Integrating Transformer and Bidirectional Long Short-Term Memory for Intelligent Breast Cancer Detection from Histopathology Biopsy Images

Breast cancer is a significant threat to the global population,affecting not only women but also a threat to the entire population.With recent advancements in digital pathology,Eosin and hematoxylin images provide enhanced clarity in examiningmicroscopic features of breast tissues based on their staining properties.Early cancer detection facilitates the quickening of the therapeutic process,thereby increasing survival rates.The analysis made by medical professionals,especially pathologists,is time-consuming and challenging,and there arises a need for automated breast cancer detection systems.The upcoming artificial intelligence platforms,especially deep learning models,play an important role in image diagnosis and prediction.Initially,the histopathology biopsy images are taken from standard data sources.Further,the gathered images are given as input to the Multi-Scale Dilated Vision Transformer,where the essential features are acquired.Subsequently,the features are subjected to the Bidirectional Long Short-Term Memory(Bi-LSTM)for classifying the breast cancer disorder.The efficacy of the model is evaluated using divergent metrics.When compared with other methods,the proposed work reveals that it offers impressive results for detection.

Dual-Path Vision Transformer用于急性缺血性脑卒中辅助诊断

急性缺血性脑卒中是由于脑组织血液供应障碍导致的脑功能障碍,数字减影脑血管造影(DSA)是诊断脑血管疾病的金标准。基于患者的正面和侧面DSA图像,对急性缺血性脑卒中的治疗效果进行分级评估,构建基于Vision Transformer的双路径图像分类智能模型DPVF。为了提高辅助诊断速度,基于EdgeViT的轻量化设计思想进行了模型的构建;为了使模型保持轻量化的同时具有较高的精度,提出空间-通道自注意力模块,促进Transformer模型捕获更全面的特征信息,提高模型的表达能力;此外,对于DPVF的两分支的特征融合,构建交叉注意力模块对两分支输出进行交叉融合,促使模型提取更丰富的特征,从而提高模型表现。实验结果显示DPVF在测试集上的准确率达98.5%,满足实际需求。

Real-time UAV path planning based on LSTM network

To address the shortcomings of single-step decision making in the existing deep reinforcement learning based unmanned aerial vehicle(UAV)real-time path planning problem,a real-time UAV path planning algorithm based on long shortterm memory(RPP-LSTM)network is proposed,which combines the memory characteristics of recurrent neural network(RNN)and the deep reinforcement learning algorithm.LSTM networks are used in this algorithm as Q-value networks for the deep Q network(DQN)algorithm,which makes the decision of the Q-value network has some memory.Thanks to LSTM network,the Q-value network can use the previous environmental information and action information which effectively avoids the problem of single-step decision considering only the current environment.Besides,the algorithm proposes a hierarchical reward and punishment function for the specific problem of UAV real-time path planning,so that the UAV can more reasonably perform path planning.Simulation verification shows that compared with the traditional feed-forward neural network(FNN)based UAV autonomous path planning algorithm,the RPP-LSTM proposed in this paper can adapt to more complex environments and has significantly improved robustness and accuracy when performing UAV real-time path planning.

Optimal search path planning of UUV in battlefeld ambush scene

Aiming at the practical application of Unmanned Underwater Vehicle(UUV)in underwater combat,this paper proposes a battlefield ambush scene with UUV considering ocean current.Firstly,by establishing these mathematical models of ocean current environment,target movement,and sonar detection,the probability calculation methods of single UUV searching target and multiple UUV cooperatively searching target are given respectively.Then,based on the Hybrid Quantum-behaved Particle Swarm Optimization(HQPSO)algorithm,the path with the highest target search probability is found.Finally,through simulation calculations,the influence of different UUV parameters and target parameters on the target search probability is analyzed,and the minimum number of UUVs that need to be deployed to complete the ambush task is demonstrated,and the optimal search path scheme is obtained.The method proposed in this paper provides a theoretical basis for the practical application of UUV in the future combat.

An Improved Bounded Conflict-Based Search for Multi-AGV Pathfinding in Automated Container Terminals

As the number of automated guided vehicles(AGVs)within automated container terminals(ACT)continues to rise,conflicts have becomemore frequent.Addressing point and edge conflicts ofAGVs,amulti-AGVconflict-free path planning model has been formulated to minimize the total path length of AGVs between shore bridges and yards.For larger terminalmaps and complex environments,the grid method is employed to model AGVs’road networks.An improved bounded conflict-based search(IBCBS)algorithmtailored to ACT is proposed,leveraging the binary tree principle to resolve conflicts and employing focal search to expand the search range.Comparative experiments involving 60 AGVs indicate a reduction in computing time by 37.397%to 64.06%while maintaining the over cost within 1.019%.Numerical experiments validate the proposed algorithm’s efficacy in enhancing efficiency and ensuring solution quality.

Short-Term Household Load Forecasting Based on Attention Mechanism and CNN-ICPSO-LSTM

Accurate load forecasting forms a crucial foundation for implementing household demand response plans andoptimizing load scheduling. When dealing with short-term load data characterized by substantial fluctuations,a single prediction model is hard to capture temporal features effectively, resulting in diminished predictionaccuracy. In this study, a hybrid deep learning framework that integrates attention mechanism, convolution neuralnetwork (CNN), improved chaotic particle swarm optimization (ICPSO), and long short-term memory (LSTM), isproposed for short-term household load forecasting. Firstly, the CNN model is employed to extract features fromthe original data, enhancing the quality of data features. Subsequently, the moving average method is used for datapreprocessing, followed by the application of the LSTM network to predict the processed data. Moreover, the ICPSOalgorithm is introduced to optimize the parameters of LSTM, aimed at boosting the model’s running speed andaccuracy. Finally, the attention mechanism is employed to optimize the output value of LSTM, effectively addressinginformation loss in LSTM induced by lengthy sequences and further elevating prediction accuracy. According tothe numerical analysis, the accuracy and effectiveness of the proposed hybrid model have been verified. It canexplore data features adeptly, achieving superior prediction accuracy compared to other forecasting methods forthe household load exhibiting significant fluctuations across different seasons.

A Time Series Short-Term Prediction Method Based on Multi-Granularity Event Matching and Alignment

Accurate forecasting of time series is crucial across various domains.Many prediction tasks rely on effectively segmenting,matching,and time series data alignment.For instance,regardless of time series with the same granularity,segmenting them into different granularity events can effectively mitigate the impact of varying time scales on prediction accuracy.However,these events of varying granularity frequently intersect with each other,which may possess unequal durations.Even minor differences can result in significant errors when matching time series with future trends.Besides,directly using matched events but unaligned events as state vectors in machine learning-based prediction models can lead to insufficient prediction accuracy.Therefore,this paper proposes a short-term forecasting method for time series based on a multi-granularity event,MGE-SP(multi-granularity event-based short-termprediction).First,amethodological framework for MGE-SP established guides the implementation steps.The framework consists of three key steps,including multi-granularity event matching based on the LTF(latest time first)strategy,multi-granularity event alignment using a piecewise aggregate approximation based on the compression ratio,and a short-term prediction model based on XGBoost.The data from a nationwide online car-hailing service in China ensures the method’s reliability.The average RMSE(root mean square error)and MAE(mean absolute error)of the proposed method are 3.204 and 2.360,lower than the respective values of 4.056 and 3.101 obtained using theARIMA(autoregressive integratedmoving average)method,as well as the values of 4.278 and 2.994 obtained using k-means-SVR(support vector regression)method.The other experiment is conducted on stock data froma public data set.The proposed method achieved an average RMSE and MAE of 0.836 and 0.696,lower than the respective values of 1.019 and 0.844 obtained using the ARIMA method,as well as the values of 1.350 and 1.172 obtained using the k-means-SVR method.

A Multi-Constraint Path Optimization Scheme Based on Information Fusion in Software Defined Network

The existingmultipath routing in Software Defined Network (SDN) is relatively blind and inefficient, and there is alack of cooperation between the terminal and network sides, making it difficult to achieve dynamic adaptationof service requirements and network resources. To address these issues, we propose a multi-constraint pathoptimization scheme based on information fusion in SDN. The proposed scheme collects network topology andnetwork state information on the network side and computes disjoint paths between end hosts. It uses the FuzzyAnalytic Hierarchy Process (FAHP) to calculate the weight coefficients of multiple constrained parameters andconstructs a composite quality evaluation function for the paths to determine the priority of the disjoint paths. TheSDN controller extracts the service attributes by analyzing the packet header and selects the optimal path for flowrule forwarding. Furthermore, the service attributes are fed back to the path composite quality evaluation function,and the path priority is dynamically adjusted to achieve dynamic adaptation between service requirements andnetwork status. By continuously monitoring and analyzing the service attributes, the scheme can ensure optimalrouting decisions in response to varying network conditions and evolving service demands. The experimentalresults demonstrated that the proposed scheme can effectively improve average throughput and link utilizationwhile meeting the Quality of Service (QoS) requirements of various applications.

Distal-scanning common path probe for optical coherence tomography

In this paper,we present a distal-scanning common path probe for optical coherence tomography(OCT)equipped with a hollow ultrasonic motor and a simple and specially designed beam-splitter.This novel probe proves to be able to effectively circumvent polarization and dispersion mismatch caused by fiber motion and is more robust to a variety of interfering factors during the imaging process,experimentally compared to a conventional noncommon path probe.Furthermore,our design counteracts the attenuation of backscattering with depth and the fall-off of the signal,resulting in a more balanced signal range and greater imaging depth.Spectral-domain OCT imaging of phantom and biological tissue is also demonstrated with a sensitivity of∼100dB and a lateral resolution of∼3μm.This low-cost probe offers simplified system configuration and excellent robustness,and is therefore particularly suitable for clinical diagnosis as one-off medical apparatus.

Predictive value of red blood cell distribution width and hematocrit for short-term outcomes and prognosis in colorectal cancer patients undergoing radical surgery

BACKGROUND Previous studies have reported that low hematocrit levels indicate poor survival in patients with ovarian cancer and cervical cancer,the prognostic value of hematocrit for colorectal cancer(CRC)patients has not been determined.The prognostic value of red blood cell distribution width(RDW)for CRC patients was controversial.AIM To investigate the impact of RDW and hematocrit on the short-term outcomes and long-term prognosis of CRC patients who underwent radical surgery.METHODS Patients who were diagnosed with CRC and underwent radical CRC resection between January 2011 and January 2020 at a single clinical center were included.The short-term outcomes,overall survival(OS)and disease-free survival(DFS)were compared among the different groups.Cox analysis was also conducted to identify independent risk factors for OS and DFS.RESULTS There were 4258 CRC patients who underwent radical surgery included in our study.A total of 1573 patients were in the lower RDW group and 2685 patients were in the higher RDW group.There were 2166 and 2092 patients in the higher hematocrit group and lower hematocrit group,respectively.Patients in the higher RDW group had more intraoperative blood loss(P<0.01)and more overall complications(P<0.01)than did those in the lower RDW group.Similarly,patients in the lower hematocrit group had more intraoperative blood loss(P=0.012),longer hospital stay(P=0.016)and overall complications(P<0.01)than did those in the higher hematocrit group.The higher RDW group had a worse OS and DFS than did the lower RDW group for tumor node metastasis(TNM)stage I(OS,P<0.05;DFS,P=0.001)and stage II(OS,P=0.004;DFS,P=0.01)than the lower RDW group;the lower hematocrit group had worse OS and DFS for TNM stage II(OS,P<0.05;DFS,P=0.001)and stage III(OS,P=0.001;DFS,P=0.001)than did the higher hematocrit group.Preoperative hematocrit was an independent risk factor for OS[P=0.017,hazard ratio(HR)=1.256,95%confidence interval(CI):1.041-1.515]and DFS(P=0.035,HR=1.194,95%CI:1.013-1.408).CONCLUSION A higher preoperative RDW and lower hematocrit were associated with more postoperative complications.However,only hematocrit was an independent risk factor for OS and DFS in CRC patients who underwent radical surgery,while RDW was not.

On traceable iterated line graph and hamiltonian path index

Xiong and Liu[21]gave a characterization of the graphs G for which the n-iterated line graph L^(n)(G)is hamiltonian,for n≥2.In this paper,we study the existence of a hamiltonian path in L^(n)(G),and give a characterization of G for which L^(n)(G)has a hamiltonian path.As applications,we use this characterization to give several upper bounds on the hamiltonian path index of a graph.

Mechanical response and dilatancy characteristics of deep marble under different stress paths:A sight from energy dissipation

Dilatancy is a fundamental volumetric growth behavior observed during loading and serves as a key index to comprehending the intricate nonlinear behavior and constitutive equation structure of rock.This study focuses on Jinping marble obtained from the Jinping Underground Laboratory in China at a depth of 2400 m.Various uniaxial and triaxial tests at different strain rates,along with constant confining pressure tests and reduced confining pressure tests under different confining pressures were conducted to analyze the mechanical response and dilatancy characteristics of the marble under four stress paths.Subsequently,a new empirical dilatancy coefficient is proposed based on the energy dissipation method.The results show that brittle failure characteristics of marble under uniaxial compression are more obvious with the strain rate increasing,and plastic failure characteristics of marble under triaxial compression are gradually strengthened.Furthermore,compared to the constant confining pressure,the volume expansion is relatively lower under unloading condition.The energy dissipation is closely linked to the process of dilatancy,with a rapid increase of dissipated energy coinciding with the beginning of dilatancy.A new empirical dilatancy coefficient is defined according to the change trend of energy dissipation rate curve,of which change trend is consistent with the actual dilatancy response in marble under different stress paths.The existing empirical and theoretical dilatancy models are analyzed,which shows that the empirical dilatancy coefficient based on the energy background is more universal.

Multi-circular formation control with reinforced transient profiles for nonholonomic vehicles:A path-following framework

This article investigates a multi-circular path-following formation control with reinforced transient profiles for nonholonomic vehicles connected by a digraph.A multi-circular formation controller endowed with the feature of spatial-temporal decoupling is devised for a group of vehicles guided by a virtual leader evolving along an implicit path,which allows for a circumnavigation on multiple circles with an anticipant angular spacing.In addition,notice that it typically imposes a stringent time constraint on time-sensitive enclosing scenarios,hence an improved prescribed performance control(IPPC)using novel tighter behavior boundaries is presented to enhance transient capabilities with an ensured appointed-time convergence free from any overshoots.The significant merits are that coordinated circumnavigation along different circles can be realized via executing geometric and dynamic assignments independently with modified transient profiles.Furthermore,all variables existing in the entire system are analyzed to be convergent.Simulation and experimental results are provided to validate the utility of suggested solution.

Short-term efficacy of microwave ablation in the treatment of liver cancer and its effect on immune function

BACKGROUND Hepatectomy is the first choice for treating liver cancer.However,inflammatory factors,released in response to pain stimulation,may suppress perioperative immune function and affect the prognosis of patients undergoing hepatectomies.AIM To determine the short-term efficacy of microwave ablation in the treatment of liver cancer and its effect on immune function.METHODS Clinical data from patients with liver cancer admitted to Suzhou Ninth People’s Hospital from January 2020 to December 2023 were retrospectively analyzed.Thirty-five patients underwent laparoscopic hepatectomy for liver cancer(liver cancer resection group)and 35 patients underwent medical image-guided microwave ablation(liver cancer ablation group).The short-term efficacy,complications,liver function,and immune function indices before and after treatment were compared between the two groups.RESULTS One month after treatment,19 patients experienced complete remission(CR),8 patients experienced partial remission(PR),6 patients experienced stable disease(SD),and 2 patients experienced disease progression(PD)in the liver cancer resection group.In the liver cancer ablation group,21 patients experienced CR,9 patients experienced PR,3 patients experienced SD,and 2 patients experienced PD.No significant differences in efficacy and complications were detected between the liver cancer ablation and liver cancer resection groups(P>0.05).After treatment,total bilirubin(41.24±7.35 vs 49.18±8.64μmol/L,P<0.001),alanine aminotransferase(30.85±6.23 vs 42.32±7.56 U/L,P<0.001),CD4+(43.95±5.72 vs 35.27±5.56,P<0.001),CD8+(20.38±3.91 vs 22.75±4.62,P<0.001),and CD4+/CD8+(2.16±0.39 vs 1.55±0.32,P<0.001)were significantly different between the liver cancer ablation and liver cancer resection groups.CONCLUSION The short-term efficacy and safety of microwave ablation and laparoscopic surgery for the treatment of liver cancer are similar,but liver function recovers quickly after microwave ablation,and microwave ablation may enhance immune function.

Ground threat prediction-based path planning of unmanned autonomous helicopter using hybrid enhanced artificial bee colony algorithm

Unmanned autonomous helicopter(UAH)path planning problem is an important component of the UAH mission planning system.Aiming to reduce the influence of non-complete ground threat information on UAH path planning,a ground threat prediction-based path planning method is proposed based on artificial bee colony(ABC)algorithm by collaborative thinking strategy.Firstly,a dynamic threat distribution probability model is developed based on the characteristics of typical ground threats.The dynamic no-fly zone of the UAH is simulated and established by calculating the distribution probability of ground threats in real time.Then,a dynamic path planning method for UAH is designed in complex environment based on the real-time prediction of ground threats.By adding the collision warning mechanism to the path planning model,the flight path could be dynamically adjusted according to changing no-fly zones.Furthermore,a hybrid enhanced ABC algorithm is proposed based on collaborative thinking strategy.The proposed algorithm applies the leader-member thinking mechanism to guide the direction of population evolution,and reduces the negative impact of local optimal solutions caused by collaborative learning update strategy,which makes the optimization performance of ABC algorithm more controllable and efficient.Finally,simulation results verify the feasibility and effectiveness of the proposed ground threat prediction path planning method.

Correlation and Pathway Analysis of the Carbon,Nitrogen,and Phosphorus in Soil-Microorganism-Plant with Main Quality Components of Tea(Camellia sinensis)

The contents of carbon(C),nitrogen(N),and phosphorus(P)in soil-microorganisms-plant significantly affect tea quality by altering the main quality components of tea,such as tea polyphenols,amino acids,and caffeine.However,few studies have quantified the effects of these factors on the main quality components of tea.The study aimed to explore the interactions of C,N,and P in soil-microorganisms-plants and the effects of these factors on the main quality components of tea by using the path analysis method.The results indicated that(1)The contents of C,N,and P in soil,microorganisms,and tea plants were highly correlated and collinear,and showed significant correlations with the main quality components of tea.(2)Optimal regression equations were established to esti-mate tea polyphenol,amino acid,catechin,caffeine,and water extract content based on C,N,and P contents in soil,microorganisms,and tea plants(R^(2)=0.923,0.726,0.954,0.848,and 0.883,respectively).(3)Pathway analysis showed that microbial biomass phosphorus(MBP),root phosphorus,branch nitrogen,and microbial biomass carbon(MBC)were the largest direct impact factors on tea polyphenol,catechin,water extracts,amino acid,and caffeine content,respectively.Leaf carbon,root phosphorus,and leaf nitrogen were the largest indirect impact factors on tea polyphenol,catechin,and water extract content,respectively.Leaf carbon indirectly affected tea polyphenol content mainly by altering MBP content.Root phosphorus indirectly affected catechin content mainly by altering soil organic carbon content.Leaf nitrogen indirectly affected water extract content mainly by altering branch nitrogen content.The research results provide the scientific basis for reasonable fertilization in tea gardens and tea quality improvement.

Heuristic Expanding Disconnected Graph:A Rapid Path Planning Method for Mobile Robots

Existing mobile robots mostly use graph search algorithms for path planning,which suffer from relatively low planning efficiency owing to high redundancy and large computational complexity.Due to the limitations of the neighborhood search strategy,the robots could hardly obtain the most optimal global path.A global path planning algorithm,denoted as EDG*,is proposed by expanding nodes using a well-designed expanding disconnected graph operator(EDG)in this paper.Firstly,all obstacles are marked and their corners are located through the map pre-processing.Then,the EDG operator is designed to find points in non-obstruction areas to complete the rapid expansion of disconnected nodes.Finally,the EDG*heuristic iterative algorithm is proposed.It selects the candidate node through a specific valuation function and realizes the node expansion while avoiding collision with a minimum offset.Path planning experiments were conducted in a typical indoor environment and on the public dataset CSM.The result shows that the proposed EDG*reduced the planning time by more than 90%and total length of paths reduced by more than 4.6%.Compared to A*,Dijkstra and JPS,EDG*does not show an exponential explosion effect in map size.The EDG*showed better performance in terms of path smoothness,and collision avoidance.This shows that the EDG*algorithm proposed in this paper can improve the efficiency of path planning and enhance path quality.

An Enhanced Ensemble-Based Long Short-Term Memory Approach for Traffic Volume Prediction

With the advancement of artificial intelligence,traffic forecasting is gaining more and more interest in optimizing route planning and enhancing service quality.Traffic volume is an influential parameter for planning and operating traffic structures.This study proposed an improved ensemble-based deep learning method to solve traffic volume prediction problems.A set of optimal hyperparameters is also applied for the suggested approach to improve the performance of the learning process.The fusion of these methodologies aims to harness ensemble empirical mode decomposition’s capacity to discern complex traffic patterns and long short-term memory’s proficiency in learning temporal relationships.Firstly,a dataset for automatic vehicle identification is obtained and utilized in the preprocessing stage of the ensemble empirical mode decomposition model.The second aspect involves predicting traffic volume using the long short-term memory algorithm.Next,the study employs a trial-and-error approach to select a set of optimal hyperparameters,including the lookback window,the number of neurons in the hidden layers,and the gradient descent optimization.Finally,the fusion of the obtained results leads to a final traffic volume prediction.The experimental results show that the proposed method outperforms other benchmarks regarding various evaluation measures,including mean absolute error,root mean squared error,mean absolute percentage error,and R-squared.The achieved R-squared value reaches an impressive 98%,while the other evaluation indices surpass the competing.These findings highlight the accuracy of traffic pattern prediction.Consequently,this offers promising prospects for enhancing transportation management systems and urban infrastructure planning.

A Reverse Path Planning Approach for Enhanced Performance of Multi-Degree-of-Freedom Industrial Manipulators

In the domain of autonomous industrial manipulators,precise positioning and appropriate posture selection in path planning are pivotal for tasks involving obstacle avoidance,such as handling,heat sealing,and stacking.While Multi-Degree-of-Freedom(MDOF)manipulators offer kinematic redundancy,aiding in the derivation of optimal inverse kinematic solutions to meet position and posture requisites,their path planning entails intricate multiobjective optimization,encompassing path,posture,and joint motion optimization.Achieving satisfactory results in practical scenarios remains challenging.In response,this study introduces a novel Reverse Path Planning(RPP)methodology tailored for industrial manipulators.The approach commences by conceptualizing the manipulator’s end-effector as an agent within a reinforcement learning(RL)framework,wherein the state space,action set,and reward function are precisely defined to expedite the search for an initial collision-free path.To enhance convergence speed,the Q-learning algorithm in RL is augmented with Dyna-Q.Additionally,we formulate the cylindrical bounding box of the manipulator based on its Denavit-Hartenberg(DH)parameters and propose a swift collision detection technique.Furthermore,the motion performance of the end-effector is refined through a bidirectional search,and joint weighting coefficients are introduced to mitigate motion in high-power joints.The efficacy of the proposed RPP methodology is rigorously examined through extensive simulations conducted on a six-degree-of-freedom(6-DOF)manipulator encountering two distinct obstacle configurations and target positions.Experimental results substantiate that the RPP method adeptly orchestrates the computation of the shortest collision-free path while adhering to specific posture constraints at the target point.Moreover,itminimizes both posture angle deviations and joint motion,showcasing its prowess in enhancing the operational performance of MDOF industrial manipulators.

A modified stochastic model for LS+AR hybrid method and its application in polar motion short-term prediction

Short-term(up to 30 days)predictions of Earth Rotation Parameters(ERPs)such as Polar Motion(PM:PMX and PMY)play an essential role in real-time applications related to high-precision reference frame conversion.Currently,least squares(LS)+auto-regressive(AR)hybrid method is one of the main techniques of PM prediction.Besides,the weighted LS+AR hybrid method performs well for PM short-term prediction.However,the corresponding covariance information of LS fitting residuals deserves further exploration in the AR model.In this study,we have derived a modified stochastic model for the LS+AR hybrid method,namely the weighted LS+weighted AR hybrid method.By using the PM data products of IERS EOP 14 C04,the numerical results indicate that for PM short-term forecasting,the proposed weighted LS+weighted AR hybrid method shows an advantage over both the LS+AR hybrid method and the weighted LS+AR hybrid method.Compared to the mean absolute errors(MAEs)of PMX/PMY sho rt-term prediction of the LS+AR hybrid method and the weighted LS+AR hybrid method,the weighted LS+weighted AR hybrid method shows average improvements of 6.61%/12.08%and 0.24%/11.65%,respectively.Besides,for the slopes of the linear regression lines fitted to the errors of each method,the growth of the prediction error of the proposed method is slower than that of the other two methods.