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
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
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
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.
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
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
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
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
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
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
In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strateg...In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.展开更多
We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expression...We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons,and we obtain the phase diagram of the model marked by the first Chern number.Furthermore,we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone.However,some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric,which leads to ill-defined non-integer topological Euler numbers.Nevertheless,the non-integer"Euler number"provides valuable insights and an upper bound for the absolute values of the Chern numbers.展开更多
In the metric-based meta-learning detection model,the distribution of training samples in the metric space has great influence on the detection performance,and this influence is usually ignored by traditional meta-det...In the metric-based meta-learning detection model,the distribution of training samples in the metric space has great influence on the detection performance,and this influence is usually ignored by traditional meta-detectors.In addition,the design of metric space might be interfered with by the background noise of training samples.To tackle these issues,we propose a metric space optimisation method based on hyperbolic geometry attention and class-agnostic activation maps.First,the geometric properties of hyperbolic spaces to establish a structured metric space are used.A variety of feature samples of different classes are embedded into the hyperbolic space with extremely low distortion.This metric space is more suitable for representing tree-like structures between categories for image scene analysis.Meanwhile,a novel similarity measure function based on Poincarédistance is proposed to evaluate the distance of various types of objects in the feature space.In addition,the class-agnostic activation maps(CCAMs)are employed to re-calibrate the weight of foreground feature information and suppress background information.Finally,the decoder processes the high-level feature information as the decoding of the query object and detects objects by predicting their locations and corresponding task encodings.Experimental evaluation is conducted on Pascal VOC and MS COCO datasets.The experiment results show that the effectiveness of the authors’method surpasses the performance baseline of the excellent few-shot detection models.展开更多
Assessment of rock mass quality significantly impacts the design and construction of underground and open-pit mines from the point of stability and economy.This study develops the novel Gromov-Hausdorff distance for r...Assessment of rock mass quality significantly impacts the design and construction of underground and open-pit mines from the point of stability and economy.This study develops the novel Gromov-Hausdorff distance for rock quality(GHDQR)methodology for rock mass quality rating based on multi-criteria grey metric space.It usually presents the quality of surrounding rock by classes(metric spaces)with specified properties and adequate interval-grey numbers.Measuring the distance between surrounding rock sample characteristics and existing classes represents the core of this study.The Gromov-Hausdorff distance is an especially useful discriminant function,i.e.,a classifier to calculate these distances,and assess the quality of the surrounding rock.The efficiency of the developed methodology is analyzed using the Mean Absolute Percentage Error(MAPE)technique.Seven existing methods,such as the Gaussian cloud method,Discriminant method,Mutation series method,Artificial neural network(ANN),Support vector machine(SVM),Grey wolf optimizer and Support vector classification method(GWO-SVC)and Rock mass rating method(RMR)are used for comparison with the proposed GHDQR method.The share of the highly accurate category of 85.71%clearly indicates compliance with actual values obtained by the compared methods.The results of comparisons showed that the model enables objective,efficient,and reliable assessment of rock mass quality.展开更多
In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to b...In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.展开更多
In this paper,we study tidal forces in the Schwarzschild black hole,whose metric explicitly includes a generalized uncertainty principle(GUP)effect.We also investigate interesting features of the geodesic equations an...In this paper,we study tidal forces in the Schwarzschild black hole,whose metric explicitly includes a generalized uncertainty principle(GUP)effect.We also investigate interesting features of the geodesic equations and tidal effects that are dependent on the GUP parameterαrelated to a minimum length.Then,by solving the geodesic deviation equations explicitly with appropriate boundary conditions,we show thatαin the effective metric affects both the radial and angular components of the geodesic equation,particularly near the singularities.展开更多
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 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 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.
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 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.
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 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In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.
基金Project supported by the Beijing Natural Science Foundation(Grant No.1232026)the Qinxin Talents Program of BISTU(Grant No.QXTCP C201711)+2 种基金the R&D Program of Beijing Municipal Education Commission(Grant No.KM202011232017)the National Natural Science Foundation of China(Grant No.12304190)the Research fund of BISTU(Grant No.2022XJJ32).
文摘We investigate the quantum metric and topological Euler number in a cyclically modulated Su-Schrieffer-Heeger(SSH)model with long-range hopping terms.By computing the quantum geometry tensor,we derive exact expressions for the quantum metric and Berry curvature of the energy band electrons,and we obtain the phase diagram of the model marked by the first Chern number.Furthermore,we also obtain the topological Euler number of the energy band based on the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone.However,some regions where the Berry curvature is identically zero in the first Brillouin zone result in the degeneracy of the quantum metric,which leads to ill-defined non-integer topological Euler numbers.Nevertheless,the non-integer"Euler number"provides valuable insights and an upper bound for the absolute values of the Chern numbers.
基金National Natural Science Foundation of China,Grant/Award Number:61602157Henan scientific and technological project,Grant/Award Number:242102210020Basal Research Fund,Grant/Award Number:NSFRF240618。
文摘In the metric-based meta-learning detection model,the distribution of training samples in the metric space has great influence on the detection performance,and this influence is usually ignored by traditional meta-detectors.In addition,the design of metric space might be interfered with by the background noise of training samples.To tackle these issues,we propose a metric space optimisation method based on hyperbolic geometry attention and class-agnostic activation maps.First,the geometric properties of hyperbolic spaces to establish a structured metric space are used.A variety of feature samples of different classes are embedded into the hyperbolic space with extremely low distortion.This metric space is more suitable for representing tree-like structures between categories for image scene analysis.Meanwhile,a novel similarity measure function based on Poincarédistance is proposed to evaluate the distance of various types of objects in the feature space.In addition,the class-agnostic activation maps(CCAMs)are employed to re-calibrate the weight of foreground feature information and suppress background information.Finally,the decoder processes the high-level feature information as the decoding of the query object and detects objects by predicting their locations and corresponding task encodings.Experimental evaluation is conducted on Pascal VOC and MS COCO datasets.The experiment results show that the effectiveness of the authors’method surpasses the performance baseline of the excellent few-shot detection models.
文摘Assessment of rock mass quality significantly impacts the design and construction of underground and open-pit mines from the point of stability and economy.This study develops the novel Gromov-Hausdorff distance for rock quality(GHDQR)methodology for rock mass quality rating based on multi-criteria grey metric space.It usually presents the quality of surrounding rock by classes(metric spaces)with specified properties and adequate interval-grey numbers.Measuring the distance between surrounding rock sample characteristics and existing classes represents the core of this study.The Gromov-Hausdorff distance is an especially useful discriminant function,i.e.,a classifier to calculate these distances,and assess the quality of the surrounding rock.The efficiency of the developed methodology is analyzed using the Mean Absolute Percentage Error(MAPE)technique.Seven existing methods,such as the Gaussian cloud method,Discriminant method,Mutation series method,Artificial neural network(ANN),Support vector machine(SVM),Grey wolf optimizer and Support vector classification method(GWO-SVC)and Rock mass rating method(RMR)are used for comparison with the proposed GHDQR method.The share of the highly accurate category of 85.71%clearly indicates compliance with actual values obtained by the compared methods.The results of comparisons showed that the model enables objective,efficient,and reliable assessment of rock mass quality.
基金Supported by the National Natural Science Foundation of China(11771020,12171005).
文摘In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.
基金supported by a Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education,NRF-2019R1I1A1A01058449supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(No.2020R1H1A2102242)。
文摘In this paper,we study tidal forces in the Schwarzschild black hole,whose metric explicitly includes a generalized uncertainty principle(GUP)effect.We also investigate interesting features of the geodesic equations and tidal effects that are dependent on the GUP parameterαrelated to a minimum length.Then,by solving the geodesic deviation equations explicitly with appropriate boundary conditions,we show thatαin the effective metric affects both the radial and angular components of the geodesic equation,particularly near the singularities.
