In a majority of cases of long-time numerical integration for initial-value problems, roundoff error has received little attention. Using twenty-nine numerical methods, the influence of round-off error on numerical so...In a majority of cases of long-time numerical integration for initial-value problems, roundoff error has received little attention. Using twenty-nine numerical methods, the influence of round-off error on numerical solutions is generally studied through a large number of numerical experiments. Here we find that there exists a strong dependence on machine precision (which is a new kind of dependence different from the sensitive dependence on initial conditions), maximally effective computation time (MECT) and optimal stepsize (OS) in solving nonlinear ordinary differential equations (ODEs) in finite machine precision. And an optimal searching method for evaluating MECT and OS under finite machine precision is presented. The relationships between MECT, OS, the order of numerical method and machine precision are found. Numerical results show that round-off error plays a significant role in the above phenomena. Moreover, we find two universal relations which are independent of the types of ODEs, initial values and numerical schemes. Based on the results of numerical experiments, we present a computational uncertainty principle, which is a great challenge to the reliability of long-time numerical integration for nonlinear ODEs.展开更多
The error propagation for general numerical method in ordinarydifferential equations ODEs is studied. Three kinds of convergence, theoretical, numerical and actual convergences, are presented. The various components o...The error propagation for general numerical method in ordinarydifferential equations ODEs is studied. Three kinds of convergence, theoretical, numerical and actual convergences, are presented. The various components of round-off error occurring in floating-point computation are fully detailed. By introducing a new kind of recurrent inequality, the classical error bounds for linear multistep methods are essentially improved, and joining probabilistic theory the “normal” growth of accumulated round-off error is derived. Moreover, a unified estimate for the total error of general method is given. On the basis of these results, we rationally interpret the various phenomena found in the numerical experiments in part I of this paper and derive two universal relations which are independent of types of ODEs, initial values and numerical schemes and are consistent with the numerical results. Furthermore, we give the explicitly mathematical expression of the computational uncertainty principle and expound the intrinsic relation between two uncertainties which result from the inaccuracies of numerical method and calculating machine.展开更多
In this work we investigate the possibility to represent physical fields as Einstein manifold. Based on the Einstein field equations in general relativity, we establish a general formulation for determining the metric...In this work we investigate the possibility to represent physical fields as Einstein manifold. Based on the Einstein field equations in general relativity, we establish a general formulation for determining the metric tensor of the Einstein manifold that represents a physical field in terms of the energy-momentum tensor that characterises the physical field. As illustrations, we first apply the general formulation to represent the perfect fluid as Einstein manifold. However, from the established relation between the metric tensor and the energy-momentum tensor, we show that if the trace of the energy-momentum tensor associated with a physical field is equal to zero then the corresponding physical field cannot be represented as an Einstein manifold. This situation applies to the electromagnetic field since the trace of the energy-momentum of the electromagnetic field vanishes. Nevertheless, we show that a system that consists of the electromagnetic field and non-interacting charged particles can be represented as an Einstein manifold since the trace of the corresponding energy-momentum of the system no longer vanishes. As a further investigation, we show that it is also possible to represent physical fields as maximally symmetric spaces of constant scalar curvature.展开更多
A {(3,4), 4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S...A {(3,4), 4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating.Let k be a positive integer,S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern.Moreover,if graph S is k-resonant for any integer k,then S is called maximally resonant.In this paper,we show that the maximally resonant{(3,4),4}-fullerene graphs are S_6,S_8,S_(10)~2,S_(12)~2,S_(12)~4,S_(12)~5,S_(14)~3,S_(14)~5,S_(16)~3,S_(18)~5,S_(24) as shown in Fig.1.As a corollary,it is shown that if a {(3,4),4}-fullerene graph is 4-resonant,then it is also maximally resonant.展开更多
This paper deals with the representation of the solutions of a polynomial system, and concentrates on the high-dimensional case. Based on the rational univari- ate representation of zero-dimensional polynomial systems...This paper deals with the representation of the solutions of a polynomial system, and concentrates on the high-dimensional case. Based on the rational univari- ate representation of zero-dimensional polynomial systems, we give a new description called rational representation for the solutions of a high-dimensional polynomial sys- tem and propose an algorithm for computing it. By this way all the solutions of any high-dimensional polynomial system can be represented by a set of so-called rational- representation sets.展开更多
Video text detection is a challenging problem, since video image background is generally complex and its subtitles often have the problems of color bleeding, fuzzy boundaries and low contrast due to video lossy compre...Video text detection is a challenging problem, since video image background is generally complex and its subtitles often have the problems of color bleeding, fuzzy boundaries and low contrast due to video lossy compression and low resolution. In this paper, we propose a robust framework to solve these problems. Firstly, we exploit gradient amplitude map （GAM） to enhance the edge of an input image, which can overcome the problems of color bleeding and fuzzy boundaries. Secondly, a two-direction morphological filtering is developed to filter background noise and enhance the contrast between background and text. Thirdly, maximally stable extremal region （MSER） is applied to detect text regions with two extreme colors, and we use the mean intensity of the regions as the graph cuts＇ label set, and the Euclidean distance of three channels in HSI color space as the graph cuts smooth term, to get optimal segmentations. Finally, we group them into text lines using the geometric characteristics of the text, and then corner detection, multi-frame verification, and some heuristic rules are used to eliminate non-text regions. We test our scheme with some challenging videos, and the results prove that our text detection framework is more robust than previous methods.展开更多
Geometric distortions are simple and effective at- tacks rendering many watermarking methods useless. They make detection and extraction of the embedded watermark difficult or even impossible by destroying the synchro...Geometric distortions are simple and effective at- tacks rendering many watermarking methods useless. They make detection and extraction of the embedded watermark difficult or even impossible by destroying the synchroniza- tion between the watermark reader and the embedded water- mark. In this paper, we propose a blind content-based image watermarking scheme against geometric distortions. Firstly, the MSER detector is adopted to extract a set of maximally stable extremal regions which are affine covariant and robust to geometric distortions and common signal processing. Sec- ondly, every original MSER is fitted into an elliptical region that was proved to be affine invariant. In order to achieve rota- tion invariance, an image normalization process is performed to transform the elliptical regions into circular ones. Finally, watermarks are repeatedly embedded into every circular disk by modifying the wavelet transform coefficients. Experimen- tal results on standard benchmark demonstrate that the pro- posed scheme is robust to geometric distortions as well as common signal processing.展开更多
Let G be a connected graph with vertex set V(G), order n=|V(G)|, minimum degree δ(G) and connectivity κ(G). The graph G is called maximally connected if κ(G) = δ(G). Define the inverse degree of G with no isolated...Let G be a connected graph with vertex set V(G), order n=|V(G)|, minimum degree δ(G) and connectivity κ(G). The graph G is called maximally connected if κ(G) = δ(G). Define the inverse degree of G with no isolated vertices as R(G) =Σv∈V(G)1/d(v) , where d(v) denotes the degree of the vertex v. We show that G is maximally connected if R(G) <1+2/δ + n-2δ+1/((n-1)(n-3)) .展开更多
Based on the first-principles density functional theory electronic structure calculation,we investigate the possible phonon-mediated superconductivity in arsenene,a two-dimensional buckled arsenic atomic sheet,under e...Based on the first-principles density functional theory electronic structure calculation,we investigate the possible phonon-mediated superconductivity in arsenene,a two-dimensional buckled arsenic atomic sheet,under electron doping.We find that the strong superconducting pairing interaction results mainly from the pz-like electrons of arsenic atoms and the A1 phonon mode around the K point,and the superconducting transition temperature can be as high as 30.8 K in the arsenene with 0.2 doped electrons per unit cell and 12%-applied biaxial tensile strain.This transition temperature is about ten times higher than that in the bulk arsenic under high pressure.It is also the highest transition temperature that is predicted for electron-doped two-dimensional elemental superconductors,including graphene,silicene,phosphorene,and borophene.展开更多
To solve the problem of wide-baseline stereo image matching based on multiple cameras,the paper puts forward an image matching method of combining maximally stable extremal regions (MSER) with Scale Invariant Feature ...To solve the problem of wide-baseline stereo image matching based on multiple cameras,the paper puts forward an image matching method of combining maximally stable extremal regions (MSER) with Scale Invariant Feature Transform (SIFT) . It uses MSER to detect feature regions instead of difference of Gaussian. After fitted into elliptical regions,those regions will be normalized into unity circles and represented with SIFT descriptors. The method estimates fundamental matrix and removes outliers by auto-maximum a posteriori sample consensus after initial matching feature points. The experimental results indicate that the method is robust to viewpoint changes,can reduce computational complexity effectively and improve matching accuracy.展开更多
We study analytically the generation of maximally entangled states （MESs） formed by a two-component Bose-Einstein condensate （BEC） trapped in an adiabatically driven single potential well. Under the condition of t...We study analytically the generation of maximally entangled states （MESs） formed by a two-component Bose-Einstein condensate （BEC） trapped in an adiabatically driven single potential well. Under the condition of the linear interaction controlled by a driven field being much stronger than the effective nonlinear interaction between the components, MESs, as some particular cases of superpositions of spin coherent states （SSCS）, may emerge periodically along with not only time evolution but also the equidifferent change of the linear coupling strength at a particular time.展开更多
Starting with the theoretical basis of quantum computing, entanglement has been explored as one of the key resources required for quantum computation, the functional dependence of the entanglement measures on spin cor...Starting with the theoretical basis of quantum computing, entanglement has been explored as one of the key resources required for quantum computation, the functional dependence of the entanglement measures on spin correlation functions has been established and the role of entanglement in implementation of QNN has been emphasized. Necessary and sufficient conditions for the general two-qubit state to be maximally entangled state (MES) have been obtained and a new set of MES constituting a very powerful and reliable eigen basis (different from magic bases) of two-qubit systems has been constructed. In terms of the MES constituting this basis, Bell’s States have been generated and all the qubits of two-qubit system have been obtained. Carrying out the correct computation of XOR function in neural network, it has been shown that QNN requires the proper correlation between the input and output qubits and the presence of appropriate entanglement in the system guarantees this correlation.展开更多
AIMTo determine the long-term effects of selective laser trabeculoplasty (SLT) on intraocular pressure (IOP) and the number of medications used up to 5y following treatment in glaucoma patients receiving maximally tol...AIMTo determine the long-term effects of selective laser trabeculoplasty (SLT) on intraocular pressure (IOP) and the number of medications used up to 5y following treatment in glaucoma patients receiving maximally tolerated medical therapy (MTMT).METHODSThe Wills Eye Hospital Glaucoma Research Center retrospectively reviewed the charts of glaucoma patients who underwent SLT after receiving MTMT. Eyes that did not achieve their target pressure within 3mo following SLT were excluded from the study. Changes in mean IOP and number of glaucoma medications used were analyzed at 1, 3, and 5y following SLT.RESULTSSeventy-five eyes of 67 patients were included in the study. Fifteen eyes that received SLT failed to achieve their target pressure within 3mo and were excluded from the study. The average follow-up time was 37.4mo (±14.4). Mean IOP was significantly reduced 1y after treatment (P=0.005). It was also reduced 3, 5y after treatment without reaching statistical significance (P=0.20 and P=0.072, respectively). There was a significant decrease in mean number of medications used 1, 3, 5y after treatment (P<0.001, P<0.001, and P=0.039, respectively). In the span of 5y, 2 eyes (2.7%) underwent repeat SLT, 7 eyes (9.3%) underwent glaucoma surgery and an additional 3 eyes (4.0%) underwent both.CONCLUSIONSLT significantly reduced the number of glaucoma medications used 5y following treatment in glaucoma patients receiving MTMT. SLT may delay operating-room surgery.展开更多
Let Q be a bounded open domain in R^n with smooth boundaryаΩ.Let X=(X1,X2…,Xm)be a system of general Grushin type vector fields defined onΩand the boundaryаΩis non-characteristic for X.For△x=∑j=1^mXj^2,we den...Let Q be a bounded open domain in R^n with smooth boundaryаΩ.Let X=(X1,X2…,Xm)be a system of general Grushin type vector fields defined onΩand the boundaryаΩis non-characteristic for X.For△x=∑j=1^mXj^2,we denoteλk as the k-th eigenvalue for the bi-subelliptic operator△X2^2 onΩ.In this paper,by using the sharp sub-elliptic estimates and maximally hypoeliptic estimates,we give the optimal lower bound estimates ofλk for the operatork△X^2.展开更多
Let D be a finite and simple digraph with vertex set V(D).The minimum degreeδof a digraph D is defined as the minimum value of its out-degrees and its in-degrees.If D is a digraph with minimum degreeδand edge-connec...Let D be a finite and simple digraph with vertex set V(D).The minimum degreeδof a digraph D is defined as the minimum value of its out-degrees and its in-degrees.If D is a digraph with minimum degreeδand edge-connectivity λ,then λ≤δ.A digraph is maximally edge-connected ifλ=δ.A digraph is called super-edge-connected if every minimum edge-cut consists of edges incident to or from a vertex of minimum degree.In this note we show that a digraph is maximally edge-connected or super-edge-connected if the number of arcs is large enough.展开更多
This paper proposes a scheme to generate, in an ion-trap, a type of multipartite maximally entangled state which was first introduced by Chen et al. [Chen P X, Zhu S Y and Guo G C 2006 Phys. Rev. A 74 032324]. The max...This paper proposes a scheme to generate, in an ion-trap, a type of multipartite maximally entangled state which was first introduced by Chen et al. [Chen P X, Zhu S Y and Guo G C 2006 Phys. Rev. A 74 032324]. The maximum entanglement property of these states is examined. It also demonstrates how to discriminate among these states in the ion-trap.展开更多
The maximally holomorphic functions of a bounded linear operator is introduced and applied to representthe spectrum and characterize the single--valued extension property. The well known results of quasi--nilpo-tent e...The maximally holomorphic functions of a bounded linear operator is introduced and applied to representthe spectrum and characterize the single--valued extension property. The well known results of quasi--nilpo-tent equivalent operators follow easily from the relation of their maximally holomorphie functions.展开更多
The sender shares six-particle maximally entangled states as quantum channel with the receiver. If the quantum channel is secure, the sender performs projective measurements and tells the measurement outcome to the re...The sender shares six-particle maximally entangled states as quantum channel with the receiver. If the quantum channel is secure, the sender performs projective measurements and tells the measurement outcome to the receiver. The receiver performs the unitary transformations and makes projective measurements on his particles to obtain the secret information. Using teleportation, the transmission of three-qubit secret information can be completed in each quantum channel展开更多
In this work,we study the local distinguishability of maximally entangled states(MESs).In particular,we are concerned with whether any fixed number of MESs can be locally distinguishable for sufficiently large dimensi...In this work,we study the local distinguishability of maximally entangled states(MESs).In particular,we are concerned with whether any fixed number of MESs can be locally distinguishable for sufficiently large dimensions.Fan and Tian et al.have already obtained two satisfactory results for the generalized Bell states(GBSs)and the qudit lattice states when applied to prime or prime power dimensions.We construct a general twist-teleportation scheme for any orthonormal basis with MESs that is inspired by the method used in[Phys.Rev.A 70,022304(2004)].Using this teleportation scheme,we obtain a sufficient and necessary condition for one-way distinguishable sets of MESs,which include the GBSs and the qudit lattice states as special cases.Moreover,we present a generalized version of the results in[Phys.Rev.A 92,042320(2015)]for the arbitrary dimensional case.展开更多
A state-dependent proof of Bell's theorem without inequalities using the product state of any two maximally entangled states (Bell states) of two qubits for two observers in an ideal condition, each of which posse...A state-dependent proof of Bell's theorem without inequalities using the product state of any two maximally entangled states (Bell states) of two qubits for two observers in an ideal condition, each of which possesses two qubits,is proposed. It is different from the other proofs in which there exists a fundamental requirement that certain specific suitable Bell states have been chosen. Moreover, in any non-ideal situation, a common Bell inequality independent of the choices of the 16-product states is derived, which is used to test the contradiction between quantum mechanics and local reality theory in the reach of current experimental technology.展开更多
文摘In a majority of cases of long-time numerical integration for initial-value problems, roundoff error has received little attention. Using twenty-nine numerical methods, the influence of round-off error on numerical solutions is generally studied through a large number of numerical experiments. Here we find that there exists a strong dependence on machine precision (which is a new kind of dependence different from the sensitive dependence on initial conditions), maximally effective computation time (MECT) and optimal stepsize (OS) in solving nonlinear ordinary differential equations (ODEs) in finite machine precision. And an optimal searching method for evaluating MECT and OS under finite machine precision is presented. The relationships between MECT, OS, the order of numerical method and machine precision are found. Numerical results show that round-off error plays a significant role in the above phenomena. Moreover, we find two universal relations which are independent of the types of ODEs, initial values and numerical schemes. Based on the results of numerical experiments, we present a computational uncertainty principle, which is a great challenge to the reliability of long-time numerical integration for nonlinear ODEs.
基金This work was supported by the Knowledge Innovation Key Project of Chinese Academy of Sciences inthe Resource Environment Field (KZCX1-203) Outstanding State Key Laboratory Project (Grant No. 49823002) the National Natural Science Foundation of C
文摘The error propagation for general numerical method in ordinarydifferential equations ODEs is studied. Three kinds of convergence, theoretical, numerical and actual convergences, are presented. The various components of round-off error occurring in floating-point computation are fully detailed. By introducing a new kind of recurrent inequality, the classical error bounds for linear multistep methods are essentially improved, and joining probabilistic theory the “normal” growth of accumulated round-off error is derived. Moreover, a unified estimate for the total error of general method is given. On the basis of these results, we rationally interpret the various phenomena found in the numerical experiments in part I of this paper and derive two universal relations which are independent of types of ODEs, initial values and numerical schemes and are consistent with the numerical results. Furthermore, we give the explicitly mathematical expression of the computational uncertainty principle and expound the intrinsic relation between two uncertainties which result from the inaccuracies of numerical method and calculating machine.
文摘In this work we investigate the possibility to represent physical fields as Einstein manifold. Based on the Einstein field equations in general relativity, we establish a general formulation for determining the metric tensor of the Einstein manifold that represents a physical field in terms of the energy-momentum tensor that characterises the physical field. As illustrations, we first apply the general formulation to represent the perfect fluid as Einstein manifold. However, from the established relation between the metric tensor and the energy-momentum tensor, we show that if the trace of the energy-momentum tensor associated with a physical field is equal to zero then the corresponding physical field cannot be represented as an Einstein manifold. This situation applies to the electromagnetic field since the trace of the energy-momentum of the electromagnetic field vanishes. Nevertheless, we show that a system that consists of the electromagnetic field and non-interacting charged particles can be represented as an Einstein manifold since the trace of the corresponding energy-momentum of the system no longer vanishes. As a further investigation, we show that it is also possible to represent physical fields as maximally symmetric spaces of constant scalar curvature.
基金Supported by NSFC(Grant Nos.11801148 and 11626089)the Foundation for the Doctor of Henan Polytechnic University(Grant No.B2014-060)。
文摘A {(3,4), 4}-fullerene graph S is a 4-regular map on the sphere whose faces are of length 3 or 4.It follows from Euler s formula that the number of triangular faces is eight.A set H of disjoint quadrangular faces of S is called resonant pattern if S has a perfect matching M such that every quadrangular face in H is M-alternating.Let k be a positive integer,S is k-resonant if any i≤k disjoint quadrangular faces of S form a resonant pattern.Moreover,if graph S is k-resonant for any integer k,then S is called maximally resonant.In this paper,we show that the maximally resonant{(3,4),4}-fullerene graphs are S_6,S_8,S_(10)~2,S_(12)~2,S_(12)~4,S_(12)~5,S_(14)~3,S_(14)~5,S_(16)~3,S_(18)~5,S_(24) as shown in Fig.1.As a corollary,it is shown that if a {(3,4),4}-fullerene graph is 4-resonant,then it is also maximally resonant.
基金The National Grand Fundamental Research 973 Program (2004CB318000) of China
文摘This paper deals with the representation of the solutions of a polynomial system, and concentrates on the high-dimensional case. Based on the rational univari- ate representation of zero-dimensional polynomial systems, we give a new description called rational representation for the solutions of a high-dimensional polynomial sys- tem and propose an algorithm for computing it. By this way all the solutions of any high-dimensional polynomial system can be represented by a set of so-called rational- representation sets.
文摘Video text detection is a challenging problem, since video image background is generally complex and its subtitles often have the problems of color bleeding, fuzzy boundaries and low contrast due to video lossy compression and low resolution. In this paper, we propose a robust framework to solve these problems. Firstly, we exploit gradient amplitude map （GAM） to enhance the edge of an input image, which can overcome the problems of color bleeding and fuzzy boundaries. Secondly, a two-direction morphological filtering is developed to filter background noise and enhance the contrast between background and text. Thirdly, maximally stable extremal region （MSER） is applied to detect text regions with two extreme colors, and we use the mean intensity of the regions as the graph cuts＇ label set, and the Euclidean distance of three channels in HSI color space as the graph cuts smooth term, to get optimal segmentations. Finally, we group them into text lines using the geometric characteristics of the text, and then corner detection, multi-frame verification, and some heuristic rules are used to eliminate non-text regions. We test our scheme with some challenging videos, and the results prove that our text detection framework is more robust than previous methods.
文摘Geometric distortions are simple and effective at- tacks rendering many watermarking methods useless. They make detection and extraction of the embedded watermark difficult or even impossible by destroying the synchroniza- tion between the watermark reader and the embedded water- mark. In this paper, we propose a blind content-based image watermarking scheme against geometric distortions. Firstly, the MSER detector is adopted to extract a set of maximally stable extremal regions which are affine covariant and robust to geometric distortions and common signal processing. Sec- ondly, every original MSER is fitted into an elliptical region that was proved to be affine invariant. In order to achieve rota- tion invariance, an image normalization process is performed to transform the elliptical regions into circular ones. Finally, watermarks are repeatedly embedded into every circular disk by modifying the wavelet transform coefficients. Experimen- tal results on standard benchmark demonstrate that the pro- posed scheme is robust to geometric distortions as well as common signal processing.
基金Supported by the Natural Science Foundation of Xinjiang University（XYl10102） Sup- ported by the of NSFXJ（2010211A06）
文摘Let G be a connected graph with vertex set V(G), order n=|V(G)|, minimum degree δ(G) and connectivity κ(G). The graph G is called maximally connected if κ(G) = δ(G). Define the inverse degree of G with no isolated vertices as R(G) =Σv∈V(G)1/d(v) , where d(v) denotes the degree of the vertex v. We show that G is maximally connected if R(G) <1+2/δ + n-2δ+1/((n-1)(n-3)) .
基金Project supported by the National Key Research and Development Program of China(Grant No.2017YFA0302901)the National Natural Science Foundation of China(Grant Nos.11474331,11404383,and 11474004)+1 种基金the Natural Science Foundation of Zhejiang Province,China(Grant No.LY17A040005)the K.C.Wong Magna Fund in Ningbo University
文摘Based on the first-principles density functional theory electronic structure calculation,we investigate the possible phonon-mediated superconductivity in arsenene,a two-dimensional buckled arsenic atomic sheet,under electron doping.We find that the strong superconducting pairing interaction results mainly from the pz-like electrons of arsenic atoms and the A1 phonon mode around the K point,and the superconducting transition temperature can be as high as 30.8 K in the arsenene with 0.2 doped electrons per unit cell and 12%-applied biaxial tensile strain.This transition temperature is about ten times higher than that in the bulk arsenic under high pressure.It is also the highest transition temperature that is predicted for electron-doped two-dimensional elemental superconductors,including graphene,silicene,phosphorene,and borophene.
基金Sponsored by the Scientific Research Common Program of Beijing Municipal Commission of Education(Grant No. KM201010772021the National High Technology Research and Development Program of China (863 Program) (Grant No. 2006AA74105)the National Natural Science Foundation of Chi-na(Grant No. 60803103)
文摘To solve the problem of wide-baseline stereo image matching based on multiple cameras,the paper puts forward an image matching method of combining maximally stable extremal regions (MSER) with Scale Invariant Feature Transform (SIFT) . It uses MSER to detect feature regions instead of difference of Gaussian. After fitted into elliptical regions,those regions will be normalized into unity circles and represented with SIFT descriptors. The method estimates fundamental matrix and removes outliers by auto-maximum a posteriori sample consensus after initial matching feature points. The experimental results indicate that the method is robust to viewpoint changes,can reduce computational complexity effectively and improve matching accuracy.
文摘We study analytically the generation of maximally entangled states （MESs） formed by a two-component Bose-Einstein condensate （BEC） trapped in an adiabatically driven single potential well. Under the condition of the linear interaction controlled by a driven field being much stronger than the effective nonlinear interaction between the components, MESs, as some particular cases of superpositions of spin coherent states （SSCS）, may emerge periodically along with not only time evolution but also the equidifferent change of the linear coupling strength at a particular time.
文摘Starting with the theoretical basis of quantum computing, entanglement has been explored as one of the key resources required for quantum computation, the functional dependence of the entanglement measures on spin correlation functions has been established and the role of entanglement in implementation of QNN has been emphasized. Necessary and sufficient conditions for the general two-qubit state to be maximally entangled state (MES) have been obtained and a new set of MES constituting a very powerful and reliable eigen basis (different from magic bases) of two-qubit systems has been constructed. In terms of the MES constituting this basis, Bell’s States have been generated and all the qubits of two-qubit system have been obtained. Carrying out the correct computation of XOR function in neural network, it has been shown that QNN requires the proper correlation between the input and output qubits and the presence of appropriate entanglement in the system guarantees this correlation.
文摘AIMTo determine the long-term effects of selective laser trabeculoplasty (SLT) on intraocular pressure (IOP) and the number of medications used up to 5y following treatment in glaucoma patients receiving maximally tolerated medical therapy (MTMT).METHODSThe Wills Eye Hospital Glaucoma Research Center retrospectively reviewed the charts of glaucoma patients who underwent SLT after receiving MTMT. Eyes that did not achieve their target pressure within 3mo following SLT were excluded from the study. Changes in mean IOP and number of glaucoma medications used were analyzed at 1, 3, and 5y following SLT.RESULTSSeventy-five eyes of 67 patients were included in the study. Fifteen eyes that received SLT failed to achieve their target pressure within 3mo and were excluded from the study. The average follow-up time was 37.4mo (±14.4). Mean IOP was significantly reduced 1y after treatment (P=0.005). It was also reduced 3, 5y after treatment without reaching statistical significance (P=0.20 and P=0.072, respectively). There was a significant decrease in mean number of medications used 1, 3, 5y after treatment (P<0.001, P<0.001, and P=0.039, respectively). In the span of 5y, 2 eyes (2.7%) underwent repeat SLT, 7 eyes (9.3%) underwent glaucoma surgery and an additional 3 eyes (4.0%) underwent both.CONCLUSIONSLT significantly reduced the number of glaucoma medications used 5y following treatment in glaucoma patients receiving MTMT. SLT may delay operating-room surgery.
基金supported by National Natural Science Foundation of China (Grants Nos. 11631011 and 11626251)
文摘Let Q be a bounded open domain in R^n with smooth boundaryаΩ.Let X=(X1,X2…,Xm)be a system of general Grushin type vector fields defined onΩand the boundaryаΩis non-characteristic for X.For△x=∑j=1^mXj^2,we denoteλk as the k-th eigenvalue for the bi-subelliptic operator△X2^2 onΩ.In this paper,by using the sharp sub-elliptic estimates and maximally hypoeliptic estimates,we give the optimal lower bound estimates ofλk for the operatork△X^2.
文摘Let D be a finite and simple digraph with vertex set V(D).The minimum degreeδof a digraph D is defined as the minimum value of its out-degrees and its in-degrees.If D is a digraph with minimum degreeδand edge-connectivity λ,then λ≤δ.A digraph is maximally edge-connected ifλ=δ.A digraph is called super-edge-connected if every minimum edge-cut consists of edges incident to or from a vertex of minimum degree.In this note we show that a digraph is maximally edge-connected or super-edge-connected if the number of arcs is large enough.
基金Project supported by the Special Funds of the National Natural Science Foundation of China (Grant No. 10947017/A05)
文摘This paper proposes a scheme to generate, in an ion-trap, a type of multipartite maximally entangled state which was first introduced by Chen et al. [Chen P X, Zhu S Y and Guo G C 2006 Phys. Rev. A 74 032324]. The maximum entanglement property of these states is examined. It also demonstrates how to discriminate among these states in the ion-trap.
文摘The maximally holomorphic functions of a bounded linear operator is introduced and applied to representthe spectrum and characterize the single--valued extension property. The well known results of quasi--nilpo-tent equivalent operators follow easily from the relation of their maximally holomorphie functions.
基金supported by the National Natural Science Foundation of China under Grant No.10704011the Research Programs of the Educational Office of Liaoning Province under Grant No.2008006
文摘The sender shares six-particle maximally entangled states as quantum channel with the receiver. If the quantum channel is secure, the sender performs projective measurements and tells the measurement outcome to the receiver. The receiver performs the unitary transformations and makes projective measurements on his particles to obtain the secret information. Using teleportation, the transmission of three-qubit secret information can be completed in each quantum channel
基金supported by the National Natural Science Foundation of China(Grant Nos.11675113,11871295,and 11901084)Beijing Municipal Commission of Education(Grant No.KM201810011009)+1 种基金Beijing Natural Science Foundation(Grant No.Z190005)the Research Startup Funds of Dongguan University of Technology(Grant No.GC300501-103)。
文摘In this work,we study the local distinguishability of maximally entangled states(MESs).In particular,we are concerned with whether any fixed number of MESs can be locally distinguishable for sufficiently large dimensions.Fan and Tian et al.have already obtained two satisfactory results for the generalized Bell states(GBSs)and the qudit lattice states when applied to prime or prime power dimensions.We construct a general twist-teleportation scheme for any orthonormal basis with MESs that is inspired by the method used in[Phys.Rev.A 70,022304(2004)].Using this teleportation scheme,we obtain a sufficient and necessary condition for one-way distinguishable sets of MESs,which include the GBSs and the qudit lattice states as special cases.Moreover,we present a generalized version of the results in[Phys.Rev.A 92,042320(2015)]for the arbitrary dimensional case.
文摘A state-dependent proof of Bell's theorem without inequalities using the product state of any two maximally entangled states (Bell states) of two qubits for two observers in an ideal condition, each of which possesses two qubits,is proposed. It is different from the other proofs in which there exists a fundamental requirement that certain specific suitable Bell states have been chosen. Moreover, in any non-ideal situation, a common Bell inequality independent of the choices of the 16-product states is derived, which is used to test the contradiction between quantum mechanics and local reality theory in the reach of current experimental technology.
