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Researchers have devoted decades to striving to create a plethora of distinctive distributions in order to meet specific objectives. The argument is that traditional distributions have typically been found to lack fit in real-world situations, which include pharmaceutical studies, the field of engineering, hydrology, environmental science, and a number of others. The Weibull-inverse Nadarajah Haghighi (WINH) distribution is developed by combining the Weibull and inverse Nadarajah Haghighi distributions. The proposed distribution's fundamental characteristics have been established and analyzed. Several plots of the distributional properties, notably probability density function (PDF) with corresponding cumulative distribution function (CDF) are displayed. The estimation of model parameter is performed via the MLE procedure. Simulation-based research is conducted to demonstrate the performance of proposed estimator's using some measure, like the average bias, variance, and associated mean square error (MSE). Two real datasets represent the morality due to COVID 19 in France and Canada are illustrated to see the practicality of the recommended model. [ABSTRACT FROM AUTHOR]

In this article, we present a comprehensive class of estimators designed for population proportion estimation by leveraging auxiliary attributes within the framework of simple random sampling. The proposed class encompasses a diverse range of estimators, each of which undergoes a thorough examination. We provide numerical expressions for both bias and mean squared error, employing a first-order approximation. The significance of the introduced class of estimators is underscored through a detailed analysis of numerical results. These findings demonstrate the marked superiority of the suggested estimators over their existing counterparts in terms of mean squared error and percentage relative efficiency, as observed in both actual and simulated data scenarios. Consequently, we advocate for the adoption of the proposed class of estimators, asserting its potential to yield improved outcomes when estimating population proportions through the utilization of simple random sampling techniques. [ABSTRACT FROM AUTHOR]

The major goal of this research study is to solve the fractional order Wolbachia invasive model (FWIM) by developing a computational framework based on the Bayesian regularization backpropagation neural network (BRB-NN) approach. The population of mosquitoes is categorized into two classes, Wolbachia-infected mosquitoes and Wolbachia-uninfected mosquitoes. We also incorporate incomplete cytoplasmic incompatibility and imperfect maternal transmission. We investigate the effects of the fractional order derivative (α) and reproduction rate of Wolbachia-infected mosquitoes ϕ w on the dynamics of mosquitoes. The proposed Bayesian regularization backpropagation scheme is applied to three distinct cases using 80% and 20% of the created dataset for training and testing, respectively, with 15 hidden neurons. Comparisons of the results are presented to verify the validity of the proposed technique for solving the model. The Bayesian regularization approach is used to lower the mean square error (MSE) for the fractional order Wolbachia invasive model. The achieved results are based on MSE, correlation, state transitions, error histograms, and regression analysis to confirm the effectiveness of the suggested approach. Additionally, the absolute error value modifies the designed approach's accuracy. [ABSTRACT FROM AUTHOR]

In this article, we offer simple random sampling (SRS) based efficient class of estimators of population mean Y ¯ utilizing additional information. The expression of the mean square error of the proposed class of estimators is deduced up to first degree approximation. The efficiency conditions are established which are enhanced numerically utilizing a simulation study consummated over symmetrical and asymmetrical populations. Real data sets are also utilized to exemplify the suggested estimators. The numerical findings are appeared rather acceptable demonstrating better advancement over the ordinary estimators. [ABSTRACT FROM AUTHOR]

The banking industry is an essential component of the world's economy. In a globalized world, the strength of a banking system is determined by each of its components, whatever its size. This calls into question the financial viability of smaller institutions like cooperative banks. Despite their tiny size, these banks play a crucial role in extending and bolstering the reach of traditional banking channels. Scheduled Urban Cooperative Banks have been examined in this research to better understand the elements that affect these organizations' success or failure. A neural network model with five input and four output variables was developed over four years, from 2019 to 2022. A neural network model was developed to aid in assessing the various performance metrics and is used to examine a prediction model to help with output value prediction. R-values were monitored to achieve the lowest possible mean square error for training, testing, and validation. 1000 epochs of experimentation were completed. The mu value for the six validation tests was found to be 1e10, and the gradient value was seen to be 1e-5. The output or input for future years, if any are available, can be predicted by authors using a neural network prediction model. [ABSTRACT FROM AUTHOR]

This article presents a useful application of the Manta Ray Foraging Optimization (MRFO) algorithm for solving the adaptive infinite impulse response (IIR) system identification problem. The effectiveness of the proposed technique is validated on four benchmark IIR models for reduced order system identification. The stability of the proposed estimated IIR system is assured by incorporating a pole-finding and initialization routine in the search procedure of the MRFO algorithm and this algorithmic modification contributes to the MRFO algorithm when seeking stable IIR filter solutions. The absence of such a scheme, which is primarily the case with the majority of the recently published literature, may lead to the generation of an unstable IIR filter for unknown real-world instances (particularly when the estimation order increases). Experiments conducted in this study highlight that the proposed technique helps to achieve a stable filter even though large bounds for the design variables are considered. The convergence rate, robustness, and computational speed of MRFO for all the considered problems are investigated. The influence of the control parameters of MRFO on the design performances is evaluated to gain insight into the interaction between the three foraging strategies of the algorithm. Extensive statistical performance analyses employing various non-parametric hypothesis tests concerning the design consistency and convergence are conducted for comparison of the proposed MRFO-based approach with six other metaheuristic search procedures to investigate the efficiency. The results on the mean square error metric also highlight the improved solution quality of the proposed approach compared to the various techniques published in the literature. [ABSTRACT FROM AUTHOR]

In the sample survey theory, the crux of survey practitioners is to provide "accurate" estimators of the parameter of choice. The conventional theory depends on the regression/difference estimators as they correspond to the best linear unbiased (B L U) estimators. This paper suggests some optimal classes of estimators by modifying the conventional estimators under stratified ranked set sampling (S R S S). The characteristics of the suggested estimators are established to the first-order approximation. The performance of the suggested class of estimators under SRSS has been theoretically and experimentally shown to be superior to traditional estimators, particularly regression (B L U) estimators. [ABSTRACT FROM AUTHOR]

In the past few decades, feedforward neural networks have gained much attraction in their hardware implementations. However, when we realize a neural network in analog circuits, the circuit-based model is sensitive to hardware nonidealities. The nonidealities, such as random offset voltage drifts and thermal noise, may lead to variation in hidden neurons and further affect neural behaviors. This paper considers that time-varying noise exists at the input of hidden neurons, with zero-mean Gaussian distribution. First, we derive lower and upper bounds on the mean square error loss to estimate the inherent noise tolerance of a noise-free trained feedforward network. Then, the lower bound is extended for any non-Gaussian noise cases based on the Gaussian mixture model concept. The upper bound is generalized for any non-zero-mean noise case. As the noise could degrade the neural performance, a new network architecture is designed to suppress the noise effect. This noise-resilient design does not require any training process. We also discuss its limitation and give a closed-form expression to describe the noise tolerance when the limitation is exceeded. [ABSTRACT FROM AUTHOR]

The study's major goal is to design a superior creative distribution by using the Kumaraswamy-G family of distributions to power Frechet distribution. The Kumaraswamy power Frechet distribution (KPFD) with four parameters is the full name of the revolutionary model. The distribution's probability density function may take numerous forms and graphs and can be used to describe complicated data sets efficiently. Several features of the new distribution are obtained, including dependability, hazard rate, quantile, and moments. The estimation of the unknown parameters of KPFD are provided using the KPFD maximum likelihood estimation technique. Furthermore, a study was performed using the Monte Carlo simulation approach to test estimator accuracy regarding average bias (AB) and mean square error (MSE). Last but not least, two genuine data sets are supplied to compare the proposed model to existing models. [ABSTRACT FROM AUTHOR]

In this work, we presented a new model called the alpha power inverse power Burr-Hatke distribution (APIPBHD). It provides several greater advantages in fitting a variety of different types of data. Estimates of the model parameters are provided and based on traditional research methods. We established the superiority of the proposed distribution by utilizing the importance and adaptability of the APIPBHD compared to other well-known distributions. The real data set includes 63 observations, all of which were manufactured to approximate the strengths of glass fibers to highlight the relevance and flexibility of the provided technique. We proved our superiority using one set of real data. Finally, major findings and conclusions are recorded at the end of the paper. Also, we added future work on the upcoming research depending on the proposed model. [ABSTRACT FROM AUTHOR]

The motive of current investigations is to design a novel radial basis neural network stochastic structure to present the numerical representations of the Zika virus spreading model (ZVSM). The mathematical ZVSM is categorized into humans and vectors based on the susceptible S (q), exposed E (q), infected I (q) and recovered R (q), i.e., SEIR. The stochastic performances are designed using the radial basis activation function, feed forward neural network, twenty-two numbers of neurons along with the optimization of Bayesian regularization in order to solve the ZVSM. A dataset is achieved using the explicit Runge-Kutta scheme, which is used to reduce the mean square error (MSE) based on the process of training for solving the nonlinear ZVSM. The division of the data is categorized into training, which is taken as 78 %, while 11 % for both authentication and testing. Three different cases of the nonlinear ZVSM have been taken, while the scheme's correctness is performed through the matching of the results. Furthermore, the reliability of the scheme is observed by applying different performances of regression, MSE, error histograms and state transition. [Display omitted] • A novel construction of the RBAF neural network is presented for the numerical representations of the ZVSM. • The numerical performances of the ZVSM are presented successfully by applying the stochastic computing RBAF neural network process. • The designed computing numerical framework using the feed forward neural network, with the structure of single, hidden and output layers is presented for solving the ZVSM. • A RBAF with twenty-two neurons is presented in the hidden layers for solving the model. • The optimization of Bayesian regularization is presented for solving the ZVSM. • The authentication of the proposed solver is observed based on the negligible absolute error (AE). [ABSTRACT FROM AUTHOR]

In this paper, two generalized class such as ratio to exponential and the difference type of estimators have been proposed for estimating the finite population mean by utilizing information on higher order moments of an auxiliary variable in the two traditional situations of non-response. The expressions of biases and mean squared errors of the estimators are derived up to first order of approximation. The efficiency comparisons of the proposed methods over other contemporary estimators are carried out on real data sets. A simulation study is also performed to support the present study. The performance of the proposed methods are better than the others existing methods. Results are interpreted and suitable recommendations are made. [ABSTRACT FROM AUTHOR]

This study introduces some novel classes of estimators using ranked set sampling to evaluate the population mean utilizing additional information on an auxiliary variable. The suggested classes of estimators include mostly prominent estimators and are found to be more efficient regarding the other existing estimators available till date. The efficiency conditions are derived under which the discussed novel estimators dominate over the existing estimators. Further, to justify the propositions of this article, a computational study is executed utilizing some real and hypothetically produced populations and the results are found to be the rather satisfactory showing improvement over all the discussed works. [ABSTRACT FROM AUTHOR]

In pattern recognition, data analysis, and decision-making, it is obvious that there are currently artificial intelligence (AI) techniques being applied and are already impacting the research in various fields of study. This research investigates the numerical evaluation of the irregular heat source by capitalizing the knacks of AI based technique multilayer predictive analysis combined with Levenberg Marquardt Algorithm abbreviated as MLPA-LMA on Carreau Nano-fluid flowing through Exponential Expanding Cylinder. The Two-dimensional axisymmetric incompressible Carreau Nanofluid Flow Model (CNFFM) over a nonlinear stretched cylinder of radius R is assumed. To apply the proposed technique, the dataset with varying values of Weissenberg parameter (We), Embedded constant parameters ( A 1 , A 2 , A 3 & A 4), Stretching index (m), Small perturbation number (ε) and Prandtl number (Pr) for the CNFFM is created. The strengths of the AI based MLPA-LMA are then applied in evaluating the dataset of CNFFM to calculate the estimated solutions. The achieved and impactful values of convergence are between the ranges of E-12 to E-16 all through the eight scenarios on CNFFM. The rationale of implementing the proposed MLPA-LMA methodology is substantiated by showing all eight graphical scenarios with mean square error (MSE), error histogram, time series, regression chart and other error-efficiency diagrams, such as error autocorrelation and input error cross correlation plots. The results obtained using the AI based MLPA-LMA technique corroborate the authenticity of the proposed technique for fairly and accurately solving the CNFFM. [ABSTRACT FROM AUTHOR]

The current investigations provides a stochastic platform using the computational Levenberg-Marquardt Backpropagation (LMB) neural network (NN) approach, i.e., LMB-NN for solving the fifth order Emden-Fowler system (FOEFS) of equations. The singular models are always considered tough due to the singularity by using the traditional schemes, hence the stochastic solvers handle efficiently the singular point exactly at zero. The solution of four types of equations based on the FOEFS is presented by using the singularity and shape factor values. To calculate the approximate solutions of the FOEFS of equations, the training, validation and testing performances are used to reduce the mean square error. The selection of the training data is 70%, while testing and validation performances are used as 10% and 20%. The scheme's correctness is performed through the result's comparison along with the negligible absolute error performances for each example of the FOEFS. Moreover, the relative study through different investigations-based error histograms, and correlation update the efficacy of the scheme. [ABSTRACT FROM AUTHOR]

In this paper, an attempt has been made in proposing some improved estimators of finite population variance when random non-response is present in the study variable, on the estimators given by Sharma and Singh (2018). Four improved regression type estimators have been proposed using information on two auxiliary variables, one of which has missing values in the data, using two-phase sampling scheme. Different robust regression methods have been applied on the proposed techniques so as to improve the efficiency of the estimators in case of outliers. It has been observed that robust estimators are more efficient than the proposed ones under some conditions. All the proposed estimators are compared with existing estimators for different values of probability of non-response and the results are verified by using empirical and simulation studies. [ABSTRACT FROM AUTHOR]

Several deep learning methods for spatial data have been developed that report good performance in a big data setting. These methods typically require the choice of an appropriate kernel and some tuning of hyperparameters, which are contributing reasons for poor performance on smaller data sets. In this paper, we propose a mathematical construction of a graph-based neural network for spatial prediction that substantially generalizes the KCN model in [Appleby, Liu and Liu (2020). Kriging convolutional networks. In Proc. AAAI Conf. AI 34, pp. 3187–3194]. In particular, our model, referred to as SPONGE, allows for integrated learning of the convolutional kernel, admits higher order neighborhood structures and can make use of the distance between locations in the neighborhood and between labels of neighboring nodes. All of this yields higher flexibility in capturing spatial correlations. We investigate in simulation studies including small, medium and (reasonably) large data sets in what situations and to what extent SPONGE comes close to or (if the conditions for optimality are violated) even beats universal Kriging, whose predictions incur a high computational cost if n is large. Furthermore we study the improvement for general SPONGE in comparison with the usual KCN. Finally, we compare various graph-based neural network models on larger real world data sets and apply our method to the prediction of soil organic carbon in the southern part of Malawi. [ABSTRACT FROM AUTHOR]

This paper investigates the optimal state estimation of finite-field networks (FFNs) with stochastic disturbances. The stochastic disturbances are regarded as independent noise process. The optimal state estimation problem of FFNs in the sense of minimum mean square error (MMSE) is proposed, and a necessary and sufficient condition is proposed to find the optimal state estimator by minimizing the mean square error (MSE). Moreover, the multi-valued Kalman filter is established, including prediction step and update step, based on which, both optimal state estimator and MMSE can be calculated effectively. [ABSTRACT FROM AUTHOR]

Along with the explosive growing of data, semi-supervised learning attracts increasing attention in the past years due to its powerful capability in labeling unlabeled data and knowledge mining. As an emerging method, the semi-supervised extreme learning machine (SSELM), that builds on ELM, has been developed for data classification and shown superiorities in learning efficiency and accuracy. However, the optimization of SSELM as well as most of the other ELMs is generally based on the mean square error (MSE) criterion, which has been shown less effective in dealing with non-Gaussian noises. In this paper, a robust regularized correntropy criterion based SSELM (RC-SSELM) is developed. The optimization of the output weight matrix of RC-SSELM is derived by the fixed-point iteration based approach. A convergent analysis of the proposed RC-SSELM is presented based on the half-quadratic optimization technique. Experimental results on 4 synthetic datasets and 13 benchmark UCI datasets are provided to show the superiorities of the proposed RC-SSELM over SSELM and other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

The current study provides numerical solutions to the human balancing system using novel framework-based artificial neural networks and the hybrid competency of global heuristic genetic algorithm and local search sequential quadratic programming. These networks tend to handle complicated tasks and perform contemporary performance in different areas. The neural networks performances based on the hybridization schemes are presented using the discretization of the model to express the fitness function in the sense of mean square error. The numerical representations are presented for three cases of the delay terms-based human balancing model in order to validate the consistency and efficacy of the proposed stochastic scheme. The acceptability of the proposed solver is oppressed through the overlapping of obtained and reference results. The negligible values of absolute error also provide the accuracy of the scheme. Additionally, the graphs based on the statistical interpretations provide the precision, and convergence of stochastic computing solver. [ABSTRACT FROM AUTHOR]

Abstract The conventional complex Kalman filter is based on the well-known mean square error criterion, which is optimal under the circular Gaussian assumption. When a real-world complex signal is involved, the state noise and the observation noise often present non-circular properties to some degree, and thus the conventional complex Kalman filter does not perform well under these circumstances. We propose a new complex Kalman filter in which the Gaussian entropy is adopted as the optimality criterion in place of the mean square error. Performance analysis shows that the steady-state error of the new algorithm decreases with the increase of the degree of non-circularity. Simulations are used to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract Adaptive multiple subfilters (MSF)-based algorithms have gained attention in recent times for their applications in acoustic echo cancellation (AEC). The most advanced combined-error MSF algorithm maintains a trade-off between the different-error and common-error subfilter-based algorithms, and it is employed for echo cancellation applications which need faster convergence. Variable tap-length adaptive filtering algorithms find the optimum filter length and are used for optimizing the tap-length of the subfilters in MSF-based echo cancellers. In case of a long room impulse response, the MSF-based variable tap-length algorithm achieves a pseudo-optimum tap-length, which renders the overall design undermodelled. Therefore, it becomes necessary to analyze the effects of the undermodelled adaptive filter on the performance of the variable tap-length MSF (VT-MSF)-based echo cancellers. In this paper, we present a mathematical investigation of convergence, steady-state MSE, stability and tracking capability of the VT-MSF echo cancellers having deficient tap-length adaptive subfilters. Simulation results are presented in support of the analysis for the VT-MSF algorithm for AEC. [ABSTRACT FROM AUTHOR]

Abstract This article proposes a method for sensor fusion between odometers, gyroscope, accelerometer, magnetometer and visual landmark localization system. The method is designed for estimation of all 6 degrees of freedom (both translation and attitude) of a wheeled robot moving in uneven terrain. The fusion method is based on continuous estimation of the mean square error of each estimated value and allows different sampling rates of each sensor. Due to the simple implementation, it is suitable for real-time processing in the low-cost hardware. In order to evaluate the precision of the estimated position, stochastical models of sensors (with parameters matching real hardware sensors) were used and random trajectories were simulated. The virtual experiments showed that the method is resistant to the failure of any sensor except the odometers; however, each sensor provides improvement in the resultant precision. Highlights • Article proposes new sensor fusion method combining variety of sensors' readings. • Method utilizes inertial sensors, landmarks, odometers and magnetometer. • The method is suitable for estimating the position of a wheeled vehicle. • The simplicity of the method allows its implementation into low-cost hardware. [ABSTRACT FROM AUTHOR]

Logarithmic Mean Divisia Index Decomposition Analysis (IDA-LMDI) is a widely used statistical technique in the engineering, economics, energy, and environmental sciences. The main application of the IDA-LMDI method is to identify the drivers that explain the change in carbon dioxide emissions of a country or region over a given time span. Therefore, proper selection of each time period is fundamental to ensure that its implemented accurately and meaningful results are obtained. In the literature, decomposition periods have been defined based on a single-, n-, or one-year period. However, in all these cases, the duration of each period was fixed and depended on arbitrary criteria. The adoption of fixed periods did not capture specific changing trends in the time series under analysis. Therefore, this study presents a new methodology for defining the number of periods and their extent to obtain unbiased drivers using the IDA-LMDI technique. The period selection was defined according to the mean square error of all feasible combinations. We illustrated the application of this method in two cases. First, an illustrative example was successfully validated using multivariate linear regression. Second, we obtained the Kaya factors of the Organisation for Economic Co-operation and Development countries of Europe. The results were compared with the decomposition results provided by the International Energy Agency on 10–7 year fixed periods. The results showed that the application of fixed periods in IDA-LMDI dismissed critical drivers that could only be captured with the proper selection of each period under analysis. Therefore, the proposed methodology will aid in accurate information analysis and decision making in energy policy and other applications. The proposed method has a broad application and could be applied to any decomposition method in the Divisia family. • Decomposition IDA-LMDI analysis is increasingly used in energy and environmental fields. • Method for defining period number and extent to obtain unbiased explanatory drivers. • Adequate determination of the explanatory drivers is crucial to guide energy policy. [ABSTRACT FROM AUTHOR]

It is an established fact that the existence of measurement errors (M E) vitiates the conventional properties of the estimators. The impact of correlated measurement errors (C M E) was first assessed by Shalabh and Tsai (2017) using classical ratio and product estimators. This article makes a modest attempt to suggest some classes of robust estimators of population mean in the presence of C M E. The bias and mean square error of the suggested estimators are reported with the first-order approximation and the efficiency conditions are derived. The theoretical results are extended with the help of a simulation study executed over a hypothetically rendered population. Apart from this, the effect of M E on the suggested estimators is also studied both theoretically and empirically. • To examine robustness of the proposed estimators under correlated measurement errors. • To provide a comparative study. • To provide an empirical study using real and artificially generated populations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the mean square error of numerical methods for SPDEs driven by Gaussian and non-Gaussian noises. The Gaussian noise considered here is a Hilbert space valued Q -Wiener process and the non-Gaussian noise is defined through compensated Poisson random measure associated to a Lévy process. As the models consider the influences of Gaussian and non-Gaussian noises simultaneously, this makes the models more realistic when the models are also influenced by some randomly abrupt factors, but more complicated. As a consequence, the numerical analysis of the problems becomes more involved. We first study the regularity for the mild solution. Next, we propose a semidiscrete finite element scheme in space and a fully discrete linear implicit Euler scheme for the SPDEs, and rigorously obtain their error estimates. Both the regularity results of the mild solution and error estimates obtained in the paper are novel. [ABSTRACT FROM AUTHOR]

Time-Series data has been of great importance to the research field of prediction models. Over the past two decades, multitudinous fuzzy time series blueprints have been put forth for agricultural yield production. However, most of these predictions were based on 7th interval partitioning. A surprising insight was that nobody gave a sound reason to justify the choice of that particular interval. So, this paper focuses on predicting data values on a large spectrum of fuzzy logic computations based on second and third-degree relationships. This paper showcases work on 4 different types of the fuzzy interval, where each interval is tested with 4 degrees of regression equations. Each of these 16 cases is performed for the fuzzy logic relationship (FLR) 2 and 3 separately. Apart from this, the robustness of algorithm is a testament to an incredible solution for the time series model. In addition to this, A Regression analysis model has been enforced to accomplish the efficient defuzzification operation. To elucidate the process of forecasting, the historical data of wheat yield of University of Agriculture and Technology has been used. [ABSTRACT FROM AUTHOR]

Image denoising could be a major concern within the field of medical imaging. An ultrasound is also referred to as ultrasonography, which is a device that is used to create images of the inner body by using high frequency sound waves. Ultrasound is an imaging technique which is noninvasive, nonradioactive and also inexpensive and is used for diagnosis and treatment. Presence of noise in ultrasound images is a major issue as it can lead to improper diagnosis of the disease. It is very important to restore the quality of the images so as to gain information from the medical images. It is important to preserve the features of the image by reducing the noise levels. This work explains about the various kinds of noises present within the ultrasound medical images and also the filters that are used for the noise removal purpose. The noises were introduced in the ultrasound images are Salt and Pepper Noise (impulse or spike noise), Poisson noise (shot noise), Gaussian or amplifier noise and Speckle Noise. For the noise reduction from ultrasound images, a study is carried out by using Gaussian filter, bilateral filter, Order statistic filter, Mean filter and Laplacian filter for efficient noise reduction from the images. The results we obtained after performing the experiments shows the performance and comparisons of different filters supported their PSNR (Peak signal to noise ratio), MSE (Mean Square Error), and RMSE (Root Mean Square Error) values. This paper explains about the Image Noises and Filtering techniques used in effective removal of the Image Noises and performance of different Filters is analyzed on the basis of the PSNR, MSE and RMSE values. [ABSTRACT FROM AUTHOR]

This study aimed to propose a scientific method depending on neural networks technique to determine the optimal proportions of some impurities (Bi 2 O 3 , Nb 2 O 5 , MnO 2 , Co 3 O 4 , Cr 2 O 3 , NiO, La 2 O 3 , Ce 2 O 3) used in manufacturing the ZnO-based varistors. The technique enables obtaining varistors with high structural homogeneity, high performance, and surge energy absorption capability. A nonlinear neural model between the nonlinear coefficient and the proportion of each impurity was accurately created. Subsequently, the neural models have been trained to approximate the correlation factor to the optimum value (R = 1), which proves the accuracy of the models. Then, using the optimization toolbox in MATLAB, the proportion of each impurity producing the highest nonlinear coefficient was determined. Afterwards, a nonlinear neural model representing the relationship between the most influential impurities combined (MnO 2 , NiO, Ce 2 O 3 , La 2 O 3) and the nonlinear coefficient was built. Through training the neural model, the correlation factor was R = 0.99516, and the mean square error was MSE = 0.1078, proving the model's accuracy. Depending on the optimal solutions based on the Lagrange-Newton algorithm in MATLAB, the optimal proportions of impurities combined corresponding to the highest value of the nonlinear coefficient were determined. The accuracy of the proposed method was practically confirmed by preparing a varistor according to the optimal proportions and performing the measurements. The relative error between the theoretical value (α = 99.7522) and the practical value (α = 99.41) of the nonlinear coefficient was RE = 0.0035. That confirms that the proposed method has high reliability and accuracy to be adopted. • Improving the reliability of ZnO-based varistors • Optimizing the impurities used in varistors compositions • Using the neural network to optimize the manufacture and performance of ZnO-based varistors [ABSTRACT FROM AUTHOR]

This study acquaints an efficient class of estimators for variance estimation in simple random sampling. Some existing prominent estimators are established to be the particular cases of the suggested estimators. The mathematical expressions of bias and mean square error of the suggested estimators are determined to the approximation of order one. The efficacious execution of the suggested estimators is examined against all distinguished estimators available till date. Further, numerical illustrations and Monte Carlo simulations are accomplished to extend the findings of the study. [ABSTRACT FROM AUTHOR]

• Numerical solutions of the Wolbachia invasive model (WIM), • The neural network Levenberg-Marquardt (NN-LM) backpropagation technique, • The dynamics of the Wolbachia model is categorized into four classes, • Wolbachia-uninfected aquatic mosquitoes (A n ∗ ), • Wolbachia-uninfected adult female mosquitoes (F n ∗ ), • Wolbachia-infected aquatic mosquitoes (A w ∗ ), • Wolbachia-infected adult female mosquitoes (F w ∗ ). • The Runge-Kutta (RK) numerical method. The current study presents the numerical solutions of the Wolbachia invasive model (WIM) using the neural network Levenberg-Marquardt (NN-LM) backpropagation technique. The dynamics of the Wolbachia model is categorized into four classes, namely Wolbachia-uninfected aquatic mosquitoes (A n ∗ ), Wolbachia-uninfected adult female mosquitoes (F n ∗ ), Wolbachia-infected aquatic mosquitoes (A w ∗ ), and Wolbachia-infected adult female mosquitoes (F w ∗ ). A reference dataset for the proposed NN-LM technique is created by solving the Wolbachia model using the Runge-Kutta (RK) numerical method. The reference dataset is used for validation, training, and testing of the proposed NN-LM technique for three different cases. The obtained numerical results from the proposed neural network technique are compared with the results obtained from the RK method for accuracy, correctness, and efficiency of the designed methodology. The validation of the proposed solution methodology is checked through the mean square error (MSE), error histograms, error plots, regression plots, and fitness plots. [ABSTRACT FROM AUTHOR]

Biodiesel is receiving increasing attention each passing day because of its fuel properties and compatibility. This study investigates the performance and emission characteristics of single cylinder four stroke indirect diesel injection (IDI) engine fueled with Rice Bran Methyl Ester (RBME) with Isopropanol additive. The investigation is done through a combination of experimental data analysis and artificial neural network (ANN) modeling. The study used IDI engine experimental data to evaluate nine engine performance and emission parameters including Exhaust Gas Temperature (E.G.T), Brake Specific Fuel Consumption (BSFC), Brake Thermal Efficiency (B.The) and various emissions like Hydrocarbons (HC), Carbon monoxide (CO), Carbon dioxide (CO 2 ), Oxygen (O 2 ), Nitrogen oxides (NO X ) and smoke. For the ANN modeling standard back propagation algorithm was found to be the optimum choice for training the model. A multi-layer perception (MLP) network was used for non-linear mapping between the input and output parameters. It was found that ANN was able to predict the engine performance and exhaust emissions with a correlation coefficient of 0.995, 0.980, 0.999, 0.985, 0.999, 0.999, 0.980, 0.999, and 0.999 for E.G.T, BSFC, B.The, HC, O 2 , CO 2 , CO, NO X , smoke respectively. [ABSTRACT FROM AUTHOR]

Widely linear estimation plays an important role in quaternion signal processing, as it caters for both proper and improper quaternion signals. However, widely linear algorithms are computationally expensive owing to the use of augmented variables and statistics. To reduce the computation cost while maintaining the performance level, we propose a four-channel estimation framework as an efficient alternative to quaternion widely linear estimation. This is achieved by using four linear models to estimate the four components of quaternion signals. We also show that any of the four channels is able to replace a strictly linear quaternion estimator when estimating strictly linear systems. The proposed method is shown to reduce computational complexity and provide more flexible algorithms, while preserving the physical meaning inherent in the quaternion domain. The proposed framework is next applied to quaternion minimum mean square error estimation to yield the reduced-complexity versions of the quaternion least mean square (QLMS), quaternion recursive least squares (QRLS), and quaternion nonlinear gradient decent (QNGD) algorithms. For the proposed QLMS algorithm, an adaptive step-size strategy is also explored. The effectiveness of the so introduced estimation techniques is validated by simulations on synthetic and real-world signals. [ABSTRACT FROM AUTHOR]

Helical milling is an eco-friendly hole-making process considering energy economy, tool inventory reduction, tool life cycle increase, set-up and non-productive times reduction due to tools changes and better borehole quality. In order to achieve the best results in terms of the sustainable manufacturing aspects energy, quality, and productivity, the present paper proposes to optimize the multi-objective helical milling process of the aluminum alloy Al 7075. With consideration to sustainable objectives, the axial cutting force component, related to energy consumption, the total roundness, related to borehole geometrical quality, and the material removal rate, related to productivity, were taken into account. The process factors axial and tangential feed per tooth and cutting velocity were selected, besides the noise factor tool overhang length, allowing to optimize bias and variance of cutting force and roundness together with the deterministic response material removal rate. In order to achieve a complete exploitation of the Pareto frontier, the new multi-objective optimization method augmented-enhanced normalized normal constraint method was proposed. It was obtained a set of Pareto optimal solutions for the mean square error of the axial cutting force, mean square error of the total roundness, and material removal rate, achieving the trade-off among energy, quality, and productivity. Therefore, different optimization scenarios were obtained, allowing to the experimenter the possibility of choice, guaranteeing a sustainable hole-making process. Furthermore, besides allowing the possibility of choosing different solutions, the TOPSIS decision-making approach was performed so that the best compromise solution was found among the Pareto optimal solutions. The helical milling of the aluminum alloy Al 7075 is presented as a green machining process. [ABSTRACT FROM AUTHOR]

In multivariate multiple linear regression with normal errors, the statistics corresponding to Mallows’ C p and its unbiased estimators are dealt with. When a model is not underfitted, the expectations and variances of the statistics are given. In the special case of univariate multiple regression, when a model may or may not be underfitted, accurate distributions of the statistics are obtained as linear functions of a noncentral F distribution. Using these results, it is possible to obtain the multiplicative constants for unbiased estimators, while minimizing their mean square errors. Simulations for model selection show that shrinkage estimators that use the minimizing constants give a substantially higher proportion of selecting correct models than the estimators using current criteria under normality and non-normality. [ABSTRACT FROM AUTHOR]

This paper theoretically analyzes the Mean Square Error (MSE) on the steady-state frequency estimation realized by the all-pass-based adaptive notch filtering algorithms with the normalized lattice structure. The adaptive algorithms to be considered are the Simplified Lattice Algorithm (SLA) proposed by Regalia and the Affine Combination Lattice Algorithm (ACLA) proposed by the authors. For these two algorithms, we derive the frequency estimation MSE in closed-form. The derivation is based on construction of a linear time-invariant model for generation of frequency estimation error, and division of this model into two submodels of which output signals are statistically uncorrelated to each other. This strategy leads to more accurate theoretical MSE expressions than the direct use of the existing analysis methods. Simulation results demonstrate that our theoretical MSE expressions are in very good agreement with the simulated MSE values. [ABSTRACT FROM AUTHOR]

In this work, noise enhanced parameter estimation problems are investigated for a general nonlinear system, where an additive noise is added to the nonlinear system input and a Bayesian estimator is developed based on the noise modified output. The optimal probability distribution of the additive noises is formulated successively for minimizing the mean square error (MSE) of the optimal Bayesian estimation and the Cramer–Rao lower bound (CRLB). Then the optimal additive noises for the two different noise enhanced optimization problems are explicitly derived as constant vectors, which implies the randomization of constant vectors is not beneficial to these optimizations. Finally, numerical results are presented to illustrate the theoretical results. • Exploration for the Mechanism of SR benefits Bayesian estimation problem. • Formulation of the noise enhanced Bayesian estimation model for nonlinear system. • Derivation of the noise minimizes MSE between parameter and its Bayesian estimator. • Investigation of the noise that minimizes CRLB of MSE. [ABSTRACT FROM AUTHOR]

This article is concerned with the predictions in linear mixed models under stochastic linear restrictions. Mixed and stochastic restricted ridge predictors are introduced by using Gilmour's approach. We also investigate assumptions that the variance parameters are not known under stochastic linear restrictions and attain estimators of variance parameters. Superiorities the linear combinations of the predictors are done in the sense of mean square error matrix criterion. Finally, a hypothetical data set is considered to illustrate the findings. [ABSTRACT FROM AUTHOR]

In this paper, the characteristics of an electrostatic separator were modeled using artificial neural network (ANN). The model was constructed by considering the misclassified middling product during separation, where system parameters (voltage level, rotation speed, electrode position, etc) were varied. The ANN architecture was optimized through the variation in the neuron number, percentage of testing data and percentage of validation data. Performance of the network was assessed by the error indicators, namely mean square error (MSE) and coefficient of determination (R-square). It is found that, lesser number of neurons and lower percentage of both training and validation dataset contributes to better network performance. Additionally, network architecture thus derived was selected for a detailed study on the various combinations performance corresponding to the input and output variables. The results consequently suggest a simplified network structure with reduced number of input variables for modeling of this nonlinear process. [ABSTRACT FROM AUTHOR]

In this paper a population based evolutionary optimization methodology called firefly algorithm (FFA) is applied for the optimization of system coefficients of the infinite impulse response (IIR) system identification problem. FFA is inspired by the flash pattern and characteristics of fireflies. In FFA technique, behaviour of flashing firefly towards its competent mate is structured. In this algorithm attractiveness depends on brightness of light and a bright firefly feels more attraction for the brighter one. For this optimization problem, brightness varies inversely proportional to the error fitness value, so the position of the brightest firefly gives the optimum result corresponding to the least error fitness in multidimensional search space. Incorporation of different control parameters in basic movement equation results in balancing of exploration and exploitation of search space. The proposed FFA based system identification approach has alleviated from inherent drawbacks of premature convergence and stagnation, unlike genetic algorithm (GA), particle swarm optimization (PSO) and differential evolution (DE). The simulation results obtained for some well known benchmark examples justify the efficacy of the proposed system identification approach using FFA over GA, PSO and DE in terms of convergence speed, identifying plant coefficients and mean square error (MSE) fitness values produced for both same order and reduced order models of adaptive IIR filters. [ABSTRACT FROM AUTHOR]

Metrics between fuzzy values are a topic with interest for different purposes. Among them, statistics with fuzzy data is growing in modelling and techniques largely through the use of suitable distances between such data. This paper introduces a generalized (actually, parameterized) L 2 metric between fuzzy vectors which is based on their representation in terms of their support function and Steiner points. Consequently, the metric takes into account the deviation in ‘central location’ (represented by the Steiner points) and the deviation in ‘shape’ (represented by a deviation defined in terms of the support function and Steiner points). Then, sufficient conditions can be given for this representation to characterize fuzzy vectors, which is valuable for different aims, like optimization studies. Properties of the metric are analyzed and its application to quantify the mean (square) error of a fuzzy value in estimating the value of a fuzzy vector-valued random element is examined. Some immediate implications from this mean error are finally described. [ABSTRACT FROM AUTHOR]

The digital pre-distortion (DPD) signal processing is an effective way to mitigate the power amplifier (PA) nonlinearity effect. For communication systems containing DPD and PA, it is difficult to acquire performance metrics closed-forms for any DPD architecture since there was no mathematical expression for each DPD coefficient. Usually, researchers look for more efficient DPD algorithms for DPD coefficients (compared to the existing ones) in terms of computational complexity, delay, power consumption, etc. Consequently, the performance is evaluated through intensive simulation. In this paper, we show how one can exploit the results of our recent work to mathematically model the indirect learning architecture (ILA) DPD and efficiently derive important measures in communication systems, e.g. normalized mean square error (NMSE), achievable rate, and signal-to-noise plus distortion ratio (SNDR). The author would like to clarify that this work might be the first one to provide closed-form analysis for DPD systems. We think the provided framework/analysis will open the door to other researchers/engineers to plug their own assumptions and derive the performance metrics. The derived expressions of the performance metrics (NMSE, SNDR, and achievable rate) are validated through Monte Carlo simulations. We also derive a closed-form expression for the achievable rate bound for the transmit chain. Moreover, we analytically study the effect of the thermal noise and the quantization noise, in the analog-digital conversion (ADC) process, on the NMSE and achievable rate. The analytical expressions are validated through numerical simulations. [ABSTRACT FROM AUTHOR]

The settlement data of oil storage tanks made of steel are measured by the measurement points located around the base of the tank wall. The measured settlement data need to be curve fitted in order to reflect the settlement distribution around the whole tank wall base. Considering about the disadvantage of measured settlement data treatment methods on tanks in current standards, an optimization method of curve fitting on the measured settlement data is presented. The Fourier series expansion is used to analyze the measured settlement data, the fitting curves and mean square error according to different order are obtained. The fitting curve with minimum mean square error is selected as the most appropriate one that reflects the actual displacement of the tank base. The optimization method of curve fitting present is applied to analyze the measured settlement data obtained from the floating roof tank and the fixed roof tank. Results show that different effects can be obtained with different order of the fitting curve. Curve fitting referring to different order is necessary to the measured settlement data in actual engineering in order to find the most appropriate one that reflects the real tank base displacement distribution. [ABSTRACT FROM AUTHOR]

The ordered values of a sample of observations are called the order statistics of the sample and are among the most important functions of a set of random variables in probability and statistics. However the study of ordered estimates seems to have been overlooked in maximum-likelihood estimation. Therefore it is the aim of this communication to give an insight into the relevance of order statistics in maximum-likelihood estimation by providing a second-order statistical prediction of ordered normally distributed estimates. Indeed, this second-order statistical prediction allows to refine the asymptotic performance analysis of the mean square error (MSE) of maximum likelihood estimators (MLEs) of a subset of the parameters. A closer look to the bivariate case highlights the possible impact of estimates ordering on MSE, impact which is not negligible in (very) high resolution scenarios. [ABSTRACT FROM AUTHOR]

Coal seam degasification improves coal mine safety by reducing the gas content of coal seams and also by generating added value as an energy source. Coal seam reservoir simulation is one of the most effective ways to help with these two main objectives. As in all modeling and simulation studies, how the reservoir is defined and whether observed productions can be predicted are important considerations. Using geostatistical realizations as spatial maps of different coal reservoir properties is a more realistic approach than assuming uniform properties across the field. In fact, this approach can help with simultaneous history matching of multiple wellbores to enhance the confidence in spatial models of different coal properties that are pertinent to degasification. The problem that still remains is the uncertainty in geostatistical simulations originating from the partial sampling of the seam that does not properly reflect the stochastic nature of coal property realizations. Stochastic simulations and using individual realizations, rather than E-type, make evaluation of uncertainty possible. This work is an advancement over Karacan et al. (2014) in the sense of assessing uncertainty that stems from geostatistical maps. In this work, we batched 100 individual realizations of 10 coal properties that were randomly generated to create 100 bundles and used them in 100 separate coal seam reservoir simulations for simultaneous history matching. We then evaluated the history matching errors for each bundle and defined the single set of realizations that would minimize the error for all wells. We further compared the errors with those of E-type and the average realization of the best matches. Unlike in Karacan et al. (2014), which used E-type maps and average of quantile maps, using these 100 bundles created 100 different history match results from separate simulations, and distributions of results for in-place gas quantity, for example, from which uncertainty in coal property realizations could be evaluated. The study helped to determine the realization bundle that consisted of the spatial maps of coal properties, which resulted in minimum error. In addition, it was shown that both E-type and the average of realizations that gave the best match for invidual approximated the same properties resonably. Moreover, the determined realization bundle showed that the study field initially had 151.5 million m 3 (cubic meter) of gas and 1.04 million m 3 water in the coal, corresponding to Q90 of the entire range of probability for gas and close to Q75 for water. In 2013, in-place fluid amounts decreased to 138.9 million m 3 and 0.997 million m 3 for gas and water, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we examine the problem of estimating the parameters of the proposed Diagonal of the Modified Riesz Distribution (DMRD) defined in R r . Several methods can be used for estimating the parameters of the DMRD. In the present work, we address the issue of estimating the parameters of the DMRD through a Bayesian approach associated with Monte Carlo methods. The proposed approach is compared via a simulation study with maximum likelihood method and method of moments by calculating the Mean Square Error (MSE). [ABSTRACT FROM AUTHOR]