the PCI Spk′$ S^{\prime }_{pk}$ has been considered for normal random variable. The article attempts to study the classical and the Bayesian estimation of Spk′$ S^{\prime }_{pk}$ for type‐II progressive right censored sample under symmetric as well as asymmetric loss functions, namely squared error loss function, and LINEX loss function, respectively. The Markov chain Monte Carlo simulation technique has been efficiently used here to have the approximate solution for Spk′$S^{\prime }_{pk}$. Through an extensive Monte Carlo simulation study along with two real life examples related to electronic industry, we compare the performances of the classical and the Bayes estimates based on symmetric and asymmetric loss functions and compared among the asymptotic confidence interval and highest posterior density credible intervals, in terms of average width and corresponding coverage probabilities of Spk′$S^{\prime }_{pk}$, respectively. [ABSTRACT FROM AUTHOR]

AbstractThis article proposes an enhanced proportional topology optimization (EPTO) method to solve the structural topology optimization problem of minimizing compliance under material volume constraints. In the proposed method, a new filtering weight function based on the improved Heaviside threshold function is adopted to filter element density during the optimization process. The optimization process of the EPTO method consists of an inner loop and an outer loop. In the inner loop, density distribution is modified in combination with a new filtering weight function. By locally averaging the weighted element compliance, an improved density distribution function in the inner loop is put forward to make the topology configuration of the optimized structure more reasonable. In addition, the projection method is used to reduce the number of intermediate density elements, thereby obtaining optimization results with clear boundaries. In the outer loop, a new termination criterion is adopted, which terminates the optimization process by determining that the relative error of the objective function in several consecutive iterations is less than the specified value. The effectiveness and efficiency of the proposed method are demonstrated through several numerical examples involving two-dimensional (2D) and three-dimensional (3D) topology optimization problems. The results of numerical examples show that the proposed method can not only accelerate the convergence of optimization iterations, but also obtain optimized structures with smaller objective function values and better topology configurations. HIGHLIGHTSA new density filtering weight function is proposed based on an improved Heaviside threshold function.An improved inner loop density distribution formula is proposed by combining a new filtering weight function.Using projection based methods to suppress the appearance of intermediate density elements.Verify the effectiveness of the proposed algorithm by comparing the optimization results with existing algorithms such as top88 and PTO.A new density filtering weight function is proposed based on an improved Heaviside threshold function.An improved inner loop density distribution formula is proposed by combining a new filtering weight function.Using projection based methods to suppress the appearance of intermediate density elements.Verify the effectiveness of the proposed algorithm by comparing the optimization results with existing algorithms such as top88 and PTO. [ABSTRACT FROM AUTHOR]

The paper addresses the construction of an error correction code for quantum computations based on squeezed Fock states. It is shown that the use of squeezed Fock states makes it possible to satisfy the Knill-Laflamme (KL) criteria for bosonic error correction codes. It is shown that the first squeezed Fock state corrects both particle loss and dephasing errors better than higher-order states. A comparison of the proposed code with a code based on the squeezed Schrodinger's cat states is carried out on the basis of the KL cost function. Using this function, we show that the squeezed first Fock state is competitive in protecting information in a channel with particle loss and dephasing. [ABSTRACT FROM AUTHOR]

In recent years, our research on biomechanical and biophysical problems has involved a series of symmetry issues. We found that the fundamental laws of the aforementioned problems can all be characterized by fractal operators, and each type of operator possesses rich invariant properties. Based on the invariant properties of fractal operators, we discovered that the symmetry evolution laws of functional fractal trees in the physical fractal space can reveal the intrinsic correlations between special functions. This article explores the fractional-order correlation between special functions inspired by bone fractal operators. Specifically, the following contents are included: (1) showing the intrinsic expression in the convolutional kernel function of bone fractal operators and its correlation with special functions; (2) proving the following proposition: the convolutional kernel function of bone fractal operators is still related to the special functions under different input signals (external load, external stimulus); (3) using the bone fractal operators as the background and error function as the core, deriving the fractional-order correlation between different special functions. [ABSTRACT FROM AUTHOR]

Twist error exists when continuously generating grinding helical gears with lead modification, which leads to problems such as meshing impact and low load bearing. To improve the meshing performance of helical gears with twist error, a multi-objective optimization design method is proposed. Firstly, the mathematical equation of helical gear tooth surface with twist error is established. With helix angle and the modified amount as design variables, the maximum contact stress and amplitude of loaded transmission error as objective functions, the loaded tooth contact analysis (LTCA) was carried out by finite element method (FEM) and 25 sets of data were obtained. Then the function model was constructed by the BP neural network, and a fast elitist nondominated sorting genetic algorithm (NSGA-II) is used to solve the model. The results show that the maximum contact stress and amplitude of loaded transmission error after optimization are reduced by 29.6 % and 92.2 % respectively. [ABSTRACT FROM AUTHOR]

We present efficient algorithms for multi-precision and multi-accuracy calculation of error functions and the Dawson integral, all with complex arguments. These algorithms achieve exceptional accuracies, ranging from 26 significant digits (SD) up to 30 SD depending on the function. In addition to the Faddeyeva or Faddeeva function, or the scaled complementary error function, , the list of functions considered include the error function, erf z ; the complementary error function, erfc z ; the imaginary error function, erfi (z) ; and the Dawson integral Daw (z) . These algorithms are integrated into a modern Fortran module confirming the claimed accuracies and superior efficiency compared to other competitive codes in the literature. Additionally, we highlight an observation regarding the built-in " Erfc _ Scaled (x) " function included in a widely used Fortran compiler, which exhibits a significant decline in accuracy when employed in quadruple-precision arithmetic. [ABSTRACT FROM AUTHOR]

We obtain an expression for the error in the approximation of f(A)b$$ f(A)\boldsymbol{b} $$ and bTf(A)b$$ {\boldsymbol{b}}^Tf(A)\boldsymbol{b} $$ with rational Krylov methods, where A$$ A $$ is a symmetric matrix, b$$ \boldsymbol{b} $$ is a vector and the function f$$ f $$ admits an integral representation. The error expression is obtained by linking the matrix function error with the error in the approximate solution of shifted linear systems using the same rational Krylov subspace, and it can be exploited to derive both a priori and a posteriori error bounds. The error bounds are a generalization of the ones given in Chen et al. for the Lanczos method for matrix functions. A technique that we employ in the rational Krylov context can also be applied to refine the bounds for the Lanczos case. [ABSTRACT FROM AUTHOR]

In this paper, the issue of projective synchronisation of bipartite networks (BNs) with multiple time-varying delays and nonlinear couplings has been studied. To reduce wasted communication resources, the novel quantised event-triggered controllers and the measurement error functions are introduced. In particular, the event-triggered schemes without Zeno behaviour are designed, which can determine whether controllers need to be updated or not. For the purpose of investigating the synchronisation with isolated nodes, comparing to the usual 1-norm and 2-norm, generalised $ \{\xi,1\} $ { ξ , 1 } -norm has been utilised to derive sufficient conditions. Furthermore, in the proof of the theorem, constant time-delays and time-varying time delays are dealt with by utilising novel Lyapunov functions, and then some valid criteria are established to achieve different types of projective synchronisation. Lastly, numerical simulations are well provided to confirm the given theoretical results. [ABSTRACT FROM AUTHOR]

To address the shortcomings of the widely-linear complex-valued distributed adaptive filtering algorithm that cannot combine convergence speed and steady-state performance when using a fixed step-size strategy. In this paper, by making the partial derivative of the square of the sum of a priori error and a posteriori error with respect to step-size equal to zero, we propose a novel variable step-size (VSS) strategy, which is formulated as a function of a priori error and a posteriori error. In addition, a corresponding adaptive filtering algorithm is proposed by using the VSS strategy. Then in the process of parameter update, the moving average method is used to avoid large perturbations in iteration of the algorithm. Secondly, the theoretically analysis of the transient and steady-state performance of the proposed algorithm is provided. Finally, in the numerical simulation experiments, the effect of each parameter on the algorithm is tested, the result of the comparison with the fixed-step algorithm illustrates that the proposed algorithm has more superiority, and the high degree of matching between theory and experiment also verifies the feasibility and accuracy of the theoretical analysis method. [ABSTRACT FROM AUTHOR]

The main reaction parameters examined were the amount of blast furnace slag, the hydration duration, ammonium acetate concentration, and temperature. The Response surface methodology was employed to quantify their impact on the sorbent's surface area. Using a central composite design, the surface area of the resulting sorbent corresponding to Brunauer-Emmett-Teller (BET) was investigated. The sorbents produced range in surface area from 49.89 to 155.33 m2/g. Additionally, the effectiveness and response prediction capacities of the Response Surface Methodology (RSM) and Artificial Neural Network (ANN) modeling methodologies were investigated. The models were assessed using various statistical metrics, including (MSE) mean squared error, (ARE) average relative errors, the (SSE) sum of squared errors, (HYBRID) Hybrid fractional error function, (SAE) Sum of the absolute errors, (R2)coefficient of determination, and Root means square. According to statistical evidence, the ANN approach surpassed the RSM-CCD model approach. The surface area of the sorbent was shown to be significantly influenced by interactions between variables in addition to all the individual variables examined. The sorbent was made from a material with substantial structural porosity based on SEM. The functional groups were identified using FTIR. The XRF determined the elemental composition of BFS-based sorbents. [ABSTRACT FROM AUTHOR]

In the grey prediction, the GM(N, 1) model is an important type. There are relatively more studies on the GM(2, 1) model, but most scholars used the GM(2, 1) model to explore the prediction problem of monotone time sequences and only a few scholars used the GM(2, 1) model to predict non-monotone time sequences, such as the quarterly variation sequence. The paper uses the GM(2, 1) model to predict quarterly variation sequences. To improve the modeling precision, the paper makes improvements in the following three aspects: (1) to improve quarterly data's adaptability to the model, the paper improves the original time sequence, i.e. introducing a quarterly multiple factor for a data transformation of the original time sequence; (2) to make the model present quarterly data's variation characteristics, the paper improves the traditional GM(2, 1) model's structure, i.e. introducing a superposed trigonometric function to extend the model's grey action; (3) to improve the model's simulation and prediction precision, the paper improves the parameter optimization method, i.e. considering the minimum of the maximum of average simulation and prediction relative errors as the objective function. The results of this study are as follows: (1) the introduction of seasonal multiplication factor enhances the adaptability of quarterly data to the model; (2) the expanded model can reflect the characteristics of seasonal data changes; (3) examples show that the simulation and prediction accuracies of the expanded model are very high, and the average simulation relative error is only 1.44%, and the average prediction relative error is only 1.43%. The errors are very small; (4) the simulation and prediction accuracies of the extended model are significantly higher than those of the traditional and comparative models. [ABSTRACT FROM AUTHOR]

Errors in administrative processes cost clientele and organizations, yet are understudied. Beyond efficiency losses, errors impose administrative burdens on clientele. Automation is a common tool for reducing errors. Little is known, however, about the factors that may augment automation's effectiveness. We theorize that administrative errors are a function of program complexity. We expect automation to improve accuracy in less complex programs but worsen with increased complexity. With U.S. Unemployment Insurance program audit data, we use longitudinal Poisson analysis to test our expectations. Complexity is associated with greater incidences of administrative errors. As expected, automation's effects vary with level of complexity. [ABSTRACT FROM AUTHOR]

In visual Simultaneous Localization and Mapping (SLAM), operational efficiency and localization accuracy are equally crucial evaluation metrics. We propose an enhanced visual SLAM method to ensure stable localization accuracy while improving system efficiency. It can maintain localization accuracy even after reducing the number of feature pyramid levels by 50%. Firstly, we innovatively incorporate the principal direction error, which represents the global geometric features of feature points, into the error function for pose estimation, utilizing Pareto optimal solutions to improve the localization accuracy. Secondly, for loop-closure detection, we construct a feature matrix by integrating the grayscale and gradient direction of an image. This matrix is then dimensionally reduced through aggregation, and a multi-layer detection approach is employed to ensure both efficiency and accuracy. Finally, we optimize the feature extraction levels and integrate our method into the visual system to speed up the extraction process and mitigate the impact of the reduced levels. We comprehensively evaluate the proposed method on local and public datasets. Experiments show that the SLAM method maintained high localization accuracy after reducing the tracking time by 24% compared with ORB SLAM3. Additionally, the proposed loop-closure-detection method demonstrated superior computational efficiency and detection accuracy compared to the existing methods. [ABSTRACT FROM AUTHOR]

In this paper, Artificial Neural Networks are used to solve Delay Differential Equations. We have suggested an appropriate approximation function based on ANN and then by solving an optimization problem of error function, the neural network is trained. The advantage of this technique is that the proposed approximation functions, with a slight modification, can be used for most types of delay differential equations, including DDE with constant delay, time dependent delay and pantograph delay. To demonstrate the effectiveness of the method, various examples have been tested and validity and efficiency of the method have been shown. [ABSTRACT FROM AUTHOR]

Sinc numerical methods are essential approaches for solving nonlinear problems. In this work, based on this method, the sinc neural networks (SNNs) are designed and applied to solve the fractional optimal control problem (FOCP) in the sense of the Riemann–Liouville (RL) derivative. To solve the FOCP, we first approximate the RL derivative using Grunwald–Letnikov ofaators. Then, according to Pontryagin's minimum principle for FOCP and using an error function, we construct an unconstrained minimization problem. We approximate the solution of the ordinary differential equation obtained from the Hamiltonian condition using the SNN. Simulation results show the efficiencies of the proposed approach. [ABSTRACT FROM AUTHOR]

The aluminum terephthalate (MIL-53) metal–organic framework (MOF) (MIL-53(Al)) was evaluated as an adsorbent for removing phosphates from aqueous solutions. XRD and FTIR were used to confirm the molecular structure. TGA/DSC was used to measure its stability. The green synthesizing MIL-53(Al) showed good performance as a highly efficient adsorbent. The adsorbed MIL-53(Al) nanoparticles still retain their original morphology according to SEM, allowing it to be easily separated from the aqueous solution via filtration. Additionally, the thermal stability of synthesized MIL-53(Al) is capable of withstanding temperatures up to 500 °C, as confirmed by TGA/DSC. Using different initial concentrations of Na2HPO4 and ICP-OES measurements, we determined the adsorption values of Na2HPO4 by MIL-53(Al) as a function of time. Three kinetic models (pseudo-first-order, pseudo-second-order, and Elovich) and three isotherm models (Langmuir, Freundlich, and Temkin) were used to evaluate the phosphate adsorption behavior of MIL-53(Al) powder in Na2HPO4 aqueous solution. Error functions are used to evaluate various kinetic and isotherm models related to different physical processes. From the analysis of the adsorption experiments, the Elovich model is the best-fitting kinetic model, showing that the adsorption rate decreases with increasing adsorption capacity. Furthermore, error function analysis identified the Freundlich model as the most suitable, indicating that complicated adsorption coexists with physisorption, and chemisorption synergistically drives the adsorption process. The module utilizing MIL-53(Al) hollow fibers also demonstrated preliminary attempts at phosphate adsorption and desorption for the first time. This work demonstrated that MIL-53(Al) is an exceptionally stable adsorbent for removing phosphate from contaminated wastewater. [ABSTRACT FROM AUTHOR]

For the Gauss–Jacobi quadrature on [-1,1], the location is estimated where the kernel of the error functional for functions analytic on an ellipse and its interior in the complex plane attains its maximum modulus. For the Jacobi weight (1-t)^\alpha (1+t)^\beta (\alpha >-1, \beta >-1) except for the Gegenbauer weight (\alpha =\beta), the location is the intersection point of the ellipse with the real axis in the complex plane. For the Gegenbauer weight, it is the intersection point(s) with either the real or the imaginary axis or other axes with angle \tfrac {1}{4}\pi and \tfrac {3}{4}\pi. Our results support the empirical results provided by Gautschi and Varga [SIAM J. Numer. Anal, 20 (1983), pp. 1170–1186] for the Jacobi weight, the Gegenbauer weight and the Legendre weight. The results obtained are also illustrated numerically. [ABSTRACT FROM AUTHOR]

In the past, manual inspection was often used for equipment inspection in indoor environments such as substation rooms and chemical plant rooms. This way often accompanies high labor intensity, low inspection efficiency, and low safety, which is difficult to meet the increasingly stringent requirements of indoor equipment operation and maintenance management. For dealing with these issues, a VIORB-SLAM2 algorithm based on the integration of IMU and visual information, was proposed by this paper. Firstly, the IMU data and image data were integrated to restore scale information of cameras, and then an error function was established to enhance the algorithm's robustness. Secondly, in order to improve the accuracy of the algorithm, the random sampling consensus method was used to eliminate the wrong matching points in feature point matching, and the normalized cross-correlation matching was employed to constrain key frame matching conditions. Finally, through the iterative closest point method to stitch the point clouds, a dense map for navigation was constructed. The experimental results show that the algorithm designed by this paper has solved the shortcomings of applying the ORB-SLAM2 algorithm to indoor inspection robots while achieving high positioning accuracy, which can be combined with other algorithms in the field of artificial intelligence for object detection and semantic map construction in the future. [ABSTRACT FROM AUTHOR]

Background: This study aims to investigate the errors in structure volume and shape caused by the replication, expansion, and merging operations of the Monaco system and analyze their influence on dosimetry evaluation. Methods: A retrospective collection of 30 patients undergoing radiotherapy was utilized. Cylinders with radii of 5, 10, and 30 mm were delineated in computerized tomography (CT) images from 10 patients with thoracic and abdominal issues, and the Margins function in Monaco was used to expand the margins by 0, 3, 5, and 10 mm in 2D mode. In 10 patients with vertebral metastases, the Margins function was utilized to replicate and merge targets, and the Copy Structure function was employed to replicate targets. Cross-CT replication was performed for the targets of 10 patients with nasopharyngeal carcinoma. The deviation between the processed structure volume and the ideal value was compared. The difference in the maximum dose (Dmax) before and after lens replication was evaluated in 10 patients undergoing whole-brain radiotherapy. Results: Monaco's Margins function increased the volume of the processed structure during the copying procedure. The margin error was equivalent to expanding the structure by 0.3–0.4 mm, and a margin error of 0.3–0.4 mm was produced in each expansion instance. The volume deviation for a cylinder with a radius of 5 mm was 12.99%. The Merge function of Margins copied substructures and merged them. The Copy Structure function did not alter the structure during copying, but the volume was reduced by less than 1% after copying across CT. Dmax after lens replication was higher than that before replication, with a median difference of 31.3 cGy for the left lenses. Conclusion: Monaco's Margins function introduces errors in organ replication, expansion, and merging, resulting in incorrect dose assessment. Physicians should be mindful of the potential effects when utilizing them. [ABSTRACT FROM AUTHOR]

A novel neural network adaptive filter algorithm is proposed to address the challenge of weak spectral signals and low accuracy in micro-spectrometer detection. This algorithm bases on error backpropagation (BP) and least mean square (LMS), introduces an innovative BP neural network model incorporating instantaneous error function and error factor to optimize the learning process. It establishes a network relationship through the input signal, output signal, error and step factor of the adaptive filter, and defines a training optimization learning method for this relationship. To validate the effectiveness of the algorithm, experiments were conducted on simulated noisy signals and actual spectral signals. Results show that the algorithm effectively denoises signals, reduces noise interference, and enhances signal quality, the SNR of the proposed algorithm is 3-4 dB higher than that of the traditional algorithm. The experimental spectral results showed that the proposed neural network adaptive filter algorithm combined with partial least squares regression is suitable for simultaneous detection of copper and cobalt based on ultravioletvisible spectroscopy, and has broad application prospects. [ABSTRACT FROM AUTHOR]

This study employs Cantera code to investigate the laminar burning velocity of different ammonia–hydrogen mixtures. Suitable models were selected from recent literature, and the one with the lowest root mean square error (RMSE) against experimental data was identified through the error function method. Bao mechanism shows an RMSE value of 4.71 at atmospheric pressure for ammonia–hydrogen mixtures, while the Otomo mechanism exhibits an RMSE of 2.11 under high‐pressure conditions. Additionally, sensitivity analysis was conducted to highlight critical reactions within each mechanism, emphasizing distinctions between different pressures. This approach aims to choose the proper mechanism to reduce computational and experimental costs in the early stages of ammonia–hydrogen research. [ABSTRACT FROM AUTHOR]

This paper investigates the control problem of spacecraft rendezvous with obstacle constraint, considering the external disturbance forces caused by orbit perturbation. Firstly, the translational dynamic model of spacecraft rendezvous is given and then rewritten into a second‐order fully‐actuated system form. Then, by employing the prescribed performance control method, the performance function and error transformation are determined, pre‐defining the prescribed performance bounds. Moreover, the fully‐actuated system approach is used to linearize the original nonlinear system, which simplifies the processes of control law design and ensures model accuracy. After that, to ensure that the spacecraft could avoid the dangerous zone during its manoeuvre, the artificial potential function is introduced, based on which a sliding mode surface is designed. Finally, the prescribed performance control–artificial potential function‐based control law is derived, further adopting the neuro‐adaptive method to deal with external interferences. The stability of the close‐loop control system is analysed through the Lyapunov approach and the effectiveness of the proposed control scheme is verified by carrying out a numerical simulation. [ABSTRACT FROM AUTHOR]