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Phase-only nulling with low sidelobe level is a problem of interest in array synthesis which is a tedious problem without an analytical solution. In this communication, a novel framework for the phase-only nulling based on radial basis function neural network (RBFNN) is proposed to predict the phase adjustment for the array pattern nulling with sidelobe control. In the process of network training, the parameters of the RBFNN are optimized simultaneously based on the self-adaptive differential evolution (SADE) algorithm, which aims to improve the approximation ability and reduce the complexity of the network. Simulation results of the optimized RBFNN models show compact network structure and form the array pattern under desired performance with good generalization capability.

Electric power generated in a centralized station is transmitted through the transmission system and supplied to the consumer end through an electric distribution substation. Electric power losses ...

HighlightsAs a non-invasive temperature detection technology, IRT can provide dynamic information on skin temperature changes caused by physiological processes of livestock.IRT will become a more valuable detection tool for evaluating various signs and behavior changes of livestock.With the continuous development of information technology, it is necessary to use IRT to explore more expected and innovative information.Abstract. Infrared thermography (IRT) is a non-invasive temperature detection technology characterized by non-destructive, long-distance measurement and high sensitivity. IRT measures mid-wave to long-wave infrared radiation emanating from objects and converts this radiation into visual images or videos of the temperature distribution and temperature changes. Because temperature is an important environmental parameter that affects livestock physiology and metabolic heat production, measurement of animal temperature and energy exchange in field environments is a useful tool for understanding physiological changes in animals. Traditional measurement methods of animal temperature are extremely time-consuming and labor-intensive. As a non-contact method, IRT provides a new method for physiological data acquisition. However, IRT is also subject to a number of uncertainties, thus requiring optimal modeling using built-in software. Therefore, this study reviews applications of IRT in livestock production, including reproduction, growth, and diseases, and discusses some of the better-known approaches and the latest research findings for IRT in livestock production. Keywords: Diseases, Growth, Infrared thermography, Reproduction.

Image processing continues to be a challenging topic in many scientific fields such as medicine, computational physics and informatics especially with the discovery and development of 3D cases. Therefore, development of suitable tools that guarantee a best treatment is a necessity. Spherical shapes are a big class of 3D images whom processing necessitates adoptable tools. This encourages researchers to develop special mathematical bases suitable for 3D spherical shapes. The present work lies in this whole topic with the application of special spherical harmonics bases. In Jallouli et al. (Soft Comput 2018. https://doi.org/10.1007/s00500-018-3596-9), theoretical framework of spherical harmonics filters adapted to image processing has been developed. In the present paper, new approach based on Jallouli et al. (Soft Comput 2018. https://doi.org/10.1007/s00500-018-3596-9) is proposed for the reconstruction of images provided with spherical harmonics Shannon-type entropy to evaluate the order/disorder of the reconstructed image. Efficiency and accuracy of the approach are demonstrated by a simulation study on several spherical models.

A simplified procedure has been developed to optimize the molding processes of thermosetting resins. The proposed methodology involves the classical finite element commercial package (NISA II v. 17). Here, the theoretical background and numerical implementation of the procedure are described. Various design variables that can describe the RIM are discussed. The solved example represents the influence of the heating regime on the curing process. The results are compared with the results obtained with the use of full analysis conducted with the aid of the finite volume analysis (filling and curing stages). They demonstrate the evident advantages of using the simplified optimization approach.

This paper introduces an accelerated algorithm for evaluating criteria for comparing the spectral similarity of color, Bidirectional Texture Functions (BTF), and hyperspectral textures. The criteria credibly compare texture pixels by simultaneously considering the pixels with similar values and their mutual ratios. Such a comparison can determine the optimal modeling or acquisition setup by comparing the original data with their synthetic simulations. Other applications of the criteria can be spectral-based texture retrieval or classification. Together with existing alternatives, the suggested methods were extensively tested and compared on a wide variety of color, BTF, and hyper-spectral textures. The methods’ performance quality was examined in a long series of specially designed experiments where proposed ones outperform all tested alternatives.

Objective. The purpose of this study was to investigate the feasibility of applying handcrafted radiomics (HCR) and deep learning-based radiomics (DLR) for the accurate preoperative classification of glioblastoma (GBM) and solitary brain metastasis (BM). Methods. A retrospective analysis of the magnetic resonance imaging (MRI) data of 140 patients (110 in the training dataset and 30 in the test dataset) with GBM and 128 patients (98 in the training dataset and 30 in the test dataset) with BM confirmed by surgical pathology was performed. The regions of interest (ROIs) on T1-weighted imaging (T1WI), T2-weighted imaging (T2WI), and contrast-enhanced T1WI (T1CE) were drawn manually, and then, HCR and DLR analyses were performed. On this basis, different machine learning algorithms were implemented and compared to find the optimal modeling method. The final classifiers were identified and validated for different MRI modalities using HCR features and HCR + DLR features. By analyzing the receiver operating characteristic (ROC) curve, the area under the curve (AUC), accuracy, sensitivity, and specificity were calculated to evaluate the predictive efficacy of different methods. Results. In multiclassifier modeling, random forest modeling showed the best distinguishing performance among all MRI modalities. HCR models already showed good results for distinguishing between the two types of brain tumors in the test dataset (T1WI, AUC = 0.86; T2WI, AUC = 0.76; T1CE, AUC = 0.93). By adding DLR features, all AUCs showed significant improvement (T1WI, AUC = 0.87; T2WI, AUC = 0.80; T1CE, AUC = 0.97; p < 0.05 ). The T1CE-based radiomic model showed the best classification performance (AUC = 0.99 in the training dataset and AUC = 0.97 in the test dataset), surpassing the other MRI modalities ( p < 0.05 ). The multimodality radiomic model also showed robust performance (AUC = 1 in the training dataset and AUC = 0.84 in the test dataset). Conclusion. Machine learning models using MRI radiomic features can help distinguish GBM from BM effectively, especially the combination of HCR and DLR features.

Computational cardiology is rapidly becoming the gold standard for innovative medical treatments and device development. Despite a worldwide effort in mathematical and computational modeling research, the complexity and intrinsic multiscale nature of the heart still limit our predictability power raising the question of the optimal modeling choice for large-scale whole-heart numerical investigations. We propose an extended numerical analysis among two different electrophysiological modeling approaches: a simplified phenomenological one and a detailed biophysical one. To achieve this, we considered three-dimensional healthy and infarcted swine heart geometries. Heterogeneous electrophysiological properties, fine-tuned DT-MRI -based anisotropy features, and non-conductive ischemic regions were included in a custom-built finite element code. We provide a quantitative comparison of the electrical behaviors during steady pacing and sustained ventricular fibrillation for healthy and diseased cases analyzing cardiac arrhythmias dynamics. Action potential duration (APD) restitution distributions, vortex filament counting, and pseudo-electrocardiography (ECG) signals were numerically quantified, introducing a novel statistical description of restitution patterns and ventricular fibrillation sustainability. Computational cost and scalability associated with the two modeling choices suggests that ventricular fibrillation signatures are mainly controlled by anatomy and structural parameters, rather than by regional restitution properties. Finally, we discuss limitations and translational perspectives of the different modeling approaches in view of large-scale whole-heart in silico studies.

To assess outcomes of a variant of traditional modeling ("optimal modeling," OM) in patients with residual curvature following prosthesis implantation.We performed a retrospective review of all patients who underwent penile implant insertion. Patients with30° of residual curvature after cylinder placement and inflation underwent OM and were compared 1:1 to a demographically-matched cohort who received implantation without ancillary straightening. Optimal modeling was performed by forcibly bending the erect penis in the direction opposite the point of maximal curvature while maintaining glanular pressure to prevent urethral injury. This was performed for 90-second intervals for as many cycles as necessary to achieve15° curvature.Eighty patients were included in the final analysis; 40 (50.0%) underwent optimal modeling while 40 (50.0%) did not need additional straightening following surgery. The mean premodeling curvature was 47.8° (range 30°-90°) while post-modeling curvature improved to a mean of 10.6° (range 0°-30°, P.001); 87.5% of patients had15° of residual curvature. Patients in the OM cohort experienced longer operative times (82.7 vs 75.8 min, P = .15). No patient in either group experienced an intraoperative or postoperative complication at a mean follow-up of 29.9 months.Although many prosthetic urologists forego manual modeling in cases of moderate-severe penile curvature, our contemporary series shows it to be both safe and effective. OM may preclude the need for more time-consuming and complex surgical procedures.

C3and C4are major functional types in terrestrial biosphere models, with photosynthesis traits as important input parameters. The evolution of C4required reorganizations of Calvin-Benson-cycle and coordination of C4-cycle enzymes, resulting in divergences of physiological traits between C3and C4. In addition, photosynthesis further optimized after the evolution of C4causing diversification within C4lineages due to different evolutionary histories. We combined optimality modeling, physiological measurements and phylogenetic analysis to examine how various aspects of C4photosynthetic machinery were reorganized and coordinated within C4lineages and as compared to closely-related C3in grasses. Optimality models and measurements indicated a higher maximal electron transport to maximal Rubisco carboxylation ratio (Jmax/Vcmax) in C4than C3, consistent with the optimal prediction to maximize photosynthesis. The coordination between Calvin-Benson and C4cycles (Vpmax/Vcmax), however, is in line with the optimal modeling results under 200 ppm, as opposed to current CO2. Such inconsistencies can be explained by a slowly declining assimilation rate beyond optimalVpmax/Vcmax. Although rapid coordination occurred early in C4evolution, C4is still under optimizing processes and photosynthetic measures have continued to increase across time. Lastly, better understandings ofJmax/Vcmax,Vpmax/Vcmaxand fluorescence-based-electron-transport proffer enhanced approaches to parameterize terrestrial biosphere models.

In this paper, we develop a forecasting model for the growth of Cryogenic Electron Microscopy (Cryo-EM) experimental data time series using autoregressive (AR) model. We employ the optimal modeling order that maximizes the estimation accuracy while maintaining the least normalized prediction error. The proposed model has been efficiently used to forecast the growth of cryo-EM data for the next 10 years, 2019–2028. The time series for the number of released three-dimensional Electron Microscopy (3DEM) images along with the time series of the annual number of 3DEM achieving resolution 10 A or better are used. The data was collected from the public Electron Microscopy Data Bank (EMDB). The simulation results showed that the optimal model orders to estimate both datasets are \( AR\left( 5 \right) \) and \( AR\left( 6 \right) \) respectively. Consequently, the optimal models obtained an estimation accuracy of \( 96.8\%, \) and \( 85\% \) for 3DEM experiments time series and 3DEM resolutions time series, respectively. Hence, the forecasting results reveal an exponential increasing behavior in the future growth of annual released of 3DEM and, similarly, for the annual number of 3DEM achieving resolution 10 A or better.

Our proposed integral optimality criteria for mathematical modeling of relaxation/recovery processes in polymer textile materials have been developed using integral governing equations of the Boltzmann–Volterra type. Practical realization of our criteria presumes a large number of computations, which is why we need to use modern information technologies for optimal modeling and prediction of the indicated processes.

Recently, computer technologies have provided the researchers with the new approaches for modeling and better understanding the role of the factors that are involved in plant growth in vitro. To develop new models for the optimization of growth conditions, it is reasonable to use plants with a high speed of vegetative in vitro reproduction, such as duckweed (Lemnaceae family). This article focuses on the trophic levels of the two types of duckweeds (Wolffia arrhiza and Lemna minor). Using the development of the optimal modeling of the biological processes we have obtained the prescriptions for individually-balanced culture medium that enable 3.0 higher yields of the total soluble protein from each of the populations for both types of Lemnaceae.

A mathematical apparatus which foresees the use of vector analysis is offered. It provides new possibilities for the analysis of economic processes. The reduction of nonlinear tasks to the simplified linear form can result in the losses of roots, or groups of roots, system errors and solutions subject to errors. The use of linear models for the set up of and for the solutions for economic tasks is possible only in application to the practical needs of the certain, limited number of cases with a minimum set of parameters. Therefore, there was a need to change the methodological approaches to the mathematical optimal modeling in the economy. The avoidance of oversimplification gives the possibility to set up he problem in a objective mathematical way and to find the solution more precisely. The modern computing engineering and application packages allow deciding such problems in a general view – without oversimplification.

To find the optimal combination of text modeling for rapid and accurate classification of patent texts and solve the severe problem of manual classification of patent texts in the face of massive patent scientific and technological information. In order to improve the efficiency of patent text automatic classification, the patent texts are split and spliced into 15 different modeling combinations based on the content structure of patent text. Through the 360 comparative experiments, the optimal modeling combination of patent text classification under different classification levels is obtained. The experimental results show that the use of full-text content is not always the best modeling choice in patent classification task. The modeling combination of title, abstract and specification (TAD) is more suitable for patent text classification task. In the subclass level, the highest classification accuracy can be obtained by selecting the specification (d) of patent text. The patent text modeling strategy proposed in this paper provides a good support for improving the effect of patent text classification.

Information flow optimization is very important for decision-making problems in various fields. Using an innovative method of information decision-making optimization, this paper makes a thorough study and analysis of the optimization modeling and intelligent calculation of a kind of stochastic signal system in science and technology by using the big data analysis method. Thus, it provides an ideal decision-making analysis method for effectively realizing the information optimization and processing of such problems.

In this study, the ENVI 4.6 software was used to obtain the spectral reflection value of samples. The outlier samples were eliminated by the Monte Carlo method, and then SPXY (sample set partitioning based on be x-y distances) was used to divide the calibration set and prediction set. The spectral images were pretreated and characteristic wavelengths were extracted. The spectral models of full and pretreated spectra and characteristic bands were established by partial least squares regression (PLSR) and principle component regression (PCR), and the optimal modeling combination was selected. The results showed that the modeling effect of the original spectrum was the best. In full-PLSR model, the determination coefficient of the calibration set (Rc2 ), the determination coefficient of prediction set (Rp2 ), and the determination coefficient of interactive verification set (Rcv2 ) were 0.8804, 0.7375, and 0.7422, and root-mean-square error of calibration set (RMSEC), root-mean-square error of prediction (RMSEP), and root mean square error of interactive validation set (RMSECV) were 2.3630, 2.9607, and 3.4209, respectively. PLSR and PCR models were established to obtain the optimal models of CARS-PLSR and PCR-PLSR. In the CARS-PLSR model, the Rc2 , Rp2 , and Rcv2 were 0.9135, 0.7654, and 0.8171, respectively, while RMSEC, RMSEP, and RMSECV were 2.0275, 2.9306, and 2.9262, respectively. In the iRF-PCR model, Rc2 , Rp2 , and Rcv2 were 0.7952, 0.7372, and 0.7280, respectively, while RMSEC, RMSEP, and RMSECV were 3.0207, 2.8278, and 3.4288, respectively. This study has demonstrated that visible and near-infrared hyperspectral imaging system can rapidly predict the content of metmyoglobin in cooked tan mutton. PRACTICAL APPLICATION: This study has demonstrated that visible and near-infrared (Vis/NIR) hyperspectral imaging system can rapidly predict the content of MetMb in cooked tan mutton. With the advantages of nondestructive, rapid, real-time, Vis/NIR, hyperspectral imaging system can be widely expanded and applied to the detection of myoglobin in meat to evaluate the color of meat.

Two general concerns remain following this updated and corrected study of structural stigma's effect on the premature mortality of sexual minorities. First, there seem to be better and worse ways to measure structural stigma. Scholars should be invested in best-possible measures. Second, remaining questions about measures and expectations suggest more attention be paid to an optimal modeling approach to predicting health outcomes among sexual minorities, one that neither underspecifies nor overspecifies models, but aims instead at better understanding stigma processes in population-based samples, not just searching for its effects.

Fast novel texture spectral similarity criterion, capable of assessing spectral modeling resemblance of color and Bidirectional Texture Functions (BTF) textures, is presented. The criterion reliably compares the multi-spectral pixel values of two textures, and thus it allows to assist an optimal modeling or acquisition setup development by comparing the original data with its synthetic simulations. The suggested criterion, together with existing alternatives, is extensively tested in a long series of thousands specially designed monotonically degrading experiments moreover, successfully compared on a wide variety of color and BTF textures.

Multiobjective optimization (MOO) techniques are of much interest with their applications to petroleum refinery catalytic processes for finding optimal solutions in the midst of conflicting objectives. The rationale behind using MOO is that if objectives are in conflict, a set of trade-off optimal modeling solutions must be obtained to help management select the most-preferred operational solution for a refinery process. Using MOO does not involve hyperparameters thereby reducing the expensive parameter tuning tasks. A true MOO method allows numerous Pareto-based optimal solutions to be identified so that management and decision-makers' preference information can be used to finally select a single preferred solution. This review discusses MOO algorithms and their applications in petroleum and refinery processes. The survey provides insights into the fundamentals, metrics, and relevant algorithms conceived for MOO in petroleum and refinery fields. Also, it provides a deeper discussion of state-of-the-art research conducted to optimize conflicting objectives simultaneously for three main refinery processes, namely hydrotreating, desulfurization, and cracking. Finally, several research and application directions specific to refinery processes are discussed.

This study aimed to determine the composition of chemical complex by partial least square (PLS) regression models combined with uninformative variable elimination (UVE). The near-infrared (NIR) spectra of the forty samples were determined and then UVE was used to compress full NIR spectra from 12011 redundant variables to dozens of variables. Finally, 54, 16, 27, 31 and 42 variables were selected by UVE for 2,2,4-Trimethylpentane, Heptane, Cyclohexane, Ethyl formate and Butyl acetate respectively. Selected variables were used as the inputs of PLS model for quantitative analysis which made the prediction of the model more robust and accurate compared with the conventional PLS.

Aiming at the problem of electric vehicle (EV) charging path selection under different road traffic conditions, an optimal charging navigation strategy for electric vehicle is proposed under the influence of traffic information. This strategy can make the electric car charging to get the best service in the shortest time; on this basis, a charging path guidance model is established, which takes full account of the time of electric vehicle driving path, the waiting time of charging station and the shortest charging time of electric vehicle charging and the shortest charging path as the objective function.. Based on Dijkstra algorithm, the experimental results show that the charging path planning strategy of the electric vehicle can plan reasonable and effective charging routes according to different road conditions. Compared with the traditional charging path planning strategy, this method can effectively reduce the total time cost, the total distance cost and improve the convenience of the user’s travel.

Division of Forest Disaster Management, Korea Forest Research Institute(Received April 2, 2015; Revised April 9, 2015; Accepted June 28, 2015)ABSTRACTThe extreme weather conditions become frequent and severe with global warming. To prevent andcope forest disaster like a forest fire, we need an accurate micrometeorological prediction system formountainous regions. This study addressed the forest fires occurred at Bonghwa and Gangneung inMarch, 2013. We constructed and optimized the prediction system that were required to interpret andsimulate the forest micrometeorology. At first, we examined WRF physical sensitivity. Subsequently,KMA AWS observation data were assimilated using three-dimensional variation data assimilationmethod. The effectiveness of the assimilation was examined by using AWS observations enhanced withthe Forest Research Institute observations. Finally, The 100 meters spatial resolution wind data wereobtained by using the MUKLIMO for the given wind vector from WRF. Key words: Forest fire, Forest micrometeorology, 3D-var, MUKLIMO

Gradient Boosted Machines (GBM) have long been used for regression and classification purposes, and their basic premise of boosting weak learners has been adapted and improvised time and time again in search for an optimal modeling approach. One recent variant has taken the world of learning-related problems by storm, by giving the most accurate solutions to most of them, it is called eXtreme GBM. The paper evaluates eXtreme GBM in the context of human activity recognition.

The use of nanoporous anodic alumina (NAA) for the development of drug delivery systems has gained much attention in recent years. The release of drugs loaded inside NAA pores is complex and depends on the morphology of the pores. In this study, NAA, with different three-dimensional (3D) pore structures (cylindrical pores with several pore diameters, multilayered nanofunnels, and multilayered inverted funnels) were fabricated, and their respective drug delivery rates were studied and modeled using doxorubicin as a model drug. The obtained results reveal optimal modeling of all 3D pore structures, differentiating two drug release stages. Thus, an initial short-term and a sustained long-term release were successfully modeled by the Higuchi and the Korsmeyer–Peppas equations, respectively. This study demonstrates the influence of pore geometries on drug release rates, and further presents a sustained long-term drug release that exceeds 60 days without an undesired initial burst.

Optimal modeling of proton exchange membrane fuel cell (PEMFC) is extremely important for the understanding and interpretation of the overall cell behavior. Intelligent optimization technique is an effective strategy to optimally model PEMFCs because the determination of model parameters is a complex optimization problem. In this paper, an adaptive differential evolution algorithm (ADE) is proposed to accurately fit parameters of PEMFC models. The main contribution is the proposal of ADE for the parameter fitting of PEMFC models. To avoid premature convergence and increase search efficiency, ADE uses two adaptation schemes to dynamically adjust its variation operators and control parameters. The effectiveness and robustness of ADE is verified by applying it to solve benchmark functions and to extract model parameters of four PEMFCs using both noise-free or noised data. Experimental results demonstrate that the proposed method produces more accurate and robust models than several other algorithms and the polarization curves obtained by ADE match well with the experimental data in all cases. This work indicates that ADE is an effective alternative to solve the PEMFC optimal modeling problem.

Biomedical signal/image processing and analysis are always fascinating tasks in scientific researches, both theoretical and practical. One of the powerful tools in such topics is wavelet theory which has been proved to be challenging since its discovery. One of the best measures of the optimality of reconstruction of signals/images is the well-known Shannon’s entropy. In wavelet theory, this is very well known and researchers are familiar with it. In the present work, a step forward is proposed based on more general wavelet tools. New approach is proposed for the reconstruction of signals/images provided with multiwavelets Shannon-type entropy to evaluate the order/disorder of the reconstructed signals/images. Efficiency and accuracy of the approach is confirmed by a simulation study on several models such as ECG, EEG and DNA/Proteins’ signals.

PURPOSE: To identify the optimal tracer-kinetic modeling strategy for dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) data acquired at low temporal resolution. MATERIALS AND METHODS: DCE-MRI was performed on 13 patients with rheumatoid arthritis of the hand before and after anti-tumor necrosis factor alpha (TNFalpha) therapy, using a 3D sequence with a temporal resolution of 13 seconds, imaging for 4 minutes postcontrast injection. Concentration-time curves were extracted from regions of interest (ROIs) in enhancing synovium and fitted to the 3-parameter modified Tofts model (MT) and the 4-parameter two-compartment exchange model (2CXM). To assist the interpretation of the data, the same analysis was applied to simulated data with similar characteristics. RESULTS: Both models fitted the data closely, and showed similar therapy effects. The MT plasma volume was significantly lower than with 2CXM, but the differences in permeability and interstitial volume were not significant. 2CXM was less precise than MT, with larger standard deviations relative to the mean in most parameters. The additional perfusion parameter determined with 2CXM did not provide a statistically significant trend due to low precision. CONCLUSION: The standard MT model is the optimal modeling strategy at low temporal resolution. Advanced models improve the accuracy and generate an additional parameter, but these benefits are offset by low precision.

Planetary gear sets have advantages of little noise, high transmission ratio, compact arrangement, so it has been widely applied in automobile and aerospace applications over the years. Using Lagrange equation, a free vibration theoretical model of a single planetary gear set was built, which was solved with modal superposition method. Combined with theoretical results, two types of modeling methods of planetary gear structures with the simulation platform SimulationX were studied. The simulation model suitable for analyzing vibration characteristic of planetary gear sets and inherent vibration characteristic in different situation were studied with the optimal modeling method. Important influencing factors of planetary gear sets vibration characteristic were studied and reference for dynamic best designing planetary gear transmission sets were provided.

The manufacture of traditional Chinese medicine (TCM) products is always accompanied by processing complex raw materials and real-time monitoring of the manufacturing process. In this study, we investigated different modeling strategies for the extraction process of licorice. Near-infrared spectra associate with the extraction time was used to detemine the states of the extraction processes. Three modeling approaches, i.e., principal component analysis (PCA), partial least squares regression (PLSR) and parallel factor analysis-PLSR (PARAFAC-PLSR), were adopted for the prediction of the real-time status of the process. The overall results indicated that PCA, PLSR and PARAFAC-PLSR can effectively detect the errors in the extraction procedure and predict the process trajectories, which has important significance for the monitoring and controlling of the extraction processes.

Tight time coupling will require the high modeling performance, especially the minimum on/off time constraint. The authors referred to the thought of the cutting plane theory, and built 4 kinds of models ABCD of the minimum on/off time constraints, to completely demonstrate the problem. Then they gave 3 kinds of optimal modeling criterial, the solution accuracy, the node numbers and the peak memory. They clarified mathematically the model C was the optimal to reduce the time couplings of coefficient matrix. Finally, IEEE118 case was used to validate the efficiency of the model and the criterial. With the characters of inequality to adjust the constraints, the guide method could be applied in other fields.