In this paper,we introduce the notion of f-CC harmonic maps with potential H from a Riemannian manifold into sub-Riemannian manifolds,and achieve some vanishing theorems for f-CC harmonic maps with potential H via the...In this paper,we introduce the notion of f-CC harmonic maps with potential H from a Riemannian manifold into sub-Riemannian manifolds,and achieve some vanishing theorems for f-CC harmonic maps with potential H via the stress-energy tensor and the monotonicity formulas.展开更多
1 Introduction and Main Results For n≥2,let M be a n-dimensional connected smooth manifold.We take a fixed smooth measure on M with strictly positive density,and write dx as the measure when we integrate.Also,we simp...1 Introduction and Main Results For n≥2,let M be a n-dimensional connected smooth manifold.We take a fixed smooth measure on M with strictly positive density,and write dx as the measure when we integrate.Also,we simply denote the measure of a set E?M by|E|.展开更多
Multi-label feature selection(MFS)is a crucial dimensionality reduction technique aimed at identifying informative features associated with multiple labels.However,traditional centralized methods face significant chal...Multi-label feature selection(MFS)is a crucial dimensionality reduction technique aimed at identifying informative features associated with multiple labels.However,traditional centralized methods face significant challenges in privacy-sensitive and distributed settings,often neglecting label dependencies and suffering from low computational efficiency.To address these issues,we introduce a novel framework,Fed-MFSDHBCPSO—federated MFS via dual-layer hybrid breeding cooperative particle swarm optimization algorithm with manifold and sparsity regularization(DHBCPSO-MSR).Leveraging the federated learning paradigm,Fed-MFSDHBCPSO allows clients to perform local feature selection(FS)using DHBCPSO-MSR.Locally selected feature subsets are encrypted with differential privacy(DP)and transmitted to a central server,where they are securely aggregated and refined through secure multi-party computation(SMPC)until global convergence is achieved.Within each client,DHBCPSO-MSR employs a dual-layer FS strategy.The inner layer constructs sample and label similarity graphs,generates Laplacian matrices to capture the manifold structure between samples and labels,and applies L2,1-norm regularization to sparsify the feature subset,yielding an optimized feature weight matrix.The outer layer uses a hybrid breeding cooperative particle swarm optimization algorithm to further refine the feature weight matrix and identify the optimal feature subset.The updated weight matrix is then fed back to the inner layer for further optimization.Comprehensive experiments on multiple real-world multi-label datasets demonstrate that Fed-MFSDHBCPSO consistently outperforms both centralized and federated baseline methods across several key evaluation metrics.展开更多
Wo prove that there do not exist quasi-isometric embeddings of connected nonabelian nilpotent Lie groups equipped with left invariant Riemannian metrics into a metric measure space satisfying the curvature-dimension c...Wo prove that there do not exist quasi-isometric embeddings of connected nonabelian nilpotent Lie groups equipped with left invariant Riemannian metrics into a metric measure space satisfying the curvature-dimension condition RCD(Q,N)with N∈R and N>1.In fact,we can prove that a sub-Riemannian manifold whose generic degree of nonholonomy is not smaller than 2 cannot be bi-Lipschitzly embedded in any Banach space with the Radon-Nikodym property.We also get that every regular sub-Riemannian manifold do not satisfy the curvature-dimension condition CD(K,N),where K,N∈R and N>1.Along the way to the proofs,we show that the minimal weak upper gradient and the horizontal gradient coincide on the Carnot-Caratheodory spaces which may have independent interests.展开更多
In this paper,we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimens...In this paper,we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimensional twisted BCV spaces.展开更多
Flow velocity uniformity of the microchannel plate is a major factor affecting the performance of microchannel devices.In order to improve the velocity distribution uniformity of the microchannel plate,we designed two...Flow velocity uniformity of the microchannel plate is a major factor affecting the performance of microchannel devices.In order to improve the velocity distribution uniformity of the microchannel plate,we designed two new microchannel structures:V-type and A-type.The effects of various structural parameters of the manifolds on the velocity distribution are reported.The V-type and A-type microchannel plates had a more uniform velocity distribution compared to the Z-type microchannel plate.The final result showed that it is beneficial for the V-type microchannel plate to obtain a more uniform velocity distribution when the manifold structure parameters are X_(in)=-1,X_(out)=0,Y_(in)=10,Y_(out)=6,Hin=4,H_(out)=1,and R=0.5.展开更多
This paper presents a manifold-optimized Error-State Kalman Filter(ESKF)framework for unmanned aerial vehicle(UAV)pose estimation,integrating Inertial Measurement Unit(IMU)data with GPS or LiDAR to enhance estimation ...This paper presents a manifold-optimized Error-State Kalman Filter(ESKF)framework for unmanned aerial vehicle(UAV)pose estimation,integrating Inertial Measurement Unit(IMU)data with GPS or LiDAR to enhance estimation accuracy and robustness.We employ a manifold-based optimization approach,leveraging exponential and logarithmic mappings to transform rotation vectors into rotation matrices.The proposed ESKF framework ensures state variables remain near the origin,effectively mitigating singularity issues and enhancing numerical stability.Additionally,due to the small magnitude of state variables,second-order terms can be neglected,simplifying Jacobian matrix computation and improving computational efficiency.Furthermore,we introduce a novel Kalman filter gain computation strategy that dynamically adapts to low-dimensional and high-dimensional observation equations,enabling efficient processing across different sensor modalities.Specifically,for resource-constrained UAV platforms,this method significantly reduces computational cost,making it highly suitable for real-time UAV applications.展开更多
In this note we describe a logarithmic version of mirror Landau-Ginzburg model for semi-projective toric manifolds and show in an elementary and explicit way that the state space ring of the Landau-Ginzburg mirror is ...In this note we describe a logarithmic version of mirror Landau-Ginzburg model for semi-projective toric manifolds and show in an elementary and explicit way that the state space ring of the Landau-Ginzburg mirror is isomorphic to the C-valued cohomology of the toric manifold.展开更多
In this paper,we study the basic p-harmonic forms on the complete foliated Riemannian manifolds.By using the method in[1],we show that if the basic mean curvature form is bounded and co-closed,and the transversal curv...In this paper,we study the basic p-harmonic forms on the complete foliated Riemannian manifolds.By using the method in[1],we show that if the basic mean curvature form is bounded and co-closed,and the transversal curvature operator is nonnegative and positive at least one point,then we obtain a vanishing theorem for L^(p)-integrably p-harmonic r-forms.展开更多
There are all kinds of unknown and known signals in the actual electromagnetic environment,which hinders the development of practical cognitive radio applications.However,most existing signal recognition models are di...There are all kinds of unknown and known signals in the actual electromagnetic environment,which hinders the development of practical cognitive radio applications.However,most existing signal recognition models are difficult to discover unknown signals while recognizing known ones.In this paper,a compact manifold mixup feature-based open-set recognition approach(OR-CMMF)is proposed to address the above problem.First,the proposed approach utilizes the center loss to constrain decision boundaries so that it obtains the compact latent signal feature representations and extends the low-confidence feature space.Second,the latent signal feature representations are used to construct synthetic representations as substitutes for unknown categories of signals.Then,these constructed representations can occupy the extended low-confidence space.Finally,the proposed approach applies the distillation loss to adjust the decision boundaries between the known categories signals and the constructed unknown categories substitutes so that it accurately discovers unknown signals.The OR-CMMF approach outperformed other state-of-the-art open-set recognition methods in comprehensive recognition performance and running time,as demonstrated by simulation experiments on two public datasets RML2016.10a and ORACLE.展开更多
This paper introduces a new method based on deep belief networks(DBNs)to integrate intrinsic vibration information and assess the similarity of subspaces established on the Grassmann manifold for intelligent fault dia...This paper introduces a new method based on deep belief networks(DBNs)to integrate intrinsic vibration information and assess the similarity of subspaces established on the Grassmann manifold for intelligent fault diagnosis of a reciprocating compressor(RC).Initially,raw vibration signals undergo empirical mode decomposition to break them down into multiple intrinsic mode functions(IMFs).This operation can reveal inherent vibration patterns of fault and other components hidden in the original signals.Subsequently,features are refined from all the IMFs and concatenated into a high-dimensional representative vector,offering localized and comprehensive insights into RC operation.Through DBN,the fault-sensitive information is further refined from the features to enhance their performance in fault identification.Finally,similarities among subspaces on the Grassmann manifold are computed to match fault types.The efficacy of the method is validated usingfield data.Comparative analysis with traditional approaches for feature dimension reduction,feature extraction,and Euclidean distance-based fault identification underscores the effectiveness and superiority of the proposed method in RC fault diagnosis.展开更多
In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the u...In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.展开更多
The modeling of crack growth in three-dimensional(3D)space poses significant challenges in rock mechanics due to the complex numerical computation involved in simulating crack propagation and interaction in rock mater...The modeling of crack growth in three-dimensional(3D)space poses significant challenges in rock mechanics due to the complex numerical computation involved in simulating crack propagation and interaction in rock materials.In this study,we present a novel approach that introduces a 3D numerical manifold method(3D-NMM)with a geometric kernel to enhance computational efficiency.Specifically,the maximum tensile stress criterion is adopted as a crack growth criterion to achieve strong discontinuous crack growth,and a local crack tracking algorithm and an angle correction technique are incorporated to address minor limitations of the algorithm in a 3D model.The implementation of the program is carried out in Python,using object-oriented programming in two independent modules:a calculation module and a crack module.Furthermore,we propose feasible improvements to enhance the performance of the algorithm.Finally,we demonstrate the feasibility and effectiveness of the enhanced algorithm in the 3D-NMM using four numerical examples.This study establishes the potential of the 3DNMM,combined with the local tracking algorithm,for accurately modeling 3D crack propagation in brittle rock materials.展开更多
Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and ...Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.展开更多
Studies are made of the cohomology of CR_ submanifolds and integrability of the distribution D of CR_submanifolds. When dim D⊥】1, the totally umbilical non-trival CR-submanifold i n nea r Kaehler manifold is totall...Studies are made of the cohomology of CR_ submanifolds and integrability of the distribution D of CR_submanifolds. When dim D⊥】1, the totally umbilical non-trival CR-submanifold i n nea r Kaehler manifold is totally geodesic. In the end, we get:If is n ear Kaehler manifold with B】0, then is not permitt ed to have fixed foliate non-trival CR-submanifold.展开更多
基金Supported by the National Natural Science Foundation of China(12271254,12141104,12571056)supported by Natural Science Foundation of Henan(252300421791,252300421497)。
文摘In this paper,we introduce the notion of f-CC harmonic maps with potential H from a Riemannian manifold into sub-Riemannian manifolds,and achieve some vanishing theorems for f-CC harmonic maps with potential H via the stress-energy tensor and the monotonicity formulas.
基金Supported by National Natural Science Foundation of China(1163101111626251)China Postdoctoral Science Foundation(2021M703282)。
文摘1 Introduction and Main Results For n≥2,let M be a n-dimensional connected smooth manifold.We take a fixed smooth measure on M with strictly positive density,and write dx as the measure when we integrate.Also,we simply denote the measure of a set E?M by|E|.
文摘Multi-label feature selection(MFS)is a crucial dimensionality reduction technique aimed at identifying informative features associated with multiple labels.However,traditional centralized methods face significant challenges in privacy-sensitive and distributed settings,often neglecting label dependencies and suffering from low computational efficiency.To address these issues,we introduce a novel framework,Fed-MFSDHBCPSO—federated MFS via dual-layer hybrid breeding cooperative particle swarm optimization algorithm with manifold and sparsity regularization(DHBCPSO-MSR).Leveraging the federated learning paradigm,Fed-MFSDHBCPSO allows clients to perform local feature selection(FS)using DHBCPSO-MSR.Locally selected feature subsets are encrypted with differential privacy(DP)and transmitted to a central server,where they are securely aggregated and refined through secure multi-party computation(SMPC)until global convergence is achieved.Within each client,DHBCPSO-MSR employs a dual-layer FS strategy.The inner layer constructs sample and label similarity graphs,generates Laplacian matrices to capture the manifold structure between samples and labels,and applies L2,1-norm regularization to sparsify the feature subset,yielding an optimized feature weight matrix.The outer layer uses a hybrid breeding cooperative particle swarm optimization algorithm to further refine the feature weight matrix and identify the optimal feature subset.The updated weight matrix is then fed back to the inner layer for further optimization.Comprehensive experiments on multiple real-world multi-label datasets demonstrate that Fed-MFSDHBCPSO consistently outperforms both centralized and federated baseline methods across several key evaluation metrics.
基金the National Natural Science Foundation of China(Grant No.11771303)the second author was also partially supported by the Beijing Advanced Innovation Center for Imaging Theory and Technology,Capital Normal University.
文摘Wo prove that there do not exist quasi-isometric embeddings of connected nonabelian nilpotent Lie groups equipped with left invariant Riemannian metrics into a metric measure space satisfying the curvature-dimension condition RCD(Q,N)with N∈R and N>1.In fact,we can prove that a sub-Riemannian manifold whose generic degree of nonholonomy is not smaller than 2 cannot be bi-Lipschitzly embedded in any Banach space with the Radon-Nikodym property.We also get that every regular sub-Riemannian manifold do not satisfy the curvature-dimension condition CD(K,N),where K,N∈R and N>1.Along the way to the proofs,we show that the minimal weak upper gradient and the horizontal gradient coincide on the Carnot-Caratheodory spaces which may have independent interests.
基金Supported by National Natural Science Foundation of China(Grant No.11771070).
文摘In this paper,we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimensional twisted BCV spaces.
基金supported by Scientific Research Project of Guangdong Provincial Department of Education(2024KQNCX152).
文摘Flow velocity uniformity of the microchannel plate is a major factor affecting the performance of microchannel devices.In order to improve the velocity distribution uniformity of the microchannel plate,we designed two new microchannel structures:V-type and A-type.The effects of various structural parameters of the manifolds on the velocity distribution are reported.The V-type and A-type microchannel plates had a more uniform velocity distribution compared to the Z-type microchannel plate.The final result showed that it is beneficial for the V-type microchannel plate to obtain a more uniform velocity distribution when the manifold structure parameters are X_(in)=-1,X_(out)=0,Y_(in)=10,Y_(out)=6,Hin=4,H_(out)=1,and R=0.5.
基金National Natural Science Foundation of China(Grant No.62266045)National Science and Technology Major Project of China(No.2022YFE0138600)。
文摘This paper presents a manifold-optimized Error-State Kalman Filter(ESKF)framework for unmanned aerial vehicle(UAV)pose estimation,integrating Inertial Measurement Unit(IMU)data with GPS or LiDAR to enhance estimation accuracy and robustness.We employ a manifold-based optimization approach,leveraging exponential and logarithmic mappings to transform rotation vectors into rotation matrices.The proposed ESKF framework ensures state variables remain near the origin,effectively mitigating singularity issues and enhancing numerical stability.Additionally,due to the small magnitude of state variables,second-order terms can be neglected,simplifying Jacobian matrix computation and improving computational efficiency.Furthermore,we introduce a novel Kalman filter gain computation strategy that dynamically adapts to low-dimensional and high-dimensional observation equations,enabling efficient processing across different sensor modalities.Specifically,for resource-constrained UAV platforms,this method significantly reduces computational cost,making it highly suitable for real-time UAV applications.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.12201314).
文摘In this note we describe a logarithmic version of mirror Landau-Ginzburg model for semi-projective toric manifolds and show in an elementary and explicit way that the state space ring of the Landau-Ginzburg mirror is isomorphic to the C-valued cohomology of the toric manifold.
基金supported by Guangzhou Science and Technology Program(202102021174)Guangdong Basic and Applied Basic Research Foundation(2023A1515012121).The second author was supported by the Natural Science Foundation of Jiangsu Province(BK20230900)+1 种基金the Fundamental Research Funds for the Central Universities(30924010838)Both authors are partially supported by NSF in China(12141104).
文摘In this paper,we study the basic p-harmonic forms on the complete foliated Riemannian manifolds.By using the method in[1],we show that if the basic mean curvature form is bounded and co-closed,and the transversal curvature operator is nonnegative and positive at least one point,then we obtain a vanishing theorem for L^(p)-integrably p-harmonic r-forms.
基金fully supported by National Natural Science Foundation of China(61871422)Natural Science Foundation of Sichuan Province(2023NSFSC1422)Central Universities of South west Minzu University(ZYN2022032)。
文摘There are all kinds of unknown and known signals in the actual electromagnetic environment,which hinders the development of practical cognitive radio applications.However,most existing signal recognition models are difficult to discover unknown signals while recognizing known ones.In this paper,a compact manifold mixup feature-based open-set recognition approach(OR-CMMF)is proposed to address the above problem.First,the proposed approach utilizes the center loss to constrain decision boundaries so that it obtains the compact latent signal feature representations and extends the low-confidence feature space.Second,the latent signal feature representations are used to construct synthetic representations as substitutes for unknown categories of signals.Then,these constructed representations can occupy the extended low-confidence space.Finally,the proposed approach applies the distillation loss to adjust the decision boundaries between the known categories signals and the constructed unknown categories substitutes so that it accurately discovers unknown signals.The OR-CMMF approach outperformed other state-of-the-art open-set recognition methods in comprehensive recognition performance and running time,as demonstrated by simulation experiments on two public datasets RML2016.10a and ORACLE.
文摘This paper introduces a new method based on deep belief networks(DBNs)to integrate intrinsic vibration information and assess the similarity of subspaces established on the Grassmann manifold for intelligent fault diagnosis of a reciprocating compressor(RC).Initially,raw vibration signals undergo empirical mode decomposition to break them down into multiple intrinsic mode functions(IMFs).This operation can reveal inherent vibration patterns of fault and other components hidden in the original signals.Subsequently,features are refined from all the IMFs and concatenated into a high-dimensional representative vector,offering localized and comprehensive insights into RC operation.Through DBN,the fault-sensitive information is further refined from the features to enhance their performance in fault identification.Finally,similarities among subspaces on the Grassmann manifold are computed to match fault types.The efficacy of the method is validated usingfield data.Comparative analysis with traditional approaches for feature dimension reduction,feature extraction,and Euclidean distance-based fault identification underscores the effectiveness and superiority of the proposed method in RC fault diagnosis.
文摘In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.
基金supported by the National Natural Science Foundation of China(Grant Nos.42172312 and 52211540395)support from the Institut Universitaire de France(IUF).
文摘The modeling of crack growth in three-dimensional(3D)space poses significant challenges in rock mechanics due to the complex numerical computation involved in simulating crack propagation and interaction in rock materials.In this study,we present a novel approach that introduces a 3D numerical manifold method(3D-NMM)with a geometric kernel to enhance computational efficiency.Specifically,the maximum tensile stress criterion is adopted as a crack growth criterion to achieve strong discontinuous crack growth,and a local crack tracking algorithm and an angle correction technique are incorporated to address minor limitations of the algorithm in a 3D model.The implementation of the program is carried out in Python,using object-oriented programming in two independent modules:a calculation module and a crack module.Furthermore,we propose feasible improvements to enhance the performance of the algorithm.Finally,we demonstrate the feasibility and effectiveness of the enhanced algorithm in the 3D-NMM using four numerical examples.This study establishes the potential of the 3DNMM,combined with the local tracking algorithm,for accurately modeling 3D crack propagation in brittle rock materials.
文摘Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.
文摘Studies are made of the cohomology of CR_ submanifolds and integrability of the distribution D of CR_submanifolds. When dim D⊥】1, the totally umbilical non-trival CR-submanifold i n nea r Kaehler manifold is totally geodesic. In the end, we get:If is n ear Kaehler manifold with B】0, then is not permitt ed to have fixed foliate non-trival CR-submanifold.
