Mean Square Error Research Articles

Residual network improves the prediction accuracy of genomic selection.

Genetic improvement of complex traits in animal and plant breeding depends on the efficient and accurate estimation of breeding values. Deep learning methods have been shown to be not superior over traditional genomic selection (GS) methods, partially due to the degradation problem (i.e. with the increase of the model depth, the performance of the deeper model deteriorates). Since the deep learning method residual network (ResNet) is designed to solve gradient degradation, we examined its performance and factors related to its prediction accuracy in GS. Here we compared the prediction accuracy of conventional genomic best linear unbiased prediction, Bayesian methods (BayesA, BayesB, BayesC, and Bayesian Lasso), and two deep learning methods, convolutional neural network and ResNet, on three datasets (wheat, simulated and real pig data). ResNet outperformed other methods in both Pearson's correlation coefficient (PCC) and mean squared error (MSE) on the wheat and simulated data. For the pig backfat depth trait, ResNet still had the lowest MSE, whereas Bayesian Lasso had the highest PCC. We further clustered the pig data into four groups and, on one separated group, ResNet had the highest prediction accuracy (both PCC and MSE). Transfer learning was adopted and capable of enhancing the performance of both convolutional neural network and ResNet. Taken together, our findings indicate that ResNet could improve GS prediction accuracy, affected potentially by factors such as the genetic architecture of complex traits, data volume, and heterogeneity.

PCSK9 inhibitors as safer therapeutics for atherosclerotic cardiovascular disease (ASCVD): Pharmacophore design and molecular dynamics analysis.

Cardiovascular disorders are still challenging and are among the deadly diseases. As a major risk factor for atherosclerotic cardiovascular disease, dyslipidemia, and high low-density lipoprotein cholesterol in particular, can be prevented primary and secondary by lipid-lowering medications. Therefore, insights are still needed into designing new drugs with minimal side effects. Proprotein convertase subtilisin/kexin 9 (PCSK9) enzyme catalyses protein-protein interactions with low-density lipoprotein, making it a critical target for designing promising inhibitors compared to statins. Therefore, we screened for potential compounds using a redesigned PCSK9 conformational behaviour to search for a significantly extensive chemical library and investigated the inhibitory mechanisms of the final compounds using integrated computational methods, from ligand essential functional group screening to all-atoms MD simulations and MMGBSA-based binding free energy. The inhibitory mechanisms of the screened compounds compared with the standard inhibitor. K31 and K34 molecules showed stronger interactions for PCSK9, having binding energy (kcal/mol) of -33.39 and -63.51, respectively, against -27.97 of control. The final molecules showed suitable drug-likeness, non-mutagenesis, permeability, and high solubility values. The C-α atoms root mean square deviation and root mean square fluctuation of the bound-PCSK9 complexes showed stable and lower fluctuations compared to apo PCSK9. The findings present a model that unravels the mechanism by which the final molecules proposedly inhibit the PCSK9 function and could further improve the design of novel drugs against cardiovascular diseases.

A deep learning approach for prediction of air quality index in smart city

Industrial developments and consumption of massive amount of fossil fuels, vehicle pollution, and other calamities upsurges the AQI (Air Quality Index) of major cities in a drastic manner. Owing to these factors, it is important to take proactive measures for reducing the air pollution in order to avoid life- threatening consequence. Therefore, prediction of air quality is significant for improving the health of living beings as highly polluted regions have a higher concentration of pollutants mixed in the air, affecting the respiratory system and reducing the lifetime. To control pollution, AQI is used as a measure for estimating the pollutant content in the air. Even though many existing techniques have predicted AQI, enhancement is required in prediction algorithms with minimized loss. To address the challenges in traditional algorithms, the proposed smart cities-based AQI prediction intends to utilize the proposed regression algorithm in the dataset, namely Air- Quality-Data, which collected harmful pollutants on an hourly and daily basis from multiple cities in India between 2015 to 2020. To achieve prediction efficiency with reduced loss, pre-processing of input data is being performed using Deep GAN (Generative Adversarial Network). It performs the imputation of data in place of missing values to improve accurate prediction. Additionally, feature scaling normalizes independent real-data features to a fixed scale. With the processed data, regression is done through modified Stacked Attention GRU with KL divergence, which predicts Ernakulam, Chennai and Ahmedabad cities with higher, medium, and low levels of AQI in India. The performance of the proposed regression algorithm is measured using metrics such as MAE (Mean Absolute Error), MSE (Mean Square Error), R2 (Coefficient of determination), MAPE (Mean Absolute Percentage Error), and RMSE (Root Mean Square Error) and better MAE, MSE, R2, MAPE and RMSE obtained by the model is 0.1013, 0.0134, 0.9479, 0.1152 and 0.1156. Internal assessment and comparative analysis performed with existing regression algorithms exhibit lower loss values obtained from the present research, which determines the efficacy of the proposed model.

AI-based predictive approach via FFB propagation in a driven-cavity of Ostwald de-Waele fluid using CFD-ANN and Levenberg–Marquardt

The integration of Artificial Intelligence (AI) and Machine Learning (ML) techniques into computational science has ushered in a new era of innovation and efficiency in various fields, with particular significance in computational fluid dynamics (CFD). Several methods based on AI and Machine Learning (ML) have been standardized in many fields of computational science, including computational fluid dynamics (CFD). This study aims to couple CFD with artificial neural networks (ANNs) to predict the fluid forces that arise when a flowing fluid interacts with obstacles installed in the flow domain. The momentum equation elucidating the flow has been simulated by adopting the finite element method (FEM) for a range of rheological and kinematic conditions. Hydrodynamic forces, including pressure drop between the back and front of the obstacle, surface drag, and lift variations, are measured on the outer surface of the cylinder via CFD simulations. This data has subsequently been fed into a Feed-Forward Back (FFB) propagation neural network for the prediction of such forces with completely unknown data. For all cases, higher predictivity is achieved for the drag coefficient (CD) and lift coefficient (CL) since the mean square error (MSE) is within ± 2% and the coefficient of determination (R) is approximately 99% for all the cases. The influence of pertinent parameters like the power law index (n) and Reynolds number (Re) on velocity, pressure, and drag and lift coefficients is also presented for limited cases. Moreover, a significant reduction in computing time has been noticed while applying hybrid CFD-ANN approach as compared with CFD simulations only.

Application of improved DBN and GRU based on intelligent optimization algorithm in power load identification and prediction

Non intrusive load monitoring belongs to the key technologies of intelligent power management systems, playing a crucial role in smart grids. To achieve accurate identification and prediction of electricity load, intelligent optimization algorithms are introduced into deep learning optimization for improvement. A load recognition model combining sparrow search algorithm and deep confidence network is designed, as well as a gated recurrent network prediction model on the grounds of particle swarm optimization. The relevant results showed that the sparrow search algorithm used in the study performed well on the solution performance evaluation metrics with a minimum value of 0.209 for the inverse generation distance and a maximum value of 0.814 for the hyper-volume. The accuracy and recall values of the optimized load identification model designed in the study were relatively high. When the accuracy was 0.9, the recall rate could reach 0.94. The recognition accuracy of the model on the basis of the test set could reach up to 0.924. The lowest classification error was only 0.05. The maximum F1 value of the harmonic evaluation index of the bidirectional gated recurrent network optimized by particle swarm optimization converged to 90.06%. The loss function had been optimized by particle swarm optimization, and both the convergence value and convergence speed had been markedly enhanced. The average absolute error and root mean square error of the prediction model were both below 0.3. Compared to the bidirectional gated recurrent model before optimization, the particle swarm optimization strategy had a significant improvement effect on prediction details. In addition, the research method had superior recognition response speed and adaptability in real application environments. This study helps to understand the load demand of the power system, optimize the operation of the power grid, and strengthen the reliability, efficiency, and sustainability of the power system.

Density dependent constitutive model for Bi-2212 powder compression deformation

Bi-2212 HTS materials are fabricated into multi-filamentary wires via powder-in-tube (PIT) method followed by proper heat treatment to obtain superconductivity, but how to predict the large compression deformation behaviors of the Bi-2212 powder is critical to design the processing of the Bi-2212 HTS wire. Drucker Prager/Cap (DPC) model was the most commonly used model for powders including Bi-2212 with soil-like mechanical behavior to consider its shear failure as well as hydrostatic compression. However, the parameters for DPC Cap evolve with densities change and the original model is inadequate to precisely describe the densification process of Bi-2212 powder with large strain. In this study, the modified DPC model with density dependent parameters was introduced for Bi-2212 powder compressions by measuring the failure strength and hydrostatic compressive behavior under different density states. The DPC yield surface was plotted with an evolution trend of non-linear outward expansion with density increased. FEM model of uniaxial compression based on the as-introduced model was built with subroutine VUSDFLD applied. The distribution of Mises stress and relative density were analyzed. The axial stress-density curve for FEM and experimental results were normalized and quantitively evaluated by Mean Square Error (MSE). The introduced model shows good convergence and could match the experimental results well with normalized MSE of 0.000207 and Root Mean Square Error (RMSE) of 0.0144, indicating the mean error percentage of 1.44%. The model introduced in this article provides supports toward large strain deformation simulation of Bi-2212 powder.

Advancing 100m sprint performance prediction: A machine learning approach to velocity curve modeling and performance correlation.

This study presents a novel approach to modeling the velocity-time curve in 100m sprinting by integrating machine learning algorithms. It critically addresses the limitations of traditional speed models, which often require extensive and intricate data collection, by proposing a more accessible and accurate method using fewer variables. The research utilized data from various international track events from 1987 to 2019. Two machine learning models, Random Forest (RF) and Neural Network (NN), were employed to predict the velocity-time curve, focusing on the acceleration phase of the sprint. The models were evaluated against the traditional exponential speed model using Mean Squared Error (MSE), with the NN model demonstrating superior performance. Additionally, the study explored the correlation between maximum velocity, the time of maximum velocity occurrence, the duration of the maximum speed phase, and the overall 100m sprint time. The findings indicate a strong negative correlation between maximum velocity and final time, offering new insights into the dynamics of sprinting performance. This research contributes significantly to the field of sports science, particularly in optimizing training and performance analysis in sprinting.

Transfer-Learning-Enhanced Regression Generative Adversarial Networks for Optimal eVTOL Takeoff Trajectory Prediction

Electric vertical takeoff and landing (eVTOL) aircraft represent a crucial aviation technology to transform future transportation systems. The unique characteristics of eVTOL aircraft include reduced noise, low pollutant emission, efficient operating cost, and flexible maneuverability, which in the meantime pose critical challenges to advanced power retention techniques. Thus, optimal takeoff trajectory design is essential due to immense power demands during eVTOL takeoffs. Conventional design optimizations, however, adopt high-fidelity simulation models in an iterative manner resulting in a computationally intensive mechanism. In this work, we implement a surrogate-enabled inverse mapping optimization architecture, i.e., directly predicting optimal designs from design requirements (including flight conditions and design constraints). A trained inverse mapping surrogate performs real-time optimal eVTOL takeoff trajectory predictions with no need for running optimizations; however, one training sample requires one design optimization in this inverse mapping setup. The excessive training cost of inverse mapping and the characteristics of optimal eVTOL takeoff trajectories necessitate the development of the regression generative adversarial network (regGAN) surrogate. We propose to further enhance regGAN predictive performance through the transfer learning (TL) technique, creating a scheme termed regGAN-TL. In particular, the proposed regGAN-TL scheme leverages the generative adversarial network (GAN) architecture consisting of a generator network and a discriminator network, with a combined loss of the mean squared error (MSE) and binary cross-entropy (BC) losses, for regression tasks. In this work, the generator employs design requirements as input and produces optimal takeoff trajectory profiles, while the discriminator differentiates the generated profiles and real optimal profiles in the training set. The combined loss facilitates the generator training in the dual aspects: the MSE loss targets minimum differences between generated profiles and training counterparts, while the BC loss drives the generated profiles to share analogous patterns with the training set. We demonstrated the utility of regGAN-TL on optimal takeoff trajectory designs for the Airbus A3 Vahana and compared its performance against representative surrogates, including the multi-output Gaussian process, the conditional GAN, and the vanilla regGAN. Results showed that regGAN-TL reached the 99.5% generalization accuracy threshold with only 200 training samples while the best reference surrogate required 400 samples. The 50% reduction in training expense and reduced standard deviations of generalization accuracy achieved by regGAN-TL confirmed its outstanding predictive performance and broad engineering application potential.

SchNetPack Hyperparameter Optimization for a More Reliable Top Docking Scores Prediction.

Options to improve the extrapolation power of the neural network designed using the SchNetPack package with respect to top docking scores prediction are presented. It is shown that hyperparameter tuning of the atomistic model representation (in the schnetpack.representation) improves the prediction of the top scoring compounds, which have characteristically a low incidence in randomized data sets for training of machine learning models. The prediction robustness is evaluated according to the mean square error (MSE) and the entropy of the average loss landscape decrease. Admittedly, the improvement of the top scoring compounds' prediction accuracy comes with the penalty of worsening the overall prediction power. It is revealed that the most impactful hyperparameter is the cutoff (5 Å is reported as the optimal choice). Other parameters (e.g., number of radial basis functions, number of interaction layers of the neural network, feature vector size or its batch size) are found to not affect the prediction robustness of the top scoring compounds in any comparable way relative to the cutoff. The MSE of the best docking score prediction (below -13 kcal/mol) improves from ca. 3.5 to 0.9 kcal/mol, while the prediction of less potent compounds (-13 to -11 kcal/mol) shows a lesser improvement, i.e., a decrease of MSE from 1.6 to 1.3 kcal/mol. Additionally, oversampling and undersampling of the training set with respect to the top scoring compounds' abundance is presented. The results indicate that the cutoff choice performs better than over- or undersampling of the training set, with undersampling performing better than oversampling.

Metaheuristic and Heuristic Algorithms-Based Identification Parameters of a Direct Current Motor

Direct current motors are widely used in industry applications, and it has become necessary to carry out studies and experiments for their optimization. In this manuscript, a comparison between heuristic and metaheuristic algorithms is presented, specifically, the Steiglitz–McBride, Jaya, Genetic Algorithm (GA), and Grey Wolf Optimizer (GWO) algorithms. They were used to estimate the parameters of a dynamic model that approximates the actual responses of current and angular velocity of a DC motor. The inverse of the Euclidean distance between the current and velocity errors was defined as the fitness function for the metaheuristic algorithms. For a more comprehensive comparison between algorithms, other indicators such as mean squared error (MSE), standard deviation, computation time, and key points of the current and velocity responses were used. Simulations were performed with MATLAB/Simulink 2010 using the estimated parameters and compared to the experiments. The results showed that Steiglitz–McBride and GWO are better parametric estimators, performing better than Jaya and GA in real signals and nominal parameters. Indicators say that GWO is more accurate for parametric estimation, with an average MSE of 0.43%, but it requires a high computational cost. On the contrary, Steiglitz–McBride performed with an average MSE of 3.32% but required a much lower computational cost. The GWO presented an error of 1% in the dynamic response using the corresponding indicators. If a more accurate parametric estimation is required, it is recommended to use GWO; however, the heuristic algorithm performed better overall. The performance of the algorithms presented in this paper may change if different error functions are used.

The analysis of ecological security and tourist satisfaction of ice-and-snow tourism under deep learning and the Internet of Things

This paper aims to propose a prediction method based on Deep Learning (DL) and Internet of Things (IoT) technology, focusing on the ecological security and tourist satisfaction of Ice-and-Snow Tourism (IST) to solve practical problems in this field. Accurate predictions of ecological security and tourist satisfaction in IST have been achieved by collecting and analyzing environment and tourist behavior data and combining with DL models, such as convolutional and recurrent neural networks. The experimental results show that the proposed method has significant advantages in performance indicators, such as accuracy, F1 score, Mean Squared Error (MSE), and correlation coefficient. Compared to other similar methods, the method proposed improves accuracy by 3.2%, F1 score by 0.03, MSE by 0.006, and correlation coefficient by 0.06. These results emphasize the important role of combining DL with IoT technology in predicting ecological security and tourist satisfaction in IST.

Adaptive neuro fuzzy technology to enhance PID performances within VCA for grid-connected wind system under nonlinear behaviors: FPGA hardware implementation

Wind Energy Conversion Systems (WECSs) exhibit nonlinear behavior due to internal and external disturbances, which can significantly impact the control performance. Firstly, this paper proposes a Vector Control Approach (VCA) based on Adaptive Neuro Fuzzy (ANF) of Proportional Integral Derivative (PID) controllers for a variable speed Permanent Magnet Synchronous Generator (PMSG)-based WECS connected to the grid to address these issues. The proposed ANF-PID controller combines the robustness of the fuzzy logic with the neural network's performance to ensure high accuracy, excellent tracking, and robustness against the WECS's nonlinear behavior. The neural network automates the placement of fuzzy logic membership functions. Secondly, this paper suggests a real-time hardware implementation of the VCA based on ANF-PID using a Field Programmable Gate Array (FPGA) to reduce the processing time and the WECS's sampling period. The effectiveness of the VCA based on ANF-PID controllers is validated by conducting a numerical simulation within the Matlab-Simulink using the Xilinx System Generator tool, alongside an experimental in-the-loop hardware implementation using FPGA board. Different scenarios are conducted to validate the robustness and stability of the proposed VCA based on ANF-PID control schemes, which is compared to Conventional Fuzzy PID (C-FPID) and PID controllers. The results exhibit that the VCA based on ANF-PID controllers outperforms VCA-C-FPID and VCA-PID controllers in terms of precision, tracking accuracy, and robustness against the WECS's nonlinear behavior and the PMSG parameter variations. The performances of the proposed controllers are tested under some criteria. In fact, the proposed ANF-PID controller provides a Mean Absolute Error (MAE), a Mean Squared Error (MSE) and a Root Mean Squared Error (RMSE) of 8.1911 × 10−04, 8.4181 × 10−05 and 0.0092, respectively. Compared to the C-FPID controller, the proposed controller offers an improvement gain of 98.96 %, 99.61 %, and 93.79 % of MAE, MSE, and RMSE, respectively. When compared to the PID controller, its improvement is even more significant, with a reduction of 99.9919 %, 99.9999 %, and 99.9288 % of MAE, MSE, and RMSE, respectively. In addition, the ANF-PID-based VCA utilizes hardware resources on the FPGA efficiently, requiring only 65.60 % slices LUT, 0.28 % LUTRAM, and 22.99 % FF. This makes it a more cost-effective option compared to the VCA-C-FPID controller for diverse control systems.

Radar-Based Precipitation Nowcasting Based on Improved U-Net Model

Rainfall nowcasting is the basis of extreme rainfall monitoring, flood prevention, and water resource scheduling. Based on the structural features of the U-Net model, we proposed the Double Recurrent Residual Attention Gates U-Net (DR2A-UNet) deep-learning model to carry out radar echo extrapolation. The model was trained with mean square error (MSE) and balanced mean square error (BMSE) as loss functions, respectively. The dynamic Z-R relationship was applied for quantitative rainfall estimation. The reference U-Net model, U-Net++, and the ConvLSTM were used as control experiments to carry out radar echo extrapolation. The results showed that the model trained by BMSE had better extrapolation. For 1 h lead time, the rainfall nowcasted by each model could reflect the actual rainfall process. DR2A-UNet performed significantly better than other models for intense rainfall, with a higher extrapolation accuracy for echo intensity and variability processes. At the 2 h lead time, the nowcast accuracy of each model was significantly reduced, but the echo extrapolation and rainfall nowcasting of DR2A-UNet were better.

Research on the application of deep learning techniques in stock market prediction and investment decision-making in financial management

Introduction: This paper introduces a deep learning approach based on Convolutional Neural Networks (CNN), Bidirectional Long Short-Term Memory Networks (BiLSTM), and attention mechanism for stock market prediction and investment decision making in financial management. These methods leverage the advantages of deep learning to capture complex patterns and dependencies in financial time series data. Stock market prediction and investment decision-making have always been important issues in financial management.Methods: Traditional statistical models often struggle to handle nonlinear relationships and complex temporal dependencies, thus necessitating the use of deep learning methods to improve prediction accuracy and decision effectiveness. This paper adopts a hybrid deep learning model incorporating CNN, BiLSTM, and attention mechanism. CNN can extract meaningful features from historical price or trading volume data, while BiLSTM can capture dependencies between past and future sequences. The attention mechanism allows the model to focus on the most relevant parts of the data. These methods are integrated to create a comprehensive stock market prediction model. We validate the effectiveness of the proposed methods through experiments on real stock market data. Compared to traditional models, the deep learning model utilizing CNN, BiLSTM, and attention mechanism demonstrates superior performance in stock market prediction and investment decision-making.Results and Discussion: Through ablation experiments on the dataset, our deep learning model achieves the best performance across all metrics. For example, the Mean Absolute Error (MAE) is 15.20, the Mean Absolute Percentage Error (MAPE) is 4.12%, the Root Mean Square Error (RMSE) is 2.13, and the Mean Squared Error (MSE) is 4.56. This indicates that these methods can predict stock market trends and price fluctuations more accurately, providing financial managers with more reliable decision guidance. This research holds significant implications for the field of financial management. It offers investors and financial institutions an innovative approach to better understand and predict stock market behavior, enabling them to make wiser investment decisions.

Graph Neural Networks to Simulate Flexible Pavement Responses Using Three-Dimensional Finite Element Analysis Data

The significant computational costs and efforts required for accurate three-dimensional (3D) finite element (FE) pavement response calculations necessitate an expedited approach. This study proposes a graph neural network (GNN)-based simulator for the modeling of 3D pavement structural responses under tire loading. The GNN model was trained using 240 simulations of 3D pavement FE data of flexible pavement structures. The simulator represented the state of pavement structure meshes in FE analysis at any given timestep as a graph, with FE nodes encoded as graph nodes and mesh edges as graph edges. The dynamic behaviors of pavement FEs were computed via learned message-passing between two graphs within two continuous timesteps. The one-step mean squared error (MSE) and rollout MSE were used as evaluation metrics for the GNN model. The results showed that, given an initial state of FE responses, the model could perform accurate one-step predictions, extending to trajectory predictions with one-step MSE as low as [Formula: see text] and rollout MSE around [Formula: see text]. The prediction framework is efficient; it requires a week of model training but only a mere 5 min of prediction for each single case. This a contrast to traditional 3D FE analyses that can span hours to weeks for a single case. The hyperparameters, including the number of message-passing steps M and the number of historical timesteps C, were established as 10 and 1, respectively, based on model performance and computation time. It was also observed that data normalization before training could significantly reduce model simulation noise.

An ensemble learning model for forecasting water-pipe leakage

Based on the benefits of different ensemble methods, such as bagging and boosting, which have been studied and adopted extensively in research and practice, where bagging and boosting focus more on reducing variance and bias, this paper presented an optimization ensemble learning-based model for a large pipe failure dataset of water pipe leakage forecasting, something that was not previously considered by others. It is known that tuning the hyperparameters of each base learned inside the ensemble weight optimization process can produce better-performing ensembles, so it effectively improves the accuracy of water pipe leakage forecasting based on the pipeline failure rate. To evaluate the proposed model, the results are compared with the results of the bagging ensemble and boosting ensemble models using the root-mean-square error (RMSE), the mean square error (MSE), the mean absolute error (MAE), and the coefficient of determination (R2) of the bagging ensemble technique, the boosting ensemble technique and optimizable ensemble technique are higher than other models. The experimental result shows that the optimizable ensemble model has better prediction accuracy. The optimizable ensemble model has achieved the best prediction of water pipe failure rate at the 14th iteration, with the least RMSE = 0.00231 and MAE = 0.00071513 when building the model that predicts water pipe leakage forecasting via pipeline failure rate.

A complexity efficient penta-diagonal quantum smoothing filter for bio-medical signal denoising: a study on ECG

Extracting information-bearing signal from a noisy environment has been a practical challenge in both classical and quantum computing formalism, especially in critical signal processing applications. To filter out the effect of noise, we propose a quantum smoothing filter built upon quantum formalism-based circuits applied for electrocardiogram signal denoising. The proposed quantum filter is a conceptually novel framework with an advantage in computational complexity as compared to the existing classical filters, such as discrete wavelet transform and empirical mode decomposition, whereas it achieves similar performance metrics for the accuracy of the filter. Further, we exploit the penta-diagonal Toeplitz structure of the smoothing filter, which gives approximately 48%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$48\\%$$\\end{document} gate cost reduction for 10 qubit circuit compared to the standard Hamiltonian simulation without structure. The run-time complexity using the quantum matrix inversion technique for the structured matrix is given by O~κ2poly(logN)εP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ilde{{\\mathscr {O}}}\\left( \\frac{\\kappa ^2 \ ext {poly}(\\log {N})}{\\varepsilon _P}\\right)$$\\end{document} for condition number κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa$$\\end{document} of the N×N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N\ imes N$$\\end{document} filter matrix within precision εP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon _P$$\\end{document}. Embedding fixed sparsity of the banded matrix, the quantum filter shows potentially better run-time complexity than classical filtering techniques. For the quantifiable research results of our work, we have shown several performance metrics, such as mean-square error and peak signal-to-noise ratio analysis, with a bound of error due to observation noise, simulation error and quantum measurement uncertainty.

Spectroscopic Measurement of Atmospheric-pressure Non-equilibrium Ar Plasma Using Continuum and Line Spectra

Abstract A robust method for determining the electron temperature and density of atmospheric-pressure non-equilibrium argon plasmas is reported. The methodology is based on the analysis of the continuum and line spectra of the plasma. Assuming that the electron energy distribution function (EEDF) is expressed as a two-temperature generalized EEDF (GEEDF), the gamma value of the GEEDF is determined through a grid search of the continuum spectrum analysis given by the bremsstrahlung process, which minimizes the mean-squared logarithmic error (MSLE). In addition, the relationship between the gamma value and the electron temperature and density is determined. Utilizing this relationship, the electron temperature and density are determined by minimizing the MSLE between the excited-state densities obtained from the line spectrum analysis and numerically calculated using the collisional-radiative model. This methodology yielded results that satisfied both continuum and line spectrum analyses. In addition, the same analysis was conducted either by continuum spectrum analysis or by line spectrum alone to compare the results.

Optical tunability with superlattice hyperbolic metamaterial coatings

Optical tunability is demonstrated with multi-metal hyperbolic metamaterial (HMM) structures on varying substrate surfaces. A systematic uniaxial modeling methodology is adapted from classical approaches to extract the anisotropic permittivity of the films to identify epsilon-near-zero (ENZ) behavior over a wide range of metal volume fractions (φ). The anisotropic model accuracy is quantified by a mean squared error (MSE) with the presented modeling routine resulting in a MSE < 35 for all samples. The optical model thicknesses were verified with transmission electron microscopy (TEM) imaging and measurements. This study also demonstrates the ability to tune the optical responses in the visible-to-infrared frequencies with surface microtexturing and applied strain with HMM coatings on flexible Kapton substrates. Furthermore, the structured films and modeling procedure lay the groundwork for future studies on coupling the anisotropic optical and thermal properties for control over advanced multifunctional thin-film coatings.

Machine learning prediction of health risk and spatial dependence of geogenic contaminated groundwater from the Hetao Basin, China

Geogenic contaminated groundwater (GCG), characterized by elevated arsenic, fluoride, and iodine levels, present a significant challenge to public health and government management. Conventional survey-based approaches of collecting groundwater samples, conducting physicochemical tests, and performing spatial interpolation to obtain regional groundwater chemical component maps are inefficient and costly. More importantly, it does not take into account the actual hydrogeological conditions or the characteristics of pollutant transport and enrichment. To address this issue, we utilized Support Vector Machine (SVM), Random Forest (RF), Adaptive Boosting (AdaBoost), and Extreme Gradient Boosting (XGBoost) to analyze the likelihood of occurrence of arsenic, fluoride, and iodine as well as their spatial distribution in shallow groundwater from the Hetao Basin. Our study incorporated 20 indicators related to meteorology, soil physicochemical properties, and groundwater conditions, along with 1505 labeled samples consisting of groundwater arsenic, fluoride, and iodine concentrations and their corresponding coordinates. Subsequently, the study automatically analyzed the meteorological, soil physicochemical properties and groundwater conditions by constructing a machine learning model using the available data. In order to optimise and select the best prediction model, this paper presents a quantitative evaluation of the prediction performance of various machine learning models. The accuracy (AC), area under curve (AUC) and mean squared error (MSE) were calculated to predict the spatial distribution of CGC. Subsequently, the optimized model for predicting the spatial distribution of GCG was selected. The results showed that the XGBoost algorithm provided optimal predictions for groundwater with arsenic concentrations above 10 μg/L and fluoride concentrations exceeding 1.5 mg/L, whereas the RF model provided the best predictions for groundwater with arsenic concentrations surpassing 50 μg/L and iodine concentrations exceeding 100 μg/L. Subsequently, groundwater health risk zones were delineated based on an optimal prediction model, and demographic analysis was conducted in both the direct and potential groundwater risk zones. Model predictions indicated that hundreds of thousands of people in the Hetao Basin were facing a public health crisis caused by high concentrations of arsenic, fluoride and iodine in groundwater. These findings underscore the significant health challenge in the study area. Considering the agricultural development and increasing groundwater use in the area, our findings can guide local governments in managing the extent of groundwater development, establishing control zones, and enhancing protection measures for populations at risk from groundwater contamination.