Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V<sub>1</sub> ∪ V<sub>2</sub> and V<sub>1</sub> ∩ V<sub>2</sub> = ∅. If a bipartition satis...Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V<sub>1</sub> ∪ V<sub>2</sub> and V<sub>1</sub> ∩ V<sub>2</sub> = ∅. If a bipartition satisfies ∥V<sub>1</sub>∣ - ∣V<sub>2</sub>∥ ≤ 1, we call it a bisection. The research in this paper is mainly based on a conjecture proposed by Bollobás and Scott. The conjecture is that every graph G has a bisection (V<sub>1</sub>, V<sub>2</sub>) such that ∀v ∈ V<sub>1</sub>, at least half minuses one of the neighbors of v are in the V<sub>2</sub>;∀v ∈ V<sub>2</sub>, at least half minuses one of the neighbors of v are in the V<sub>1</sub>. In this paper, we confirm this conjecture for some bipartite graphs, crown graphs and windmill graphs.展开更多
Due to the exponential growth of video data,aided by rapid advancements in multimedia technologies.It became difficult for the user to obtain information from a large video series.The process of providing an abstract ...Due to the exponential growth of video data,aided by rapid advancements in multimedia technologies.It became difficult for the user to obtain information from a large video series.The process of providing an abstract of the entire video that includes the most representative frames is known as static video summarization.This method resulted in rapid exploration,indexing,and retrieval of massive video libraries.We propose a framework for static video summary based on a Binary Robust Invariant Scalable Keypoint(BRISK)and bisecting K-means clustering algorithm.The current method effectively recognizes relevant frames using BRISK by extracting keypoints and the descriptors from video sequences.The video frames’BRISK features are clustered using a bisecting K-means,and the keyframe is determined by selecting the frame that is most near the cluster center.Without applying any clustering parameters,the appropriate clusters number is determined using the silhouette coefficient.Experiments were carried out on a publicly available open video project(OVP)dataset that contained videos of different genres.The proposed method’s effectiveness is compared to existing methods using a variety of evaluation metrics,and the proposed method achieves a trade-off between computational cost and quality.展开更多
Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement...Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid Chttp：//lsec. cc. ac. cn/phg/）, a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simukaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the biseetioning refinement procedure.展开更多
The computation algorithm of knot point planning for Cartesian trajectorygeneration of manipulator is investigated, A novel inheritance bisection algorithm (IBA) based onconventional bisection algorithm (B A) is propo...The computation algorithm of knot point planning for Cartesian trajectorygeneration of manipulator is investigated, A novel inheritance bisection algorithm (IBA) based onconventional bisection algorithm (B A) is proposed. IBA has two steps. The first step is the 1 stknot point planning under lower set position accuracy; the second step is the 2nd knot pointplanning that inherits the results of the 1st planning under higher set position accuracy. Thesimulation results reveal that the number of inverse kinematical calculation (IKC) caused by IBA isdecreased compared with BA. IBA is more efficient to plan knot points.展开更多
A successive quadratic programming algorithm for solving SDP relaxation of Max- Bisection is provided and its convergence result is given. The step-size in the algorithm is obtained by solving n easy quadratic equatio...A successive quadratic programming algorithm for solving SDP relaxation of Max- Bisection is provided and its convergence result is given. The step-size in the algorithm is obtained by solving n easy quadratic equations without using the linear search technique. The numerical experiments show that this algorithm is rather faster than the interior-point method.展开更多
In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strateg...In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.展开更多
Indoor positioning is a key technology in today’s intelligent environments,and it plays a crucial role in many application areas.This paper proposed an unscented Kalman filter(UKF)based on the maximum correntropy cri...Indoor positioning is a key technology in today’s intelligent environments,and it plays a crucial role in many application areas.This paper proposed an unscented Kalman filter(UKF)based on the maximum correntropy criterion(MCC)instead of the minimummean square error criterion(MMSE).This innovative approach is applied to the loose coupling of the Inertial Navigation System(INS)and Ultra-Wideband(UWB).By introducing the maximum correntropy criterion,the MCCUKF algorithm dynamically adjusts the covariance matrices of the system noise and the measurement noise,thus enhancing its adaptability to diverse environmental localization requirements.Particularly in the presence of non-Gaussian noise,especially heavy-tailed noise,the MCCUKF exhibits superior accuracy and robustness compared to the traditional UKF.The method initially generates an estimate of the predicted state and covariance matrix through the unscented transform(UT)and then recharacterizes the measurement information using a nonlinear regression method at the cost of theMCC.Subsequently,the state and covariance matrices of the filter are updated by employing the unscented transformation on the measurement equations.Moreover,to mitigate the influence of non-line-of-sight(NLOS)errors positioning accuracy,this paper proposes a k-medoid clustering algorithm based on bisection k-means(Bikmeans).This algorithm preprocesses the UWB distance measurements to yield a more precise position estimation.Simulation results demonstrate that MCCUKF is robust to the uncertainty of UWB and realizes stable integration of INS and UWB systems.展开更多
文摘Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V<sub>1</sub> ∪ V<sub>2</sub> and V<sub>1</sub> ∩ V<sub>2</sub> = ∅. If a bipartition satisfies ∥V<sub>1</sub>∣ - ∣V<sub>2</sub>∥ ≤ 1, we call it a bisection. The research in this paper is mainly based on a conjecture proposed by Bollobás and Scott. The conjecture is that every graph G has a bisection (V<sub>1</sub>, V<sub>2</sub>) such that ∀v ∈ V<sub>1</sub>, at least half minuses one of the neighbors of v are in the V<sub>2</sub>;∀v ∈ V<sub>2</sub>, at least half minuses one of the neighbors of v are in the V<sub>1</sub>. In this paper, we confirm this conjecture for some bipartite graphs, crown graphs and windmill graphs.
基金The authors would like to thank Research Supporting Project Number(RSP2024R444)King Saud University,Riyadh,Saudi Arabia.
文摘Due to the exponential growth of video data,aided by rapid advancements in multimedia technologies.It became difficult for the user to obtain information from a large video series.The process of providing an abstract of the entire video that includes the most representative frames is known as static video summarization.This method resulted in rapid exploration,indexing,and retrieval of massive video libraries.We propose a framework for static video summary based on a Binary Robust Invariant Scalable Keypoint(BRISK)and bisecting K-means clustering algorithm.The current method effectively recognizes relevant frames using BRISK by extracting keypoints and the descriptors from video sequences.The video frames’BRISK features are clustered using a bisecting K-means,and the keyframe is determined by selecting the frame that is most near the cluster center.Without applying any clustering parameters,the appropriate clusters number is determined using the silhouette coefficient.Experiments were carried out on a publicly available open video project(OVP)dataset that contained videos of different genres.The proposed method’s effectiveness is compared to existing methods using a variety of evaluation metrics,and the proposed method achieves a trade-off between computational cost and quality.
基金supported by the 973 Program of China 2005CB321702China NSF 10531080.
文摘Local mesh refinement is one of the key steps in the implementations of adaptive finite element methods. This paper presents a parallel algorithm for distributed memory parallel computers for adaptive local refinement of tetrahedral meshes using bisection. This algorithm is used in PHG, Parallel Hierarchical Grid Chttp：//lsec. cc. ac. cn/phg/）, a toolbox under active development for parallel adaptive finite element solutions of partial differential equations. The algorithm proposed is characterized by allowing simukaneous refinement of submeshes to arbitrary levels before synchronization between submeshes and without the need of a central coordinator process for managing new vertices. Using the concept of canonical refinement, a simple proof of the independence of the resulting mesh on the mesh partitioning is given, which is useful in better understanding the behaviour of the biseetioning refinement procedure.
基金This project is supported by National 863 Hi-tech Foundation of China(No. 2001AA422210).
文摘The computation algorithm of knot point planning for Cartesian trajectorygeneration of manipulator is investigated, A novel inheritance bisection algorithm (IBA) based onconventional bisection algorithm (B A) is proposed. IBA has two steps. The first step is the 1 stknot point planning under lower set position accuracy; the second step is the 2nd knot pointplanning that inherits the results of the 1st planning under higher set position accuracy. Thesimulation results reveal that the number of inverse kinematical calculation (IKC) caused by IBA isdecreased compared with BA. IBA is more efficient to plan knot points.
文摘A successive quadratic programming algorithm for solving SDP relaxation of Max- Bisection is provided and its convergence result is given. The step-size in the algorithm is obtained by solving n easy quadratic equations without using the linear search technique. The numerical experiments show that this algorithm is rather faster than the interior-point method.
文摘In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.
基金supported by the National Natural Science Foundation of China under Grant Nos.62273083 and 61803077Natural Science Foundation of Hebei Province under Grant No.F2020501012.
文摘Indoor positioning is a key technology in today’s intelligent environments,and it plays a crucial role in many application areas.This paper proposed an unscented Kalman filter(UKF)based on the maximum correntropy criterion(MCC)instead of the minimummean square error criterion(MMSE).This innovative approach is applied to the loose coupling of the Inertial Navigation System(INS)and Ultra-Wideband(UWB).By introducing the maximum correntropy criterion,the MCCUKF algorithm dynamically adjusts the covariance matrices of the system noise and the measurement noise,thus enhancing its adaptability to diverse environmental localization requirements.Particularly in the presence of non-Gaussian noise,especially heavy-tailed noise,the MCCUKF exhibits superior accuracy and robustness compared to the traditional UKF.The method initially generates an estimate of the predicted state and covariance matrix through the unscented transform(UT)and then recharacterizes the measurement information using a nonlinear regression method at the cost of theMCC.Subsequently,the state and covariance matrices of the filter are updated by employing the unscented transformation on the measurement equations.Moreover,to mitigate the influence of non-line-of-sight(NLOS)errors positioning accuracy,this paper proposes a k-medoid clustering algorithm based on bisection k-means(Bikmeans).This algorithm preprocesses the UWB distance measurements to yield a more precise position estimation.Simulation results demonstrate that MCCUKF is robust to the uncertainty of UWB and realizes stable integration of INS and UWB systems.
