Face recognition(FR) is a practical application of pattern recognition(PR) and remains a compelling topic in the study of computer vision. However, in real-world FR systems, interferences in images, including illumina...Face recognition(FR) is a practical application of pattern recognition(PR) and remains a compelling topic in the study of computer vision. However, in real-world FR systems, interferences in images, including illumination condition, occlusion, facial expression and pose variation, make the recognition task challenging. This study explored the impact of those interferences on FR performance and attempted to alleviate it by taking face symmetry into account. A novel and robust FR method was proposed by combining multi-mirror symmetry with local binary pattern(LBP), namely multi-mirror local binary pattern(MMLBP). To enhance FR performance with various interferences, the MMLBP can 1) adaptively compensate lighting under heterogeneous lighting conditions, and 2) generate extracted image features that are much closer to those under well-controlled conditions(i.e., frontal facial images without expression). Therefore, in contrast with the later variations of LBP, the symmetrical singular value decomposition representation(SSVDR) algorithm utilizing the facial symmetry and a state-of-art non-LBP method, the MMLBP method is shown to successfully handle various image interferences that are common in FR applications without preprocessing operation and a large number of training images. The proposed method was validated with four public data sets. According to our analysis, the MMLBP method was demonstrated to achieve robust performance regardless of image interferences.展开更多
We introduce the notion of ungraded matrix factorization as a mirror of non-orientable Lagrangian submanifolds.An ungraded matrix factorization of a polynomial W,with coefficients in a field of characteristic 2,is a s...We introduce the notion of ungraded matrix factorization as a mirror of non-orientable Lagrangian submanifolds.An ungraded matrix factorization of a polynomial W,with coefficients in a field of characteristic 2,is a square matrix Q of polynomial entries satisfying Q^(2)=W·Id.We then show that non-orientable Lagrangians correspond to ungraded matrix factorizations under the localized mirror functor and illustrate this construction in a few instances.Our main example is the Lagrangian submanifold RP^(2)⊂CP^(2)and its mirror ungraded matrix factorization,which we construct and study.In particular,we prove a version of Homological Mirror Symmetry in this setting.展开更多
In the standard model QCD Lagrangian,a term of CP violating gluon density is theoretically expected to have a physical coefficientθ¯,which is typically on the order of unity.However,the upper bound on the electr...In the standard model QCD Lagrangian,a term of CP violating gluon density is theoretically expected to have a physical coefficientθ¯,which is typically on the order of unity.However,the upper bound on the electric dipole moment of the neutron enforces the value ofθ¯to be extremely small.The significant discrepancy between theoretical expectations and experimental results in this context is widely recognized as the strong CP problem.To solve this puzzle in an appealing context of two Higgs doublets,we propose aθ¯-characterized mirror symmetry between two Higgs singlets with respective discrete symmetries.In our scenario,the parameterθ¯can completely disappear from the full Lagrangian after the standard model fermions take a proper phase rotation as well as the Higgs doublets and singlets.Moreover,all of new physics for solving the strong CP problem can be allowed near the TeV scale.展开更多
This paper,largely written in 2009/2010,fits Landau-Ginzburg models into the mirror symmetry program pursued by the last author jointly with Mark Gross since 2001.This point of view transparently brings in tropical di...This paper,largely written in 2009/2010,fits Landau-Ginzburg models into the mirror symmetry program pursued by the last author jointly with Mark Gross since 2001.This point of view transparently brings in tropical disks of Maslov index 2 via the notion of broken lines,previously introduced in two dimensions by Mark Gross in his study of mirror symmetry for P2.A ma jor insight is the equivalence of properness of the Landau-Ginzburg potential with smoothness of the anticanonical divisor on the mirror side.We obtain proper superpotentials which agree on an open part with those classically known for toric varieties.Examples include mirror LG models for non-singular and singular del Pezzo surfaces,Hirzebruch surfaces and some Fano threefolds.展开更多
Dual topological insulator(DTI),which simultaneously hosts topological insulator(TI)and topological crystalline insulator(TCI)phases,has attracted extensive attention since it has a better robustness of topological na...Dual topological insulator(DTI),which simultaneously hosts topological insulator(TI)and topological crystalline insulator(TCI)phases,has attracted extensive attention since it has a better robustness of topological nature and broad application prospects in spintronics.However,the realization of DTI phase in two-dimensional(2D)system is extremely scarce.By first-principles calculations,we predict that the 2D rectangular bismuth(R–Bi)bilayer is a novel DTI,featured by topological invariant=1,mirror Chern number C_(M)=–1,and metallic edge states within the bulk band gap.More interestingly,the TCI phase in bilayer is protected by horizontal glide mirror symmetries,rather than the usual mirror symmetry.The bulk band gap can be effectively tuned by vertical electric field and strain.Besides,the electric field can trigger the transition between TI and metallic phases for the bilayer,accompanied by the annihilation of TCI phase.On this basis,a topological field effect transistor is proposed,which can rapidly manipulate spin and charge carriers via electric field.The KBr(110)surface is demonstrated as an ideal substrate for the deposition of bilayer.These findings provide not only a new strategy for exploiting 2D DTI,but also a promising candidate for spintronic applications.展开更多
This paper presents Symm Sketch—a system for creating symmetric 3D free-form shapes from 2D sketches. The reconstruction task usually separates a 3D symmetric shape into two types of shape components, that is, the se...This paper presents Symm Sketch—a system for creating symmetric 3D free-form shapes from 2D sketches. The reconstruction task usually separates a 3D symmetric shape into two types of shape components, that is, the self-symmetric shape component and the mutual-symmetric shape components. Each type can be created in an intuitive manner. Using a uniform symmetry plane, the user first draws 2D sketch lines for each shape component on a sketching plane. The z-depth information of the hand-drawn input sketches can be calculated using their property of mirror symmetry to generate 3D construction curves. In order to provide more freedom for controlling the local geometric features of the reconstructed free-form shapes(e.g., non-circular crosssections), our modeling system creates each shape component from four construction curves. Using one pair of symmetric curves and one pair of general curves, an improved cross-sectional surface blending scheme is applied to generate a parametric surface for each component. The final symmetric free-form shape is progressively created, and is represented by 3D triangular mesh. Experimental results illustrate that our system can generate complex symmetric free-form shapes effectively and conveniently.展开更多
Nodal-line semimetals have become a research hot-spot due to their novel properties and great potential application in spin electronics. It is more challenging to find 2D nodal-line semimetals that can resist the spin...Nodal-line semimetals have become a research hot-spot due to their novel properties and great potential application in spin electronics. It is more challenging to find 2D nodal-line semimetals that can resist the spin–orbit coupling(SOC)effect. Here, we predict that 2D tetragonal Zn B is a nodal-line semimetal with great transport properties. There are two crossing bands centered on the S point at the Fermi surface without SOC, which are mainly composed of the pxy orbitals of Zn and B atoms and the pz orbitals of the B atom. Therefore, the system presents a nodal line centered on the S point in its Brillouin zone(BZ). And the nodal line is protected by the horizontal mirror symmetry M_(z). We further examine the robustness of a nodal line under biaxial strain by applying up to-4% in-plane compressive strain and 5% tensile strain on the Zn B monolayer, respectively. The transmission along the a direction is significantly stronger than that along the b direction in the conductive channel. The current in the a direction is as high as 26.63 μA at 0.8 V, and that in the b direction reaches 8.68 μA at 0.8 V. It is interesting that the transport characteristics of Zn B show the negative differential resistance(NDR) effect after 0.8 V along the a(b) direction. The results provide an ideal platform for research of fundamental physics of 2D nodal-line fermions and nanoscale spintronics, as well as the design of new quantum devices.展开更多
基金supported by National Natural Science Foundation of China (No. 51305392)Youth Funds of the State Key Laboratory of Fluid Power Transmission and Control (No. SKLoFP_QN_1501)+1 种基金Zhejiang Provincial Natural Science Foundation of China (Nos. LY17E050009 and LZ15E050001)the Fundamental Rsesearch Funds for the Central Universities (No. 2018QNA4008)
文摘Face recognition(FR) is a practical application of pattern recognition(PR) and remains a compelling topic in the study of computer vision. However, in real-world FR systems, interferences in images, including illumination condition, occlusion, facial expression and pose variation, make the recognition task challenging. This study explored the impact of those interferences on FR performance and attempted to alleviate it by taking face symmetry into account. A novel and robust FR method was proposed by combining multi-mirror symmetry with local binary pattern(LBP), namely multi-mirror local binary pattern(MMLBP). To enhance FR performance with various interferences, the MMLBP can 1) adaptively compensate lighting under heterogeneous lighting conditions, and 2) generate extracted image features that are much closer to those under well-controlled conditions(i.e., frontal facial images without expression). Therefore, in contrast with the later variations of LBP, the symmetrical singular value decomposition representation(SSVDR) algorithm utilizing the facial symmetry and a state-of-art non-LBP method, the MMLBP method is shown to successfully handle various image interferences that are common in FR applications without preprocessing operation and a large number of training images. The proposed method was validated with four public data sets. According to our analysis, the MMLBP method was demonstrated to achieve robust performance regardless of image interferences.
基金supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(Grant No.2020R1A5A1016126)。
文摘We introduce the notion of ungraded matrix factorization as a mirror of non-orientable Lagrangian submanifolds.An ungraded matrix factorization of a polynomial W,with coefficients in a field of characteristic 2,is a square matrix Q of polynomial entries satisfying Q^(2)=W·Id.We then show that non-orientable Lagrangians correspond to ungraded matrix factorizations under the localized mirror functor and illustrate this construction in a few instances.Our main example is the Lagrangian submanifold RP^(2)⊂CP^(2)and its mirror ungraded matrix factorization,which we construct and study.In particular,we prove a version of Homological Mirror Symmetry in this setting.
基金Supported in part by the National Natural Science Foundation of China (12175038)and in part by the Fundamental Research Funds for the Central Universities。
文摘In the standard model QCD Lagrangian,a term of CP violating gluon density is theoretically expected to have a physical coefficientθ¯,which is typically on the order of unity.However,the upper bound on the electric dipole moment of the neutron enforces the value ofθ¯to be extremely small.The significant discrepancy between theoretical expectations and experimental results in this context is widely recognized as the strong CP problem.To solve this puzzle in an appealing context of two Higgs doublets,we propose aθ¯-characterized mirror symmetry between two Higgs singlets with respective discrete symmetries.In our scenario,the parameterθ¯can completely disappear from the full Lagrangian after the standard model fermions take a proper phase rotation as well as the Higgs doublets and singlets.Moreover,all of new physics for solving the strong CP problem can be allowed near the TeV scale.
基金supported by the Studienstiftung des deutschen Volkessupported by NSF grant DMS-1903437。
文摘This paper,largely written in 2009/2010,fits Landau-Ginzburg models into the mirror symmetry program pursued by the last author jointly with Mark Gross since 2001.This point of view transparently brings in tropical disks of Maslov index 2 via the notion of broken lines,previously introduced in two dimensions by Mark Gross in his study of mirror symmetry for P2.A ma jor insight is the equivalence of properness of the Landau-Ginzburg potential with smoothness of the anticanonical divisor on the mirror side.We obtain proper superpotentials which agree on an open part with those classically known for toric varieties.Examples include mirror LG models for non-singular and singular del Pezzo surfaces,Hirzebruch surfaces and some Fano threefolds.
基金supported by the National Natural Science Foundation of China(Grant No.12004137)the Taishan Scholar Project of Shandong Province(No.ts20190939)the Natural Science Foundation of Shandong Province(Grant No.ZR2020QA052).
文摘Dual topological insulator(DTI),which simultaneously hosts topological insulator(TI)and topological crystalline insulator(TCI)phases,has attracted extensive attention since it has a better robustness of topological nature and broad application prospects in spintronics.However,the realization of DTI phase in two-dimensional(2D)system is extremely scarce.By first-principles calculations,we predict that the 2D rectangular bismuth(R–Bi)bilayer is a novel DTI,featured by topological invariant=1,mirror Chern number C_(M)=–1,and metallic edge states within the bulk band gap.More interestingly,the TCI phase in bilayer is protected by horizontal glide mirror symmetries,rather than the usual mirror symmetry.The bulk band gap can be effectively tuned by vertical electric field and strain.Besides,the electric field can trigger the transition between TI and metallic phases for the bilayer,accompanied by the annihilation of TCI phase.On this basis,a topological field effect transistor is proposed,which can rapidly manipulate spin and charge carriers via electric field.The KBr(110)surface is demonstrated as an ideal substrate for the deposition of bilayer.These findings provide not only a new strategy for exploiting 2D DTI,but also a promising candidate for spintronic applications.
基金supported by the National Natural Science Foundation of China under Grant Nos. 61272309 and 61303138
文摘This paper presents Symm Sketch—a system for creating symmetric 3D free-form shapes from 2D sketches. The reconstruction task usually separates a 3D symmetric shape into two types of shape components, that is, the self-symmetric shape component and the mutual-symmetric shape components. Each type can be created in an intuitive manner. Using a uniform symmetry plane, the user first draws 2D sketch lines for each shape component on a sketching plane. The z-depth information of the hand-drawn input sketches can be calculated using their property of mirror symmetry to generate 3D construction curves. In order to provide more freedom for controlling the local geometric features of the reconstructed free-form shapes(e.g., non-circular crosssections), our modeling system creates each shape component from four construction curves. Using one pair of symmetric curves and one pair of general curves, an improved cross-sectional surface blending scheme is applied to generate a parametric surface for each component. The final symmetric free-form shape is progressively created, and is represented by 3D triangular mesh. Experimental results illustrate that our system can generate complex symmetric free-form shapes effectively and conveniently.
基金Project supported by the Natural Science Foundation of Shandong Province, China (Grant No. ZR2019MA041)Taishan Scholar Project of Shandong Province, China (Grant No. ts20190939)the National Natural Science Foundation of China (Grant No. 62071200)。
文摘Nodal-line semimetals have become a research hot-spot due to their novel properties and great potential application in spin electronics. It is more challenging to find 2D nodal-line semimetals that can resist the spin–orbit coupling(SOC)effect. Here, we predict that 2D tetragonal Zn B is a nodal-line semimetal with great transport properties. There are two crossing bands centered on the S point at the Fermi surface without SOC, which are mainly composed of the pxy orbitals of Zn and B atoms and the pz orbitals of the B atom. Therefore, the system presents a nodal line centered on the S point in its Brillouin zone(BZ). And the nodal line is protected by the horizontal mirror symmetry M_(z). We further examine the robustness of a nodal line under biaxial strain by applying up to-4% in-plane compressive strain and 5% tensile strain on the Zn B monolayer, respectively. The transmission along the a direction is significantly stronger than that along the b direction in the conductive channel. The current in the a direction is as high as 26.63 μA at 0.8 V, and that in the b direction reaches 8.68 μA at 0.8 V. It is interesting that the transport characteristics of Zn B show the negative differential resistance(NDR) effect after 0.8 V along the a(b) direction. The results provide an ideal platform for research of fundamental physics of 2D nodal-line fermions and nanoscale spintronics, as well as the design of new quantum devices.
