Internet of things networks often suffer from early node failures and short lifespan due to energy limits.Traditional routing methods are not enough.This work proposes a new hybrid algorithm called ACOGA.It combines A...Internet of things networks often suffer from early node failures and short lifespan due to energy limits.Traditional routing methods are not enough.This work proposes a new hybrid algorithm called ACOGA.It combines Ant Colony Optimization(ACO)and the Greedy Algorithm(GA).ACO finds smart paths while Greedy makes quick decisions.This improves energy use and performance.ACOGA outperforms Hybrid Energy-Efficient(HEE)and Adaptive Lossless Data Compression(ALDC)algorithms.After 500 rounds,only 5%of ACOGA’s nodes are dead,compared to 15%for HEE and 20%for ALDC.The network using ACOGA runs for 1200 rounds before the first nodes fail.HEE lasts 900 rounds and ALDC only 850.ACOGA saves at least 15%more energy by better distributing the load.It also achieves a 98%packet delivery rate.The method works well in mixed IoT networks like Smart Water Management Systems(SWMS).These systems have different power levels and communication ranges.The simulation of proposed model has been done in MATLAB simulator.The results show that that the proposed model outperform then the existing models.展开更多
Multiple Sclerosis(MS)poses significant health risks.Patients may face neurodegeneration,mobility issues,cognitive decline,and a reduced quality of life.Manual diagnosis by neurologists is prone to limitations,making ...Multiple Sclerosis(MS)poses significant health risks.Patients may face neurodegeneration,mobility issues,cognitive decline,and a reduced quality of life.Manual diagnosis by neurologists is prone to limitations,making AI-based classification crucial for early detection.Therefore,automated classification using Artificial Intelligence(AI)techniques has a crucial role in addressing the limitations of manual classification and preventing the development of MS to advanced stages.This study developed hybrid systems integrating XGBoost(eXtreme Gradient Boosting)with multi-CNN(Convolutional Neural Networks)features based on Ant Colony Optimization(ACO)and Maximum Entropy Score-based Selection(MESbS)algorithms for early classification of MRI(Magnetic Resonance Imaging)images in a multi-class and binary-class MS dataset.All hybrid systems started by enhancing MRI images using the fusion processes of a Gaussian filter and Contrast-Limited Adaptive Histogram Equalization(CLAHE).Then,the Gradient Vector Flow(GVF)algorithm was applied to select white matter(regions of interest)within the brain and segment them from the surrounding brain structures.These regions of interest were processed by CNN models(ResNet101,DenseNet201,and MobileNet)to extract deep feature maps,which were then combined into fused feature vectors of multi-CNN model combinations(ResNet101-DenseNet201,DenseNet201-MobileNet,ResNet101-MobileNet,and ResNet101-DenseNet201-MobileNet).The multi-CNN features underwent dimensionality reduction using ACO and MESbS algorithms to remove unimportant features and retain important features.The XGBoost classifier employed the resultant feature vectors for classification.All developed hybrid systems displayed promising outcomes.For multiclass classification,the XGBoost model using ResNet101-DenseNet201-MobileNet features selected by ACO attained 99.4%accuracy,99.45%precision,and 99.75%specificity,surpassing prior studies(93.76%accuracy).It reached 99.6%accuracy,99.65%precision,and 99.55%specificity in binary-class classification.These results demonstrate the effectiveness of multi-CNN fusion with feature selection in improving MS classification accuracy.展开更多
Microperforated panels(MPP)are widely used in noise control applications due to their excellent sound absorption performance.However,traditional single-layer MPPs suffer from a narrow sound absorption bandwidth,making...Microperforated panels(MPP)are widely used in noise control applications due to their excellent sound absorption performance.However,traditional single-layer MPPs suffer from a narrow sound absorption bandwidth,making it difficult to meet the demands for broadband sound absorption.To address this limitation,this study proposes a design approach for double-layer MPPs optimized using a genetic algorithm(GA).By optimizing structural parameters such as perforation diameter,panel thickness,perforation ratio,and cavity depth,the sound absorption performance of the double-layer MPP is significantly enhanced.The results demonstrate that the optimized double-layer MPP achieves an average sound absorption coefficient of 0.71 across the 100-5000 Hz frequency range,with a peak absorption coefficient exceeding 0.8 at 500 Hz,outperforming conventional sound-absorbing products of the same category.展开更多
The Grey Wolf Optimization(GWO)algorithm is acknowledged as an effective method for rock acoustic emission localization.However,the conventional GWO algorithm encounters challenges related to solution accuracy and con...The Grey Wolf Optimization(GWO)algorithm is acknowledged as an effective method for rock acoustic emission localization.However,the conventional GWO algorithm encounters challenges related to solution accuracy and convergence speed.To address these concerns,this paper develops a Simplex Improved Grey Wolf Optimizer(SMIGWO)algorithm.The randomly generating initial populations are replaced with the iterative chaotic sequences.The search process is optimized using the convergence factor optimization algorithm based on the inverse incompleteГfunction.The simplex method is utilized to address issues related to poorly positioned grey wolves.Experimental results demonstrate that,compared to the conventional GWO algorithm-based AE localization algorithm,the proposed algorithm achieves a higher solution accuracy and showcases a shorter search time.Additionally,the algorithm demonstrates fewer convergence steps,indicating superior convergence efficiency.These findings highlight that the proposed SMIGWO algorithm offers enhanced solution accuracy,stability,and optimization performance.The benefits of the SMIGWO algorithm extend universally across various materials,such as aluminum,granite,and sandstone,showcasing consistent effectiveness irrespective of material type.Consequently,this algorithm emerges as a highly effective tool for identifying acoustic emission signals and improving the precision of rock acoustic emission localization.展开更多
The distribution of shear-wave velocities in the subsurface is generally used to assess the potential forseismic liquefaction and soil amplification effects and to classify seismic sites. Newly developeddistributed ac...The distribution of shear-wave velocities in the subsurface is generally used to assess the potential forseismic liquefaction and soil amplification effects and to classify seismic sites. Newly developeddistributed acoustic sensing (DAS) technology enables estimation of the shear-wave distribution as ahigh-density seismic observation system. This technology is characterized by low maintenance costs,high-resolution outputs, and real-time data transmission capabilities, albeit with the challenge ofmanaging massive data generation. Rapid and efficient interpretation of data is the key to advancingapplication of the DAS technology. In this study, field tests were carried out to record ambient noise overa short period using DAS technology, from which the surface-wave dispersion curves were extracted. Inorder to reduce the influence of directional effects on the results, an unsupervised clustering method isused to select appropriate clusters to extract the Green's function. A combination of a genetic algorithmand Monte Carlo (GA-MC) simulation is proposed to invert the subsurface velocity structure. Thestratigraphic profiles obtained by the GA-MC method are in agreement with the borehole profiles.Compared to other methods, the proposed optimization method not only improves the solution qualitybut also reduces the solution time.展开更多
Precisely estimating the state of health(SOH)of lithium-ion batteries is essential for battery management systems(BMS),as it plays a key role in ensuring the safe and reliable operation of battery systems.However,curr...Precisely estimating the state of health(SOH)of lithium-ion batteries is essential for battery management systems(BMS),as it plays a key role in ensuring the safe and reliable operation of battery systems.However,current SOH estimation methods often overlook the valuable temperature information that can effectively characterize battery aging during capacity degradation.Additionally,the Elman neural network,which is commonly employed for SOH estimation,exhibits several drawbacks,including slow training speed,a tendency to become trapped in local minima,and the initialization of weights and thresholds using pseudo-random numbers,leading to unstable model performance.To address these issues,this study addresses the challenge of precise and effective SOH detection by proposing a method for estimating the SOH of lithium-ion batteries based on differential thermal voltammetry(DTV)and an SSA-Elman neural network.Firstly,two health features(HFs)considering temperature factors and battery voltage are extracted fromthe differential thermal voltammetry curves and incremental capacity curves.Next,the Sparrow Search Algorithm(SSA)is employed to optimize the initial weights and thresholds of the Elman neural network,forming the SSA-Elman neural network model.To validate the performance,various neural networks,including the proposed SSA-Elman network,are tested using the Oxford battery aging dataset.The experimental results demonstrate that the method developed in this study achieves superior accuracy and robustness,with a mean absolute error(MAE)of less than 0.9%and a rootmean square error(RMSE)below 1.4%.展开更多
Complex network models are frequently employed for simulating and studyingdiverse real-world complex systems.Among these models,scale-free networks typically exhibit greater fragility to malicious attacks.Consequently...Complex network models are frequently employed for simulating and studyingdiverse real-world complex systems.Among these models,scale-free networks typically exhibit greater fragility to malicious attacks.Consequently,enhancing the robustness of scale-free networks has become a pressing issue.To address this problem,this paper proposes a Multi-Granularity Integration Algorithm(MGIA),which aims to improve the robustness of scale-free networks while keeping the initial degree of each node unchanged,ensuring network connectivity and avoiding the generation of multiple edges.The algorithm generates a multi-granularity structure from the initial network to be optimized,then uses different optimization strategies to optimize the networks at various granular layers in this structure,and finally realizes the information exchange between different granular layers,thereby further enhancing the optimization effect.We propose new network refresh,crossover,and mutation operators to ensure that the optimized network satisfies the given constraints.Meanwhile,we propose new network similarity and network dissimilarity evaluation metrics to improve the effectiveness of the optimization operators in the algorithm.In the experiments,the MGIA enhances the robustness of the scale-free network by 67.6%.This improvement is approximately 17.2%higher than the optimization effects achieved by eight currently existing complex network robustness optimization algorithms.展开更多
Accurate short-term wind power forecast technique plays a crucial role in maintaining the safety and economic efficiency of smart grids.Although numerous studies have employed various methods to forecast wind power,th...Accurate short-term wind power forecast technique plays a crucial role in maintaining the safety and economic efficiency of smart grids.Although numerous studies have employed various methods to forecast wind power,there remains a research gap in leveraging swarm intelligence algorithms to optimize the hyperparameters of the Transformer model for wind power prediction.To improve the accuracy of short-term wind power forecast,this paper proposes a hybrid short-term wind power forecast approach named STL-IAOA-iTransformer,which is based on seasonal and trend decomposition using LOESS(STL)and iTransformer model optimized by improved arithmetic optimization algorithm(IAOA).First,to fully extract the power data features,STL is used to decompose the original data into components with less redundant information.The extracted components as well as the weather data are then input into iTransformer for short-term wind power forecast.The final predicted short-term wind power curve is obtained by combining the predicted components.To improve the model accuracy,IAOA is employed to optimize the hyperparameters of iTransformer.The proposed approach is validated using real-generation data from different seasons and different power stations inNorthwest China,and ablation experiments have been conducted.Furthermore,to validate the superiority of the proposed approach under different wind characteristics,real power generation data fromsouthwestChina are utilized for experiments.Thecomparative results with the other six state-of-the-art prediction models in experiments show that the proposed model well fits the true value of generation series and achieves high prediction accuracy.展开更多
In disaster relief operations,multiple UAVs can be used to search for trapped people.In recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms...In disaster relief operations,multiple UAVs can be used to search for trapped people.In recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms to solve the problem of multi-UAV path planning.The Dung Beetle Optimization(DBO)algorithm has been widely applied due to its diverse search patterns in the above algorithms.However,the update strategies for the rolling and thieving dung beetles of the DBO algorithm are overly simplistic,potentially leading to an inability to fully explore the search space and a tendency to converge to local optima,thereby not guaranteeing the discovery of the optimal path.To address these issues,we propose an improved DBO algorithm guided by the Landmark Operator(LODBO).Specifically,we first use tent mapping to update the population strategy,which enables the algorithm to generate initial solutions with enhanced diversity within the search space.Second,we expand the search range of the rolling ball dung beetle by using the landmark factor.Finally,by using the adaptive factor that changes with the number of iterations.,we improve the global search ability of the stealing dung beetle,making it more likely to escape from local optima.To verify the effectiveness of the proposed method,extensive simulation experiments are conducted,and the result shows that the LODBO algorithm can obtain the optimal path using the shortest time compared with the Genetic Algorithm(GA),the Gray Wolf Optimizer(GWO),the Whale Optimization Algorithm(WOA)and the original DBO algorithm in the disaster search and rescue task set.展开更多
In this paper,we prove that Euclid's algorithm,Bezout's equation and Divi-sion algorithm are equivalent to each other.Our result shows that Euclid has preliminarily established the theory of divisibility and t...In this paper,we prove that Euclid's algorithm,Bezout's equation and Divi-sion algorithm are equivalent to each other.Our result shows that Euclid has preliminarily established the theory of divisibility and the greatest common divisor.We further provided several suggestions for teaching.展开更多
文摘Internet of things networks often suffer from early node failures and short lifespan due to energy limits.Traditional routing methods are not enough.This work proposes a new hybrid algorithm called ACOGA.It combines Ant Colony Optimization(ACO)and the Greedy Algorithm(GA).ACO finds smart paths while Greedy makes quick decisions.This improves energy use and performance.ACOGA outperforms Hybrid Energy-Efficient(HEE)and Adaptive Lossless Data Compression(ALDC)algorithms.After 500 rounds,only 5%of ACOGA’s nodes are dead,compared to 15%for HEE and 20%for ALDC.The network using ACOGA runs for 1200 rounds before the first nodes fail.HEE lasts 900 rounds and ALDC only 850.ACOGA saves at least 15%more energy by better distributing the load.It also achieves a 98%packet delivery rate.The method works well in mixed IoT networks like Smart Water Management Systems(SWMS).These systems have different power levels and communication ranges.The simulation of proposed model has been done in MATLAB simulator.The results show that that the proposed model outperform then the existing models.
文摘Multiple Sclerosis(MS)poses significant health risks.Patients may face neurodegeneration,mobility issues,cognitive decline,and a reduced quality of life.Manual diagnosis by neurologists is prone to limitations,making AI-based classification crucial for early detection.Therefore,automated classification using Artificial Intelligence(AI)techniques has a crucial role in addressing the limitations of manual classification and preventing the development of MS to advanced stages.This study developed hybrid systems integrating XGBoost(eXtreme Gradient Boosting)with multi-CNN(Convolutional Neural Networks)features based on Ant Colony Optimization(ACO)and Maximum Entropy Score-based Selection(MESbS)algorithms for early classification of MRI(Magnetic Resonance Imaging)images in a multi-class and binary-class MS dataset.All hybrid systems started by enhancing MRI images using the fusion processes of a Gaussian filter and Contrast-Limited Adaptive Histogram Equalization(CLAHE).Then,the Gradient Vector Flow(GVF)algorithm was applied to select white matter(regions of interest)within the brain and segment them from the surrounding brain structures.These regions of interest were processed by CNN models(ResNet101,DenseNet201,and MobileNet)to extract deep feature maps,which were then combined into fused feature vectors of multi-CNN model combinations(ResNet101-DenseNet201,DenseNet201-MobileNet,ResNet101-MobileNet,and ResNet101-DenseNet201-MobileNet).The multi-CNN features underwent dimensionality reduction using ACO and MESbS algorithms to remove unimportant features and retain important features.The XGBoost classifier employed the resultant feature vectors for classification.All developed hybrid systems displayed promising outcomes.For multiclass classification,the XGBoost model using ResNet101-DenseNet201-MobileNet features selected by ACO attained 99.4%accuracy,99.45%precision,and 99.75%specificity,surpassing prior studies(93.76%accuracy).It reached 99.6%accuracy,99.65%precision,and 99.55%specificity in binary-class classification.These results demonstrate the effectiveness of multi-CNN fusion with feature selection in improving MS classification accuracy.
文摘Microperforated panels(MPP)are widely used in noise control applications due to their excellent sound absorption performance.However,traditional single-layer MPPs suffer from a narrow sound absorption bandwidth,making it difficult to meet the demands for broadband sound absorption.To address this limitation,this study proposes a design approach for double-layer MPPs optimized using a genetic algorithm(GA).By optimizing structural parameters such as perforation diameter,panel thickness,perforation ratio,and cavity depth,the sound absorption performance of the double-layer MPP is significantly enhanced.The results demonstrate that the optimized double-layer MPP achieves an average sound absorption coefficient of 0.71 across the 100-5000 Hz frequency range,with a peak absorption coefficient exceeding 0.8 at 500 Hz,outperforming conventional sound-absorbing products of the same category.
基金support from the National Science Foundation of China(52304137,5192780752274124,52325403)Tiandi Science and Technology Co.,Ltd.(2022-2-TDMS012 and SKLIS202417)Sichuan University(SKHL2215).
文摘The Grey Wolf Optimization(GWO)algorithm is acknowledged as an effective method for rock acoustic emission localization.However,the conventional GWO algorithm encounters challenges related to solution accuracy and convergence speed.To address these concerns,this paper develops a Simplex Improved Grey Wolf Optimizer(SMIGWO)algorithm.The randomly generating initial populations are replaced with the iterative chaotic sequences.The search process is optimized using the convergence factor optimization algorithm based on the inverse incompleteГfunction.The simplex method is utilized to address issues related to poorly positioned grey wolves.Experimental results demonstrate that,compared to the conventional GWO algorithm-based AE localization algorithm,the proposed algorithm achieves a higher solution accuracy and showcases a shorter search time.Additionally,the algorithm demonstrates fewer convergence steps,indicating superior convergence efficiency.These findings highlight that the proposed SMIGWO algorithm offers enhanced solution accuracy,stability,and optimization performance.The benefits of the SMIGWO algorithm extend universally across various materials,such as aluminum,granite,and sandstone,showcasing consistent effectiveness irrespective of material type.Consequently,this algorithm emerges as a highly effective tool for identifying acoustic emission signals and improving the precision of rock acoustic emission localization.
基金supported by the National Natural Science Foundation of China(Grant Nos.42225702 and 42077235)the Natural Science Foundation of Jiangsu Province(Grant No.BK20211086)the open fund of the Key Laboratory of Earth Fissures Geological Disaster,Ministry of Natural Resources.
文摘The distribution of shear-wave velocities in the subsurface is generally used to assess the potential forseismic liquefaction and soil amplification effects and to classify seismic sites. Newly developeddistributed acoustic sensing (DAS) technology enables estimation of the shear-wave distribution as ahigh-density seismic observation system. This technology is characterized by low maintenance costs,high-resolution outputs, and real-time data transmission capabilities, albeit with the challenge ofmanaging massive data generation. Rapid and efficient interpretation of data is the key to advancingapplication of the DAS technology. In this study, field tests were carried out to record ambient noise overa short period using DAS technology, from which the surface-wave dispersion curves were extracted. Inorder to reduce the influence of directional effects on the results, an unsupervised clustering method isused to select appropriate clusters to extract the Green's function. A combination of a genetic algorithmand Monte Carlo (GA-MC) simulation is proposed to invert the subsurface velocity structure. Thestratigraphic profiles obtained by the GA-MC method are in agreement with the borehole profiles.Compared to other methods, the proposed optimization method not only improves the solution qualitybut also reduces the solution time.
基金supported by the National Natural Science Foundation of China(NSFC)under Grant(No.51677058).
文摘Precisely estimating the state of health(SOH)of lithium-ion batteries is essential for battery management systems(BMS),as it plays a key role in ensuring the safe and reliable operation of battery systems.However,current SOH estimation methods often overlook the valuable temperature information that can effectively characterize battery aging during capacity degradation.Additionally,the Elman neural network,which is commonly employed for SOH estimation,exhibits several drawbacks,including slow training speed,a tendency to become trapped in local minima,and the initialization of weights and thresholds using pseudo-random numbers,leading to unstable model performance.To address these issues,this study addresses the challenge of precise and effective SOH detection by proposing a method for estimating the SOH of lithium-ion batteries based on differential thermal voltammetry(DTV)and an SSA-Elman neural network.Firstly,two health features(HFs)considering temperature factors and battery voltage are extracted fromthe differential thermal voltammetry curves and incremental capacity curves.Next,the Sparrow Search Algorithm(SSA)is employed to optimize the initial weights and thresholds of the Elman neural network,forming the SSA-Elman neural network model.To validate the performance,various neural networks,including the proposed SSA-Elman network,are tested using the Oxford battery aging dataset.The experimental results demonstrate that the method developed in this study achieves superior accuracy and robustness,with a mean absolute error(MAE)of less than 0.9%and a rootmean square error(RMSE)below 1.4%.
基金National Natural Science Foundation of China(11971211,12171388).
文摘Complex network models are frequently employed for simulating and studyingdiverse real-world complex systems.Among these models,scale-free networks typically exhibit greater fragility to malicious attacks.Consequently,enhancing the robustness of scale-free networks has become a pressing issue.To address this problem,this paper proposes a Multi-Granularity Integration Algorithm(MGIA),which aims to improve the robustness of scale-free networks while keeping the initial degree of each node unchanged,ensuring network connectivity and avoiding the generation of multiple edges.The algorithm generates a multi-granularity structure from the initial network to be optimized,then uses different optimization strategies to optimize the networks at various granular layers in this structure,and finally realizes the information exchange between different granular layers,thereby further enhancing the optimization effect.We propose new network refresh,crossover,and mutation operators to ensure that the optimized network satisfies the given constraints.Meanwhile,we propose new network similarity and network dissimilarity evaluation metrics to improve the effectiveness of the optimization operators in the algorithm.In the experiments,the MGIA enhances the robustness of the scale-free network by 67.6%.This improvement is approximately 17.2%higher than the optimization effects achieved by eight currently existing complex network robustness optimization algorithms.
基金supported by Yunnan Provincial Basic Research Project(202401AT070344,202301AT070443)National Natural Science Foundation of China(62263014,52207105)+1 种基金Yunnan Lancang-Mekong International Electric Power Technology Joint Laboratory(202203AP140001)Major Science and Technology Projects in Yunnan Province(202402AG050006).
文摘Accurate short-term wind power forecast technique plays a crucial role in maintaining the safety and economic efficiency of smart grids.Although numerous studies have employed various methods to forecast wind power,there remains a research gap in leveraging swarm intelligence algorithms to optimize the hyperparameters of the Transformer model for wind power prediction.To improve the accuracy of short-term wind power forecast,this paper proposes a hybrid short-term wind power forecast approach named STL-IAOA-iTransformer,which is based on seasonal and trend decomposition using LOESS(STL)and iTransformer model optimized by improved arithmetic optimization algorithm(IAOA).First,to fully extract the power data features,STL is used to decompose the original data into components with less redundant information.The extracted components as well as the weather data are then input into iTransformer for short-term wind power forecast.The final predicted short-term wind power curve is obtained by combining the predicted components.To improve the model accuracy,IAOA is employed to optimize the hyperparameters of iTransformer.The proposed approach is validated using real-generation data from different seasons and different power stations inNorthwest China,and ablation experiments have been conducted.Furthermore,to validate the superiority of the proposed approach under different wind characteristics,real power generation data fromsouthwestChina are utilized for experiments.Thecomparative results with the other six state-of-the-art prediction models in experiments show that the proposed model well fits the true value of generation series and achieves high prediction accuracy.
基金supported by the National Natural Science Foundation of China(No.62373027).
文摘In disaster relief operations,multiple UAVs can be used to search for trapped people.In recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms to solve the problem of multi-UAV path planning.The Dung Beetle Optimization(DBO)algorithm has been widely applied due to its diverse search patterns in the above algorithms.However,the update strategies for the rolling and thieving dung beetles of the DBO algorithm are overly simplistic,potentially leading to an inability to fully explore the search space and a tendency to converge to local optima,thereby not guaranteeing the discovery of the optimal path.To address these issues,we propose an improved DBO algorithm guided by the Landmark Operator(LODBO).Specifically,we first use tent mapping to update the population strategy,which enables the algorithm to generate initial solutions with enhanced diversity within the search space.Second,we expand the search range of the rolling ball dung beetle by using the landmark factor.Finally,by using the adaptive factor that changes with the number of iterations.,we improve the global search ability of the stealing dung beetle,making it more likely to escape from local optima.To verify the effectiveness of the proposed method,extensive simulation experiments are conducted,and the result shows that the LODBO algorithm can obtain the optimal path using the shortest time compared with the Genetic Algorithm(GA),the Gray Wolf Optimizer(GWO),the Whale Optimization Algorithm(WOA)and the original DBO algorithm in the disaster search and rescue task set.
基金Supported by the Natural Science Foundation of Chongqing(General Program,NO.CSTB2022NSCQ-MSX0884)Discipline Teaching Special Project of Yangtze Normal University(csxkjx14)。
文摘In this paper,we prove that Euclid's algorithm,Bezout's equation and Divi-sion algorithm are equivalent to each other.Our result shows that Euclid has preliminarily established the theory of divisibility and the greatest common divisor.We further provided several suggestions for teaching.
