In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of ...In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of weakly A-harmonic tensors due to B. Stroffolini.展开更多
A new kind of weight-Ar^λ3 （λ1, λ2, Ω）-weight is used to prove the local and global integral inequalities for conjugate A-harmonic tensors, which can be regarded as generalizations of the classical results. Some...A new kind of weight-Ar^λ3 （λ1, λ2, Ω）-weight is used to prove the local and global integral inequalities for conjugate A-harmonic tensors, which can be regarded as generalizations of the classical results. Some applications of the above results to quasiregular mappings are given.展开更多
In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, bas...In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. And directly establish the optimal Holder exponent for the derivative of a weak solution.展开更多
In this paper,the following result is given by using Hodge decomposition: There exists r(0) = r(0)(n,p,a,b), such that if u is an element of W-loc(1,r)(Omega) is a very weak solution of (1.1),with C max{1,p - 1} < ...In this paper,the following result is given by using Hodge decomposition: There exists r(0) = r(0)(n,p,a,b), such that if u is an element of W-loc(1,r)(Omega) is a very weak solution of (1.1),with C max{1,p - 1} < r < p and u is an element of W-0(1,r)(Omega;partial derivativeOmega\E) where E subset of partial derivativeOmega is a closed set and small in an appropriate capacity sense, then u = 0, a.e. in Omega provided that r(0) < r < p.展开更多
In this article,we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition.The proof is based on the A-harmo...In this article,we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition.The proof is based on the A-harmonic approximation technique.In this article,we extend the result of Shuhong Chen and Zhong Tan[7]and Giaquinta and Modica[18]to the stationary Navier-Stokes system with subquadratic growth.展开更多
In this paper, the following result is given by using Hodge decomposition and weak reverse Holder inequality： For every r1 with P-（2^n＋1 100^n^2 p（2^3＋n/（P-1）＋1）b/a）^-1〈r1〈p,there exists the exponent r2 =...In this paper, the following result is given by using Hodge decomposition and weak reverse Holder inequality： For every r1 with P-（2^n＋1 100^n^2 p（2^3＋n/（P-1）＋1）b/a）^-1〈r1〈p,there exists the exponent r2 = r2（n, r1,p） 〉 p, such that for every very weak solution u∈W^1r1,loc（Ω） to A-harmonic equation, u also belongs to W^1r2,loc（Ω） . In particular, u is the weak solution to A-harmonic equation in the usual sense.展开更多
Extremum principle for very weak solutions of A-harmonic equation div A(x,▽u)=0 is obtained, where the operator A:Ω × Rn→Rnsatisfies some coercivity and controllable growth conditions with Mucken-houpt weight.
In this paper,we established a class of parallel algorithm for solving low-rank tensor completion problem.The main idea is that N singular value decompositions are implemented in N different processors for each slice ...In this paper,we established a class of parallel algorithm for solving low-rank tensor completion problem.The main idea is that N singular value decompositions are implemented in N different processors for each slice matrix under unfold operator,and then the fold operator is used to form the next iteration tensor such that the computing time can be decreased.In theory,we analyze the global convergence of the algorithm.In numerical experiment,the simulation data and real image inpainting are carried out.Experiment results show the parallel algorithm outperform its original algorithm in CPU times under the same precision.展开更多
Aiming at the problem that infrared small target detection faces low contrast between the background and the target and insufficient noise suppression ability under the complex cloud background,an infrared small targe...Aiming at the problem that infrared small target detection faces low contrast between the background and the target and insufficient noise suppression ability under the complex cloud background,an infrared small target detection method based on the tensor nuclear norm and direction residual weighting was proposed.Based on converting the infrared image into an infrared patch tensor model,from the perspective of the low-rank nature of the background tensor,and taking advantage of the difference in contrast between the background and the target in different directions,we designed a double-neighborhood local contrast based on direction residual weighting method(DNLCDRW)combined with the partial sum of tensor nuclear norm(PSTNN)to achieve effective background suppression and recovery of infrared small targets.Experiments show that the algorithm is effective in suppressing the background and improving the detection ability of the target.展开更多
The monitoring signals of bearings from single-source sensor often contain limited information for characterizing various working condition,which may lead to instability and uncertainty of the class-imbalanced intelli...The monitoring signals of bearings from single-source sensor often contain limited information for characterizing various working condition,which may lead to instability and uncertainty of the class-imbalanced intelligent fault diagnosis.On the other hand,the vectorization of multi-source sensor signals may not only generate high-dimensional vectors,leading to increasing computational complexity and overfitting problems,but also lose the structural information and the coupling information.This paper proposes a new method for class-imbalanced fault diagnosis of bearing using support tensor machine(STM)driven by heterogeneous data fusion.The collected sound and vibration signals of bearings are successively decomposed into multiple frequency band components to extract various time-domain and frequency-domain statistical parameters.A third-order hetero-geneous feature tensor is designed based on multisensors,frequency band components,and statistical parameters.STM-based intelligent model is constructed to preserve the structural information of the third-order heterogeneous feature tensor for bearing fault diagnosis.A series of comparative experiments verify the advantages of the proposed method.展开更多
This paper proposed a moment tensor regression prediction technology based on ResNet for microseismic events.Taking the great advantages of deep networks in classification and regression tasks,it can realize the great...This paper proposed a moment tensor regression prediction technology based on ResNet for microseismic events.Taking the great advantages of deep networks in classification and regression tasks,it can realize the great potential of fast and accurate inversion of microseismic moment tensors after the network trained.This ResNet-based moment tensor prediction technology,whose input is raw recordings,does not require the extraction of data features in advance.First,we tested the network using synthetic data and performed a quantitative assessment of the errors.The results demonstrate that the network exhibits high accuracy and efficiency during the prediction phase.Next,we tested the network using real microseismic data and compared the results with those from traditional inversion methods.The error in the results was relatively small compared to traditional methods.However,the network operates more efficiently without requiring manual intervention,making it highly valuable for near-real-time monitoring applications.展开更多
Absorption compensation is a process involving the exponential amplification of reflection amplitudes.This process amplifies the seismic signal and noise,thereby substantially reducing the signal-tonoise ratio of seis...Absorption compensation is a process involving the exponential amplification of reflection amplitudes.This process amplifies the seismic signal and noise,thereby substantially reducing the signal-tonoise ratio of seismic data.Therefore,this paper proposes a multichannel inversion absorption compensation method based on structure tensor regularization.First,the structure tensor is utilized to extract the spatial inclination of seismic signals,and the spatial prediction filter is designed along the inclination direction.The spatial prediction filter is then introduced into the regularization condition of multichannel inversion absorption compensation,and the absorption compensation is realized under the framework of multichannel inversion theory.The spatial predictability of seismic signals is also introduced into the objective function of absorption compensation inversion.Thus,the inversion system can effectively suppress the noise amplification effect during absorption compensation and improve the recovery accuracy of high-frequency signals.Synthetic and field data tests are conducted to demonstrate the accuracy and effectiveness of the proposed method.展开更多
Computing free energy is a fundamental problem in statistical physics.Recently,two distinct methods have been developed and have demonstrated remarkable success:the tensor-network-based contraction method and the neur...Computing free energy is a fundamental problem in statistical physics.Recently,two distinct methods have been developed and have demonstrated remarkable success:the tensor-network-based contraction method and the neural-network-based variational method.Tensor networks are accurate,but their application is often limited to low-dimensional systems due to the high computational complexity in high-dimensional systems.The neural network method applies to systems with general topology.However,as a variational method,it is not as accurate as tensor networks.In this work,we propose an integrated approach,tensor-network-based variational autoregressive networks(TNVAN),that leverages the strengths of both tensor networks and neural networks:combining the variational autoregressive neural network’s ability to compute an upper bound on free energy and perform unbiased sampling from the variational distribution with the tensor network’s power to accurately compute the partition function for small sub-systems,resulting in a robust method for precisely estimating free energy.To evaluate the proposed approach,we conducted numerical experiments on spin glass systems with various topologies,including two-dimensional lattices,fully connected graphs,and random graphs.Our numerical results demonstrate the superior accuracy of our method compared to existing approaches.In particular,it effectively handles systems with longrange interactions and leverages GPU efficiency without requiring singular value decomposition,indicating great potential in tackling statistical mechanics problems and simulating high-dimensional complex systems through both tensor networks and neural networks.展开更多
Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either dire...Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either directly or by reducing it to other problems.This paper introduces the Julia ecosystem for solving and analyzing CSPs with a focus on the programming practices.We introduce some important CSPs and show how these problems are reduced to each other.We also show how to transform CSPs into tensor networks,how to optimize the tensor network contraction orders,and how to extract the solution space properties by contracting the tensor networks with generic element types.Examples are given,which include computing the entropy constant,analyzing the overlap gap property,and the reduction between CSPs.展开更多
The quantum geometric tensor(QGT)is a fundamental quantity for characterizing the geometric properties of quantum states and plays an essential role in elucidating various physical phenomena.The traditional QGT,defned...The quantum geometric tensor(QGT)is a fundamental quantity for characterizing the geometric properties of quantum states and plays an essential role in elucidating various physical phenomena.The traditional QGT,defned only for pure states,has limited applicability in realistic scenarios where mixed states are common.To address this limitation,we generalize the defnition of the QGT to mixed states using the purifcation bundle and the covariant derivative.Notably,our proposed defnition reduces to the traditional QGT when mixed states approach pure states.In our framework,the real and imaginary parts of this generalized QGT correspond to the Bures metric and the mean gauge curvature,respectively,endowing it with a broad range of potential applications.Additionally,using our proposed mixed-state QGT,we derive the geodesic equation applicable to mixed states.This work establishes a unifed framework for the geometric analysis of both pure and mixed states,thereby deepening our understanding of the geometric properties of quantum states.展开更多
Dear Editor,This letter proposes the graph tensor alliance attention network(GT-A^(2)T)to represent a dynamic graph(DG)precisely.Its main idea includes 1)Establishing a unified spatio-temporal message propagation fram...Dear Editor,This letter proposes the graph tensor alliance attention network(GT-A^(2)T)to represent a dynamic graph(DG)precisely.Its main idea includes 1)Establishing a unified spatio-temporal message propagation framework on a DG via the tensor product for capturing the complex cohesive spatio-temporal interdependencies precisely and 2)Acquiring the alliance attention scores by node features and favorable high-order structural correlations.展开更多
When plants respond to drought stress,dynamic cellular changes occur,accompanied by alterations in gene expression,which often act through trans-regulation.However,the detection of trans-acting genetic variants and ne...When plants respond to drought stress,dynamic cellular changes occur,accompanied by alterations in gene expression,which often act through trans-regulation.However,the detection of trans-acting genetic variants and networks of genes is challenged by the large number of genes and markers.Using a tensor decomposition method,we identify trans-acting expression quantitative trait loci(trans-eQTLs)linked to gene modules,rather than individual genes,which were associated with maize drought response.Module-to-trait association analysis demonstrates that half of the modules are relevant to drought-related traits.Genome-wide association studies of the expression patterns of each module identify 286 trans-eQTLs linked to drought-responsive modules,the majority of which cannot be detected based on individual gene expression.Notably,the trans-eQTLs located in the regions selected during maize improvement tend towards relatively strong selection.We further prioritize the genes that affect the transcriptional regulation of multiple genes in trans,as exemplified by two transcription factor genes.Our analyses highlight that multidimensional reduction could facilitate the identification of trans-acting variations in gene expression in response to dynamic environments and serve as a promising technique for high-order data processing in future crop breeding.展开更多
In this study,we employed Bayesian inversion coupled with the summation-by-parts and simultaneousapproximation-term(SBP-SAT)forward simulation method to elucidate the mechanisms behind mininginduced seismic events cau...In this study,we employed Bayesian inversion coupled with the summation-by-parts and simultaneousapproximation-term(SBP-SAT)forward simulation method to elucidate the mechanisms behind mininginduced seismic events caused by fault slip and their potential effects on rockbursts.Through Bayesian inversion,it is determined that the sources near fault FQ14 have a significant shear component.Additionally,we analyzed the stress and displacement fields of high-energy events,along with the hypocenter distribution of aftershocks,which aided in identifying the slip direction of the critically stressed fault FQ14.We also performed forward modeling to capture the complex dynamics of fault slip under varying friction laws and shear fracture modes.The selection of specific friction laws for fault slip models was based on their ability to accurately replicate observed slip behavior under various external loading conditions,thereby enhancing the applicability of our findings.Our results suggest that the slip behavior of fault FQ14 can be effectively understood by comparing different scenarios.展开更多
The tensor force changes the nuclear shell structure and thus may result in underlying influence of the collectivity and decay properties of the nucleus.We carefully examined the impact of the monopole and multipole e...The tensor force changes the nuclear shell structure and thus may result in underlying influence of the collectivity and decay properties of the nucleus.We carefully examined the impact of the monopole and multipole effects originating from the tensor force on both the collectivity and the matrix element for the neutrinoless double-β(0νββ)decay,using the generatorcoordinate method with an effective interaction.To analyze the effect of the tensor force,we employed an effective Hamiltonian associated with the monopole-based universal interaction that explicitly consists of the central,tensor,and spin-orbit coupling terms.The interferences among the shell structure,quadrupole collectivity,nucleon occupancy,and 0νββmatrix elements were analyzed in detail.A better understanding of the tensor force would be of great importance in reducing the theoretical uncertainty in 0νββnuclear matrix element calculations.展开更多
The era of big data brings new challenges for information network systems(INS),simultaneously offering unprecedented opportunities for advancing intelligent intrusion detection systems.In this work,we propose a data-d...The era of big data brings new challenges for information network systems(INS),simultaneously offering unprecedented opportunities for advancing intelligent intrusion detection systems.In this work,we propose a data-driven intrusion detection system for Distributed Denial of Service(DDoS)attack detection.The system focuses on intrusion detection from a big data perceptive.As intelligent information processing methods,big data and artificial intelligence have been widely used in information systems.The INS system is an important information system in cyberspace.In advanced INS systems,the network architectures have become more complex.And the smart devices in INS systems collect a large scale of network data.How to improve the performance of a complex intrusion detection system with big data and artificial intelligence is a big challenge.To address the problem,we design a novel intrusion detection system(IDS)from a big data perspective.The IDS system uses tensors to represent large-scale and complex multi-source network data in a unified tensor.Then,a novel tensor decomposition(TD)method is developed to complete big data mining.The TD method seamlessly collaborates with the XGBoost(eXtreme Gradient Boosting)method to complete the intrusion detection.To verify the proposed IDS system,a series of experiments is conducted on two real network datasets.The results revealed that the proposed IDS system attained an impressive accuracy rate over 98%.Additionally,by altering the scale of the datasets,the proposed IDS system still maintains excellent detection performance,which demonstrates the proposed IDS system’s robustness.展开更多
基金Supported by the National Natural Science Foundation of China (10971224)the Hebei Natural ScienceFoundation (07M003)
文摘In this paper, we give the definition of weak WT2-class of differential forms, and then obtain its weak reverse Holder inequality. As an application, we give an alternative proof of the higher integrability result of weakly A-harmonic tensors due to B. Stroffolini.
基金Supported by the Natural Science Foundation of Hebei Province(07M003)the Doctoral Fund of Hebei Provincial Commission of Education(B2004103)
文摘A new kind of weight-Ar^λ3 （λ1, λ2, Ω）-weight is used to prove the local and global integral inequalities for conjugate A-harmonic tensors, which can be regarded as generalizations of the classical results. Some applications of the above results to quasiregular mappings are given.
基金Supported by NSF of China(10531020)the Program of 985 Innovation Engieering on Information in Xiamen University(2004-2007).
文摘In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. And directly establish the optimal Holder exponent for the derivative of a weak solution.
文摘In this paper,the following result is given by using Hodge decomposition: There exists r(0) = r(0)(n,p,a,b), such that if u is an element of W-loc(1,r)(Omega) is a very weak solution of (1.1),with C max{1,p - 1} < r < p and u is an element of W-0(1,r)(Omega;partial derivativeOmega\E) where E subset of partial derivativeOmega is a closed set and small in an appropriate capacity sense, then u = 0, a.e. in Omega provided that r(0) < r < p.
文摘In this article,we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition.The proof is based on the A-harmonic approximation technique.In this article,we extend the result of Shuhong Chen and Zhong Tan[7]and Giaquinta and Modica[18]to the stationary Navier-Stokes system with subquadratic growth.
文摘In this paper, the following result is given by using Hodge decomposition and weak reverse Holder inequality： For every r1 with P-（2^n＋1 100^n^2 p（2^3＋n/（P-1）＋1）b/a）^-1〈r1〈p,there exists the exponent r2 = r2（n, r1,p） 〉 p, such that for every very weak solution u∈W^1r1,loc（Ω） to A-harmonic equation, u also belongs to W^1r2,loc（Ω） . In particular, u is the weak solution to A-harmonic equation in the usual sense.
文摘Extremum principle for very weak solutions of A-harmonic equation div A(x,▽u)=0 is obtained, where the operator A:Ω × Rn→Rnsatisfies some coercivity and controllable growth conditions with Mucken-houpt weight.
基金Supported by National Nature Science Foundation(12371381)Nature Science Foundation of Shanxi(202403021222270)。
文摘In this paper,we established a class of parallel algorithm for solving low-rank tensor completion problem.The main idea is that N singular value decompositions are implemented in N different processors for each slice matrix under unfold operator,and then the fold operator is used to form the next iteration tensor such that the computing time can be decreased.In theory,we analyze the global convergence of the algorithm.In numerical experiment,the simulation data and real image inpainting are carried out.Experiment results show the parallel algorithm outperform its original algorithm in CPU times under the same precision.
基金Supported by the Key Laboratory Fund for Equipment Pre-Research(6142207210202)。
文摘Aiming at the problem that infrared small target detection faces low contrast between the background and the target and insufficient noise suppression ability under the complex cloud background,an infrared small target detection method based on the tensor nuclear norm and direction residual weighting was proposed.Based on converting the infrared image into an infrared patch tensor model,from the perspective of the low-rank nature of the background tensor,and taking advantage of the difference in contrast between the background and the target in different directions,we designed a double-neighborhood local contrast based on direction residual weighting method(DNLCDRW)combined with the partial sum of tensor nuclear norm(PSTNN)to achieve effective background suppression and recovery of infrared small targets.Experiments show that the algorithm is effective in suppressing the background and improving the detection ability of the target.
基金supported by the National Natural Science Foundation of China(No.52275104)the Science and Technology Innovation Program of Hunan Province(No.2023RC3097).
文摘The monitoring signals of bearings from single-source sensor often contain limited information for characterizing various working condition,which may lead to instability and uncertainty of the class-imbalanced intelligent fault diagnosis.On the other hand,the vectorization of multi-source sensor signals may not only generate high-dimensional vectors,leading to increasing computational complexity and overfitting problems,but also lose the structural information and the coupling information.This paper proposes a new method for class-imbalanced fault diagnosis of bearing using support tensor machine(STM)driven by heterogeneous data fusion.The collected sound and vibration signals of bearings are successively decomposed into multiple frequency band components to extract various time-domain and frequency-domain statistical parameters.A third-order hetero-geneous feature tensor is designed based on multisensors,frequency band components,and statistical parameters.STM-based intelligent model is constructed to preserve the structural information of the third-order heterogeneous feature tensor for bearing fault diagnosis.A series of comparative experiments verify the advantages of the proposed method.
基金supported by the National Natural Science dation Foun-of China(Grant Number 42272204)Key Laboratory of Coal sources Re-Exploration and Comprehensive Utilization,Ministry of Natural Resources,Canada(SMDZ-KF2024-4)+1 种基金the Fundamental Research Funds for the Central Universities,China(Grant No.2024JCCXDC06)supported in part by open fund project of State Key Laboratory for Fine Exploration and Intelligent Development of Coal Research(SKLCRSM23KFA04)。
文摘This paper proposed a moment tensor regression prediction technology based on ResNet for microseismic events.Taking the great advantages of deep networks in classification and regression tasks,it can realize the great potential of fast and accurate inversion of microseismic moment tensors after the network trained.This ResNet-based moment tensor prediction technology,whose input is raw recordings,does not require the extraction of data features in advance.First,we tested the network using synthetic data and performed a quantitative assessment of the errors.The results demonstrate that the network exhibits high accuracy and efficiency during the prediction phase.Next,we tested the network using real microseismic data and compared the results with those from traditional inversion methods.The error in the results was relatively small compared to traditional methods.However,the network operates more efficiently without requiring manual intervention,making it highly valuable for near-real-time monitoring applications.
基金funded by the National Key R&D Program of China(Grant no.2018YFA0702504)the Sinopec research project(P22162).
文摘Absorption compensation is a process involving the exponential amplification of reflection amplitudes.This process amplifies the seismic signal and noise,thereby substantially reducing the signal-tonoise ratio of seismic data.Therefore,this paper proposes a multichannel inversion absorption compensation method based on structure tensor regularization.First,the structure tensor is utilized to extract the spatial inclination of seismic signals,and the spatial prediction filter is designed along the inclination direction.The spatial prediction filter is then introduced into the regularization condition of multichannel inversion absorption compensation,and the absorption compensation is realized under the framework of multichannel inversion theory.The spatial predictability of seismic signals is also introduced into the objective function of absorption compensation inversion.Thus,the inversion system can effectively suppress the noise amplification effect during absorption compensation and improve the recovery accuracy of high-frequency signals.Synthetic and field data tests are conducted to demonstrate the accuracy and effectiveness of the proposed method.
基金supported by Projects 12325501,12047503,and 12247104 of the National Natural Science Foundation of ChinaProject ZDRW-XX-2022-3-02 of the Chinese Academy of Sciencessupported by the Innovation Program for Quantum Science and Technology project 2021ZD0301900。
文摘Computing free energy is a fundamental problem in statistical physics.Recently,two distinct methods have been developed and have demonstrated remarkable success:the tensor-network-based contraction method and the neural-network-based variational method.Tensor networks are accurate,but their application is often limited to low-dimensional systems due to the high computational complexity in high-dimensional systems.The neural network method applies to systems with general topology.However,as a variational method,it is not as accurate as tensor networks.In this work,we propose an integrated approach,tensor-network-based variational autoregressive networks(TNVAN),that leverages the strengths of both tensor networks and neural networks:combining the variational autoregressive neural network’s ability to compute an upper bound on free energy and perform unbiased sampling from the variational distribution with the tensor network’s power to accurately compute the partition function for small sub-systems,resulting in a robust method for precisely estimating free energy.To evaluate the proposed approach,we conducted numerical experiments on spin glass systems with various topologies,including two-dimensional lattices,fully connected graphs,and random graphs.Our numerical results demonstrate the superior accuracy of our method compared to existing approaches.In particular,it effectively handles systems with longrange interactions and leverages GPU efficiency without requiring singular value decomposition,indicating great potential in tackling statistical mechanics problems and simulating high-dimensional complex systems through both tensor networks and neural networks.
基金funded by the National Key R&D Program of China(Grant No.2024YFE0102500)the National Natural Science Foundation of China(Grant No.12404568)+1 种基金the Guangzhou Municipal Science and Technology Project(Grant No.2023A03J00904)the Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area,China and the Undergraduate Research Project from HKUST(Guangzhou).
文摘Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either directly or by reducing it to other problems.This paper introduces the Julia ecosystem for solving and analyzing CSPs with a focus on the programming practices.We introduce some important CSPs and show how these problems are reduced to each other.We also show how to transform CSPs into tensor networks,how to optimize the tensor network contraction orders,and how to extract the solution space properties by contracting the tensor networks with generic element types.Examples are given,which include computing the entropy constant,analyzing the overlap gap property,and the reduction between CSPs.
基金supported by the National Natural Science Foundation of China(Grant Nos.12347104,U24A2017,12461160276,and 12175075)the National Key Research and Development Program of China(Grant No.2023YFC2205802)+1 种基金the Natural Science Foundation of Jiangsu Province(Grant Nos.BK20243060 and BK20233001)in part by the State Key Laboratory of Advanced Optical Communication Systems and Networks,China。
文摘The quantum geometric tensor(QGT)is a fundamental quantity for characterizing the geometric properties of quantum states and plays an essential role in elucidating various physical phenomena.The traditional QGT,defned only for pure states,has limited applicability in realistic scenarios where mixed states are common.To address this limitation,we generalize the defnition of the QGT to mixed states using the purifcation bundle and the covariant derivative.Notably,our proposed defnition reduces to the traditional QGT when mixed states approach pure states.In our framework,the real and imaginary parts of this generalized QGT correspond to the Bures metric and the mean gauge curvature,respectively,endowing it with a broad range of potential applications.Additionally,using our proposed mixed-state QGT,we derive the geodesic equation applicable to mixed states.This work establishes a unifed framework for the geometric analysis of both pure and mixed states,thereby deepening our understanding of the geometric properties of quantum states.
基金supported in part by the National Natural Science Foundation of China(62372385).
文摘Dear Editor,This letter proposes the graph tensor alliance attention network(GT-A^(2)T)to represent a dynamic graph(DG)precisely.Its main idea includes 1)Establishing a unified spatio-temporal message propagation framework on a DG via the tensor product for capturing the complex cohesive spatio-temporal interdependencies precisely and 2)Acquiring the alliance attention scores by node features and favorable high-order structural correlations.
基金supported by the Biological Breeding-National Science and Technology Major Project(2023ZD04076)the Guangxi Key Research and Development Projects of China(GuikeAB21238004)the Agricultural Science and Technology Innovation Program.
文摘When plants respond to drought stress,dynamic cellular changes occur,accompanied by alterations in gene expression,which often act through trans-regulation.However,the detection of trans-acting genetic variants and networks of genes is challenged by the large number of genes and markers.Using a tensor decomposition method,we identify trans-acting expression quantitative trait loci(trans-eQTLs)linked to gene modules,rather than individual genes,which were associated with maize drought response.Module-to-trait association analysis demonstrates that half of the modules are relevant to drought-related traits.Genome-wide association studies of the expression patterns of each module identify 286 trans-eQTLs linked to drought-responsive modules,the majority of which cannot be detected based on individual gene expression.Notably,the trans-eQTLs located in the regions selected during maize improvement tend towards relatively strong selection.We further prioritize the genes that affect the transcriptional regulation of multiple genes in trans,as exemplified by two transcription factor genes.Our analyses highlight that multidimensional reduction could facilitate the identification of trans-acting variations in gene expression in response to dynamic environments and serve as a promising technique for high-order data processing in future crop breeding.
基金the Graduate Innovation Program of China University of Mining and Technology,the Fundamental Research Funds for the Central Universities(Grant No.2023WLKXJ017)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX23_2776)the Shandong Energy Group(Grant No.SNKJ2022BJ03-R28)。
文摘In this study,we employed Bayesian inversion coupled with the summation-by-parts and simultaneousapproximation-term(SBP-SAT)forward simulation method to elucidate the mechanisms behind mininginduced seismic events caused by fault slip and their potential effects on rockbursts.Through Bayesian inversion,it is determined that the sources near fault FQ14 have a significant shear component.Additionally,we analyzed the stress and displacement fields of high-energy events,along with the hypocenter distribution of aftershocks,which aided in identifying the slip direction of the critically stressed fault FQ14.We also performed forward modeling to capture the complex dynamics of fault slip under varying friction laws and shear fracture modes.The selection of specific friction laws for fault slip models was based on their ability to accurately replicate observed slip behavior under various external loading conditions,thereby enhancing the applicability of our findings.Our results suggest that the slip behavior of fault FQ14 can be effectively understood by comparing different scenarios.
基金supported by the National Natural Science Foundation of China(No.12275369)the Fundamental Research Funds for the Central Universities,Sun Yat-sen University(No.22qntd3101)the Guangdong Major Project of Basic and Applied Basic Research(2021B0301030006)。
文摘The tensor force changes the nuclear shell structure and thus may result in underlying influence of the collectivity and decay properties of the nucleus.We carefully examined the impact of the monopole and multipole effects originating from the tensor force on both the collectivity and the matrix element for the neutrinoless double-β(0νββ)decay,using the generatorcoordinate method with an effective interaction.To analyze the effect of the tensor force,we employed an effective Hamiltonian associated with the monopole-based universal interaction that explicitly consists of the central,tensor,and spin-orbit coupling terms.The interferences among the shell structure,quadrupole collectivity,nucleon occupancy,and 0νββmatrix elements were analyzed in detail.A better understanding of the tensor force would be of great importance in reducing the theoretical uncertainty in 0νββnuclear matrix element calculations.
基金supported in part by the National Nature Science Foundation of China under Project 62166047in part by the Yunnan International Joint Laboratory of Natural Rubber Intelligent Monitor and Digital Applications under Grant 202403AP140001in part by the Xingdian Talent Support Program under Grant YNWR-QNBJ-2019-270.
文摘The era of big data brings new challenges for information network systems(INS),simultaneously offering unprecedented opportunities for advancing intelligent intrusion detection systems.In this work,we propose a data-driven intrusion detection system for Distributed Denial of Service(DDoS)attack detection.The system focuses on intrusion detection from a big data perceptive.As intelligent information processing methods,big data and artificial intelligence have been widely used in information systems.The INS system is an important information system in cyberspace.In advanced INS systems,the network architectures have become more complex.And the smart devices in INS systems collect a large scale of network data.How to improve the performance of a complex intrusion detection system with big data and artificial intelligence is a big challenge.To address the problem,we design a novel intrusion detection system(IDS)from a big data perspective.The IDS system uses tensors to represent large-scale and complex multi-source network data in a unified tensor.Then,a novel tensor decomposition(TD)method is developed to complete big data mining.The TD method seamlessly collaborates with the XGBoost(eXtreme Gradient Boosting)method to complete the intrusion detection.To verify the proposed IDS system,a series of experiments is conducted on two real network datasets.The results revealed that the proposed IDS system attained an impressive accuracy rate over 98%.Additionally,by altering the scale of the datasets,the proposed IDS system still maintains excellent detection performance,which demonstrates the proposed IDS system’s robustness.
