We show that the volume of the projection bodyΠ(Z)of an n-dimensional zonotope Z with n+1 generators and of volume 1 is always exactly 2^(n).Moroever,we point out that an upper bound on the volume ofΠ(K)of a central...We show that the volume of the projection bodyΠ(Z)of an n-dimensional zonotope Z with n+1 generators and of volume 1 is always exactly 2^(n).Moroever,we point out that an upper bound on the volume ofΠ(K)of a centrally symmetric n-dimensional convex body of volume 1 is at least 2^(n)(9/8)^([n/3]).展开更多
Quantum coherence serves as a defining characteristic of quantum mechanics,finding extensive applications in quantum computing and quantum communication processing.This study explores quantum block coherence in the co...Quantum coherence serves as a defining characteristic of quantum mechanics,finding extensive applications in quantum computing and quantum communication processing.This study explores quantum block coherence in the context of projective measurements,focusing on the quantification of such coherence.Firstly,we define the correlation function between the two general projective measurements P and Q,and analyze the connection between sets of block incoherent states related to two compatible projective measurements P and Q.Secondly,we discuss the measure of quantum block coherence with respect to projective measurements.Based on a given measure of quantum block coherence,we characterize the existence of maximal block coherent states through projective measurements.This research integrates the compatibility of projective measurements with the framework of quantum block coherence,contributing to the advancement of block coherence measurement theory.展开更多
In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm ineq...In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.展开更多
Active target time projection chambers are state-of-the-art tools in the field of low-energy nuclear physics and are particularly suitable for experiments using low-intensity radioactive ion beams or gamma rays.The Fu...Active target time projection chambers are state-of-the-art tools in the field of low-energy nuclear physics and are particularly suitable for experiments using low-intensity radioactive ion beams or gamma rays.The Fudan multi-purpose active target time projection chamber(fMeta-TPC)with 2048 channels was developed to studyα-clustering nuclei.This study focused on the photonuclear reaction with a laser Compton scattering gamma source,particularly for the decay of the highly excitedαcluster state.The design of fMeta-TPC is described in this paper.A comprehensive evaluation of its offline performance was conducted using an ultraviolet laser and ^(241)Amαsource.The results showed that the intrinsic angular resolution of the detector was within 0.30°,and the detector had an energy resolution of 6.85%for 3.0 MeVαparticles.The gain uniformity of the detector was approximately 10%(RMS/Mean),as tested by the ^(55)Fe X-ray source.展开更多
A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gr...A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method.Under some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection technique.Finally,the effectiveness and application prospects of the proposed method are verified by numerical experiments.展开更多
Taiji-2 project is the second step of Taiji program,which is to verify the required technology for Taiji-3 mission.The feasibility study of Taiji-2 is successfully finished,and some of the main progress is introduced ...Taiji-2 project is the second step of Taiji program,which is to verify the required technology for Taiji-3 mission.The feasibility study of Taiji-2 is successfully finished,and some of the main progress is introduced here.展开更多
The Chinese Meridian Project(CMP)is a major national science and technology infrastructure constructed in two steps.The first phase of the CMP has been operating for more than a solar cycle.From 2022 to 2023,utilizing...The Chinese Meridian Project(CMP)is a major national science and technology infrastructure constructed in two steps.The first phase of the CMP has been operating for more than a solar cycle.From 2022 to 2023,utilizing the monitoring data collected by the CMP,scientists made major breakthroughs in fields of ionosphere,middle and upper atmosphere,and coupling between layers.The construction of the second phase of the CMP is nearly finished,and the project is expected to operate as a whole in 2025 after national acceptance of the second phase.The whole project was built in an architecture of so-called“One Chain,Three Networks and Four Focuses”.It is promising to make a three-dimensional observation of the whole solar-terrestrial space.The science community is looking forward to the great contribution of the CMP to space weather and space physics research.展开更多
The advantages of a flat-panel X-ray source(FPXS)make it a promising candidate for imaging applications.Accurate imaging-system modeling and projection simulation are critical for analyzing imaging performance and res...The advantages of a flat-panel X-ray source(FPXS)make it a promising candidate for imaging applications.Accurate imaging-system modeling and projection simulation are critical for analyzing imaging performance and resolving overlapping projection issues in FPXS.The conventional analytical ray-tracing approach is limited by the number of patterns and is not applicable to FPXS-projection calculations.However,the computation time of Monte Carlo(MC)simulation is independent of the size of the patterned arrays in FPXS.This study proposes two high-efficiency MC projection simulators for FPXS:a graphics processing unit(GPU)-based phase-space sampling MC(gPSMC)simulator and GPU-based fluence sampling MC(gFSMC)simulator.The two simulators comprise three components:imaging-system modeling,photon initialization,and physical-interaction simulations in the phantom.Imaging-system modeling was performed by modeling the FPXS,imaging geometry,and detector.The gPSMC simulator samples the initial photons from the phase space,whereas the gFSMC simulator performs photon initialization from the calculated energy spectrum and fluence map.The entire process of photon interaction with the geometry and arrival at the detector was simulated in parallel using multiple GPU kernels,and projections based on the two simulators were calculated.The accuracies of the two simulators were evaluated by comparing them with the conventional analytical ray-tracing approach and acquired projections,and the efficiencies were evaluated by comparing the computation time.The results of simulated and realistic experiments illustrate the accuracy and efficiency of the proposed gPSMC and gFSMC simulators in the projection calculation of various phantoms.展开更多
This paper introduces a new method of calculating crown projection area(CPA),the area of level ground covered by a vertical projection of a tree crown from measured crown radii through numerical interpolation and inte...This paper introduces a new method of calculating crown projection area(CPA),the area of level ground covered by a vertical projection of a tree crown from measured crown radii through numerical interpolation and integration.This novel method and other four existing methods of calculating CPA were compared using detailed crown radius measurements from 30 tall trees of Eucalyptus pilularis variable in crown size,shape,and asymmetry.The four existing methods included the polygonal approach and three ways of calculating CPA as the area of a circle using the arithmetic,geometric and quadratic mean radius.Comparisons were made across a sequence of eight non-consecutive numbers(from 2 to 16)of measured crown radii for each tree over the range of crown asymmetry of the 30 trees through generalized linear models and multiple comparisons of means.The sequence covered the range of the number of crown radii measured for calculating the CPA of a tree in the literature.A crown asymmetry index within the unit interval was calculated for each tree to serve as a normative measure.With a slight overestimation of 2.2%on average and an overall mean error size of 7.9%across the numbers of crown radii that were compared,our new method was the least biased and most accurate.Calculating CPA as a circle using the quadratic mean crown radius was the second best,which had an average overestimation of 4.5%and overall mean error size of 8.8%.These two methods remained by and large unbiased as crown asymmetry increased,while the other three methods showed larger bias of underestimation.For the conventional method of using the arithmetic mean crown radius to calculate CPA as a circle,bias correction factors were developed as a function of crown asymmetry index to delineate the increasing magnitude of bias associated with greater degrees of crown asymmetry.This study reveals and demonstrates such relationships between the accuracy of CPA calculations and crown asymmetry and will help increase awareness among researchers and practitioners on the existence of bias in their CPA calculations and for the need to use an unbiased method in the future.Our new method is recommended for calculating CPA where at least four crown radius measurements per tree are available because that is the minimum number required for its use.展开更多
This paper introduces a hybrid approach combining Green’s function Monte Carlo(GFMC)method with projected entangled pair state(PEPS)ansatz.This hybrid method regards PEPS as a trial state and a guiding wave function ...This paper introduces a hybrid approach combining Green’s function Monte Carlo(GFMC)method with projected entangled pair state(PEPS)ansatz.This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC.By leveraging PEPS’s proficiency in capturing quantum state entanglement and GFMC’s efficient parallel architecture,the hybrid method is well-suited for the accurate and efficient treatment of frustrated quantum spin systems.As a benchmark,we applied this approach to study the frustrated J_(1)–J_(2) Heisenberg model on a square lattice with periodic boundary conditions(PBCs).Compared with other numerical methods,our approach integrating PEPS and GFMC shows competitive accuracy in the performance of ground-state energy.This paper provides systematic and comprehensive discussion of the approach of our previous work[Phys.Rev.B 109235133(2024)].展开更多
文摘We show that the volume of the projection bodyΠ(Z)of an n-dimensional zonotope Z with n+1 generators and of volume 1 is always exactly 2^(n).Moroever,we point out that an upper bound on the volume ofΠ(K)of a centrally symmetric n-dimensional convex body of volume 1 is at least 2^(n)(9/8)^([n/3]).
基金partially supported by the National Natural Science Foundations of China (Grant No.11901317)the China Postdoctoral Science Foundation (Grant No.2020M680480)+1 种基金the Fundamental Research Funds for the Central Universities (Grant No.2023MS078)the Beijing Natural Science Foundation (Grant No.1232021)。
文摘Quantum coherence serves as a defining characteristic of quantum mechanics,finding extensive applications in quantum computing and quantum communication processing.This study explores quantum block coherence in the context of projective measurements,focusing on the quantification of such coherence.Firstly,we define the correlation function between the two general projective measurements P and Q,and analyze the connection between sets of block incoherent states related to two compatible projective measurements P and Q.Secondly,we discuss the measure of quantum block coherence with respect to projective measurements.Based on a given measure of quantum block coherence,we characterize the existence of maximal block coherent states through projective measurements.This research integrates the compatibility of projective measurements with the framework of quantum block coherence,contributing to the advancement of block coherence measurement theory.
文摘In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.
基金supported by the National Key R&D Program of China(Nos.2022YFA1602402,2020YFE0202001,2023YFA1606900)the National Natural Science Foundation of China(NSFC)(Nos.12235003,11835002,11925502,11705031,12275053,12147101).
文摘Active target time projection chambers are state-of-the-art tools in the field of low-energy nuclear physics and are particularly suitable for experiments using low-intensity radioactive ion beams or gamma rays.The Fudan multi-purpose active target time projection chamber(fMeta-TPC)with 2048 channels was developed to studyα-clustering nuclei.This study focused on the photonuclear reaction with a laser Compton scattering gamma source,particularly for the decay of the highly excitedαcluster state.The design of fMeta-TPC is described in this paper.A comprehensive evaluation of its offline performance was conducted using an ultraviolet laser and ^(241)Amαsource.The results showed that the intrinsic angular resolution of the detector was within 0.30°,and the detector had an energy resolution of 6.85%for 3.0 MeVαparticles.The gain uniformity of the detector was approximately 10%(RMS/Mean),as tested by the ^(55)Fe X-ray source.
基金supported by the Guangxi Science and Technology base and Talent Project(AD22080047)the National Natural Science Foundation of Guangxi Province(2023GXNFSBA 026063)+1 种基金the Innovation Funds of Chinese University(2021BCF03001)the special foundation for Guangxi Ba Gui Scholars.
文摘A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method.Under some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection technique.Finally,the effectiveness and application prospects of the proposed method are verified by numerical experiments.
基金Supported by the Strategic Priority Research Program of the Chinese Academy of Sciences(XDA15021100)the National Natural Science Foundation of China(12147103)the Fundamental Research Funds for the Central Universities。
文摘Taiji-2 project is the second step of Taiji program,which is to verify the required technology for Taiji-3 mission.The feasibility study of Taiji-2 is successfully finished,and some of the main progress is introduced here.
基金Supported by National Major Science and Technology Infrastructure Construction Project:the Chinese Meridian Project(2017-000052-73-01-002390)。
文摘The Chinese Meridian Project(CMP)is a major national science and technology infrastructure constructed in two steps.The first phase of the CMP has been operating for more than a solar cycle.From 2022 to 2023,utilizing the monitoring data collected by the CMP,scientists made major breakthroughs in fields of ionosphere,middle and upper atmosphere,and coupling between layers.The construction of the second phase of the CMP is nearly finished,and the project is expected to operate as a whole in 2025 after national acceptance of the second phase.The whole project was built in an architecture of so-called“One Chain,Three Networks and Four Focuses”.It is promising to make a three-dimensional observation of the whole solar-terrestrial space.The science community is looking forward to the great contribution of the CMP to space weather and space physics research.
文摘The advantages of a flat-panel X-ray source(FPXS)make it a promising candidate for imaging applications.Accurate imaging-system modeling and projection simulation are critical for analyzing imaging performance and resolving overlapping projection issues in FPXS.The conventional analytical ray-tracing approach is limited by the number of patterns and is not applicable to FPXS-projection calculations.However,the computation time of Monte Carlo(MC)simulation is independent of the size of the patterned arrays in FPXS.This study proposes two high-efficiency MC projection simulators for FPXS:a graphics processing unit(GPU)-based phase-space sampling MC(gPSMC)simulator and GPU-based fluence sampling MC(gFSMC)simulator.The two simulators comprise three components:imaging-system modeling,photon initialization,and physical-interaction simulations in the phantom.Imaging-system modeling was performed by modeling the FPXS,imaging geometry,and detector.The gPSMC simulator samples the initial photons from the phase space,whereas the gFSMC simulator performs photon initialization from the calculated energy spectrum and fluence map.The entire process of photon interaction with the geometry and arrival at the detector was simulated in parallel using multiple GPU kernels,and projections based on the two simulators were calculated.The accuracies of the two simulators were evaluated by comparing them with the conventional analytical ray-tracing approach and acquired projections,and the efficiencies were evaluated by comparing the computation time.The results of simulated and realistic experiments illustrate the accuracy and efficiency of the proposed gPSMC and gFSMC simulators in the projection calculation of various phantoms.
基金supported by the Natural Science Foundation of China (32071758)the Fundamental Research Funds for the Central Universities of China (No. 2572020BA01)
文摘This paper introduces a new method of calculating crown projection area(CPA),the area of level ground covered by a vertical projection of a tree crown from measured crown radii through numerical interpolation and integration.This novel method and other four existing methods of calculating CPA were compared using detailed crown radius measurements from 30 tall trees of Eucalyptus pilularis variable in crown size,shape,and asymmetry.The four existing methods included the polygonal approach and three ways of calculating CPA as the area of a circle using the arithmetic,geometric and quadratic mean radius.Comparisons were made across a sequence of eight non-consecutive numbers(from 2 to 16)of measured crown radii for each tree over the range of crown asymmetry of the 30 trees through generalized linear models and multiple comparisons of means.The sequence covered the range of the number of crown radii measured for calculating the CPA of a tree in the literature.A crown asymmetry index within the unit interval was calculated for each tree to serve as a normative measure.With a slight overestimation of 2.2%on average and an overall mean error size of 7.9%across the numbers of crown radii that were compared,our new method was the least biased and most accurate.Calculating CPA as a circle using the quadratic mean crown radius was the second best,which had an average overestimation of 4.5%and overall mean error size of 8.8%.These two methods remained by and large unbiased as crown asymmetry increased,while the other three methods showed larger bias of underestimation.For the conventional method of using the arithmetic mean crown radius to calculate CPA as a circle,bias correction factors were developed as a function of crown asymmetry index to delineate the increasing magnitude of bias associated with greater degrees of crown asymmetry.This study reveals and demonstrates such relationships between the accuracy of CPA calculations and crown asymmetry and will help increase awareness among researchers and practitioners on the existence of bias in their CPA calculations and for the need to use an unbiased method in the future.Our new method is recommended for calculating CPA where at least four crown radius measurements per tree are available because that is the minimum number required for its use.
基金Project supported by the National Natural Science Foundation of China(Grant No.11934020)the Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302402).
文摘This paper introduces a hybrid approach combining Green’s function Monte Carlo(GFMC)method with projected entangled pair state(PEPS)ansatz.This hybrid method regards PEPS as a trial state and a guiding wave function in GFMC.By leveraging PEPS’s proficiency in capturing quantum state entanglement and GFMC’s efficient parallel architecture,the hybrid method is well-suited for the accurate and efficient treatment of frustrated quantum spin systems.As a benchmark,we applied this approach to study the frustrated J_(1)–J_(2) Heisenberg model on a square lattice with periodic boundary conditions(PBCs).Compared with other numerical methods,our approach integrating PEPS and GFMC shows competitive accuracy in the performance of ground-state energy.This paper provides systematic and comprehensive discussion of the approach of our previous work[Phys.Rev.B 109235133(2024)].
