Anchor-free object-detection methods achieve a significant advancement in field of computer vision,particularly in the realm of real-time inferences.However,in remote sensing object detection,anchor-free methods often...Anchor-free object-detection methods achieve a significant advancement in field of computer vision,particularly in the realm of real-time inferences.However,in remote sensing object detection,anchor-free methods often lack of capability in separating the foreground and background.This paper proposes an anchor-free method named probability-enhanced anchor-free detector(ProEnDet)for remote sensing object detection.First,a weighted bidirectional feature pyramid is used for feature extraction.Second,we introduce probability enhancement to strengthen the classification of the object’s foreground and background.The detector uses the logarithm likelihood as the final score to improve the classification of the foreground and background of the object.ProEnDet is verified using the DIOR and NWPU-VHR-10 datasets.The experiment achieved mean average precisions of 61.4 and 69.0 on the DIOR dataset and NWPU-VHR-10 dataset,respectively.ProEnDet achieves a speed of 32.4 FPS on the DIOR dataset,which satisfies the real-time requirements for remote-sensing object detection.展开更多
The accuracy of spot centroid positioning has a significant impact on the tracking accuracy of the system and the stability of the laser link construction.In satellite laser communication systems,the use of short-wave...The accuracy of spot centroid positioning has a significant impact on the tracking accuracy of the system and the stability of the laser link construction.In satellite laser communication systems,the use of short-wave infrared wavelengths as beacon light can reduce atmospheric absorption and signal attenuation.However,there are strong non-uniformity and blind pixels in the short-wave infrared image,which makes the image distorted and leads to the decrease of spot centroid positioning accuracy.Therefore,the high-precision localization of the spot centroid of the short-wave infrared images is of great research significance.A high-precision spot centroid positioning model for short-wave infrared is proposed to correct for non-uniformity and blind pixels in short-wave infrared images and quantify the localization errors caused by the two,further model-based localization error simulations are performed,and a novel spot centroid positioning payload for satellite laser communications has been designed using the latest 640×512 planar array InGaAs shortwave infrared detector.The experimental results show that the non-uniformity of the corrected image is reduced from 7%to 0.6%,the blind pixels rejection rate reaches 100%,the frame rate can be up to 2000 Hz,and the spot centroid localization accuracy is as high as 0.1 pixel point,which realizes high-precision spot centroid localization of high-frame-frequency short-wave infrared images.展开更多
With the development of modern society,people put forward higher requirements for building safety,which makes the construction project face new challenges.Reinforced concrete frame structure as a common engineering ty...With the development of modern society,people put forward higher requirements for building safety,which makes the construction project face new challenges.Reinforced concrete frame structure as a common engineering type,although the construction technology has been relatively mature,but its earthquake collapse ability still needs to be strengthened.This paper analyzes the specific factors that affect the seismic collapse ability of reinforced concrete frame structure,summarizes the previous research results,and puts forward innovative application of fiber-reinforced polymer(FRP)composite materials,play the role of smart materials,improve the isolation and energy dissipation devices,etc.,to promote the continuous optimization of reinforced concrete frame structure design,and show better seismic performance.展开更多
High-voltage electrical post equipment is generally installed on steel supports,which amplifies the seismic inputs and degrades the seismic performance of equipment.This study proposed a variable cross-section damped ...High-voltage electrical post equipment is generally installed on steel supports,which amplifies the seismic inputs and degrades the seismic performance of equipment.This study proposed a variable cross-section damped steel support frame(VCDFS)with viscous dampers to reduce seismic responses of both tall and low-rise electrical equipment.The VCDFS contains a trapezoidal damper layer to generate rocking motions,enabling the diagonal viscous dampers to dissipate seismic inputs.A theoretical model of post equipment with VCDFS is established,and an optimal design procedure is proposed.The analysis shows that the remaining static stiffness ratio λ_(k) is the key parameter that determines the effectiveness of the VCDFS.The VCDFS reduces the average displacement and stress response of a post insulator by 39.4%and 44.6%,respectively,together with a significant decrease in the dynamic amplification factor.Therefore,it is recommended to use the VCDFS instead of the conventional latticed-steel frame in earthquake zones.展开更多
To ensure the operational safety of railways in the landslide-prone areas of mountainous regions,a large-scale model test and numerical simulation were conducted to study the bending moment distribution,internal force...To ensure the operational safety of railways in the landslide-prone areas of mountainous regions,a large-scale model test and numerical simulation were conducted to study the bending moment distribution,internal force distribution,deformation development,and crack propagation characteristics of a framed anti-sliding structure(FAS)under landslide thrust up to the point of failure.Results show that the maximum bending moment and its increase rate in the fore pile are greater than those in the rear pile,with the maximum bending moment of the fore pile approximately 1.1 times that of the rear pile.When the FAS fails,the displacement at the top of the fore pile is significantly greater,about 1.27 times that of the rear pile in the experiment.Major cracks develop at locations corresponding to the peak bending moments.Small transverse cracks initially appear on the upper surface at the intersection between the primary beam and rear pile and then spread to the side of the structure.At the failure stage,major cracks are observed at the pil-beam intersections and near the anchor points.Strengthening flexural stiffness at intersections where major cracks occur can improve the overall thrust-deformation coordination of the FAS,thereby maximizing its performance.展开更多
针对目前Anchor-free目标检测方法CenterNet(Objects as Points)生成热力图不准确、检测精度不足的问题,提出了一种基于特征迭代聚合的高分辨率表征网络CenterNet-DHRNet。首先,引入高分辨率表征骨干网络,并用迭代聚合的方式对不同分辨...针对目前Anchor-free目标检测方法CenterNet(Objects as Points)生成热力图不准确、检测精度不足的问题,提出了一种基于特征迭代聚合的高分辨率表征网络CenterNet-DHRNet。首先,引入高分辨率表征骨干网络,并用迭代聚合的方式对不同分辨率的特征图进行融合,提高网络的分辨率,有效减少图像在下采样过程中损失的空间语义信息。其次,使用高效通道注意力机制对高分辨率表征骨干网络的输出进行优化。最后,利用结合空洞卷积的空间金字塔池化操作增强网络对不同尺度物体的感受野。实验在PASCAL VOC数据集和KITTI数据集上进行,结果表明:CenterNet-DHRNet精度更高,满足实时检测的性能要求,具有良好的鲁棒性。展开更多
Geographic location of nodes is very useful in a sensor network. Previous localization algorithms assume that there exist some anchor nodes in this kind of network, and then other nodes are estimated to create their c...Geographic location of nodes is very useful in a sensor network. Previous localization algorithms assume that there exist some anchor nodes in this kind of network, and then other nodes are estimated to create their coordinates. Once there are not anchors to be deployed, those localization algorithms will be invalidated. Many papers in this field focus on anchor-based solutions. The use of anchors introduces many limitations, since anchors require external equipments such as global position system, cause additional power consumption. A novel positioning algorithm is proposed to use a virtual coordinate system based on a new concept--virtual anchor. It is executed in a distributed fashion according to the connectivity of a node and the measured distances to its neighbors. Both the adjacent member information and the ranging distance result are combined to generate the estimated position of a network, one of which is independently adopted for localization previously. At the position refinement stage the intermediate estimation of a node begins to be evaluated on its reliability for position mutation; thus the positioning optimization process of the whole network is avoided falling into a local optimal solution. Simulation results prove that the algorithm can resolve the distributed localization problem for anchor-free sensor networks, and is superior to previous methods in terms of its positioning capability under a variety of circumstances.展开更多
In anchor-free environments,where no devices with known positions are available,the error growth of autonomous underwater vehicle(AUV)localization and target tracking is unbounded due to the lack of references and the...In anchor-free environments,where no devices with known positions are available,the error growth of autonomous underwater vehicle(AUV)localization and target tracking is unbounded due to the lack of references and the accumulated errors in inertial measurements.This paper aims to improve the localization and tracking accuracy by involving current information as extra references.We first integrate current measurements and maps with belief propagation and design a distributed current-aided message-passing scheme that theoretically solves the localization and tracking problems.Based on this scheme,we propose particle-based cooperative localization and target tracking algorithms,named CaCL and CaTT,respectively.In AUV localization,CaCL uses the current measurements to correct the predicted and transmitted position information and alleviates the impact of the accumulated errors in inertial measurements.With target tracking,the current maps are applied in CaTT to modify the position prediction of the target which is calculated through historical estimates.The effectiveness and robustness of the proposed methods are validated through various simulations by comparisons with alternative methods under different trajectories and current conditions.展开更多
Interactive holography offers unmatched levels of immersion and user engagement in the field of future display.Despite of the substantial progress has been made in dynamic meta-holography,the realization of real-time,...Interactive holography offers unmatched levels of immersion and user engagement in the field of future display.Despite of the substantial progress has been made in dynamic meta-holography,the realization of real-time,highly smooth interactive holography remains a significant challenge due to the computational and display frame rate limitations.In this study,we introduced a dynamic interactive bitwise meta-holography with ultra-high computational and display frame rates.To our knowledge,this is the first reported practical dynamic interactive metasurface holographic system.We spa-tially divided the metasurface device into multiple distinct channels,each projecting a reconstructed sub-pattern.The switching states of these channels were mapped to bitwise operations on a set of bit values,which avoids complex holo-gram computations,enabling an ultra-high computational frame rate.Our approach achieves a computational frame rate of 800 kHz and a display frame rate of 23 kHz on a low-power Raspberry Pi computational platform.According to this methodology,we demonstrated an interactive dynamic holographic Tetris game system that allows interactive gameplay,color display,and on-the-fly hologram creation.Our technology presents an inspiration for advanced dynamic meta-holography,which is promising for a broad range of applications including advanced human-computer interaction,real-time 3D visualization,and next-generation virtual and augmented reality systems.展开更多
The Visual tracking problem can usually be solved in two parts.The first part is to extract the feature of the target and get the candidate region.The second part is to realize the classification of the target and the...The Visual tracking problem can usually be solved in two parts.The first part is to extract the feature of the target and get the candidate region.The second part is to realize the classification of the target and the regression of the bounding box.In recent years,Siameses network in visual tracking problem has always been a frontier research hotspot.In this work,it applies two branches namely search area and tracking template area for similar learning to track.Some related researches prove the feasibility of this network structure.According to the characteristics of two branch shared networks in Siamese network,we also propos a new fully convolutional Siamese network to solve the visual tracking problem.Based on the Siamese network structure,the network we designed adopt a new fusion module,which realizes the fusion of multiple feature layers at different depths.We also devise a better target state estimation criterion.The overall structure is simple,efficient and has wide applicability.We extensive experiments on challenging benchmarks including generic object tracking-10k(GOT-10K),online object tracking benckmark2015(OTB2015)and unmanned air vehicle123(UAV123),and comparisons with state-of-the-art trackers and the fusion module commonly used in the past,Finally,our network performed better under the same backbone,and achieved good tracking effect,which proved the effectiveness and universality of our designed network and feature fusion method.展开更多
Person Search is a task involving pedestrian detection and person re-identification,aiming to retrieve person images matching a given objective attribute from a large-scale image library.The Person Search models need ...Person Search is a task involving pedestrian detection and person re-identification,aiming to retrieve person images matching a given objective attribute from a large-scale image library.The Person Search models need to understand and capture the detailed features and context information of smaller objects in the image more accurately and comprehensively.The current popular Person Search models,whether end-to-end or two-step,are based on anchor boxes.However,due to the limitations of the anchor itself,the model inevitably has some disadvantages,such as unbalance of positive and negative samples and redundant calculation,which will affect the performance of models.To address the problem of fine-grained understanding of target pedestrians in complex scenes and small sizes,this paper proposes a Deformable-Attention-based Anchor-free Person Search model(DAAPS).Fully Convolutional One-Stage(FCOS),as a classic Anchor-free detector,is chosen as the model’s infrastructure.The DAAPS model is the first to combine the Anchor-free Person Search model with Deformable Attention Mechanism,applied to guide the model adaptively adjust the perceptual.The Deformable Attention Mechanism is used to help the model focus on the critical information and effectively improve the poor accuracy caused by the absence of anchor boxes.The experiment proves the adaptability of the Attention mechanism to the Anchor-free model.Besides,with an improved ResNeXt+network frame,the DAAPS model selects the Triplet-based Online Instance Matching(TOIM)Loss function to achieve a more precise end-to-end Person Search task.Simulation experiments demonstrate that the proposed model has higher accuracy and better robustness than most Person Search models,reaching 95.0%of mean Average Precision(mAP)and 95.6%of Top-1 on the CUHK-SYSU dataset,48.6%of mAP and 84.7%of Top-1 on the Person Re-identification in the Wild(PRW)dataset,respectively.展开更多
基金supported in part by the National Natural Science Foundation of China(42001408).
文摘Anchor-free object-detection methods achieve a significant advancement in field of computer vision,particularly in the realm of real-time inferences.However,in remote sensing object detection,anchor-free methods often lack of capability in separating the foreground and background.This paper proposes an anchor-free method named probability-enhanced anchor-free detector(ProEnDet)for remote sensing object detection.First,a weighted bidirectional feature pyramid is used for feature extraction.Second,we introduce probability enhancement to strengthen the classification of the object’s foreground and background.The detector uses the logarithm likelihood as the final score to improve the classification of the foreground and background of the object.ProEnDet is verified using the DIOR and NWPU-VHR-10 datasets.The experiment achieved mean average precisions of 61.4 and 69.0 on the DIOR dataset and NWPU-VHR-10 dataset,respectively.ProEnDet achieves a speed of 32.4 FPS on the DIOR dataset,which satisfies the real-time requirements for remote-sensing object detection.
基金Supported by the Short-wave Infrared Camera Systems(B025F40622024)。
文摘The accuracy of spot centroid positioning has a significant impact on the tracking accuracy of the system and the stability of the laser link construction.In satellite laser communication systems,the use of short-wave infrared wavelengths as beacon light can reduce atmospheric absorption and signal attenuation.However,there are strong non-uniformity and blind pixels in the short-wave infrared image,which makes the image distorted and leads to the decrease of spot centroid positioning accuracy.Therefore,the high-precision localization of the spot centroid of the short-wave infrared images is of great research significance.A high-precision spot centroid positioning model for short-wave infrared is proposed to correct for non-uniformity and blind pixels in short-wave infrared images and quantify the localization errors caused by the two,further model-based localization error simulations are performed,and a novel spot centroid positioning payload for satellite laser communications has been designed using the latest 640×512 planar array InGaAs shortwave infrared detector.The experimental results show that the non-uniformity of the corrected image is reduced from 7%to 0.6%,the blind pixels rejection rate reaches 100%,the frame rate can be up to 2000 Hz,and the spot centroid localization accuracy is as high as 0.1 pixel point,which realizes high-precision spot centroid localization of high-frame-frequency short-wave infrared images.
文摘With the development of modern society,people put forward higher requirements for building safety,which makes the construction project face new challenges.Reinforced concrete frame structure as a common engineering type,although the construction technology has been relatively mature,but its earthquake collapse ability still needs to be strengthened.This paper analyzes the specific factors that affect the seismic collapse ability of reinforced concrete frame structure,summarizes the previous research results,and puts forward innovative application of fiber-reinforced polymer(FRP)composite materials,play the role of smart materials,improve the isolation and energy dissipation devices,etc.,to promote the continuous optimization of reinforced concrete frame structure design,and show better seismic performance.
基金Guangdong Basic and Applied Basic Research Foundation under Grant Nos.2022A1515110561 and 2023A1515010072Natural Science Foundation of China under Grant Nos.52308488 and 52378499。
文摘High-voltage electrical post equipment is generally installed on steel supports,which amplifies the seismic inputs and degrades the seismic performance of equipment.This study proposed a variable cross-section damped steel support frame(VCDFS)with viscous dampers to reduce seismic responses of both tall and low-rise electrical equipment.The VCDFS contains a trapezoidal damper layer to generate rocking motions,enabling the diagonal viscous dampers to dissipate seismic inputs.A theoretical model of post equipment with VCDFS is established,and an optimal design procedure is proposed.The analysis shows that the remaining static stiffness ratio λ_(k) is the key parameter that determines the effectiveness of the VCDFS.The VCDFS reduces the average displacement and stress response of a post insulator by 39.4%and 44.6%,respectively,together with a significant decrease in the dynamic amplification factor.Therefore,it is recommended to use the VCDFS instead of the conventional latticed-steel frame in earthquake zones.
基金The National Natural Science Foundation of China(No.52078427).
文摘To ensure the operational safety of railways in the landslide-prone areas of mountainous regions,a large-scale model test and numerical simulation were conducted to study the bending moment distribution,internal force distribution,deformation development,and crack propagation characteristics of a framed anti-sliding structure(FAS)under landslide thrust up to the point of failure.Results show that the maximum bending moment and its increase rate in the fore pile are greater than those in the rear pile,with the maximum bending moment of the fore pile approximately 1.1 times that of the rear pile.When the FAS fails,the displacement at the top of the fore pile is significantly greater,about 1.27 times that of the rear pile in the experiment.Major cracks develop at locations corresponding to the peak bending moments.Small transverse cracks initially appear on the upper surface at the intersection between the primary beam and rear pile and then spread to the side of the structure.At the failure stage,major cracks are observed at the pil-beam intersections and near the anchor points.Strengthening flexural stiffness at intersections where major cracks occur can improve the overall thrust-deformation coordination of the FAS,thereby maximizing its performance.
文摘针对目前Anchor-free目标检测方法CenterNet(Objects as Points)生成热力图不准确、检测精度不足的问题,提出了一种基于特征迭代聚合的高分辨率表征网络CenterNet-DHRNet。首先,引入高分辨率表征骨干网络,并用迭代聚合的方式对不同分辨率的特征图进行融合,提高网络的分辨率,有效减少图像在下采样过程中损失的空间语义信息。其次,使用高效通道注意力机制对高分辨率表征骨干网络的输出进行优化。最后,利用结合空洞卷积的空间金字塔池化操作增强网络对不同尺度物体的感受野。实验在PASCAL VOC数据集和KITTI数据集上进行,结果表明:CenterNet-DHRNet精度更高,满足实时检测的性能要求,具有良好的鲁棒性。
基金the National Natural Science Foundation of China (60673054, 60773129)theExcellent Youth Science and Technology Foundation of Anhui Province of China.
文摘Geographic location of nodes is very useful in a sensor network. Previous localization algorithms assume that there exist some anchor nodes in this kind of network, and then other nodes are estimated to create their coordinates. Once there are not anchors to be deployed, those localization algorithms will be invalidated. Many papers in this field focus on anchor-based solutions. The use of anchors introduces many limitations, since anchors require external equipments such as global position system, cause additional power consumption. A novel positioning algorithm is proposed to use a virtual coordinate system based on a new concept--virtual anchor. It is executed in a distributed fashion according to the connectivity of a node and the measured distances to its neighbors. Both the adjacent member information and the ranging distance result are combined to generate the estimated position of a network, one of which is independently adopted for localization previously. At the position refinement stage the intermediate estimation of a node begins to be evaluated on its reliability for position mutation; thus the positioning optimization process of the whole network is avoided falling into a local optimal solution. Simulation results prove that the algorithm can resolve the distributed localization problem for anchor-free sensor networks, and is superior to previous methods in terms of its positioning capability under a variety of circumstances.
基金supported in part by the National Natural Science Foundation of China(62203299,61773264,61922058,61803261,61801295)the Oceanic Interdisciplinary Program of Shanghai Jiao Tong University(SL2020ZD206,SL2020MS010,SL2020MS015)。
文摘In anchor-free environments,where no devices with known positions are available,the error growth of autonomous underwater vehicle(AUV)localization and target tracking is unbounded due to the lack of references and the accumulated errors in inertial measurements.This paper aims to improve the localization and tracking accuracy by involving current information as extra references.We first integrate current measurements and maps with belief propagation and design a distributed current-aided message-passing scheme that theoretically solves the localization and tracking problems.Based on this scheme,we propose particle-based cooperative localization and target tracking algorithms,named CaCL and CaTT,respectively.In AUV localization,CaCL uses the current measurements to correct the predicted and transmitted position information and alleviates the impact of the accumulated errors in inertial measurements.With target tracking,the current maps are applied in CaTT to modify the position prediction of the target which is calculated through historical estimates.The effectiveness and robustness of the proposed methods are validated through various simulations by comparisons with alternative methods under different trajectories and current conditions.
基金supports from National Natural Science Foundation of China (Grant No.62205117,52275429)National Key Research and Development Program of China (Grant No.2021YFF0502700)+3 种基金Young Elite Scientists Sponsorship Program by CAST (Grant No.2022QNRC001)West Light Foundation of the Chinese Academy of Sciences (Grant No.xbzg-zdsys-202206)Knowledge Innovation Program of Wuhan-Shuguang,Innovation project of Optics Valley Laboratory (Grant No.OVL2021ZD002)Hubei Provincial Natural Science Foundation of China (Grant No.2022CFB792).
文摘Interactive holography offers unmatched levels of immersion and user engagement in the field of future display.Despite of the substantial progress has been made in dynamic meta-holography,the realization of real-time,highly smooth interactive holography remains a significant challenge due to the computational and display frame rate limitations.In this study,we introduced a dynamic interactive bitwise meta-holography with ultra-high computational and display frame rates.To our knowledge,this is the first reported practical dynamic interactive metasurface holographic system.We spa-tially divided the metasurface device into multiple distinct channels,each projecting a reconstructed sub-pattern.The switching states of these channels were mapped to bitwise operations on a set of bit values,which avoids complex holo-gram computations,enabling an ultra-high computational frame rate.Our approach achieves a computational frame rate of 800 kHz and a display frame rate of 23 kHz on a low-power Raspberry Pi computational platform.According to this methodology,we demonstrated an interactive dynamic holographic Tetris game system that allows interactive gameplay,color display,and on-the-fly hologram creation.Our technology presents an inspiration for advanced dynamic meta-holography,which is promising for a broad range of applications including advanced human-computer interaction,real-time 3D visualization,and next-generation virtual and augmented reality systems.
文摘The Visual tracking problem can usually be solved in two parts.The first part is to extract the feature of the target and get the candidate region.The second part is to realize the classification of the target and the regression of the bounding box.In recent years,Siameses network in visual tracking problem has always been a frontier research hotspot.In this work,it applies two branches namely search area and tracking template area for similar learning to track.Some related researches prove the feasibility of this network structure.According to the characteristics of two branch shared networks in Siamese network,we also propos a new fully convolutional Siamese network to solve the visual tracking problem.Based on the Siamese network structure,the network we designed adopt a new fusion module,which realizes the fusion of multiple feature layers at different depths.We also devise a better target state estimation criterion.The overall structure is simple,efficient and has wide applicability.We extensive experiments on challenging benchmarks including generic object tracking-10k(GOT-10K),online object tracking benckmark2015(OTB2015)and unmanned air vehicle123(UAV123),and comparisons with state-of-the-art trackers and the fusion module commonly used in the past,Finally,our network performed better under the same backbone,and achieved good tracking effect,which proved the effectiveness and universality of our designed network and feature fusion method.
基金to the Natural Science Foundation of Shanghai under Grant 21ZR1426500,and the Top-Notch Innovative Talent Training Program for Graduate Students of Shanghai Maritime University under Grant 2021YBR008for their generous support and funding through the project funding program.This funding has played a pivotal role in the successful completion of our research.We are deeply appreciative of their invaluable contribution to our research efforts.
文摘Person Search is a task involving pedestrian detection and person re-identification,aiming to retrieve person images matching a given objective attribute from a large-scale image library.The Person Search models need to understand and capture the detailed features and context information of smaller objects in the image more accurately and comprehensively.The current popular Person Search models,whether end-to-end or two-step,are based on anchor boxes.However,due to the limitations of the anchor itself,the model inevitably has some disadvantages,such as unbalance of positive and negative samples and redundant calculation,which will affect the performance of models.To address the problem of fine-grained understanding of target pedestrians in complex scenes and small sizes,this paper proposes a Deformable-Attention-based Anchor-free Person Search model(DAAPS).Fully Convolutional One-Stage(FCOS),as a classic Anchor-free detector,is chosen as the model’s infrastructure.The DAAPS model is the first to combine the Anchor-free Person Search model with Deformable Attention Mechanism,applied to guide the model adaptively adjust the perceptual.The Deformable Attention Mechanism is used to help the model focus on the critical information and effectively improve the poor accuracy caused by the absence of anchor boxes.The experiment proves the adaptability of the Attention mechanism to the Anchor-free model.Besides,with an improved ResNeXt+network frame,the DAAPS model selects the Triplet-based Online Instance Matching(TOIM)Loss function to achieve a more precise end-to-end Person Search task.Simulation experiments demonstrate that the proposed model has higher accuracy and better robustness than most Person Search models,reaching 95.0%of mean Average Precision(mAP)and 95.6%of Top-1 on the CUHK-SYSU dataset,48.6%of mAP and 84.7%of Top-1 on the Person Re-identification in the Wild(PRW)dataset,respectively.
