In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the sol...In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre （PCF） parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.展开更多
全波形反演作为一种高分辨率地下成像技术,在实际应用中仍面临低频数据缺失、周期跳跃以及噪声干扰等一系列挑战,因此提出一种基于Fourier近似Wasserstein距离的隐式全波形反演方法。在目标函数层面,利用Wasserstein距离与Fourier系数...全波形反演作为一种高分辨率地下成像技术,在实际应用中仍面临低频数据缺失、周期跳跃以及噪声干扰等一系列挑战,因此提出一种基于Fourier近似Wasserstein距离的隐式全波形反演方法。在目标函数层面,利用Wasserstein距离与Fourier系数之间的有界关系,构建基于Fourier近似的低频增强型目标函数。通过对地震数据中低波数成分进行加权增强,提高模型背景速度的恢复质量,从而有效缓解周期跳跃问题。在模型重参数化层面,引入基于正弦激活函数的神经网络对速度模型进行隐式表征,利用其连续的高维映射特性替代传统的离散网格表示,在提高模型表征自由度的同时为反演过程引入由参数化带来的平滑约束。选取Marmousi、Marmousi2和SEG Salt 3个典型模型,分别在低频缺失、线性初始模型、含噪场景和强散射介质等条件下评估方法的有效性。结果表明,在初始模型较差、低频缺失、噪声干扰和强散射等复杂条件下,所提方法均表现出优异的鲁棒性与收敛性,能够有效克服周期跳跃并显著提升反演精度。展开更多
Full-color imaging is essential in digital pathology for accurate tissue analysis.Utilizing advanced optical modulation and phase retrieval algorithms,Fourier ptychographic microscopy(FPM)offers a powerful solution fo...Full-color imaging is essential in digital pathology for accurate tissue analysis.Utilizing advanced optical modulation and phase retrieval algorithms,Fourier ptychographic microscopy(FPM)offers a powerful solution for high-throughput digital pathology,combining high resolution,large field of view,and extended depth of field(DOF).However,the full-color capabilities of FPM are hindered by coherent color artifacts and reduced computational efficiency,which significantly limits its practical applications.Color-transferbased FPM(CFPM)has emerged as a potential solution,theoretically reducing both acquisition and reconstruction threefold time.Yet,existing methods fall short of achieving the desired reconstruction speed and colorization quality.In this study,we report a generalized dual-color-space constrained model for FPM colorization.This model provides a mathematical framework for model-based FPM colorization,enabling a closed-form solution without the need for redundant iterative calculations.Our approach,termed generalized CFPM(gCFPM),achieves colorization within seconds for megapixel-scale images,delivering superior colorization quality in terms of both colorfulness and sharpness,along with an extended DOF.Both simulations and experiments demonstrate that gCFPM surpasses state-of-the-art methods across all evaluated criteria.Our work offers a robust and comprehensive workflow for high-throughput full-color pathological imaging using FPM platforms,laying a solid foundation for future advancements in methodology and engineering.展开更多
Let f be a primitive holomorphic cusp form with even integral weight k≥2 for the full modular groupΓ=SL(2,Z)andλ_(sym^(j)f)(n)be the n-th coefficient of Dirichlet series of j-th symmetric L-function L(s,sym^(j)f)at...Let f be a primitive holomorphic cusp form with even integral weight k≥2 for the full modular groupΓ=SL(2,Z)andλ_(sym^(j)f)(n)be the n-th coefficient of Dirichlet series of j-th symmetric L-function L(s,sym^(j)f)attached to f.In this paper,we study the mean value distribution over a specific sparse sequence of positive integers of the following sum∑(a^(2)+b^(2)+c^(2)+d^(2)≤x(a,b,c,d)∈Z^(4))λ_(sym^(j))^(i)f(a^(2)+b^(2)+c^(2)+d^(2))where j≥2 is a given positive integer,i=2,3,4 andαis sufficiently large.We utilize Python programming to design algorithms for higher power conditions,combining Perron's formula,latest results of representations of natural integers as sums of squares,as well as analytic properties and subconvexity and convexity bounds of automorphic L-functions,to ensure the accuracy and verifiability of asymptotic formulas.The conclusion we obtained improves previous results and extends them to a more general settings.展开更多
Fourier Ptychographic Microscopy(FPM)is a high-throughput computational optical imaging technology reported in 2013.It effectively breaks through the trade-off between high-resolution imaging and wide-field imaging.In...Fourier Ptychographic Microscopy(FPM)is a high-throughput computational optical imaging technology reported in 2013.It effectively breaks through the trade-off between high-resolution imaging and wide-field imaging.In recent years,it has been found that FPM is not only a tool to break through the trade-off between field of view and spatial resolution,but also a paradigm to break through those trade-off problems,thus attracting extensive attention.Compared with previous reviews,this review does not introduce its concept,basic principles,optical system and series of applications once again,but focuses on elaborating the three major difficulties faced by FPM technology in the process from“looking good”in the laboratory to“working well”in practical applications:mismatch between numerical model and physical reality,long reconstruction time and high computing power demand,and lack of multi-modal expansion.It introduces how to achieve key technological innovations in FPM through the dual drive of Artificial Intelligence(AI)and physics,including intelligent reconstruction algorithms introducing machine learning concepts,optical-algorithm co-design,fusion of frequency domain extrapolation methods and generative adversarial networks,multi-modal imaging schemes and data fusion enhancement,etc.,gradually solving the difficulties of FPM technology.Conversely,this review deeply considers the unique value of FPM technology in potentially feeding back to the development of“AI+optics”,such as providing AI benchmark tests under physical constraints,inspirations for the balance of computing power and bandwidth in miniaturized intelligent microscopes,and photoelectric hybrid architectures.Finally,it introduces the industrialization path and frontier directions of FPM technology,pointing out that with the promotion of the dual drive of AI and physics,it will generate a large number of industrial application case,and looks forward to the possibilities of future application scenarios and expansions,for instance,body fluid biopsy and point-of-care testing at the grassroots level represent the expansion of the growth market.展开更多
In this paper,the convergence of the split-step theta method for stochastic differential equations is analyzed using stochastic C-stability and stochastic B-consistency.The fact that the numerical scheme,which is both...In this paper,the convergence of the split-step theta method for stochastic differential equations is analyzed using stochastic C-stability and stochastic B-consistency.The fact that the numerical scheme,which is both stochastically C-stable and stochastically B-consistent,is convergent has been proved in a previous paper.In order to analyze the convergence of the split-step theta method(θ∈[1/2,1]),the stochastic C-stability and stochastic B-consistency under the condition of global monotonicity have been researched,and the rate of convergence 1/2 has been explored in this paper.It can be seen that the convergence does not require the drift function should satisfy the linear growth condition whenθ=1/2 Furthermore,the rate of the convergence of the split-step scheme for stochastic differential equations with additive noise has been researched and found to be 1.Finally,an example is given to illustrate the convergence with the theoretical results.展开更多
We present the Fourier lightfield multiview stereoscope(FiLM-Scope).This imaging device combines concepts from Fourier lightfield microscopy and multiview stereo imaging to capture high-resolution 3D videos over large...We present the Fourier lightfield multiview stereoscope(FiLM-Scope).This imaging device combines concepts from Fourier lightfield microscopy and multiview stereo imaging to capture high-resolution 3D videos over large fields of view.The FiLM-Scope optical hardware consists of a multicamera array,with 48 individual microcameras,placed behind a high-throughput primary lens.This allows the FiLM-Scope to simultaneously capture 48 unique 12.8 megapixel images of a 28×37 mm field-of-view,from unique angular perspectives over a 21 deg×29 deg range,with down to 22μm lateral resolution.We also describe a self-supervised algorithm to reconstruct 3D height maps from these images.Our approach demonstrates height accuracy down to 11μm.To showcase the utility of our system,we perform tool tracking over the surface of an ex vivo rat skull and visualize the 3D deformation in stretching human skin,with videos captured at up to 100 frames per second.The FiLM-Scope has the potential to improve 3D visualization in a range of microsurgical settings.展开更多
文摘In this paper, the generalized nonlinear Schrodinger equation （GNLSE） is solved by an adaptive split-step Fourier method （ASSFM）. It is found that ASSFM must be used to solve GNLSE to ensure precision when the soliton selffrequency shift is remarkable and the photonic crystal fibre （PCF） parameters vary with the frequency considerably. The precision of numerical simulation by using ASSFM is higher than that by using split-step Fourier method in the process of laser pulse propagation in PCFs due to the fact that the variation of fibre parameters with the peak frequency in the pulse spectrum can be taken into account fully.
文摘全波形反演作为一种高分辨率地下成像技术,在实际应用中仍面临低频数据缺失、周期跳跃以及噪声干扰等一系列挑战,因此提出一种基于Fourier近似Wasserstein距离的隐式全波形反演方法。在目标函数层面,利用Wasserstein距离与Fourier系数之间的有界关系,构建基于Fourier近似的低频增强型目标函数。通过对地震数据中低波数成分进行加权增强,提高模型背景速度的恢复质量,从而有效缓解周期跳跃问题。在模型重参数化层面,引入基于正弦激活函数的神经网络对速度模型进行隐式表征,利用其连续的高维映射特性替代传统的离散网格表示,在提高模型表征自由度的同时为反演过程引入由参数化带来的平滑约束。选取Marmousi、Marmousi2和SEG Salt 3个典型模型,分别在低频缺失、线性初始模型、含噪场景和强散射介质等条件下评估方法的有效性。结果表明,在初始模型较差、低频缺失、噪声干扰和强散射等复杂条件下,所提方法均表现出优异的鲁棒性与收敛性,能够有效克服周期跳跃并显著提升反演精度。
基金supported by the National Natural Science Foundation of China(Grant Nos.12104500 and 82430062)the Key Research and Development Projects of Shaanxi Province(Grant No.2023-YBSF-263),the Shenzhen Engineering Research Centre(Grant No.XMHT20230115004)the Shenzhen Science and Technology Innovation Commission(Grant No.KCXFZ20201221173207022).
文摘Full-color imaging is essential in digital pathology for accurate tissue analysis.Utilizing advanced optical modulation and phase retrieval algorithms,Fourier ptychographic microscopy(FPM)offers a powerful solution for high-throughput digital pathology,combining high resolution,large field of view,and extended depth of field(DOF).However,the full-color capabilities of FPM are hindered by coherent color artifacts and reduced computational efficiency,which significantly limits its practical applications.Color-transferbased FPM(CFPM)has emerged as a potential solution,theoretically reducing both acquisition and reconstruction threefold time.Yet,existing methods fall short of achieving the desired reconstruction speed and colorization quality.In this study,we report a generalized dual-color-space constrained model for FPM colorization.This model provides a mathematical framework for model-based FPM colorization,enabling a closed-form solution without the need for redundant iterative calculations.Our approach,termed generalized CFPM(gCFPM),achieves colorization within seconds for megapixel-scale images,delivering superior colorization quality in terms of both colorfulness and sharpness,along with an extended DOF.Both simulations and experiments demonstrate that gCFPM surpasses state-of-the-art methods across all evaluated criteria.Our work offers a robust and comprehensive workflow for high-throughput full-color pathological imaging using FPM platforms,laying a solid foundation for future advancements in methodology and engineering.
文摘Let f be a primitive holomorphic cusp form with even integral weight k≥2 for the full modular groupΓ=SL(2,Z)andλ_(sym^(j)f)(n)be the n-th coefficient of Dirichlet series of j-th symmetric L-function L(s,sym^(j)f)attached to f.In this paper,we study the mean value distribution over a specific sparse sequence of positive integers of the following sum∑(a^(2)+b^(2)+c^(2)+d^(2)≤x(a,b,c,d)∈Z^(4))λ_(sym^(j))^(i)f(a^(2)+b^(2)+c^(2)+d^(2))where j≥2 is a given positive integer,i=2,3,4 andαis sufficiently large.We utilize Python programming to design algorithms for higher power conditions,combining Perron's formula,latest results of representations of natural integers as sums of squares,as well as analytic properties and subconvexity and convexity bounds of automorphic L-functions,to ensure the accuracy and verifiability of asymptotic formulas.The conclusion we obtained improves previous results and extends them to a more general settings.
基金National Natural Science Foundation of China(No.12574332)the Space Optoelectronic Measurement and Perception Lab.,Beijing Institute of Control Engineering(No.LabSOMP-2023-10)Major Science and Technology Innovation Program of Xianyang City(No.L2024-ZDKJ-ZDCGZH-0021)。
文摘Fourier Ptychographic Microscopy(FPM)is a high-throughput computational optical imaging technology reported in 2013.It effectively breaks through the trade-off between high-resolution imaging and wide-field imaging.In recent years,it has been found that FPM is not only a tool to break through the trade-off between field of view and spatial resolution,but also a paradigm to break through those trade-off problems,thus attracting extensive attention.Compared with previous reviews,this review does not introduce its concept,basic principles,optical system and series of applications once again,but focuses on elaborating the three major difficulties faced by FPM technology in the process from“looking good”in the laboratory to“working well”in practical applications:mismatch between numerical model and physical reality,long reconstruction time and high computing power demand,and lack of multi-modal expansion.It introduces how to achieve key technological innovations in FPM through the dual drive of Artificial Intelligence(AI)and physics,including intelligent reconstruction algorithms introducing machine learning concepts,optical-algorithm co-design,fusion of frequency domain extrapolation methods and generative adversarial networks,multi-modal imaging schemes and data fusion enhancement,etc.,gradually solving the difficulties of FPM technology.Conversely,this review deeply considers the unique value of FPM technology in potentially feeding back to the development of“AI+optics”,such as providing AI benchmark tests under physical constraints,inspirations for the balance of computing power and bandwidth in miniaturized intelligent microscopes,and photoelectric hybrid architectures.Finally,it introduces the industrialization path and frontier directions of FPM technology,pointing out that with the promotion of the dual drive of AI and physics,it will generate a large number of industrial application case,and looks forward to the possibilities of future application scenarios and expansions,for instance,body fluid biopsy and point-of-care testing at the grassroots level represent the expansion of the growth market.
基金Supported by the National Natural Science Foundation of China (Grant No. 12301521)the Natural Science Foundation of Shanxi Province (Grant No. 20210302124081)。
文摘In this paper,the convergence of the split-step theta method for stochastic differential equations is analyzed using stochastic C-stability and stochastic B-consistency.The fact that the numerical scheme,which is both stochastically C-stable and stochastically B-consistent,is convergent has been proved in a previous paper.In order to analyze the convergence of the split-step theta method(θ∈[1/2,1]),the stochastic C-stability and stochastic B-consistency under the condition of global monotonicity have been researched,and the rate of convergence 1/2 has been explored in this paper.It can be seen that the convergence does not require the drift function should satisfy the linear growth condition whenθ=1/2 Furthermore,the rate of the convergence of the split-step scheme for stochastic differential equations with additive noise has been researched and found to be 1.Finally,an example is given to illustrate the convergence with the theoretical results.
基金supported by the National Cancer Institute(NCI)of the National Institutes of Health(Grant No.R44CA250877)the Office of Research Infrastructure Programs(ORIP),Office of the Director,National Institutes of Health,and the National Institute of Environmental Health Sciences(NIEHS)of the National Institutes of Health(Grant No.R44OD024879)+2 种基金the National Institute of Biomedical Imaging and Bioengineering(NIBIB)of the National Institutes of Health(Grant No.R43EB030979)the National Science Foundation(Grant Nos.2036439 and 2238845)the Duke Coulter Translational Part-nership Award,the Fitzpatrick Institute at the Duke University.
文摘We present the Fourier lightfield multiview stereoscope(FiLM-Scope).This imaging device combines concepts from Fourier lightfield microscopy and multiview stereo imaging to capture high-resolution 3D videos over large fields of view.The FiLM-Scope optical hardware consists of a multicamera array,with 48 individual microcameras,placed behind a high-throughput primary lens.This allows the FiLM-Scope to simultaneously capture 48 unique 12.8 megapixel images of a 28×37 mm field-of-view,from unique angular perspectives over a 21 deg×29 deg range,with down to 22μm lateral resolution.We also describe a self-supervised algorithm to reconstruct 3D height maps from these images.Our approach demonstrates height accuracy down to 11μm.To showcase the utility of our system,we perform tool tracking over the surface of an ex vivo rat skull and visualize the 3D deformation in stretching human skin,with videos captured at up to 100 frames per second.The FiLM-Scope has the potential to improve 3D visualization in a range of microsurgical settings.
