In this paper,we obtain a vector bundle valued mixed hard Lefschetz theorem.The argument is mainly based on the works of Tien-Cuong Dinh and Viet-Anh Nguyen.
In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family...In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family of vertex operator algebras V_(√kA_(1)) associated to rank-one positive definite even lattices √kA_(1) for arbitrary positive integers k to characterize these even lattice vertex operator algebras.In such a family of lattice vertex operator algebras V_(√kA_(1)),the vertex operator algebra V_(√2A_(1)) is different from others.Hence we describe the varieties of semi-conformal vectors of V_(√2A_(1)) and the fixed vertex operator subalgebra V^(+)√2A_(1).Moreover,as applications,we study the relations between vertex operator algebras V_(√kA_(1) )and L_(sl_(2))(k,0)for arbitrary positive integers k by the viewpoint of semi-conformal homomorphisms of vertex operator algebras.For case k=2,in the series of rational simple affine vertex operator algebras L_(sl_(2))(k,0)for positive integers k,we show that L_(sl_(2))(2,0)is a unique frame vertex operator algebra with rank 3.展开更多
On-chip devices for generating pre-designed vectorial optical fields(VOFs)under surface wave(SW)excitations are highly desired in integrated photonics.However,conventional devices are usually of large footprints,low e...On-chip devices for generating pre-designed vectorial optical fields(VOFs)under surface wave(SW)excitations are highly desired in integrated photonics.However,conventional devices are usually of large footprints,low efficiencies,and limited wave-control capabilities.Here,we present a generic approach to design ultra-compact on-chip devices that can efficiently generate pre-designed VOFs under SW excitations,and experimentally verify the concept in terahertz(THz)regime.We first describe how to design SW-excitation metasurfaces for generating circularly polarized complex beams,and experimentally demonstrate two meta-devices to realize directional emission and focusing of THz waves with oppo-site circular polarizations,respectively.We then establish a systematic approach to construct an integrated device via merging two carefully designed metasurfaces,which,under SW excitations,can separately produce pre-designed far-field patterns with different circular polarizations and generate target VOF based on their interference.As a proof of con-cept,we demonstrate experimentally a meta-device that can generate a radially polarized Bessel beam under SW excita-tion at~0.4 THz.Experimental results agree well with full-wave simulations,collectively verifying the performance of our device.Our study paves the road to realizing highly integrated on-chip functional THz devices,which may find many ap-plications in biological sensing,communications,displays,image multiplexing,and beyond.展开更多
The Bessel-like vector vortex beam(BlVVB)has gained increasing significance across numerous applications.However,its practical application is restricted by manufacturing difficulties and polarization manipulation.Thus...The Bessel-like vector vortex beam(BlVVB)has gained increasing significance across numerous applications.However,its practical application is restricted by manufacturing difficulties and polarization manipulation.Thus,the ability to manipulate its degrees of freedom is highly desirable.In this paper,the full-domain polarization modulation of BlVVB within a hot atomic ensemble has been investigated.We begin with the theoretical analysis of the resonant magneto-optical effect of atoms with a horizontal linear-polarized beam and experimentally demonstrate precise manipulation of the polarization state across the entire domain of the BlVVB,achieving an error margin of less than 3°at various cross-sectional points.Our study provides a novel approach for the modulation of BlVVB based on atomic media,which holds potential applications in sensitive vector magnetometers,optical communications,and signal processing.展开更多
Accurate positioning is one of the essential requirements for numerous applications of remote sensing data,especially in the event of a noisy or unreliable satellite signal.Toward this end,we present a novel framework...Accurate positioning is one of the essential requirements for numerous applications of remote sensing data,especially in the event of a noisy or unreliable satellite signal.Toward this end,we present a novel framework for aircraft geo-localization in a large range that only requires a downward-facing monocular camera,an altimeter,a compass,and an open-source Vector Map(VMAP).The algorithm combines the matching and particle filter methods.Shape vector and correlation between two building contour vectors are defined,and a coarse-to-fine building vector matching(CFBVM)method is proposed in the matching stage,for which the original matching results are described by the Gaussian mixture model(GMM).Subsequently,an improved resampling strategy is designed to reduce computing expenses with a huge number of initial particles,and a credibility indicator is designed to avoid location mistakes in the particle filter stage.An experimental evaluation of the approach based on flight data is provided.On a flight at a height of 0.2 km over a flight distance of 2 km,the aircraft is geo-localized in a reference map of 11,025 km~2using 0.09 km~2aerial images without any prior information.The absolute localization error is less than 10 m.展开更多
Hamilton energy,which reflects the energy variation of systems,is one of the crucial instruments used to analyze the characteristics of dynamical systems.Here we propose a method to deduce Hamilton energy based on the...Hamilton energy,which reflects the energy variation of systems,is one of the crucial instruments used to analyze the characteristics of dynamical systems.Here we propose a method to deduce Hamilton energy based on the existing systems.This derivation process consists of three steps:step 1,decomposing the vector field;step 2,solving the Hamilton energy function;and step 3,verifying uniqueness.In order to easily choose an appropriate decomposition method,we propose a classification criterion based on the form of system state variables,i.e.,type-I vector fields that can be directly decomposed and type-II vector fields decomposed via exterior differentiation.Moreover,exterior differentiation is used to represent the curl of low-high dimension vector fields in the process of decomposition.Finally,we exemplify the Hamilton energy function of six classical systems and analyze the relationship between Hamilton energy and dynamic behavior.This solution provides a new approach for deducing the Hamilton energy function,especially in high-dimensional systems.展开更多
The distribution of data has a significant impact on the results of classification.When the distribution of one class is insignificant compared to the distribution of another class,data imbalance occurs.This will resu...The distribution of data has a significant impact on the results of classification.When the distribution of one class is insignificant compared to the distribution of another class,data imbalance occurs.This will result in rising outlier values and noise.Therefore,the speed and performance of classification could be greatly affected.Given the above problems,this paper starts with the motivation and mathematical representing of classification,puts forward a new classification method based on the relationship between different classification formulations.Combined with the vector characteristics of the actual problem and the choice of matrix characteristics,we firstly analyze the orderly regression to introduce slack variables to solve the constraint problem of the lone point.Then we introduce the fuzzy factors to solve the problem of the gap between the isolated points on the basis of the support vector machine.We introduce the cost control to solve the problem of sample skew.Finally,based on the bi-boundary support vector machine,a twostep weight setting twin classifier is constructed.This can help to identify multitasks with feature-selected patterns without the need for additional optimizers,which solves the problem of large-scale classification that can’t deal effectively with the very low category distribution gap.展开更多
The vector vortex beam(VVB)has attracted significant attention due to its intrinsic diversity of information and has found great applications in both classical and quantum communications.However,a VVB is unavoidably a...The vector vortex beam(VVB)has attracted significant attention due to its intrinsic diversity of information and has found great applications in both classical and quantum communications.However,a VVB is unavoidably affected by atmospheric turbulence(AT)when it propagates through the free-space optical communication environment,which results in detection errors at the receiver.In this paper,we propose a VVB classification scheme to detect VVBs with continuously changing polarization states under AT,where a diffractive deep neural network(DDNN)is designed and trained to classify the intensity distribution of the input distorted VVBs,and the horizontal direction of polarization of the input distorted beam is adopted as the feature for the classification through the DDNN.The numerical simulations and experimental results demonstrate that the proposed scheme has high accuracy in classification tasks.The energy distribution percentage remains above 95%from weak to medium AT,and the classification accuracy can remain above 95%for various strengths of turbulence.It has a faster convergence and better accuracy than that based on a convolutional neural network.展开更多
The perfect hybrid vector vortex beam(PHVVB)with helical phase wavefront structure has aroused significant concern in recent years,as its beam waist does not expand with the topological charge(TC).In this work,we inve...The perfect hybrid vector vortex beam(PHVVB)with helical phase wavefront structure has aroused significant concern in recent years,as its beam waist does not expand with the topological charge(TC).In this work,we investigate the spatial quantum coherent modulation effect with PHVVB based on the atomic medium,and we observe the absorption characteristic of the PHVVB with different TCs under variant magnetic fields.We find that the transmission spectrum linewidth of PHVVB can be effectively maintained regardless of the TC.Still,the width of transmission peaks increases slightly as the beam size expands in hot atomic vapor.This distinctive quantum coherence phenomenon,demonstrated by the interaction of an atomic medium with a hybrid vector-structured beam,might be anticipated to open up new opportunities for quantum coherence modulation and accurate magnetic field measurement.展开更多
The application of the vector magnetometry based on nitrogen-vacancy(NV)ensembles has been widely investigatedin multiple areas.It has the superiority of high sensitivity and high stability in ambient conditions with ...The application of the vector magnetometry based on nitrogen-vacancy(NV)ensembles has been widely investigatedin multiple areas.It has the superiority of high sensitivity and high stability in ambient conditions with microscale spatialresolution.However,a bias magnetic field is necessary to fully separate the resonance lines of optically detected magneticresonance(ODMR)spectrum of NV ensembles.This brings disturbances in samples being detected and limits the rangeof application.Here,we demonstrate a method of vector magnetometry in zero bias magnetic field using NV ensembles.By utilizing the anisotropy property of fluorescence excited from NV centers,we analyzed the ODMR spectrum of NVensembles under various polarized angles of excitation laser in zero bias magnetic field with a quantitative numerical modeland reconstructed the magnetic field vector.The minimum magnetic field modulus that can be resolved accurately is downto~0.64 G theoretically depending on the ODMR spectral line width(1.8 MHz),and~2 G experimentally due to noisesin fluorescence signals and errors in calibration.By using 13C purified and low nitrogen concentration diamond combinedwith improving calibration of unknown parameters,the ODMR spectral line width can be further decreased below 0.5 MHz,corresponding to~0.18 G minimum resolvable magnetic field modulus.展开更多
为了探究Vector 3D Tiles格式在三维矢量地物表达方面的效果和性能,研究了一套Vector 3D Tiles格式生产和表达工具,用于在Cesium平台上对矢量数据进行可视化展示。主要工作包括两部分:一是将数据从传统的矢量格式转换为Vector 3D Tiles...为了探究Vector 3D Tiles格式在三维矢量地物表达方面的效果和性能,研究了一套Vector 3D Tiles格式生产和表达工具,用于在Cesium平台上对矢量数据进行可视化展示。主要工作包括两部分:一是将数据从传统的矢量格式转换为Vector 3D Tiles格式,二是在Cesium平台上展示转换后的Vector 3D Tiles数据。为了验证方法可行性,采用广州市地下管线数据开展了实验,对Shapefile、GeoJSON二维矢量格式进行处理,生成Vector 3D Tiles格式后,在Cesium平台上进行三维可视化展示。通过不同格式数据的加载效率和呈现效果比较,证明了矢量切片数据比原始矢量格式加载更快、渲染更平滑。在此基础上,对矢量切片数据基于自定义三维样式的渲染能力进行了验证。展开更多
基金supported by the National key R and D Program of China 2020YFA0713100the NSFC(12141104,12371062 and 12431004).
文摘In this paper,we obtain a vector bundle valued mixed hard Lefschetz theorem.The argument is mainly based on the works of Tien-Cuong Dinh and Viet-Anh Nguyen.
基金Supported by National Natural Science Foundation of China(Grant No.12475002).
文摘In this paper,we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors.We first give the varieties of semi-conformal vectors of a family of vertex operator algebras V_(√kA_(1)) associated to rank-one positive definite even lattices √kA_(1) for arbitrary positive integers k to characterize these even lattice vertex operator algebras.In such a family of lattice vertex operator algebras V_(√kA_(1)),the vertex operator algebra V_(√2A_(1)) is different from others.Hence we describe the varieties of semi-conformal vectors of V_(√2A_(1)) and the fixed vertex operator subalgebra V^(+)√2A_(1).Moreover,as applications,we study the relations between vertex operator algebras V_(√kA_(1) )and L_(sl_(2))(k,0)for arbitrary positive integers k by the viewpoint of semi-conformal homomorphisms of vertex operator algebras.For case k=2,in the series of rational simple affine vertex operator algebras L_(sl_(2))(k,0)for positive integers k,we show that L_(sl_(2))(2,0)is a unique frame vertex operator algebra with rank 3.
基金the financial support from National Natural Science Foundation of China (Nos. 62192771, 12374344, 12221004)National Key Research and Development Program of China (2022YFA1204700, 2020YFA0710100)+1 种基金Natural Science Foundation of Shanghai (Grant No. 23dz2260100)China Postdoctoral Science Foundation 2021TQ0077
文摘On-chip devices for generating pre-designed vectorial optical fields(VOFs)under surface wave(SW)excitations are highly desired in integrated photonics.However,conventional devices are usually of large footprints,low efficiencies,and limited wave-control capabilities.Here,we present a generic approach to design ultra-compact on-chip devices that can efficiently generate pre-designed VOFs under SW excitations,and experimentally verify the concept in terahertz(THz)regime.We first describe how to design SW-excitation metasurfaces for generating circularly polarized complex beams,and experimentally demonstrate two meta-devices to realize directional emission and focusing of THz waves with oppo-site circular polarizations,respectively.We then establish a systematic approach to construct an integrated device via merging two carefully designed metasurfaces,which,under SW excitations,can separately produce pre-designed far-field patterns with different circular polarizations and generate target VOF based on their interference.As a proof of con-cept,we demonstrate experimentally a meta-device that can generate a radially polarized Bessel beam under SW excita-tion at~0.4 THz.Experimental results agree well with full-wave simulations,collectively verifying the performance of our device.Our study paves the road to realizing highly integrated on-chip functional THz devices,which may find many ap-plications in biological sensing,communications,displays,image multiplexing,and beyond.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12033007,61801458,12103058,12203058,12074309,and 61875205)the Key Project of Frontier Science Research of the Chinese Academy of Sciences(Grant No.QYZDB-SSW-SLH007)+2 种基金the Strategic Priority Research Program of CAS(Grant No.XDC07020200)the Youth Innovation Promotion Association,CAS(Grant Nos.2021408,2022413,and 2023425)the Research on Highly Sensitive Long-Wave Receiver Based on Rydberg Atoms(Grant No.1P2024000059)。
文摘The Bessel-like vector vortex beam(BlVVB)has gained increasing significance across numerous applications.However,its practical application is restricted by manufacturing difficulties and polarization manipulation.Thus,the ability to manipulate its degrees of freedom is highly desirable.In this paper,the full-domain polarization modulation of BlVVB within a hot atomic ensemble has been investigated.We begin with the theoretical analysis of the resonant magneto-optical effect of atoms with a horizontal linear-polarized beam and experimentally demonstrate precise manipulation of the polarization state across the entire domain of the BlVVB,achieving an error margin of less than 3°at various cross-sectional points.Our study provides a novel approach for the modulation of BlVVB based on atomic media,which holds potential applications in sensitive vector magnetometers,optical communications,and signal processing.
文摘Accurate positioning is one of the essential requirements for numerous applications of remote sensing data,especially in the event of a noisy or unreliable satellite signal.Toward this end,we present a novel framework for aircraft geo-localization in a large range that only requires a downward-facing monocular camera,an altimeter,a compass,and an open-source Vector Map(VMAP).The algorithm combines the matching and particle filter methods.Shape vector and correlation between two building contour vectors are defined,and a coarse-to-fine building vector matching(CFBVM)method is proposed in the matching stage,for which the original matching results are described by the Gaussian mixture model(GMM).Subsequently,an improved resampling strategy is designed to reduce computing expenses with a huge number of initial particles,and a credibility indicator is designed to avoid location mistakes in the particle filter stage.An experimental evaluation of the approach based on flight data is provided.On a flight at a height of 0.2 km over a flight distance of 2 km,the aircraft is geo-localized in a reference map of 11,025 km~2using 0.09 km~2aerial images without any prior information.The absolute localization error is less than 10 m.
基金the National Natural Science Foundation of China(Grant Nos.12305054,12172340,and 12371506)。
文摘Hamilton energy,which reflects the energy variation of systems,is one of the crucial instruments used to analyze the characteristics of dynamical systems.Here we propose a method to deduce Hamilton energy based on the existing systems.This derivation process consists of three steps:step 1,decomposing the vector field;step 2,solving the Hamilton energy function;and step 3,verifying uniqueness.In order to easily choose an appropriate decomposition method,we propose a classification criterion based on the form of system state variables,i.e.,type-I vector fields that can be directly decomposed and type-II vector fields decomposed via exterior differentiation.Moreover,exterior differentiation is used to represent the curl of low-high dimension vector fields in the process of decomposition.Finally,we exemplify the Hamilton energy function of six classical systems and analyze the relationship between Hamilton energy and dynamic behavior.This solution provides a new approach for deducing the Hamilton energy function,especially in high-dimensional systems.
基金Hebei Province Key Research and Development Project(No.20313701D)Hebei Province Key Research and Development Project(No.19210404D)+13 种基金Mobile computing and universal equipment for the Beijing Key Laboratory Open Project,The National Social Science Fund of China(17AJL014)Beijing University of Posts and Telecommunications Construction of World-Class Disciplines and Characteristic Development Guidance Special Fund “Cultural Inheritance and Innovation”Project(No.505019221)National Natural Science Foundation of China(No.U1536112)National Natural Science Foundation of China(No.81673697)National Natural Science Foundation of China(61872046)The National Social Science Fund Key Project of China(No.17AJL014)“Blue Fire Project”(Huizhou)University of Technology Joint Innovation Project(CXZJHZ201729)Industry-University Cooperation Cooperative Education Project of the Ministry of Education(No.201902218004)Industry-University Cooperation Cooperative Education Project of the Ministry of Education(No.201902024006)Industry-University Cooperation Cooperative Education Project of the Ministry of Education(No.201901197007)Industry-University Cooperation Collaborative Education Project of the Ministry of Education(No.201901199005)The Ministry of Education Industry-University Cooperation Collaborative Education Project(No.201901197001)Shijiazhuang science and technology plan project(236240267A)Hebei Province key research and development plan project(20312701D)。
文摘The distribution of data has a significant impact on the results of classification.When the distribution of one class is insignificant compared to the distribution of another class,data imbalance occurs.This will result in rising outlier values and noise.Therefore,the speed and performance of classification could be greatly affected.Given the above problems,this paper starts with the motivation and mathematical representing of classification,puts forward a new classification method based on the relationship between different classification formulations.Combined with the vector characteristics of the actual problem and the choice of matrix characteristics,we firstly analyze the orderly regression to introduce slack variables to solve the constraint problem of the lone point.Then we introduce the fuzzy factors to solve the problem of the gap between the isolated points on the basis of the support vector machine.We introduce the cost control to solve the problem of sample skew.Finally,based on the bi-boundary support vector machine,a twostep weight setting twin classifier is constructed.This can help to identify multitasks with feature-selected patterns without the need for additional optimizers,which solves the problem of large-scale classification that can’t deal effectively with the very low category distribution gap.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62375140 and 62001249)the Open Research Fund of National Laboratory of Solid State Microstructures(Grant No.M36055).
文摘The vector vortex beam(VVB)has attracted significant attention due to its intrinsic diversity of information and has found great applications in both classical and quantum communications.However,a VVB is unavoidably affected by atmospheric turbulence(AT)when it propagates through the free-space optical communication environment,which results in detection errors at the receiver.In this paper,we propose a VVB classification scheme to detect VVBs with continuously changing polarization states under AT,where a diffractive deep neural network(DDNN)is designed and trained to classify the intensity distribution of the input distorted VVBs,and the horizontal direction of polarization of the input distorted beam is adopted as the feature for the classification through the DDNN.The numerical simulations and experimental results demonstrate that the proposed scheme has high accuracy in classification tasks.The energy distribution percentage remains above 95%from weak to medium AT,and the classification accuracy can remain above 95%for various strengths of turbulence.It has a faster convergence and better accuracy than that based on a convolutional neural network.
基金Project supported by the Youth Innovation Promotion Association CASState Key Laboratory of Transient Optics and Photonics Open Topics (Grant No. SKLST202222)
文摘The perfect hybrid vector vortex beam(PHVVB)with helical phase wavefront structure has aroused significant concern in recent years,as its beam waist does not expand with the topological charge(TC).In this work,we investigate the spatial quantum coherent modulation effect with PHVVB based on the atomic medium,and we observe the absorption characteristic of the PHVVB with different TCs under variant magnetic fields.We find that the transmission spectrum linewidth of PHVVB can be effectively maintained regardless of the TC.Still,the width of transmission peaks increases slightly as the beam size expands in hot atomic vapor.This distinctive quantum coherence phenomenon,demonstrated by the interaction of an atomic medium with a hybrid vector-structured beam,might be anticipated to open up new opportunities for quantum coherence modulation and accurate magnetic field measurement.
基金supported by the National Key R&D Program of China(Grant Nos.2021YFB3202800 and 2023YF0718400)Chinese Academy of Sciences(Grant No.ZDZBGCH2021002)+2 种基金Chinese Academy of Sciences(Grant No.GJJSTD20200001)Innovation Program for Quantum Science and Technology(Grant No.2021ZD0303204)Anhui Initiative in Quantum Information Technologies,USTC Tang Scholar,and the Fundamental Research Funds for the Central Universities.
文摘The application of the vector magnetometry based on nitrogen-vacancy(NV)ensembles has been widely investigatedin multiple areas.It has the superiority of high sensitivity and high stability in ambient conditions with microscale spatialresolution.However,a bias magnetic field is necessary to fully separate the resonance lines of optically detected magneticresonance(ODMR)spectrum of NV ensembles.This brings disturbances in samples being detected and limits the rangeof application.Here,we demonstrate a method of vector magnetometry in zero bias magnetic field using NV ensembles.By utilizing the anisotropy property of fluorescence excited from NV centers,we analyzed the ODMR spectrum of NVensembles under various polarized angles of excitation laser in zero bias magnetic field with a quantitative numerical modeland reconstructed the magnetic field vector.The minimum magnetic field modulus that can be resolved accurately is downto~0.64 G theoretically depending on the ODMR spectral line width(1.8 MHz),and~2 G experimentally due to noisesin fluorescence signals and errors in calibration.By using 13C purified and low nitrogen concentration diamond combinedwith improving calibration of unknown parameters,the ODMR spectral line width can be further decreased below 0.5 MHz,corresponding to~0.18 G minimum resolvable magnetic field modulus.
文摘为了探究Vector 3D Tiles格式在三维矢量地物表达方面的效果和性能,研究了一套Vector 3D Tiles格式生产和表达工具,用于在Cesium平台上对矢量数据进行可视化展示。主要工作包括两部分:一是将数据从传统的矢量格式转换为Vector 3D Tiles格式,二是在Cesium平台上展示转换后的Vector 3D Tiles数据。为了验证方法可行性,采用广州市地下管线数据开展了实验,对Shapefile、GeoJSON二维矢量格式进行处理,生成Vector 3D Tiles格式后,在Cesium平台上进行三维可视化展示。通过不同格式数据的加载效率和呈现效果比较,证明了矢量切片数据比原始矢量格式加载更快、渲染更平滑。在此基础上,对矢量切片数据基于自定义三维样式的渲染能力进行了验证。
