A novel motion-blur-based method for measuring the angular amplitude of a high-frequency rotational vibration is schemed. The proposed approach combines the active vision concept and the mechanism of motion-from-blur,...A novel motion-blur-based method for measuring the angular amplitude of a high-frequency rotational vibration is schemed. The proposed approach combines the active vision concept and the mechanism of motion-from-blur, generates motion blur on the image plane actively by extending exposure time, and utilizes the motion blur information in polar images to estimate the angular amplitude of a high-frequency rotational vibration. This method obtains the analytical results of the angular vibration amplitude from the geometric moments of a motion blurred polar image and an unblurred image for reference. Experimental results are provided to validate the presented scheme.展开更多
We analyze the dynamics of geometric measure of discord (GMOD) and measurement-induced non-locality (MIN) in the presence of initial system-reservoir correlations without Born and Markov approximation. Although th...We analyze the dynamics of geometric measure of discord (GMOD) and measurement-induced non-locality (MIN) in the presence of initial system-reservoir correlations without Born and Markov approximation. Although the initial system-environment states have the same reduced density matrices for both the system and environment, the effects of different initial system-environment correlations have been shown to fundamentally alter the time evolution of GMOD and MIN between two quantum systems in both Markovian and non-Markovian regimes. In general, both GMOD and MIN experience a sudden increase for initially quantum-correlated states, and a sudden decrease for classical-correlated states before they reach the same stationary values with initially factorized states.展开更多
A symmetric measure of quantum correlation based on the Hilbert–Schmidt distance is presented in this paper. For two-qubit states, we considerably simplify the optimization procedure so that numerical evaluation can ...A symmetric measure of quantum correlation based on the Hilbert–Schmidt distance is presented in this paper. For two-qubit states, we considerably simplify the optimization procedure so that numerical evaluation can be performed efficiently. Analytical expressions for the quantum correlation are attained for some special states. We further investigate the dynamics of quantum correlation of the system qubits in the presence of independent dissipative environments. Several nontrivial aspects are demonstrated. We find that the quantum correlation can increase even if the system state is suffering from dissipative noise. Sudden changes occur, even twice, in the time evolution of quantum correlation. There exists a certain correspondence between the evolution of quantum correlation in the systems and that in the environments, and the quantum correlation in the systems will be transferred into the environments completely and asymptotically.展开更多
Some techniques in the Geometric Measure Theory are used to study the hypersurfaces in Euclidean spaces and some fundamental properties with this subject are discussed in this article.
In this article, we establish the Gauss Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very general by using the geometric measure theoretic me...In this article, we establish the Gauss Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very general by using the geometric measure theoretic method. The Cauchy-Pompeiu formula for Clifford-valued functions under the weak condition will be derived as their simple application. Furthermore, Cauchy formula for monogenic functions under the weak condition is derived directly from the Cauchy-Pompeiu formula.展开更多
We investigate the characteristics of three kinds of quantum correlations, measured by pairwise quantum discord (QD), geometric measure of quantum discord (GMQD), and measurement-induced disturbance (MID), in th...We investigate the characteristics of three kinds of quantum correlations, measured by pairwise quantum discord (QD), geometric measure of quantum discord (GMQD), and measurement-induced disturbance (MID), in the systems of three- and four-dipole arrays. The influence of the temperature on the three quantum correlations and entanglement of the systems is also analyzed numerically. It is found that novel quantum correlation switches called QD, GMQD, and MID respectively can be constructed with the qubits consisting of electric dipoles coupled by the dipole-dipole interaction and oriented along or against the external electric field. Moreover, with the increase of temperature, QD, GMQD, and MID are more robust than entanglement against the thermal environment. It is also found that for each dipole pair of the three- and four-dipole arrangements, the MID is always the largest and the GMQD the smallest.展开更多
Similarity measurement has been a prevailing research topic geographic information science.Geometric similarity measurement inin scaling transformation(GSM_ST)is critical to ensure spatial data quality while balancing...Similarity measurement has been a prevailing research topic geographic information science.Geometric similarity measurement inin scaling transformation(GSM_ST)is critical to ensure spatial data quality while balancing detailed information with distinctive features.However,GSM_ST is an uncertain problem due to subjective spatial cognition,global and local concerns,and geometric complexity.Traditional rule-based methods considering multiple consistent conditions require subjective adjustments to characteristics and weights,leading to poor robustness in addressing GSM_ST.This study proposes an unsupervised representation learning framework for automated GSM_ST,using a Graph Autoencoder Network(GAE)and drainage networks as an example.The framework involves constructing a drainage graph,designing the GAE architecture for GSM_ST,and using Cosine similarity to measure similarity based on the GAE-derived drainage embeddings in different scales.We perform extensive experiments and compare methods across 71 drainage networks duringfive scaling transformations.The results show that the proposed GAE method outperforms other methods with a satisfaction ratio of around 88%and has strong robustness.Moreover,our proposed method also can be applied to other scenarios,such as measuring similarity between geographical entities at different times and data from different datasets.展开更多
Inevitable geometric variations significantly affect the performance of turbines or even that of entire engines;thus,it is necessary to determine their actual characteristics and accurately estimate their impact on pe...Inevitable geometric variations significantly affect the performance of turbines or even that of entire engines;thus,it is necessary to determine their actual characteristics and accurately estimate their impact on performance.In this study,based on 1781 measured profiles of a typical turbine blade,the statistical characteristics of the geometric variations and the uncertainty impact are analyzed,and some commonly used uncertainty modelling methods based on Principal-Component Analysis(PCA)are verified.The geometric variations are found to be evident,asymmetric,and non-uniform,and the non-normality of the random distributions is non-negligible.The performance is notably affected,which is manifested as an overall offset,a notable scattering,and significant deterioration in several extreme cases.Additionally,it is demonstrated that the PCA reconstruction model is effective in characterizing major uncertainty characteristics of the geometric variations and their impact on the performance with almost the first 10 PCA modes.Based on a reasonable profile error and mean geometric deviation,the Gaussian assumption and stochasticprocess-based model are also found to be effective in predicting the mean values and standard deviations of the performance variations.However,they fail to predict the probability of some extreme cases with high loss.Finally,a Chi-square-based correction model is proposed to compensate for this deficiency.The present work can provide a useful reference for uncertainty analysis of the impact of geometric variations,and the corresponding uncertainty design of turbine blades.展开更多
We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels: amplitude damping channel, phase damping channel, depolarizing channel and bit flit ...We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels: amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qnbit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by l1 norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative α-entropies, while the bit flit channel does change for some special cases.展开更多
The problem of computing geometric measure of quantum entanglement for symmetric pure states can be regarded as the problem of finding the largest unitary symmetric eigenvalue(US-eigenvalue)for symmetric complex tenso...The problem of computing geometric measure of quantum entanglement for symmetric pure states can be regarded as the problem of finding the largest unitary symmetric eigenvalue(US-eigenvalue)for symmetric complex tensors,which can be taken as a multilinear optimization problem in complex number field.In this paper,we convert the problem of computing the geometric measure of entanglement for symmetric pure states to a real polynomial optimization problem.Then we use Jacobian semidefinite relaxation method to solve it.Some numerical examples are presented.展开更多
We extend the classical Gibbs theory for smooth potentials to the geometric Gibbs theory for certain continuous potentials.We study the existence and uniqueness and the compatibility of geometric Gibbs measures associ...We extend the classical Gibbs theory for smooth potentials to the geometric Gibbs theory for certain continuous potentials.We study the existence and uniqueness and the compatibility of geometric Gibbs measures associated with these continuous potentials.We introduce a complex Banach manifold structure on the space of these continuous potentials as well as on the space of all geometric Gibbs measures.We prove that with this complex Banach manifold structure,the space is complete and,moreover,is the completion of the space of all smooth potentials as well as the space of all classical Gibbs measures.There is a maximum metric on the space,which is incomplete.We prove that the topology induced by the newly introduced complex Banach manifold structure and the topology induced by the maximal metric are the same.We prove that a geometric Gibbs measure is an equilibrium state,and the in mum of the metric entropy function on the space is zero.展开更多
基金This project is supported by National Natural Science Foundation of China (No. 50375099, No. 50390064)
文摘A novel motion-blur-based method for measuring the angular amplitude of a high-frequency rotational vibration is schemed. The proposed approach combines the active vision concept and the mechanism of motion-from-blur, generates motion blur on the image plane actively by extending exposure time, and utilizes the motion blur information in polar images to estimate the angular amplitude of a high-frequency rotational vibration. This method obtains the analytical results of the angular vibration amplitude from the geometric moments of a motion blurred polar image and an unblurred image for reference. Experimental results are provided to validate the presented scheme.
基金supported by the Special Funds of the National Natural Science Foundation of China(Grant Nos.11247006 and 11247207)the Scientific Research Foundation of Jiangxi Provincial Education Department(Grant Nos.GJJ12355 and GJJ13651)the Natural Science Foundation of Jiangxi Province,China(Grant Nos.20122BAB212004 and 20132BAB212008)
文摘We analyze the dynamics of geometric measure of discord (GMOD) and measurement-induced non-locality (MIN) in the presence of initial system-reservoir correlations without Born and Markov approximation. Although the initial system-environment states have the same reduced density matrices for both the system and environment, the effects of different initial system-environment correlations have been shown to fundamentally alter the time evolution of GMOD and MIN between two quantum systems in both Markovian and non-Markovian regimes. In general, both GMOD and MIN experience a sudden increase for initially quantum-correlated states, and a sudden decrease for classical-correlated states before they reach the same stationary values with initially factorized states.
基金Project supported by the National Fundamental Research Program of China (Grant No. 2007CB925200)the National Natural Science Foundation of China(Grant No. 11275083)the Natural Science Foundation of Anhui Province of China (Grant No. KJ2012B180)
文摘A symmetric measure of quantum correlation based on the Hilbert–Schmidt distance is presented in this paper. For two-qubit states, we considerably simplify the optimization procedure so that numerical evaluation can be performed efficiently. Analytical expressions for the quantum correlation are attained for some special states. We further investigate the dynamics of quantum correlation of the system qubits in the presence of independent dissipative environments. Several nontrivial aspects are demonstrated. We find that the quantum correlation can increase even if the system state is suffering from dissipative noise. Sudden changes occur, even twice, in the time evolution of quantum correlation. There exists a certain correspondence between the evolution of quantum correlation in the systems and that in the environments, and the quantum correlation in the systems will be transferred into the environments completely and asymptotically.
基金Supported by a Grant-in-Aid for scicntific Research from Nanjing University of Science and Technology (AB96137) partly by NNSP(10471063)
文摘Some techniques in the Geometric Measure Theory are used to study the hypersurfaces in Euclidean spaces and some fundamental properties with this subject are discussed in this article.
基金supported by NNSF of China(11171260)RFDP of Higher Education of China(20100141110054)
文摘In this article, we establish the Gauss Green type theorems for Clifford-valued functions in Clifford analysis. The boundary conditions in theorems obtained are very general by using the geometric measure theoretic method. The Cauchy-Pompeiu formula for Clifford-valued functions under the weak condition will be derived as their simple application. Furthermore, Cauchy formula for monogenic functions under the weak condition is derived directly from the Cauchy-Pompeiu formula.
基金supported by the National Natural Science Foundation of China(Grant Nos.11174081,11034002,11134003,11104075,and 60708003)the National Basic Research Program of China(Grant Nos.2011CB921602 and 2012CB821302)the Open Fund from the State Key Laboratory of Precision Spectroscopy of East China Normal University,China
文摘We investigate the characteristics of three kinds of quantum correlations, measured by pairwise quantum discord (QD), geometric measure of quantum discord (GMQD), and measurement-induced disturbance (MID), in the systems of three- and four-dipole arrays. The influence of the temperature on the three quantum correlations and entanglement of the systems is also analyzed numerically. It is found that novel quantum correlation switches called QD, GMQD, and MID respectively can be constructed with the qubits consisting of electric dipoles coupled by the dipole-dipole interaction and oriented along or against the external electric field. Moreover, with the increase of temperature, QD, GMQD, and MID are more robust than entanglement against the thermal environment. It is also found that for each dipole pair of the three- and four-dipole arrangements, the MID is always the largest and the GMQD the smallest.
基金supported by the National Natural Science Foundation of China[grant number 41531180]the National Natural Science Foundation of China[grant number 42071450]the China Scholarship Council(CSC)[grant number 202206270076].
文摘Similarity measurement has been a prevailing research topic geographic information science.Geometric similarity measurement inin scaling transformation(GSM_ST)is critical to ensure spatial data quality while balancing detailed information with distinctive features.However,GSM_ST is an uncertain problem due to subjective spatial cognition,global and local concerns,and geometric complexity.Traditional rule-based methods considering multiple consistent conditions require subjective adjustments to characteristics and weights,leading to poor robustness in addressing GSM_ST.This study proposes an unsupervised representation learning framework for automated GSM_ST,using a Graph Autoencoder Network(GAE)and drainage networks as an example.The framework involves constructing a drainage graph,designing the GAE architecture for GSM_ST,and using Cosine similarity to measure similarity based on the GAE-derived drainage embeddings in different scales.We perform extensive experiments and compare methods across 71 drainage networks duringfive scaling transformations.The results show that the proposed GAE method outperforms other methods with a satisfaction ratio of around 88%and has strong robustness.Moreover,our proposed method also can be applied to other scenarios,such as measuring similarity between geographical entities at different times and data from different datasets.
基金supported by the National Science and Technology Major Project, China (No. J2019-II-0012-0032)
文摘Inevitable geometric variations significantly affect the performance of turbines or even that of entire engines;thus,it is necessary to determine their actual characteristics and accurately estimate their impact on performance.In this study,based on 1781 measured profiles of a typical turbine blade,the statistical characteristics of the geometric variations and the uncertainty impact are analyzed,and some commonly used uncertainty modelling methods based on Principal-Component Analysis(PCA)are verified.The geometric variations are found to be evident,asymmetric,and non-uniform,and the non-normality of the random distributions is non-negligible.The performance is notably affected,which is manifested as an overall offset,a notable scattering,and significant deterioration in several extreme cases.Additionally,it is demonstrated that the PCA reconstruction model is effective in characterizing major uncertainty characteristics of the geometric variations and their impact on the performance with almost the first 10 PCA modes.Based on a reasonable profile error and mean geometric deviation,the Gaussian assumption and stochasticprocess-based model are also found to be effective in predicting the mean values and standard deviations of the performance variations.However,they fail to predict the probability of some extreme cases with high loss.Finally,a Chi-square-based correction model is proposed to compensate for this deficiency.The present work can provide a useful reference for uncertainty analysis of the impact of geometric variations,and the corresponding uncertainty design of turbine blades.
文摘We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels: amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qnbit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by l1 norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative α-entropies, while the bit flit channel does change for some special cases.
基金the Research Programme of National University of Defense Technology(No.ZK16-03-45).
文摘The problem of computing geometric measure of quantum entanglement for symmetric pure states can be regarded as the problem of finding the largest unitary symmetric eigenvalue(US-eigenvalue)for symmetric complex tensors,which can be taken as a multilinear optimization problem in complex number field.In this paper,we convert the problem of computing the geometric measure of entanglement for symmetric pure states to a real polynomial optimization problem.Then we use Jacobian semidefinite relaxation method to solve it.Some numerical examples are presented.
基金This work was supported by National Science Foundation of USA(Grant No.DMS-1747905)the Simons Foundation(Grant No.523341)+1 种基金Professional Sta Congress of the City University of New York Enhanced Award(Grant No.62777-0050)National Natural Science Foundation of China(Grant No.11571122).
文摘We extend the classical Gibbs theory for smooth potentials to the geometric Gibbs theory for certain continuous potentials.We study the existence and uniqueness and the compatibility of geometric Gibbs measures associated with these continuous potentials.We introduce a complex Banach manifold structure on the space of these continuous potentials as well as on the space of all geometric Gibbs measures.We prove that with this complex Banach manifold structure,the space is complete and,moreover,is the completion of the space of all smooth potentials as well as the space of all classical Gibbs measures.There is a maximum metric on the space,which is incomplete.We prove that the topology induced by the newly introduced complex Banach manifold structure and the topology induced by the maximal metric are the same.We prove that a geometric Gibbs measure is an equilibrium state,and the in mum of the metric entropy function on the space is zero.