The neuron model has been widely employed in neural-morphic computing systems and chaotic circuits.This study aims to develop a novel circuit simulation of a three-neuron Hopfield neural network(HNN)with coupled hyper...The neuron model has been widely employed in neural-morphic computing systems and chaotic circuits.This study aims to develop a novel circuit simulation of a three-neuron Hopfield neural network(HNN)with coupled hyperbolic memristors through the modification of a single coupling connection weight.The bistable mode of the hyperbolic memristive HNN(mHNN),characterized by the coexistence of asymmetric chaos and periodic attractors,is effectively demonstrated through the utilization of conventional nonlinear analysis techniques.These techniques include bifurcation diagrams,two-parameter maximum Lyapunov exponent plots,local attractor basins,and phase trajectory diagrams.Moreover,an encryption technique for color images is devised by leveraging the mHNN model and asymmetric structural attractors.This method demonstrates significant benefits in correlation,information entropy,and resistance to differential attacks,providing strong evidence for its effectiveness in encryption.Additionally,an improved modular circuit design method is employed to create the analog equivalent circuit of the memristive HNN.The correctness of the circuit design is confirmed through Multisim simulations,which align with numerical simulations conducted in Matlab.展开更多
Accurate prediction of flood events is important for flood control and risk management.Machine learning techniques contributed greatly to advances in flood predictions,and existing studies mainly focused on predicting...Accurate prediction of flood events is important for flood control and risk management.Machine learning techniques contributed greatly to advances in flood predictions,and existing studies mainly focused on predicting flood resource variables using single or hybrid machine learning techniques.However,class-based flood predictions have rarely been investigated,which can aid in quickly diagnosing comprehensive flood characteristics and proposing targeted management strategies.This study proposed a prediction approach of flood regime metrics and event classes coupling machine learning algorithms with clustering-deduced membership degrees.Five algorithms were adopted for this exploration.Results showed that the class membership degrees accurately determined event classes with class hit rates up to 100%,compared with the four classes clustered from nine regime metrics.The nonlinear algorithms(Multiple Linear Regression,Random Forest,and least squares-Support Vector Machine)outperformed the linear techniques(Multiple Linear Regression and Stepwise Regression)in predicting flood regime metrics.The proposed approach well predicted flood event classes with average class hit rates of 66.0%-85.4%and 47.2%-76.0%in calibration and validation periods,respectively,particularly for the slow and late flood events.The predictive capability of the proposed prediction approach for flood regime metrics and classes was considerably stronger than that of hydrological modeling approach.展开更多
It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics.When the domain of...It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics.When the domain of S is restricted to the space of constant scalar curvature metrics,there has been a conjecture that a critical point is also Einstein or isometric to a standard sphere.In the Riemannian case,it’s tangent space satisfies a decomposition.In this paper,we prove that if we only consider the Hermitian metrics,it also have a decomposition.Then we obtain the equation of the critical points among the Hermitian metrics.展开更多
In this paper,the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannia...In this paper,the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannian manifolds.The authors rigorously establish statistical properties of the estimators,providing formal proofs of their consistency and asymptotic behaviors.The effectiveness of our method is demonstrated through extensive simulations and applications to real-world datasets which highlight its practical utility for complex data with non-Euclidean structures.展开更多
The energy eigenvalues of a Dirac particle for the hyperbolic-type potential field have been computed approximately. It is obtained a transcendental function of energy, F(E), by writing in terms of confluent Heun func...The energy eigenvalues of a Dirac particle for the hyperbolic-type potential field have been computed approximately. It is obtained a transcendental function of energy, F(E), by writing in terms of confluent Heun functions.The numerical values of energy are then obtained by fixing the zeros on "E-axis" for both complex functions Re[F(E)]and Im[F(E)].展开更多
In this paper,we introduce and prove three analytic results related to uniform convergence,properties of Newtonian potential,and convergence of sequences in Sobolev space constrained by their Laplacian.Then,utilizing ...In this paper,we introduce and prove three analytic results related to uniform convergence,properties of Newtonian potential,and convergence of sequences in Sobolev space constrained by their Laplacian.Then,utilizing our analytic results,we develop a complete proof of a crucial estimate appearing in the results of Guofang Wang and Xiaohua Zhu,which states the classification of extremal Hermitian metrics with finite energy and area on compact Riemann surfaces and finite singularities satisfying small singular angles.展开更多
The Kelly strategy is a common approach in portfolio optimization problems that aims to maximize the expected portfolio growth rate in the long term.Its computation requires complete knowledge of the asset return dist...The Kelly strategy is a common approach in portfolio optimization problems that aims to maximize the expected portfolio growth rate in the long term.Its computation requires complete knowledge of the asset return distribution,which is obviously not observable,but can be inferred from sample data.Motivated by recent developments in data-driven optimization methods,we propose a new class of coherent Wasserstein data-driven Kelly portfolio optimization models.In particular,we establish a class of ambiguity sets based on coherent Wasserstein metrics,and these new metrics can strike a good balance between robustness and data-drivenness,thus providing richer choices for ambiguity set design.The Kelly portfolio optimization model,which is data-driven and based on coherent Wasserstein balls,can be solved efficiently as a finite-dimensional convex program.This model also provides a robust data-driven solution.In addition,we numerically investigate the proposed model and find that it outperforms the type-1 Wasserstein-Kelly portfolio,especially the classical Kelly portfolio.Moreover,it indicates that we can obtain a portfolio with higher final value and stability,especially in controlling volatility and maximum drawdown.展开更多
In a recent article, we have corrected the traditional derivation of the Schwarzschild metric, thus obtaining the formulation of the correct Schwarzschild metric, which is different from the traditional Schwarzschild ...In a recent article, we have corrected the traditional derivation of the Schwarzschild metric, thus obtaining the formulation of the correct Schwarzschild metric, which is different from the traditional Schwarzschild metric. Then, in another article by starting from this correct Schwarzschild metric, we have corrected also the Reissner-Nordstrøm, Kerr and Kerr-Newman metrics. On the other hand, in a third article, always by starting from this correct Schwarzschild metric, we have obtained the formulas of the correct gravitational potential and of the correct gravitational force in the case described by this metric. Now, in this article, by starting from these correct Reissner-Nordstrøm, Kerr and Kerr-Newman metrics and proceeding in a manner analogous to this third article, we obtain the formulas of the correct gravitational potential and of the correct gravitational force in the cases described by these metrics. Moreover, we analyze these correct results and their consequences. Finally, we propose some possible crucial experiments between the commonly accepted theory and the same theory corrected according to this article.展开更多
In this paper,we prove that for certain fiber bundles there is a k-Futaki-Ono conformally Kahler metric related to a metric in any given Kahler class for any k≥2.
The quantum metric manifested as the Riemannian metric in the parameter space of Bloch bands,characterizes the topology and geometry of quantum states.The second harmonic generation(SHG),as one of the fundamental nonl...The quantum metric manifested as the Riemannian metric in the parameter space of Bloch bands,characterizes the topology and geometry of quantum states.The second harmonic generation(SHG),as one of the fundamental nonlinear optical responses that links geometry of optical transitions to physical observables,despite being widely studied in various materials,its relation to quantum metric,especially in the dynamical regime,stays obscure.展开更多
Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X.Let Π_(C):X→C denote the generalized metric projection operator introduced by Alber in[1].In this pap...Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X.Let Π_(C):X→C denote the generalized metric projection operator introduced by Alber in[1].In this paper,we define the Gâteaux directional differentiability of Π_(C).We investigate some properties of the Gâteaux directional differentiability of Π_(C).In particular,if C is a closed ball,or a closed and convex cone(including proper closed subspaces),or a closed and convex cylinder,then,we give the exact representations of the directional derivatives of Π_(C).By comparing the results in[12]and this paper,we see the significant difference between the directional derivatives of the generalized metric projection operator Π_(C) and the Gâteaux directional derivatives of the standard metric projection operator PC.展开更多
The focus of green analytical chemistry(GAC)is to minimize the negative impacts of analytical procedures on human safety,human health,and the environment.Several factors,such as the reagents used,sample collection,sam...The focus of green analytical chemistry(GAC)is to minimize the negative impacts of analytical procedures on human safety,human health,and the environment.Several factors,such as the reagents used,sample collection,sample processing,instruments,energy consumed,and the quantities of hazardous materials and waste generated during analytical procedures,need to be considered in the evaluation of the greenness of analytical assays.In this study,we propose a greenness evaluation metric for analytical methods(GEMAM).The new greenness metric is simple,flexible,and comprehensive.The evaluation criteria are based on both the 12 principles of GAC(SIGNIFICANCE)and the 10 factors of sample preparation,and the results are presented on a 0–10 scale.The GEMAM calculation process is easy to perform,and its results are easy to interpret.The output of GEMAM is a pictogram that can provide both qualitative and quantitative information based on color and number.展开更多
In this paper,we study scalar curvature rigidity of non-smooth metrics on smooth manifolds with non-positive Yamabe invariant.We prove that if the scalar curvature is not less than the Yamabe invariant in the distribu...In this paper,we study scalar curvature rigidity of non-smooth metrics on smooth manifolds with non-positive Yamabe invariant.We prove that if the scalar curvature is not less than the Yamabe invariant in the distributional sense,then the manifold must be isometric to an Einstein manifold.This result extends Theorem 1.4 in Jiang,Sheng and Zhang[27],from a special case where the manifolds have zero Yamabe invariant to general cases where the manifolds have non-positive Yamabe invariant.展开更多
Tag recommendation systems can significantly improve the accuracy of information retrieval by recommending relevant tag sets that align with user preferences and resource characteristics.However,metric learning method...Tag recommendation systems can significantly improve the accuracy of information retrieval by recommending relevant tag sets that align with user preferences and resource characteristics.However,metric learning methods often suffer from high sensitivity,leading to unstable recommendation results when facing adversarial samples generated through malicious user behavior.Adversarial training is considered to be an effective method for improving the robustness of tag recommendation systems and addressing adversarial samples.However,it still faces the challenge of overfitting.Although curriculum learning-based adversarial training somewhat mitigates this issue,challenges still exist,such as the lack of a quantitative standard for attack intensity and catastrophic forgetting.To address these challenges,we propose a Self-Paced Adversarial Metric Learning(SPAML)method.First,we employ a metric learning model to capture the deep distance relationships between normal samples.Then,we incorporate a self-paced adversarial training model,which dynamically adjusts the weights of adversarial samples,allowing the model to progressively learn from simpler to more complex adversarial samples.Finally,we jointly optimize the metric learning loss and self-paced adversarial training loss in an adversarial manner,enhancing the robustness and performance of tag recommendation tasks.Extensive experiments on the MovieLens and LastFm datasets demonstrate that SPAML achieves F1@3 and NDCG@3 scores of 22%and 32.7%on the MovieLens dataset,and 19.4%and 29%on the LastFm dataset,respectively,outperforming the most competitive baselines.Specifically,F1@3 improves by 4.7%and 6.8%,and NDCG@3 improves by 5.0%and 6.9%,respectively.展开更多
Quantum key distribution(QKD)optical networks can provide more secure communications.However,with the increase of the QKD path requests and key updates,network blocking problems will become severe.The blocking problem...Quantum key distribution(QKD)optical networks can provide more secure communications.However,with the increase of the QKD path requests and key updates,network blocking problems will become severe.The blocking problems in the network can become more severe because each fiber link has limited resources(such as wavelengths and time slots).In addition,QKD optical networks are also affected by external disturbances such as data interception and eavesdropping,resulting in inefficient network communication.In this paper,we exploit the idea of protection path to enhance the anti-interference ability of QKD optical network.By introducing the concept of security metric,we propose a routing wavelength and time slot allocation algorithm(RWTA)based on protection path,which can lessen the blocking problem of QKD optical network.According to simulation analysis,the security-metric-based RWTA algorithm(SM-RWTA)proposed in this paper can substantially improve the success rate of security key(SK)update and significantly reduce the blocking rate of the network.It can also improve the utilization rate of resources such as wavelengths and time slots.Compared with the non-security-metric-based RWTA algorithm(NSM-RWTA),our algorithm is robust and can enhance the anti-interference ability and security of QKD optical networks.展开更多
In this paper,various extended contractions are introduced as generalizations of some existing contractions given by Kannan,Ciric,Reich and Gornicki,et al.Then,several meaningful results about asymptotically regular m...In this paper,various extended contractions are introduced as generalizations of some existing contractions given by Kannan,Ciric,Reich and Gornicki,et al.Then,several meaningful results about asymptotically regular mappings in cone metric spaces over Banach algebras are obtained,weakening the completeness of the spaces and the continuity of the mappings.Moreover,some nontrivial examples are showed to verify the innovation of the new concepts and our fxed point theorems.展开更多
Intonation refers to the use of supra-segmental features to convey pragmatic meanings at the sentence level in a linguistically structured way.The difference in intonation between the native language and a foreign lan...Intonation refers to the use of supra-segmental features to convey pragmatic meanings at the sentence level in a linguistically structured way.The difference in intonation between the native language and a foreign language may influence second language learners’acquisition of intonation.The purpose of this study is to explore the similarities and differences at the level of phonological representation between English and Chinese intonation systems.This study investigated English and Chinese intonation systems,respectively,from both form and meaning under the Auto-Segmental Metrical framework by referring to previous studies and illustrating examples.The results showed that in terms of form,there were notable differences in the structural elements and their inventories between the intonation systems of English and Chinese.In terms of meaning,assertions were represented by different structural elements in English and Chinese intonation systems;the types of structural elements in English intonation possessed the capability to convey complex and subtle meanings,contrasting with the comparatively simpler nature of Chinese intonation.The results reveal that Chinese EFL learners demonstrate considerable difficulties in the production of the structural elements of English intonation and their combinations due to L1 intonation interference.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
基金Project supported by the National Nature Science Foundation of China(Grant Nos.51737003 and 51977060)the Natural Science Foundation of Hebei Province(Grant No.E2011202051).
文摘The neuron model has been widely employed in neural-morphic computing systems and chaotic circuits.This study aims to develop a novel circuit simulation of a three-neuron Hopfield neural network(HNN)with coupled hyperbolic memristors through the modification of a single coupling connection weight.The bistable mode of the hyperbolic memristive HNN(mHNN),characterized by the coexistence of asymmetric chaos and periodic attractors,is effectively demonstrated through the utilization of conventional nonlinear analysis techniques.These techniques include bifurcation diagrams,two-parameter maximum Lyapunov exponent plots,local attractor basins,and phase trajectory diagrams.Moreover,an encryption technique for color images is devised by leveraging the mHNN model and asymmetric structural attractors.This method demonstrates significant benefits in correlation,information entropy,and resistance to differential attacks,providing strong evidence for its effectiveness in encryption.Additionally,an improved modular circuit design method is employed to create the analog equivalent circuit of the memristive HNN.The correctness of the circuit design is confirmed through Multisim simulations,which align with numerical simulations conducted in Matlab.
基金National Key Research and Development Program of China,No.2023YFC3006704National Natural Science Foundation of China,No.42171047CAS-CSIRO Partnership Joint Project of 2024,No.177GJHZ2023097MI。
文摘Accurate prediction of flood events is important for flood control and risk management.Machine learning techniques contributed greatly to advances in flood predictions,and existing studies mainly focused on predicting flood resource variables using single or hybrid machine learning techniques.However,class-based flood predictions have rarely been investigated,which can aid in quickly diagnosing comprehensive flood characteristics and proposing targeted management strategies.This study proposed a prediction approach of flood regime metrics and event classes coupling machine learning algorithms with clustering-deduced membership degrees.Five algorithms were adopted for this exploration.Results showed that the class membership degrees accurately determined event classes with class hit rates up to 100%,compared with the four classes clustered from nine regime metrics.The nonlinear algorithms(Multiple Linear Regression,Random Forest,and least squares-Support Vector Machine)outperformed the linear techniques(Multiple Linear Regression and Stepwise Regression)in predicting flood regime metrics.The proposed approach well predicted flood event classes with average class hit rates of 66.0%-85.4%and 47.2%-76.0%in calibration and validation periods,respectively,particularly for the slow and late flood events.The predictive capability of the proposed prediction approach for flood regime metrics and classes was considerably stronger than that of hydrological modeling approach.
基金Supported by National Natural Science Foundation of China(Grant No.12171140).
文摘It is well known that critical points of the total scalar curvature functional S on the space of all smooth Riemannian structures of volume 1 on a compact manifold M are exactly the Einstein metrics.When the domain of S is restricted to the space of constant scalar curvature metrics,there has been a conjecture that a critical point is also Einstein or isometric to a standard sphere.In the Riemannian case,it’s tangent space satisfies a decomposition.In this paper,we prove that if we only consider the Hermitian metrics,it also have a decomposition.Then we obtain the equation of the critical points among the Hermitian metrics.
文摘In this paper,the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannian manifolds.The authors rigorously establish statistical properties of the estimators,providing formal proofs of their consistency and asymptotic behaviors.The effectiveness of our method is demonstrated through extensive simulations and applications to real-world datasets which highlight its practical utility for complex data with non-Euclidean structures.
基金partially supported by the Scientific and Technical Research Council of Turkey
文摘The energy eigenvalues of a Dirac particle for the hyperbolic-type potential field have been computed approximately. It is obtained a transcendental function of energy, F(E), by writing in terms of confluent Heun functions.The numerical values of energy are then obtained by fixing the zeros on "E-axis" for both complex functions Re[F(E)]and Im[F(E)].
基金Supported by the National Natural Science Foundation of China(11971450)partially supported by the Project of Stable Support for Youth Team in Basic Research Field,CAS(YSBR-001)。
文摘In this paper,we introduce and prove three analytic results related to uniform convergence,properties of Newtonian potential,and convergence of sequences in Sobolev space constrained by their Laplacian.Then,utilizing our analytic results,we develop a complete proof of a crucial estimate appearing in the results of Guofang Wang and Xiaohua Zhu,which states the classification of extremal Hermitian metrics with finite energy and area on compact Riemann surfaces and finite singularities satisfying small singular angles.
基金supported by the National Natural Science Foundation of China(12401625)the China Postdoctoral Science Foundation(2024M753074)+1 种基金the Postdoctoral Fellowship Program of CPSF(GZC20232556)the Fundamental Research Funds for the Central Universities(WK2040000108).
文摘The Kelly strategy is a common approach in portfolio optimization problems that aims to maximize the expected portfolio growth rate in the long term.Its computation requires complete knowledge of the asset return distribution,which is obviously not observable,but can be inferred from sample data.Motivated by recent developments in data-driven optimization methods,we propose a new class of coherent Wasserstein data-driven Kelly portfolio optimization models.In particular,we establish a class of ambiguity sets based on coherent Wasserstein metrics,and these new metrics can strike a good balance between robustness and data-drivenness,thus providing richer choices for ambiguity set design.The Kelly portfolio optimization model,which is data-driven and based on coherent Wasserstein balls,can be solved efficiently as a finite-dimensional convex program.This model also provides a robust data-driven solution.In addition,we numerically investigate the proposed model and find that it outperforms the type-1 Wasserstein-Kelly portfolio,especially the classical Kelly portfolio.Moreover,it indicates that we can obtain a portfolio with higher final value and stability,especially in controlling volatility and maximum drawdown.
文摘In a recent article, we have corrected the traditional derivation of the Schwarzschild metric, thus obtaining the formulation of the correct Schwarzschild metric, which is different from the traditional Schwarzschild metric. Then, in another article by starting from this correct Schwarzschild metric, we have corrected also the Reissner-Nordstrøm, Kerr and Kerr-Newman metrics. On the other hand, in a third article, always by starting from this correct Schwarzschild metric, we have obtained the formulas of the correct gravitational potential and of the correct gravitational force in the case described by this metric. Now, in this article, by starting from these correct Reissner-Nordstrøm, Kerr and Kerr-Newman metrics and proceeding in a manner analogous to this third article, we obtain the formulas of the correct gravitational potential and of the correct gravitational force in the cases described by these metrics. Moreover, we analyze these correct results and their consequences. Finally, we propose some possible crucial experiments between the commonly accepted theory and the same theory corrected according to this article.
基金supported by the Nature Science Foundation of China(12171140).
文摘In this paper,we prove that for certain fiber bundles there is a k-Futaki-Ono conformally Kahler metric related to a metric in any given Kahler class for any k≥2.
基金supported by National Natural Science Foundation of China(Grant Nos.12025407,12474246,and 12450401)the National Key Research and Development Program of China(Grant No.2021YFA1400201)the Chinese Academy of Sciences(Grant Nos.YSBR-047 and XDB33030100)。
文摘The quantum metric manifested as the Riemannian metric in the parameter space of Bloch bands,characterizes the topology and geometry of quantum states.The second harmonic generation(SHG),as one of the fundamental nonlinear optical responses that links geometry of optical transitions to physical observables,despite being widely studied in various materials,its relation to quantum metric,especially in the dynamical regime,stays obscure.
文摘Let X be a real uniformly convex and uniformly smooth Banach space and C a nonempty closed and convex subset of X.Let Π_(C):X→C denote the generalized metric projection operator introduced by Alber in[1].In this paper,we define the Gâteaux directional differentiability of Π_(C).We investigate some properties of the Gâteaux directional differentiability of Π_(C).In particular,if C is a closed ball,or a closed and convex cone(including proper closed subspaces),or a closed and convex cylinder,then,we give the exact representations of the directional derivatives of Π_(C).By comparing the results in[12]and this paper,we see the significant difference between the directional derivatives of the generalized metric projection operator Π_(C) and the Gâteaux directional derivatives of the standard metric projection operator PC.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.:81603182 and 81703607)the Fundamental Research Funds for the Central Universities,China(Grant Nos.:DUT21RC(3)057,DUT23YG226,DUT24MS018,and DUT23YG228)+1 种基金the Natural Science Foundation of Liaoning Province,China(Grant No.:2023-MSBA-018)the Open Funding of Cancer Hospital of Dalian University of Technology,China(Grant No.:2024-ZLKF-33).
文摘The focus of green analytical chemistry(GAC)is to minimize the negative impacts of analytical procedures on human safety,human health,and the environment.Several factors,such as the reagents used,sample collection,sample processing,instruments,energy consumed,and the quantities of hazardous materials and waste generated during analytical procedures,need to be considered in the evaluation of the greenness of analytical assays.In this study,we propose a greenness evaluation metric for analytical methods(GEMAM).The new greenness metric is simple,flexible,and comprehensive.The evaluation criteria are based on both the 12 principles of GAC(SIGNIFICANCE)and the 10 factors of sample preparation,and the results are presented on a 0–10 scale.The GEMAM calculation process is easy to perform,and its results are easy to interpret.The output of GEMAM is a pictogram that can provide both qualitative and quantitative information based on color and number.
基金Supported by the National Key Research and Development Program of China(2022YFA1005501)the Natural Science Foundation of Jiangsu Province(BK20241433).
文摘In this paper,we study scalar curvature rigidity of non-smooth metrics on smooth manifolds with non-positive Yamabe invariant.We prove that if the scalar curvature is not less than the Yamabe invariant in the distributional sense,then the manifold must be isometric to an Einstein manifold.This result extends Theorem 1.4 in Jiang,Sheng and Zhang[27],from a special case where the manifolds have zero Yamabe invariant to general cases where the manifolds have non-positive Yamabe invariant.
基金supported by the Key Research and Development Program of Zhejiang Province(No.2024C01071)the Natural Science Foundation of Zhejiang Province(No.LQ15F030006).
文摘Tag recommendation systems can significantly improve the accuracy of information retrieval by recommending relevant tag sets that align with user preferences and resource characteristics.However,metric learning methods often suffer from high sensitivity,leading to unstable recommendation results when facing adversarial samples generated through malicious user behavior.Adversarial training is considered to be an effective method for improving the robustness of tag recommendation systems and addressing adversarial samples.However,it still faces the challenge of overfitting.Although curriculum learning-based adversarial training somewhat mitigates this issue,challenges still exist,such as the lack of a quantitative standard for attack intensity and catastrophic forgetting.To address these challenges,we propose a Self-Paced Adversarial Metric Learning(SPAML)method.First,we employ a metric learning model to capture the deep distance relationships between normal samples.Then,we incorporate a self-paced adversarial training model,which dynamically adjusts the weights of adversarial samples,allowing the model to progressively learn from simpler to more complex adversarial samples.Finally,we jointly optimize the metric learning loss and self-paced adversarial training loss in an adversarial manner,enhancing the robustness and performance of tag recommendation tasks.Extensive experiments on the MovieLens and LastFm datasets demonstrate that SPAML achieves F1@3 and NDCG@3 scores of 22%and 32.7%on the MovieLens dataset,and 19.4%and 29%on the LastFm dataset,respectively,outperforming the most competitive baselines.Specifically,F1@3 improves by 4.7%and 6.8%,and NDCG@3 improves by 5.0%and 6.9%,respectively.
基金funded by Youth Program of Shaanxi Provincial Department of Science and Technology(Grant No.2024JC-YBQN-0630)。
文摘Quantum key distribution(QKD)optical networks can provide more secure communications.However,with the increase of the QKD path requests and key updates,network blocking problems will become severe.The blocking problems in the network can become more severe because each fiber link has limited resources(such as wavelengths and time slots).In addition,QKD optical networks are also affected by external disturbances such as data interception and eavesdropping,resulting in inefficient network communication.In this paper,we exploit the idea of protection path to enhance the anti-interference ability of QKD optical network.By introducing the concept of security metric,we propose a routing wavelength and time slot allocation algorithm(RWTA)based on protection path,which can lessen the blocking problem of QKD optical network.According to simulation analysis,the security-metric-based RWTA algorithm(SM-RWTA)proposed in this paper can substantially improve the success rate of security key(SK)update and significantly reduce the blocking rate of the network.It can also improve the utilization rate of resources such as wavelengths and time slots.Compared with the non-security-metric-based RWTA algorithm(NSM-RWTA),our algorithm is robust and can enhance the anti-interference ability and security of QKD optical networks.
基金Supported by Yunnan Provincial Reserve Talent Program for Young and Middle-aged Academic and Technical Leaders(202405AC350086)the Special Basic Cooperative Research Programs of Yunnan Provincial Undergraduate Universities’Association(202301BA070001-095,202301BA070001-092)+3 种基金the Natural Science Foundation of Guangdong Province(2023A1515010997)Xingzhao Talent Support ProgramEducation and Teaching Reform Research Project of Zhaotong University(Ztjx202405,Ztjx202403,Ztjx202414)2024 First-class Undergraduate Courses of Zhaotong University(Ztujk202405,Ztujk202404).
文摘In this paper,various extended contractions are introduced as generalizations of some existing contractions given by Kannan,Ciric,Reich and Gornicki,et al.Then,several meaningful results about asymptotically regular mappings in cone metric spaces over Banach algebras are obtained,weakening the completeness of the spaces and the continuity of the mappings.Moreover,some nontrivial examples are showed to verify the innovation of the new concepts and our fxed point theorems.
文摘Intonation refers to the use of supra-segmental features to convey pragmatic meanings at the sentence level in a linguistically structured way.The difference in intonation between the native language and a foreign language may influence second language learners’acquisition of intonation.The purpose of this study is to explore the similarities and differences at the level of phonological representation between English and Chinese intonation systems.This study investigated English and Chinese intonation systems,respectively,from both form and meaning under the Auto-Segmental Metrical framework by referring to previous studies and illustrating examples.The results showed that in terms of form,there were notable differences in the structural elements and their inventories between the intonation systems of English and Chinese.In terms of meaning,assertions were represented by different structural elements in English and Chinese intonation systems;the types of structural elements in English intonation possessed the capability to convey complex and subtle meanings,contrasting with the comparatively simpler nature of Chinese intonation.The results reveal that Chinese EFL learners demonstrate considerable difficulties in the production of the structural elements of English intonation and their combinations due to L1 intonation interference.
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.
