Deep learning-based methods have become alternatives to traditional numerical weather prediction systems,offering faster computation and the ability to utilize large historical datasets.However,the application of deep...Deep learning-based methods have become alternatives to traditional numerical weather prediction systems,offering faster computation and the ability to utilize large historical datasets.However,the application of deep learning to medium-range regional weather forecasting with limited data remains a significant challenge.In this work,three key solutions are proposed:(1)motivated by the need to improve model performance in data-scarce regional forecasting scenarios,the authors innovatively apply semantic segmentation models,to better capture spatiotemporal features and improve prediction accuracy;(2)recognizing the challenge of overfitting and the inability of traditional noise-based data augmentation methods to effectively enhance model robustness,a novel learnable Gaussian noise mechanism is introduced that allows the model to adaptively optimize perturbations for different locations,ensuring more effective learning;and(3)to address the issue of error accumulation in autoregressive prediction,as well as the challenge of learning difficulty and the lack of intermediate data utilization in one-shot prediction,the authors propose a cascade prediction approach that effectively resolves these problems while significantly improving model forecasting performance.The method achieves a competitive result in The East China Regional AI Medium Range Weather Forecasting Competition.Ablation experiments further validate the effectiveness of each component,highlighting their contributions to enhancing prediction performance.展开更多
Optimization problems are prevalent in various fields of science and engineering,with several real-world applications characterized by high dimensionality and complex search landscapes.Starfish optimization algorithm(...Optimization problems are prevalent in various fields of science and engineering,with several real-world applications characterized by high dimensionality and complex search landscapes.Starfish optimization algorithm(SFOA)is a recently optimizer inspired by swarm intelligence,which is effective for numerical optimization,but it may encounter premature and local convergence for complex optimization problems.To address these challenges,this paper proposes the multi-strategy enhanced crested porcupine-starfish optimization algorithm(MCPSFOA).The core innovation of MCPSFOA lies in employing a hybrid strategy to improve SFOA,which integrates the exploratory mechanisms of SFOA with the diverse search capacity of the Crested Porcupine Optimizer(CPO).This synergy enhances MCPSFOA’s ability to navigate complex and multimodal search spaces.To further prevent premature convergence,MCPSFOA incorporates Lévy flight,leveraging its characteristic long and short jump patterns to enable large-scale exploration and escape from local optima.Subsequently,Gaussian mutation is applied for precise solution tuning,introducing controlled perturbations that enhance accuracy and mitigate the risk of insufficient exploitation.Notably,the population diversity enhancement mechanism periodically identifies and resets stagnant individuals,thereby consistently revitalizing population variety throughout the optimization process.MCPSFOA is rigorously evaluated on 24 classical benchmark functions(including high-dimensional cases),the CEC2017 suite,and the CEC2022 suite.MCPSFOA achieves superior overall performance with Friedman mean ranks of 2.208,2.310 and 2.417 on these benchmark functions,outperforming 11 state-of-the-art algorithms.Furthermore,the practical applicability of MCPSFOA is confirmed through its successful application to five engineering optimization cases,where it also yields excellent results.In conclusion,MCPSFOA is not only a highly effective and reliable optimizer for benchmark functions,but also a practical tool for solving real-world optimization problems.展开更多
Existing feature selection methods for intrusion detection systems in the Industrial Internet of Things often suffer from local optimality and high computational complexity.These challenges hinder traditional IDS from...Existing feature selection methods for intrusion detection systems in the Industrial Internet of Things often suffer from local optimality and high computational complexity.These challenges hinder traditional IDS from effectively extracting features while maintaining detection accuracy.This paper proposes an industrial Internet ofThings intrusion detection feature selection algorithm based on an improved whale optimization algorithm(GSLDWOA).The aim is to address the problems that feature selection algorithms under high-dimensional data are prone to,such as local optimality,long detection time,and reduced accuracy.First,the initial population’s diversity is increased using the Gaussian Mutation mechanism.Then,Non-linear Shrinking Factor balances global exploration and local development,avoiding premature convergence.Lastly,Variable-step Levy Flight operator and Dynamic Differential Evolution strategy are introduced to improve the algorithm’s search efficiency and convergence accuracy in highdimensional feature space.Experiments on the NSL-KDD and WUSTL-IIoT-2021 datasets demonstrate that the feature subset selected by GSLDWOA significantly improves detection performance.Compared to the traditional WOA algorithm,the detection rate and F1-score increased by 3.68%and 4.12%.On the WUSTL-IIoT-2021 dataset,accuracy,recall,and F1-score all exceed 99.9%.展开更多
We investigate the null tests of cosmic accelerated expansion by using the baryon acoustic oscillation(BAO)data measured by the dark energy spectroscopic instrument(DESI)and reconstruct the dimensionless Hubble parame...We investigate the null tests of cosmic accelerated expansion by using the baryon acoustic oscillation(BAO)data measured by the dark energy spectroscopic instrument(DESI)and reconstruct the dimensionless Hubble parameter E(z)from the DESI BAO Alcock-Paczynski(AP)data using Gaussian process to perform the null test.We find strong evidence of accelerated expansion from the DESI BAO AP data.By reconstructing the deceleration parameter q(z) from the DESI BAO AP data,we find that accelerated expansion persisted until z■0.7 with a 99.7%confidence level.Additionally,to provide insights into the Hubble tension problem,we propose combining the reconstructed E(z) with D_(H)/r_(d) data to derive a model-independent result r_(d)h=99.8±3.1 Mpc.This result is consistent with measurements from cosmic microwave background(CMB)anisotropies using the ΛCDM model.We also propose a model-independent method for reconstructing the comoving angular diameter distance D_(M)(z) from the distance modulus μ,using SNe Ia data and combining this result with DESI BAO data of D_(M)/r_(d) to constrain the value of r_(d).We find that the value of r_(d),derived from this model-independent method,is smaller than that obtained from CMB measurements,with a significant discrepancy of at least 4.17σ.All the conclusions drawn in this paper are independent of cosmological models and gravitational theories.展开更多
Advances in software and hardware technologies have facilitated the production of quadrotor unmanned aerial vehicles(UAVs).Nowadays,people actively use quadrotor UAVs in essential missions such as search and rescue,co...Advances in software and hardware technologies have facilitated the production of quadrotor unmanned aerial vehicles(UAVs).Nowadays,people actively use quadrotor UAVs in essential missions such as search and rescue,counter-terrorism,firefighting,surveillance,and cargo transportation.While performing these tasks,quadrotors must operate in noisy environments.Therefore,a robust controller design that can control the altitude and attitude of the quadrotor in noisy environments is of great importance.Many researchers have focused only on white Gaussian noise in their studies,whereas researchers need to consider the effects of all colored noises during the operation of the quadrotor.This study aims to design a robust controller that is resistant to all colored noises.Firstly,a nonlinear quadrotormodel was created with MATLAB.Then,a backstepping controller resistant to colored noises was designed.Thedesigned backstepping controller was tested under Gaussian white,pink,brown,blue,and purple noises.PID and Lyapunov-based controller designswere also carried out,and their time responses(rise time,overshoot,settling time)were compared with those of the backstepping controller.In the simulations,time was in seconds,altitude was in meters,and roll,pitch,and yaw references were in radians.Rise and settling time values were in seconds,and overshoot value was in percent.When the obtained values are examined,simulations prove that the proposed backstepping controller has the least overshoot and the shortest settling time under all noise types.展开更多
针对现有SLAM算法在渲染真实感、内存占用和复杂场景适应性方面的不足,提出了一种基于3D Gaussians Splatting的密集SLAM算法——TIGO-SLAM(tensor illumination and Gaussian optimization for indoor SLAM)。该算法集成了基于神经网...针对现有SLAM算法在渲染真实感、内存占用和复杂场景适应性方面的不足,提出了一种基于3D Gaussians Splatting的密集SLAM算法——TIGO-SLAM(tensor illumination and Gaussian optimization for indoor SLAM)。该算法集成了基于神经网络的张量光照模型、改进的高斯遮罩算法以及网格化神经场的几何和颜色属性表示,具体创新包括:a)基于神经网络的张量光照模型,增强镜面反射与漫反射效果,从而提升了渲染真实感;b)通过冗余高斯剔除机制改进高斯遮罩算法,有效降低了内存消耗并提高了实时性;c)结合网格化神经场的几何与颜色属性表示,采用优化的码本存储方式,显著提高了渲染性能和场景重建精度。实验结果表明,TIGO-SLAM在室内场景渲染、内存优化和复杂场景适应性方面均有显著提升,特别是在动态室内环境中的渲染和重建效果表现突出,为SLAM技术在资源受限设备上的应用提供了新的可能。展开更多
Robots are key to expanding the scope of space applications.The end-to-end training for robot vision-based detection and precision operations is challenging owing to constraints such as extreme environments and high c...Robots are key to expanding the scope of space applications.The end-to-end training for robot vision-based detection and precision operations is challenging owing to constraints such as extreme environments and high computational overhead.This study proposes a lightweight integrated framework for grasp detection and imitation learning,named GD-IL;it comprises a grasp detection algorithm based on manipulability and Gaussian mixture model(manipulability-GMM),and a grasp trajectory generation algorithm based on a two-stage robot imitation learning algorithm(TS-RIL).In the manipulability-GMM algorithm,we apply GMM clustering and ellipse regression to the object point cloud,propose two judgment criteria to generate multiple candidate grasp bounding boxes for the robot,and use manipulability as a metric for selecting the optimal grasp bounding box.The stages of the TS-RIL algorithm are grasp trajectory learning and robot pose optimization.In the first stage,the robot grasp trajectory is characterized using a second-order dynamic movement primitive model and Gaussian mixture regression(GMM).By adjusting the function form of the forcing term,the robot closely approximates the target-grasping trajectory.In the second stage,a robot pose optimization model is built based on the derived pose error formula and manipulability metric.This model allows the robot to adjust its configuration in real time while grasping,thereby effectively avoiding singularities.Finally,an algorithm verification platform is developed based on a Robot Operating System and a series of comparative experiments are conducted in real-world scenarios.The experimental results demonstrate that GD-IL significantly improves the effectiveness and robustness of grasp detection and trajectory imitation learning,outperforming existing state-of-the-art methods in execution efficiency,manipulability,and success rate.展开更多
In engineering practice,it is often necessary to determine functional relationships between dependent and independent variables.These relationships can be highly nonlinear,and classical regression approaches cannot al...In engineering practice,it is often necessary to determine functional relationships between dependent and independent variables.These relationships can be highly nonlinear,and classical regression approaches cannot always provide sufficiently reliable solutions.Nevertheless,Machine Learning(ML)techniques,which offer advanced regression tools to address complicated engineering issues,have been developed and widely explored.This study investigates the selected ML techniques to evaluate their suitability for application in the hot deformation behavior of metallic materials.The ML-based regression methods of Artificial Neural Networks(ANNs),Support Vector Machine(SVM),Decision Tree Regression(DTR),and Gaussian Process Regression(GPR)are applied to mathematically describe hot flow stress curve datasets acquired experimentally for a medium-carbon steel.Although the GPR method has not been used for such a regression task before,the results showed that its performance is the most favorable and practically unrivaled;neither the ANN method nor the other studied ML techniques provide such precise results of the solved regression analysis.展开更多
To further understand the performance of the energy harvesters under the influence of the wind force and the random excitation,this paper investigates the stochastic response of the bio-inspired energy harvesters subj...To further understand the performance of the energy harvesters under the influence of the wind force and the random excitation,this paper investigates the stochastic response of the bio-inspired energy harvesters subjected to Gaussian white noise and galloping excitation,simulating the flapping pattern of a seagull and its interaction with wind force.The equivalent linearization method is utilized to convert the original nonlinear model into the Itôstochastic differential equation by minimizing the mean squared error.Then,the second-order steady-state moments about the displacement,velocity,and voltage are derived by combining the moment analysis theory.The theoretical results are simulated numerically to analyze the stochastic response performance under different noise intensities,wind speeds,stiffness coefficients,and electromechanical coupling coefficients,time domain analysis is also conducted to study the performance of the harvester with different parameters.The results reveal that the mean square displacement and voltage increase with increasing the noise intensity and wind speed,larger absolute values of stiffness coefficient correspond to smaller mean square displacement and voltage,and larger electromechanical coupling coefficients can enhance the mean square voltage.Finally,the influence of wind speed and electromechanical coupling coefficient on the stationary probability density function(SPDF)is investigated,revealing the existence of a bimodal distribution under varying environmental conditions.展开更多
基金supported by the National Natural Science Foundation of China[grant number 62376217]the Young Elite Scientists Sponsorship Program by CAST[grant number 2023QNRC001]the Joint Research Project for Meteorological Capacity Improvement[grant number 24NLTSZ003]。
文摘Deep learning-based methods have become alternatives to traditional numerical weather prediction systems,offering faster computation and the ability to utilize large historical datasets.However,the application of deep learning to medium-range regional weather forecasting with limited data remains a significant challenge.In this work,three key solutions are proposed:(1)motivated by the need to improve model performance in data-scarce regional forecasting scenarios,the authors innovatively apply semantic segmentation models,to better capture spatiotemporal features and improve prediction accuracy;(2)recognizing the challenge of overfitting and the inability of traditional noise-based data augmentation methods to effectively enhance model robustness,a novel learnable Gaussian noise mechanism is introduced that allows the model to adaptively optimize perturbations for different locations,ensuring more effective learning;and(3)to address the issue of error accumulation in autoregressive prediction,as well as the challenge of learning difficulty and the lack of intermediate data utilization in one-shot prediction,the authors propose a cascade prediction approach that effectively resolves these problems while significantly improving model forecasting performance.The method achieves a competitive result in The East China Regional AI Medium Range Weather Forecasting Competition.Ablation experiments further validate the effectiveness of each component,highlighting their contributions to enhancing prediction performance.
基金supported by the National Natural Science Foundation of China(Grant No.12402139,No.52368070)supported by Hainan Provincial Natural Science Foundation of China(Grant No.524QN223)+3 种基金Scientific Research Startup Foundation of Hainan University(Grant No.RZ2300002710)State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Dalian University of Technology(Grant No.GZ24107)the Horizontal Research Project(Grant No.HD-KYH-2024022)Innovative Research Projects for Postgraduate Students in Hainan Province(Grant No.Hys2025-217).
文摘Optimization problems are prevalent in various fields of science and engineering,with several real-world applications characterized by high dimensionality and complex search landscapes.Starfish optimization algorithm(SFOA)is a recently optimizer inspired by swarm intelligence,which is effective for numerical optimization,but it may encounter premature and local convergence for complex optimization problems.To address these challenges,this paper proposes the multi-strategy enhanced crested porcupine-starfish optimization algorithm(MCPSFOA).The core innovation of MCPSFOA lies in employing a hybrid strategy to improve SFOA,which integrates the exploratory mechanisms of SFOA with the diverse search capacity of the Crested Porcupine Optimizer(CPO).This synergy enhances MCPSFOA’s ability to navigate complex and multimodal search spaces.To further prevent premature convergence,MCPSFOA incorporates Lévy flight,leveraging its characteristic long and short jump patterns to enable large-scale exploration and escape from local optima.Subsequently,Gaussian mutation is applied for precise solution tuning,introducing controlled perturbations that enhance accuracy and mitigate the risk of insufficient exploitation.Notably,the population diversity enhancement mechanism periodically identifies and resets stagnant individuals,thereby consistently revitalizing population variety throughout the optimization process.MCPSFOA is rigorously evaluated on 24 classical benchmark functions(including high-dimensional cases),the CEC2017 suite,and the CEC2022 suite.MCPSFOA achieves superior overall performance with Friedman mean ranks of 2.208,2.310 and 2.417 on these benchmark functions,outperforming 11 state-of-the-art algorithms.Furthermore,the practical applicability of MCPSFOA is confirmed through its successful application to five engineering optimization cases,where it also yields excellent results.In conclusion,MCPSFOA is not only a highly effective and reliable optimizer for benchmark functions,but also a practical tool for solving real-world optimization problems.
基金supported by the Major Science and Technology Programs in Henan Province(No.241100210100)Henan Provincial Science and Technology Research Project(No.252102211085,No.252102211105)+3 种基金Endogenous Security Cloud Network Convergence R&D Center(No.602431011PQ1)The Special Project for Research and Development in Key Areas of Guangdong Province(No.2021ZDZX1098)The Stabilization Support Program of Science,Technology and Innovation Commission of Shenzhen Municipality(No.20231128083944001)The Key scientific research projects of Henan higher education institutions(No.24A520042).
文摘Existing feature selection methods for intrusion detection systems in the Industrial Internet of Things often suffer from local optimality and high computational complexity.These challenges hinder traditional IDS from effectively extracting features while maintaining detection accuracy.This paper proposes an industrial Internet ofThings intrusion detection feature selection algorithm based on an improved whale optimization algorithm(GSLDWOA).The aim is to address the problems that feature selection algorithms under high-dimensional data are prone to,such as local optimality,long detection time,and reduced accuracy.First,the initial population’s diversity is increased using the Gaussian Mutation mechanism.Then,Non-linear Shrinking Factor balances global exploration and local development,avoiding premature convergence.Lastly,Variable-step Levy Flight operator and Dynamic Differential Evolution strategy are introduced to improve the algorithm’s search efficiency and convergence accuracy in highdimensional feature space.Experiments on the NSL-KDD and WUSTL-IIoT-2021 datasets demonstrate that the feature subset selected by GSLDWOA significantly improves detection performance.Compared to the traditional WOA algorithm,the detection rate and F1-score increased by 3.68%and 4.12%.On the WUSTL-IIoT-2021 dataset,accuracy,recall,and F1-score all exceed 99.9%.
基金supported in part by the National Key Research and Development Program of China (Grant No.2020YFC2201504)the National Natural Science Foundation of China (Grant Nos.12588101 and 12535002)。
文摘We investigate the null tests of cosmic accelerated expansion by using the baryon acoustic oscillation(BAO)data measured by the dark energy spectroscopic instrument(DESI)and reconstruct the dimensionless Hubble parameter E(z)from the DESI BAO Alcock-Paczynski(AP)data using Gaussian process to perform the null test.We find strong evidence of accelerated expansion from the DESI BAO AP data.By reconstructing the deceleration parameter q(z) from the DESI BAO AP data,we find that accelerated expansion persisted until z■0.7 with a 99.7%confidence level.Additionally,to provide insights into the Hubble tension problem,we propose combining the reconstructed E(z) with D_(H)/r_(d) data to derive a model-independent result r_(d)h=99.8±3.1 Mpc.This result is consistent with measurements from cosmic microwave background(CMB)anisotropies using the ΛCDM model.We also propose a model-independent method for reconstructing the comoving angular diameter distance D_(M)(z) from the distance modulus μ,using SNe Ia data and combining this result with DESI BAO data of D_(M)/r_(d) to constrain the value of r_(d).We find that the value of r_(d),derived from this model-independent method,is smaller than that obtained from CMB measurements,with a significant discrepancy of at least 4.17σ.All the conclusions drawn in this paper are independent of cosmological models and gravitational theories.
文摘Advances in software and hardware technologies have facilitated the production of quadrotor unmanned aerial vehicles(UAVs).Nowadays,people actively use quadrotor UAVs in essential missions such as search and rescue,counter-terrorism,firefighting,surveillance,and cargo transportation.While performing these tasks,quadrotors must operate in noisy environments.Therefore,a robust controller design that can control the altitude and attitude of the quadrotor in noisy environments is of great importance.Many researchers have focused only on white Gaussian noise in their studies,whereas researchers need to consider the effects of all colored noises during the operation of the quadrotor.This study aims to design a robust controller that is resistant to all colored noises.Firstly,a nonlinear quadrotormodel was created with MATLAB.Then,a backstepping controller resistant to colored noises was designed.Thedesigned backstepping controller was tested under Gaussian white,pink,brown,blue,and purple noises.PID and Lyapunov-based controller designswere also carried out,and their time responses(rise time,overshoot,settling time)were compared with those of the backstepping controller.In the simulations,time was in seconds,altitude was in meters,and roll,pitch,and yaw references were in radians.Rise and settling time values were in seconds,and overshoot value was in percent.When the obtained values are examined,simulations prove that the proposed backstepping controller has the least overshoot and the shortest settling time under all noise types.
文摘针对现有SLAM算法在渲染真实感、内存占用和复杂场景适应性方面的不足,提出了一种基于3D Gaussians Splatting的密集SLAM算法——TIGO-SLAM(tensor illumination and Gaussian optimization for indoor SLAM)。该算法集成了基于神经网络的张量光照模型、改进的高斯遮罩算法以及网格化神经场的几何和颜色属性表示,具体创新包括:a)基于神经网络的张量光照模型,增强镜面反射与漫反射效果,从而提升了渲染真实感;b)通过冗余高斯剔除机制改进高斯遮罩算法,有效降低了内存消耗并提高了实时性;c)结合网格化神经场的几何与颜色属性表示,采用优化的码本存储方式,显著提高了渲染性能和场景重建精度。实验结果表明,TIGO-SLAM在室内场景渲染、内存优化和复杂场景适应性方面均有显著提升,特别是在动态室内环境中的渲染和重建效果表现突出,为SLAM技术在资源受限设备上的应用提供了新的可能。
基金Supported by National Natural Science Foundation of China(Grant No.52475280)Shaanxi Provincial Natural Science Basic Research Program(Grant No.2025SYSSYSZD-105).
文摘Robots are key to expanding the scope of space applications.The end-to-end training for robot vision-based detection and precision operations is challenging owing to constraints such as extreme environments and high computational overhead.This study proposes a lightweight integrated framework for grasp detection and imitation learning,named GD-IL;it comprises a grasp detection algorithm based on manipulability and Gaussian mixture model(manipulability-GMM),and a grasp trajectory generation algorithm based on a two-stage robot imitation learning algorithm(TS-RIL).In the manipulability-GMM algorithm,we apply GMM clustering and ellipse regression to the object point cloud,propose two judgment criteria to generate multiple candidate grasp bounding boxes for the robot,and use manipulability as a metric for selecting the optimal grasp bounding box.The stages of the TS-RIL algorithm are grasp trajectory learning and robot pose optimization.In the first stage,the robot grasp trajectory is characterized using a second-order dynamic movement primitive model and Gaussian mixture regression(GMM).By adjusting the function form of the forcing term,the robot closely approximates the target-grasping trajectory.In the second stage,a robot pose optimization model is built based on the derived pose error formula and manipulability metric.This model allows the robot to adjust its configuration in real time while grasping,thereby effectively avoiding singularities.Finally,an algorithm verification platform is developed based on a Robot Operating System and a series of comparative experiments are conducted in real-world scenarios.The experimental results demonstrate that GD-IL significantly improves the effectiveness and robustness of grasp detection and trajectory imitation learning,outperforming existing state-of-the-art methods in execution efficiency,manipulability,and success rate.
基金supported by the SP2024/089 Project by the Faculty of Materials Science and Technology,VˇSB-Technical University of Ostrava.
文摘In engineering practice,it is often necessary to determine functional relationships between dependent and independent variables.These relationships can be highly nonlinear,and classical regression approaches cannot always provide sufficiently reliable solutions.Nevertheless,Machine Learning(ML)techniques,which offer advanced regression tools to address complicated engineering issues,have been developed and widely explored.This study investigates the selected ML techniques to evaluate their suitability for application in the hot deformation behavior of metallic materials.The ML-based regression methods of Artificial Neural Networks(ANNs),Support Vector Machine(SVM),Decision Tree Regression(DTR),and Gaussian Process Regression(GPR)are applied to mathematically describe hot flow stress curve datasets acquired experimentally for a medium-carbon steel.Although the GPR method has not been used for such a regression task before,the results showed that its performance is the most favorable and practically unrivaled;neither the ANN method nor the other studied ML techniques provide such precise results of the solved regression analysis.
文摘To further understand the performance of the energy harvesters under the influence of the wind force and the random excitation,this paper investigates the stochastic response of the bio-inspired energy harvesters subjected to Gaussian white noise and galloping excitation,simulating the flapping pattern of a seagull and its interaction with wind force.The equivalent linearization method is utilized to convert the original nonlinear model into the Itôstochastic differential equation by minimizing the mean squared error.Then,the second-order steady-state moments about the displacement,velocity,and voltage are derived by combining the moment analysis theory.The theoretical results are simulated numerically to analyze the stochastic response performance under different noise intensities,wind speeds,stiffness coefficients,and electromechanical coupling coefficients,time domain analysis is also conducted to study the performance of the harvester with different parameters.The results reveal that the mean square displacement and voltage increase with increasing the noise intensity and wind speed,larger absolute values of stiffness coefficient correspond to smaller mean square displacement and voltage,and larger electromechanical coupling coefficients can enhance the mean square voltage.Finally,the influence of wind speed and electromechanical coupling coefficient on the stationary probability density function(SPDF)is investigated,revealing the existence of a bimodal distribution under varying environmental conditions.
