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We deal with the problem of optimal estimation of linear functionals constructed from the missed values of a continuous time stochastic process ξ ⁢ (t) with periodically stationary increments at points t ∈ [ 0 ; (N + 1) ⁢ T ] based on observations of this process with periodically stationary noise. To solve the problem, a sequence of stochastic functions { ξ j (d) ⁢ (u) = ξ j (d) ⁢ (u + j ⁢ T , τ) , u ∈ [ 0 , T) , j ∈ ℤ } is constructed. It forms an L 2 ⁢ ([ 0 , T) ; H) -valued stationary increment sequence { ξ j (d) , j ∈ ℤ } or corresponding to it an (infinite-dimensional) vector stationary increment sequence { ξ → j (d) = (ξ k ⁢ j (d) , k = 1 , 2 , ...) ⊤ , j ∈ ℤ } . In the case of a known spectral density, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of the functionals. Formulas determining the least favorable spectral densities and the minimax (robust) spectral characteristics of the optimal linear estimates of functionals are derived in the case where the sets of admissible spectral densities are given. [ABSTRACT FROM AUTHOR]

We consider a two‐dimensional time‐inhomogeneous birth‐death process to model the time‐evolution of fake news in a population. The two components of the process represent, respectively: (i) the number of individuals (say spreaders) who know the rumor and intend to spread it and (ii) the number of individuals (say inactives) who have forgotten the rumor previously received. We employ the probability generating function‐based approach to obtain the moments and the covariance of the two‐dimensional process. We also analyze a new adimensional index to study the correlation between the two components. Some special cases are considered in which both the expected numbers of spreaders and inactives are equal to suitable sigmoidal curves, which are often adopted in modeling growth phenomena. Finally, we provide an application based on real data related to the diffusion of fake news, in which the optimal choice of the sigmoidal curve that fit the datasets is based on the minimization of the mean square error and of the relative absolute error. [ABSTRACT FROM AUTHOR]

This paper may be the first meta-analysis that presents a comprehensive synthesis of scientific works spanning the last five years, focusing on methodologies and results related to the analysis of nanocomposite using nanoparticles. The primary objective is to identify the optimal algorithm using software information and leading to better classification methodology. Specifically, this study comes up with the advantages and the drawbacks of the most used algorithms and proposes an enhancement and performance of Recurrent Neural Networks based on Long Short Term Memory (LSTM) neurons. Besides, a comparison of Deep Learning methods for the classification of polymeric nanoparticles, with polypropylene serving as a case study will be implemented. Experiment comparisons are conducted to assess with one physical property, later expanded to four properties and finally to eight properties. Neural networks, including Artificial Neural Networks (ANN), Recurrent Neural Networks (RNN), and Recurrent Neural Networks-Monte Carlo, are employed for simulations. The evaluation criteria encompass accuracy, calculation time, mean square error (MSE) and other metrics. The findings contribute to the selection of an optimal algorithm for the analysis of polymeric nanoparticles, emphasizing the potential of Deep Learning methodologies, particularly Recurrent Neural Networks Monte Carlo, in advancing classification accuracy and efficiency. [ABSTRACT FROM AUTHOR]

ABSTRACT To address the issue of underreporting faults in the detection of tiny faults by dynamic factor analysis (DFA), a novel fault detection and diagnosis method based on DFA‐sliding window combined with mean square error (DFA‐SWMSE) is proposed. Firstly, the data matrix is augmented by introducing time lag shifts. Secondly, factor analysis (FA) is applied to the augmented data matrix, achieving dimensionality reduction and feature extraction while retaining most of the original data's information. Then, the sliding window technique is applied to calculate the mean square error of the dimensionally reduced data, allowing for the monitoring of the system's current state and the detection of tiny faults. Finally, effective fault diagnosis is achieved through the analysis of fault factors and variable contributions. The proposed method is validated using a complex dynamic numerical example and a three‐tank system process named Sim3Tanks. This system has gained widespread application in the field of process fault detection due to its ability to simulate and generate various types of faults. The proposed method is compared with principal component analysis (PCA), dynamic principal component analysis (DPCA), PCA similarity factor (SPCA), FA, and DFA. The experimental results thoroughly validate the effectiveness of the proposed method in detecting and diagnosing tiny faults in dynamic processes. [ABSTRACT FROM AUTHOR]

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]

Dimensionality reduction is a method used in machine learning and data science to reduce the dimensions in a dataset. While linear methods are generally less effective at dimensionality reduction than nonlinear methods, they can provide a linear relationship between the original data and the dimensionality-reduced representation, leading to better interpretability. In this research, we present a tied-weight autoencoder as a dimensionality reduction model with the merit of both linear and nonlinear methods. Although the tied-weight autoencoder is a nonlinear dimensionality reduction model, we approximate it to function as a linear model. This is achieved by removing the hidden layer units that are largely inactivated by the input data, while preserving the model's effectiveness. We evaluate the proposed model by comparing its performance with other linear and nonlinear models using benchmark datasets. Our results show that the proposed model performs comparably to the nonlinear model of a similar autoencoder structure to the proposed model. More importantly, we show that the proposed model outperforms the linear models in various metrics, including the mean square error, data reconstruction, and the classification of low-dimensional projections of the input data. Thus, our study provides general recommendations for best practices in dimensionality reduction. [ABSTRACT FROM AUTHOR]

Accurately predicting lithium-ion batteries' state of temperature (SOT) is crucial for effective battery safety and health management. This study introduces a novel approach to SOT prediction based on voltage and temperature profiles during the abusive discharging process, aiming for enhanced prediction accuracy and evaluating the safety range. The duration of equal voltage discharge and temperature variation during discharge are considered temperature indicators. Linear regression and R2 analyses are employed to assess the relationship and variance over different discharge–charge cycles of varied duration between the complete life cycle and its temperature variance. In this study, a decision tree (DT) and an artificial neural network (ANN) are employed to estimate the SOT of a Li-ion battery. The effectiveness and accuracy of the proposed methods are validated using ageing data from eVTOL charge–discharge cycles through numerical simulations. The results demonstrate that for the short cruise range of 600 s, the DT algorithm with an R2 regression value of 6.17% demonstrates better performance than ANN, whereas for the bigger cruise range of 1000 s, the ANN model with an R2 regression value of 5.06 percent was better suited than DT. It is concluded that both DT and ANN outperform other methods in predicting the SOT of lithium-ion batteries. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel ranked set generalized randomized response estimator designed for accurately estimating the mean of sensitive variables while maintaining the privacy of sensitive information. This method incorporates an additive scramble response technique, which effectively addresses the challenge of estimating the mean of such variables. Through a rigorous analysis, we derive expressions for both bias and mean square error (MSE) pertaining to the proposed estimator and its constituent estimators, to the first-order of approximation. By identifying specific conditions, we highlight scenarios in which the performance of the suggested estimator surpasses alternatives. To substantiate the effectiveness of our approach, we conduct efficiency comparisons, a comprehensive simulation and real data study. These analyses collectively demonstrate the superior performance of our proposed estimator within the framework of ranked set sampling (RSS) for sensitive variables. [ABSTRACT FROM AUTHOR]

High-precision measurement of temperature value distributions in production scenarios is of great significance for industrial production, but traditional temperature field reconstruction algorithms rely on the design of manual feature extraction methods with high computational complexity and poor generalization ability. In this paper, we propose a high-precision temperature field reconstruction algorithm based on deep learning, using an efficient adaptive feature extraction method for temperature field reconstruction. We design an improved temperature field reconstruction algorithm based on the ResNet18 neural network; introduce the CBAM attention mechanism in the model; and design a feature pyramid, using M-FPN, a multi-scale feature aggregation network fusing PAN and FPN, to make the extracted feature information propagate multi-dimensionally among different layers to improve the feature characterization ability. Finally, the mean square error is used to guide the model to optimize the training so that the model pays more attention to the data and reduces the large error to ensure that the gap between the predicted value and the real value is small. The experimental results show that the reconstruction accuracy of the improved algorithm presented in this paper is significantly better than that of the original algorithm in the case of typical peaked temperature field distributions. [ABSTRACT FROM AUTHOR]

In wireless communication systems, the information is transferred as digital symbols that get affected by noise interference while transmitting through the wireless channel. In today's world, the increased demand for rapid data transmission rates leads to more inter-symbol interference in the received signal. To diminish the effects of inter-symbol interference, adaptive channel equalization is utilized in digital communication. In this paper, the inter-symbol interference effect in the finite impulse response channel is reduced in terms of an adaptive equalizer method. The weights/coefficients of the equalizer are optimized through a tunicate swarm algorithm. Channel equalization involves optimizing the channel coefficients to mitigate the impact of inter-symbol interference. This equalization process can be viewed as an iterative optimization task, aimed at lessening the mean square error among the transmitted signal and the equalizer's output. The implementation of the proposed method is executed using MATLAB software. We assess its effectiveness through a comparative analysis, considering metrics such as mean square error, learning rate, bit error rate, convergence rate, and computational time. Furthermore, we conduct a comparative evaluation with other optimization approaches, including the Bat Algorithm, Slime Mould Algorithm, and Harris Hawks Optimization Algorithm. This comparison demonstrates the superiority of the proposed algorithm over traditional optimization techniques. [ABSTRACT FROM AUTHOR]

In sample survey analysis, accurate population mean estimation is an important task, but traditional approaches frequently ignore the intricacies of real-world data, leading to biassed results. In order to handle uncertainties, indeterminacies, and ambiguity, this work presents an innovative approach based on neutrosophic statistics. We proposed novel neutrosophic factor type exponential estimators that use auxiliary information to improve population mean precision. The suggested estimators are highly useful for computing results while working with unclear, hazy, and neutrosophic-type data. These estimators produce answers that are interval-form rather than single-valued, which may give our population parameter a better chance of being off. Since we now have an estimated interval with the population mean's unknown value supplied a minimal MSE or highest Percentage Relative Efficiency (PRE), the estimators are more effective. The investigation of alpha constants in the neutrosophic framework, extending from −1 to +1, is at the heart of this research. These constants have a significant impact on how estimates are made and enable flexible accuracy modification. We choose the best neutrosophic values for characterizing constants, emphasizing their importance in obtaining precise estimations. This study further expands its originality by including preexisting estimators into the neutrosophic framework, showcasing its versatility and adaptability. We demonstrate the estimators' superiority to traditional techniques through empirical assessments employing neutrosophic temperature information and simulation assessments. The ensuing interval-based results, influenced by alpha constants, offer concrete insights into the world of uncertainty, enabling more well-informed decision-making. [ABSTRACT FROM AUTHOR]

The aim of this paper is to improve the parameter estimation accuracy of the system to be identified by using measurements from a known system. By introducing the transfer gain matrix and setting the effective identification criterion, a novel transfer sparse identification method is raised, which deals with the sparse issues more precise. Besides, the unbiased form is given in the parameter analysis and the recursion form can prevent the dimension catastrophe related problems. Moreover, in order to test the effects of the transfer and avoid bad performance, a negative transfer analysis condition is carried out. Finally, the simulation verifies the enhancements and benefits of the proposed transfer sparse identification method, confirming that the transfer performance outperforms better than that of no transfer, especially on the zero parameters identification. [ABSTRACT FROM AUTHOR]

According to existing literature, the ordinary least squares (OLS) estimators are not the best in presence of multicollinearity. The inability of OLS estimators against multicollinearity has paved the way for the development of various ridge type estimators for circumventing the problem of multicollinearity. In this paper improved two-parameter ridge (ITPR) estimators are proposed. A simulation study is used to evaluate the performance of proposed estimators based on minimum mean squared error (MSE) criterion. The simulative results reveal that, based on minimum MSE, ITPR2 was the most efficient estimator compared to the considered estimators in the study. Finally, a real-life dataset is analyzed to demonstrate the applications of the proposed estimators and also checked their efficacy for mitigation of multicollinearity. [ABSTRACT FROM AUTHOR]

To refine the displacement field of the background-oriented Schlieren method, a novel super-resolution method based on deep learning has been proposed and compared with the bicubic interpolation in this study. The gradient loss functions were first introduced into the hybrid downsampled skip-connection/multi-scale model to improve the reconstruction effect. The reconstruction effects of the new loss functions were compared with that of the traditional mean square error (MSE) loss function. The results show that the Laplace operator with average pooling exhibits better performance than the origin loss function in all the indexes including peak signal-to-noise ratio, MSE, MSE of the gradient, and the maximum MSE. In these four indexes, the MSE of the gradient and the maximum MSE performed especially better than the others, where the MSE of the gradient was reduced from 3. 0× 10−05 to 3.30 × 10−05, and the maximum MSE was reduced from 0.392 to 0.360. [ABSTRACT FROM AUTHOR]

Nowadays, high latency in Edge Computing (EC) for Internet of Things (IoT) devices due to network congestion and online traffic reduces the acquired precision, performance, and processing power of the network. Data overload in IoT significantly impacts the real-time capabilities of user experience, decision- making efficiency, operational costs, and security in EC. By combining EC innovation and three Machine Learning (ML) models, namely Decision Trees (DT), Support Vector Machines (SVMs), and Convolutional Neural Networks (CNNs), this research aims to tackle the inactivity of IoT devices and information cleaning from errors. Its purpose is to preserve information astuteness and highlight the efficacy of each model's execution by using the essential components of previous approaches. The proposed model evaluates the precision, performance, and quality enhancement by measuring the Mean Square Error (MSE), coefficient of determination (R²), and accuracy. [ABSTRACT FROM AUTHOR]

Abstract Dimensionality reduction is a method used in machine learning and data science to reduce the dimensions in a dataset. While linear methods are generally less effective at dimensionality reduction than nonlinear methods, they can provide a linear relationship between the original data and the dimensionality-reduced representation, leading to better interpretability. In this research, we present a tied-weight autoencoder as a dimensionality reduction model with the merit of both linear and nonlinear methods. Although the tied-weight autoencoder is a nonlinear dimensionality reduction model, we approximate it to function as a linear model. This is achieved by removing the hidden layer units that are largely inactivated by the input data, while preserving the model’s effectiveness. We evaluate the proposed model by comparing its performance with other linear and nonlinear models using benchmark datasets. Our results show that the proposed model performs comparably to the nonlinear model of a similar autoencoder structure to the proposed model. More importantly, we show that the proposed model outperforms the linear models in various metrics, including the mean square error, data reconstruction, and the classification of low-dimensional projections of the input data. Thus, our study provides general recommendations for best practices in dimensionality reduction.

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 Time-based surveys often experience missing data due to several reasons, like non-response or data collection limitations. Imputation methods play an essential role in incorporating these missing values to secure the accuracy and reliability of the survey outcomes. This manuscript proposes some optimal class of memory type imputation methods for imputing missing data in time-based surveys by utilizing exponentially weighted moving average (EWMA) statistics. The insights into the optimal conditions for incorporating our proposed methods are provided. A comprehensive examination of the proposed method utilizing simulated and real-life datasets is conducted. Comparative analyses against the existing imputation methods exhibit the superior performance of our methods, particularly in the scenarios characterized by developing trends and dynamic response patterns. The outcomes highlight the effectiveness of utilizing EWMA statistics into memory type imputation methods, displaying their flexibility to changing survey dynamics.

Typically, most researchers rely on precise data for estimating population parameters using classical statistical methods. However, there are scenarios where dealing with uncertain and imprecise data in the form of intervals becomes necessary. To tackle this challenge, various adaptations of classical estimators, such as the neutrosophic ratio estimator and their improved ones, have emerged. This article introduces a novel estimator known as the neutrosophic ratio-cum-product exponential estimator combining two auxiliary variables, specifically designed for the elevated estimation of population mean in such situations. Performance evaluation is conducted using metrics like Mean Square Error (MSE) and Percentage Relative Efficiency (PRE). The effectiveness of the proposed estimator is demonstrated through both empirical and simulation studies. Additionally, its practical applicability is showcased using agricultural data. The results illustrate that the proposed estimator surpasses all other estimators discussed in this paper. To justify the usefulness of neutrosophic estimators over their classical ones, a simulation study is also made. Simulation results obtained for classical estimators have also been compared with their neutrosophic adaptations. [ABSTRACT FROM AUTHOR]

Abstract This article aims to suggest an improved estimator for estimation of population median using auxiliary information under simple random sampling. The expression for the bias and mean square error are obtained up to first order approximation. We determine the MLE of the optimal values of the describing scalars. The proficiency of the suggested estimator is evaluated in comparison to the preliminary estimators using the MSE threshold. The suggested estimators are compared numerically to the ones that are currently studied in this study. The performance and novelty of the estimators was evaluated using real data sets and a simulation study. To check the efficiency of estimators empirical and theoretical study has been studied. Based on numerical result it is to be noted that our suggested estimator is more efficient as compared to existing estimators which is considered in this article in terms of least MSE and greater PRE.

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.

In underwater communications for 6G, Doppler effects cause the coherent time to become similar to or shorter than the orthogonal frequency division multiplexing (OFDM) symbol length. Conventional time and frequency synchronization methods require additional training symbols for synchronization, which reduces the traffic data rate. This paper proposes the Zadoff–Chu sequence (ZCS) pilot-based OFDM for time and frequency synchronization. The proposed method transmits ZCS as a pilot for OFDM symbols and simultaneously transmits traffic data to increase the traffic data rate while estimating the CFO at each coherence time. For time–frequency synchronization, the correlation of the ZCS pilot is used to perform coarse and fine time and frequency synchronization in two stages. Since the traffic data cause interference with the correlation of ZCS pilots, we theoretically analyzed the relationship between the amount of traffic data and interference and verified it through computer simulations. The synchronization and BER performance of the proposed ZCS pilot-based OFDM were evaluated by conduction computer simulations and a practical ocean experiment. Compared to the methods of Ren, Yang, and Avrashi, the proposed method demonstrated a 6.3% to 14.3% increase in traffic data rate with similar BER performance and a 2 dB to 3.8 dB SNR gain for a 14.3% to 23.8% decrease in traffic data rate. [ABSTRACT FROM AUTHOR]

This paper offers a novel approach to formulate efficient ratio estimator of the population variance using a transformed auxiliary variable. The impact of transformation on auxiliary information has also been discussed. It is observed that incorporating a transformed auxiliary variable result in a high gain in efficiency. Theoretical properties of the newly developed estimators have been derived. The empirical and simulation studies show that the suggested estimators outperformed the existing estimators. [ABSTRACT FROM AUTHOR]

The present study concerns the issue of estimating the population mean and presents novel and improved regressed exponential estimators using different parameters of an auxiliary character based on sub-sampling non-respondents. The bias and mean square error (MSE) of the proposed estimators for the most pragmatic simple random sampling without replacement (SRSWOR) scheme have been derived up to the first order of approximation (i.e. the expression containing errors up to the power of two so that the expectation comes only in terms of the mean, variance and covariance). The optimum value of the MSE of the estimators is found, along with the necessary conditions for optimising the MSE. The effectiveness of the suggested estimators, outperforming the existing ones in terms of their MSE, has been studied theoretically, while the empirical as well as the simulation studies have confirmed these findings. [ABSTRACT FROM AUTHOR]

This paper proposes nonparametric estimates for the two information measures extropy and entropy when a progressively Type-I interval censored data is available. Different nonparametric approaches are used for deriving the estimates, including: moments of the empirical cumulative distribution function and linear regression. The performance of the proposed estimates is studied under various censoring schemes via simulation studies. Furthermore, different real data sets are analyzed for illustrative purposes. The estimates based on linear approximation J^2 and H^2 outperform the other estimate in the majority of studied cases. [ABSTRACT FROM AUTHOR]

Accurate and efficient channel estimation (CE) is critical in the context of autonomous driving. This paper addresses the issue of orthogonal frequency-division multiplexing (OFDM) channel estimation in 5G communication systems by proposing a channel estimation model based on the Parrot Optimizer (PO). The model optimizes for the minimum bit error rate (BER) and the minimum mean square error (MMSE) using the Parrot Optimizer to estimate the optimal channel characteristics. Simulation experiments compared the performance of PO-CE with the Least Squares (LS) method and the MMSE method under various signal-to-noise ratios (SNR) and modulation schemes. The results demonstrate that PO-CE's performance approximates that of MMSE under high SNR conditions and significantly outperforms LS in the absence of prior information. The experiments specifically included scenarios with different modulation schemes (QPSK, 16QAM, 64QAM, and 256QAM) and pilot densities (1/3, 1/6, 1/9, and 1/12). The findings indicate that PO-CE has substantial potential for application in 5G channel estimation, offering an effective method for optimizing wireless communication systems. [ABSTRACT FROM AUTHOR]

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

In this article we study the prediction problem in small geographic areas in the situation where the survey data does not cover a substantial percentage of these areas. In such situation, the application of the Spatial Fay–Herriot model may involve a difficult and subtle process of determining neighboring areas. Ambiguity in definition of neighbors can potentially produce a problem of sensitivity of the conclusions to these definitions. In this article, we attempt to remedy this problem by incorporating random effects for higher level administrative divisions into the model. In this setting, only the higher-level random effects are supposed to have spatial correlations. This may potentially reduce the problem of ambiguity in the definition of spatial neighbors, provided that all higher level administrative divisions are represented in the sample. We also show that predicting in non-sampled areas is considerably more straightforward under the proposed model, as opposed to the case where the Spatial Fay–Herriot model is applied. In addition, we propose two new predictors for out-of-sample areas, under the spatial Fay–Herriot model. In order to compare the performance of the aforementioned models, we use the data from the Demographic and Family Health Survey of the year 2021, and the National Census carried out in 2017. [ABSTRACT FROM AUTHOR]

In many areas, such as speech processing, communication, and measurement systems, where the actual signal is not directly available, Wiener deconvolution is a widely used signal restoration technique. The accuracy of the estimated signal in Wiener deconvolution is determined by the unknown filter parameter. To compute this unknown parameter, complex and time-consuming numerical as well as iterative computation approaches were proposed in the literature, which also often compute an unoptimized unknown filter parameter. To address the computational problem and estimate a more accurate unknown filter parameter, the authors reported an analytical solution in a prior work for a given signal to noise ratio. However, it was revealed that the actual optimum parameter value also varies with noise also. In this paper, the authors propose a new analytical solution for optimum parameter estimation that includes noise as well. The authors compared the modified analytical solution to existing numerical computation methods for different values of Signal to Noise Ratio and demonstrated that the proposed methods' optimum parameter estimation is always close to the actual optimum value, which resulted in more accurate signal deconvolution. Proposed mathematical solutions are also verified with experimental signals, acquired in a laboratory. [ABSTRACT FROM AUTHOR]

The pretty good measurement is a fundamental analytical tool in quantum information theory, giving a method for inferring the classical label that identifies a quantum state chosen probabilistically from an ensemble. Identifying and constructing the pretty good measurement for the class of bosonic Gaussian states is of immediate practical relevance in quantum information processing tasks. Holevo recently showed that the pretty good measurement for a bosonic Gaussian ensemble is a bosonic Gaussian measurement that attains the accessible information of the ensemble [IEEE Trans. Inf. Theory 66(9) (2020) 5634]. In this paper, we provide an alternate proof of Gaussianity of the pretty good measurement for a Gaussian ensemble of multimode bosonic states, with a focus on establishing an explicit and efficiently computable Gaussian description of the measurement. We also compute an explicit form of the mean square error of the pretty good measurement, which is relevant when using it for parameter estimation. Generalizing the pretty good measurement is a quantum instrument, called the pretty good instrument. We prove that the post-measurement state of the pretty good instrument is a faithful Gaussian state if the input state is a faithful Gaussian state whose covariance matrix satisfies a certain condition. Combined with our previous finding for the pretty good measurement and provided that the same condition holds, it follows that the expected output state is a faithful Gaussian state as well. In this case, we compute an explicit Gaussian description of the post-measurement and expected output states. Our findings imply that the pretty good instrument for bosonic Gaussian ensembles is no longer merely an analytical tool, but that it can also be implemented experimentally in quantum optics laboratories. [ABSTRACT FROM AUTHOR]

In survey research, the issue of measurement errors (ME) has been sorted out by various authors, but the issue of correlated measurement errors (CME) has only been studied by Shalabh and Tsai (2017) till date. This article provides a modest acquaintance to evaluate the performance of few novel logarithmic estimators of population mean in the existence of CME under simple random sampling (SRS). The mean square error of the proposed estimators has been obtained. It has been exhibited theoretically under certain conditions that the proposed class of estimators dominates their conventional counterparts. Furthermore, the theoretical findings have been assessed with a Monte Carlo simulation using a hypothetically gendered population and proper suggestions have been forwarded to the survey professionals. [ABSTRACT FROM AUTHOR]

Pressure sensors prepared from sapphire exhibit excellent characteristics, including high-temperature resistance, high hardness, and resistance to electromagnetic interference. A Fast Fourier Transform and Mean Square Error (FFT-MSE) demodulation algorithm was employed to demodulate a sapphire sandwich-structure Fabry–Perot (F-P) pressure sensor. Through simulation analysis, the experimental results indicated that the demodulation error of the air cavity length in the range of 206 μm to 216 μm was less than 0.0008%. Compared to single demodulation methods and combined demodulation methods based on FFT or Minimum Mean Square Error (MMSE), the method proposed in this work reduced the demodulation error by more than three times and increased accuracy by more than six times. The algorithm was utilized to demodulate the sapphire sandwich-structure F-P pressure sensor, and the test results indicated that the fitting error of the sensor was less than 0.025% within the pressure range of 0 MPa to 10 MPa. The repeatability error was less than 0.066%, the zero-point deviation was 1.26%, and the maximum stability deviation was 0.0063% per 30 min. The algorithm effectively demodulated the actual cavity length variation in the sapphire sandwich-structure F-P pressure sensor, providing a solution for the performance evaluation of the sapphire sandwich-structure F-P pressure sensor. [ABSTRACT FROM AUTHOR]

A neural network method has been developed for helicopter turboshaft engine residual life determination, the basis of which is a hierarchical system, which is represented in neural network model form, consisting of four layers, which determines the numerical value of the residual life. To implement a hierarchical system, a justified multilayer perceptron is used. A multilayer perceptron training algorithm has been developed, which, by introducing an initial parameter to the output layer, yields a prediction accuracy of up to 99.3%, and the adaptive Adam training rate ensures an accuracy of up to 99.4% in helicopter turboshaft engine residual life determination. A method for constructing a degradation curve has been developed that takes into account both the parameter predictions and similarities with past patterns, allowing you to determine the range of possible values of the residual life estimate, with a probability of up to 95%. The article considers an example of solving the task of determining the thermally stressed state of helicopter turboshaft engine compressor turbine blades and assessing their residual life. A computational experiment was carried out to determine the residual life of helicopter turboshaft engine compressor turbine blades, and the results, with 160 training epochs, recorded an accuracy of 99.3%, with a reduction in losses from 2.5% to 0.5% thanks to training process optimization by applying an adaptive training rate. The comparative analysis results showed that use of the multilayer perceptron as a hierarchical system gives better results than the classical RBF network and the least squares method. The first and second types of error were reduced by 2.23 times compared to the RBF network and by 4.74 times compared to the least squares method. [ABSTRACT FROM AUTHOR]

This study proposes the inclusion of noise variables in an experimental design to develop a predictive model of surface roughness in the face milling process of duplex stainless steel. A central composite design arrangement was conducted, incorporating controlled variables (cutting speed, feed rate, milling width, and depth of cut) and noise variables (tool flank wear, fluid flow, and protrusion length). Each experimental configuration was employed in duplex stainless steel milling, with the collection of roughness data under each condition. The collected data were used to train eight configurations of artificial neural networks, which were then applied to predict roughness. The results indicate that the 7-20-14-1 network configuration exhibited the lowest root mean square error, which is a measure of the difference between predicted and observed values of (0.063), followed by 7-64-32-1 (0.064) and 7-14-12-1 (0.068), respectively. Additionally, these configurations also demonstrated the lowest mean absolute error values, which calculate the average of the absolute differences between predicted and observed values of (0.046, 0.053, and 0.055, respectively), and the coefficient of determination, which is a statistical measure indicating the proportion of data variability explained by the statistical model of (0.914, 0.908, and 0.901, respectively). Therefore, the inclusion of noise variables alongside controllable process factors resulted in a more accurate and robust predictive model of surface roughness for duplex stainless steel face milling. [ABSTRACT FROM AUTHOR]

Distributed in-network processing has garnered much attention due to its capability to estimate the unknown parameter of interest from noisy measurements based on a set of cooperating sensor nodes. In previous studies, distributed in-network processing mainly focused on short-distance communication systems, wherein sensor nodes collect certain parameters of interest within their maximum communication distance. In addition, the estimation of certain parameter vectors of interest from noisy measurements, relying heavily on training signals, is achieved with a non-blind distributed estimation algorithm. However, in some applications, acquiring knowledge of training signals beforehand is difficult. Therefore, it is necessary to perform distributed estimation algorithms for receivers without training signals, a concept known as blind distributed estimation. In this paper, the generalized Sato algorithm is used to design the blind equalizer for the signal estimation. In addition, we consider extending the short-distance communication system to a long-distance communication system for an unmanned aerial vehicle (UAV) cooperating with sensor nodes in the wireless sensor network (WSN). In this scenario, the data signal is transmitted from a UAV to the WSN and is received by sensor nodes. However, the performance of the blind equalizer is susceptible to the transmission channel in long-distance communication systems. Here, we present a network topology reconfiguration approach to address the issue of distributed blind equalization. The objective of the proposed method is to discard the influence of ill-channels on the other sensor nodes by detecting ill-channels and redesigning the sensor node weights. Through computer simulation experiments, we evaluated the performance of the blind equalizer using the average mean square error (MSE) and average symbol error rate (SER). In the results of the computer simulation experiments, the blind equalizer using the proposed method outperformed the conventional methods in terms of prediction accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

This article aims to suggest an improved estimator for estimation of population median using auxiliary information under simple random sampling. The expression for the bias and mean square error are obtained up to first order approximation. We determine the MLE of the optimal values of the describing scalars. The proficiency of the suggested estimator is evaluated in comparison to the preliminary estimators using the MSE threshold. The suggested estimators are compared numerically to the ones that are currently studied in this study. The performance and novelty of the estimators was evaluated using real data sets and a simulation study. To check the efficiency of estimators empirical and theoretical study has been studied. Based on numerical result it is to be noted that our suggested estimator is more efficient as compared to existing estimators which is considered in this article in terms of least MSE and greater PRE. [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 present study proposes a generalized ratio estimator for estimating the population mean under the systematic sampling technique by considering auxiliary information and auxiliary attribute. Its bias and Mean Square Error (MSE) expressions have been derived. Mathematical comparisons are made by comparing the proposed estimator with the usual mean estimator, Swain (1964) estimator, Bhal and Tuteja (1991) estimator, and Singh and Singh (1998) estimator, and it is shown that the proposed estimator is more efficient than the previous estimators. A numerical comparison is also performed to demonstrate the superiority of the proposed estimator over the traditional estimators. The technique of ratio estimators based on systematic sampling is used to design an Exponentially Weighted Moving Average (EWMA) control chart. The Control chart is a significant industrial tool for monitoring the process mean. To evaluate performance efficiency Average run lengths (ARL) are obtained in this study. The proposed charts are compared based on out-of-control ARLs. A chart based on the proposed estimator is superior as it detects the shifts earlier than charts based on existing estimators. Empirical work is done to support the study. The suggested efficiency is further addressed utilizing real-life examples and simulations using R-Studio. [ABSTRACT FROM AUTHOR]

In real-life scenarios, encountering data with missing values is common, and if not managed carefully from the outset of a study, it can lead to significant biases in survey estimates. Various methods exist for imputing missing values in sampling procedures. Ranked set sampling (RSS) is widely recognized for its superior efficiency compared to simple random sampling. However, limited research has been conducted on ranked set sampling in the presence of missing data. This article introduces novel imputation methods designed to estimate population means in the context of missing data under RSS. These innovative estimators are developed by integrating ratio, exponential, and logarithmic estimators judiciously. Expressions for the bias and mean squared error of the proposed estimators are derived up to the first-order approximation. Through simulation studies and an application to stunting and its determinants among children in Uttar Pradesh, India's most populous state, the effectiveness of the suggested estimators in handling missing data is demonstrated. Numerical examples involving stunting in Uttar Pradesh, as well as simulated data generated using R software, confirm the superior performance of the proposed estimators over existing methods, as evidenced by comparisons of percentage relative efficiency and mean squared error. The results are promising, indicating improvement over all existing imputation methods. Additionally, pertinent recommendations are provided for survey professionals regarding future research. [ABSTRACT FROM AUTHOR]

Non-response poses a significant concern within survey sampling, occurring when individuals are either unavailable or unwilling to respond to survey questions. To address this issue, the application of non-response adjustment through auxiliary variables is widely employed to estimate missing data points. This study delves into the extensive possibilities presented by this approach, particularly focusing on calibration weighting. The study specifically investigates the challenge of non-response within the context of ranked set sampling (RSS). Within this study, we introduce two novel calibration estimators for population means. One estimator addresses scenarios of complete response, while the other pertains to cases of non-response under the ranked set sampling technique. To evaluate their performance, the Mean Square Error (MSE) and Bias expressions are derived. Furthermore, the performance of the proposed estimators is assessed through comprehensive simulation studies, encompassing both artificial and real-world datasets. For this purpose, the Mean Square Error and Bias for the ranked set samples of sizes 5, 8, 10, and 25, encompassing a total of 10,000 samples for each size category are calculated. Our findings reveal that the proposed calibration estimator, along with the imputation through calibration for non-response, consistently generates more efficient estimates compared to mean and median imputation techniques. This underscores the potential of the calibration approach in mitigating the impact of non-response, offering improved accuracy and robustness in survey sampling. [ABSTRACT FROM AUTHOR]

Based on the criterion of minimum error entropy, this paper proposes a novel conjugate gradient algorithm, called MEE-CG. This algorithm has robust performance under non-Gaussian interference. Theoretical analysis and experimental results demonstrate that the proposed algorithm displays more robust performance than the conventional conjugate gradient methods on the basis of the mean square error and the maximum correntropy criterion. Compared with the stochastic gradient minimum error entropy algorithm and the recursive minimum error entropy algorithm, the proposed algorithm provides a trade-off between computational complexity and convergence speed. [ABSTRACT FROM AUTHOR]

Ranked set sampling is widely acknowledged for its superior efficiency compared with simple random sampling. Only a small amount of work has been conducted using ranked set sampling when measurement errors are present. This study introduces innovative estimators utilizing ranked set sampling to assess the population mean when faced with both correlated and uncorrelated measurement errors. The expressions for the bias and mean squared error of the proposed estimators are derived up to the first-order approximation, revealing their superior performance compared to the other examined estimators. The efficacy of the suggested estimators in handling measurement errors was demonstrated through numerical illustration and simulation study investigations. The recommended estimators are further compared to the existing ones using the percentage relative efficiency and mean squared error, and the impact of measurement errors on the results is highlighted through the percentage computation of measurement errors. The innovative estimators suggested were formulated by judiciously incorporating ratio, exponential, and log estimators. Numerical examples involving expenditure and income, as well as simulated data generated from a normal population using R software, affirm the superior performance of the proposed estimators over existing ones such as the usual mean estimator and those proposed by Vishwakarma and Singh (2022), as evidenced by the higher percent relative efficiency and lower mean squared error. The evaluation of the percentage contribution of measurement error values confirms the impact of measurement errors on the properties of the estimators. [ABSTRACT FROM AUTHOR]

The Sine-Exponential (Sine-E) distribution is a probability distribution that combines the periodic behavior of the sine function with the decay characteristic of the exponential function. This study addresses the problem of identifying the most accurate and reliable estimation method for the parameter of the Sine-E distribution. The objective is to evaluate various parameter estimation techniques, including Maximum Likelihood Estimation (MLE), Least Squares Estimation (LSE), Weighted Least Squares Estimation (WLSE), Maximum Product of Spacing Estimation (MPSE), Cramer-von-Mises Estimation (CVME), and Anderson-Darling Estimation (ADE), using Mean Square Error (MSE) as the criterion for determining the technique with the minimum error. The study's findings reveal that as sample size increases, the parameter estimates for all techniques converge to the true parameter value, with decreases in bias, MSE, and mean relative estimates. Among the techniques evaluated, the MPSE method consistently provides estimates closest to the true parameter value and exhibits the least bias and lowest MSE across small, moderate, and large sample sizes, making it the best estimator for the Sine-E distribution. [ABSTRACT FROM AUTHOR]

The transformation technique can assist in improving the efficiency of the estimators in terms of bias and mean square error reduction. A class of ratio estimators for estimating population mean utilizing the transformation of an auxiliary variable has been proposed under stratified random sampling. The bias and mean square error of the proposed estimators up to the first order of approximation are obtained. Simulation studies and an application to rubber data in Thailand are investigated to compare the performance of the proposed class of estimators with existing estimators, the results show that the proposed class of estimators performs much better than other existing estimators under given conditions. [ABSTRACT FROM AUTHOR]

The present study suggests an enhanced class of estimators for the population mean estimation utilizing simple random sampling (SRS). The bias, mean square errors (MSE), and minimum MSE of the suggested estimators are computed to the approximation of order one. The efficiency conditions are obtained by comparing the MSE of the proposed and existing estimators. An empirical investigation is carried out using some real and artificially generated symmetric and asymmetric populations. The empirical findings are observed to be positive, clearly demonstrating the preponderance of the suggested estimators over the existing estimators.