We build a computer program to reconstruct convex bodies using even L_(p)surface area measures for p≥1.Firstly,we transform the minimization problem Pi,which is equivalent to solving the even L_(p)Minkowski problem,i...We build a computer program to reconstruct convex bodies using even L_(p)surface area measures for p≥1.Firstly,we transform the minimization problem Pi,which is equivalent to solving the even L_(p)Minkowski problem,into a convex optimization problem P4 with a finite number of constraints.This transformation makes it suitable for computational resolution.Then,we prove that the approximate solutions obtained by solving the problem P4 converge to the theoretical solution when N and k are sufficiently large.Finally,based on the convex optimization problem P_(4),we provide an algorithm for reconstructing convex bodies from even L_(p)surface area measures,and present several examples implemented using MATLAB.展开更多
There is a contradiction between the evolution rate of materials and the time resolution of SR-CT characterization in the in situ synchrotron radiation computed tomography(SR-CT)characterization of ultrafast evolution...There is a contradiction between the evolution rate of materials and the time resolution of SR-CT characterization in the in situ synchrotron radiation computed tomography(SR-CT)characterization of ultrafast evolution process.The sampling strategy of the ultra-sparse angle is an effective method for improving time resolution.Accurate reconstruction under sparse sampling conditions has always been a bottleneck problem.In recent years,convolutional neural networks have shown outstanding advantages in sparse-angle CT reconstruction given the development of deep learning.However,existing ideas did not consider the expression of high-frequency details in neural networks,limiting their application in accurate SR-CT characterization.A novel high-frequency information-constrained deep learning network(HFIC-Net)is proposed in response to this problem.Additional high-frequency information constraints are added to improve the accuracy of the reconstruction results.Further,a series of numerical reconstruction experiments are conducted to verify this new method,and the results indicate that the reconstruction results of HFIC-Net method effectively improve reconstruction quality.This new method uses only eight-angle projections to achieve the reconstruction effect of the filtered backprojection method(FBP)method in 360 projections.The results of the HFIC-Net method demonstrate clear boundaries and accurate detailed structures,correcting the misinformation caused by using other methods.For quantitative evaluation,the SSIM used to evaluate image structure similarity is increased from 0.1951,0.9212,and 0.9308 for FBP,FBP-Conv,and DDC-Net,respectively,to 0.9620 for HFIC-Net.Finally,the results of actual SR-CT experimental data indicate that the new method can suppress artifacts and achieve accurate reconstruction,and it is suitable for the in situ SR-CT accurate characterization of ultxafast evolution process.展开更多
β-ray-induced X-ray spectroscopy(BIXS)is a promising method for tritium detection in solid materials because of its unique advantages,such as large detection depth,nondestructive testing capabilities,and low requirem...β-ray-induced X-ray spectroscopy(BIXS)is a promising method for tritium detection in solid materials because of its unique advantages,such as large detection depth,nondestructive testing capabilities,and low requirements for sample preparation.However,high-accuracy reconstruction of the tritium depth profile remains a significant challenge for this technique.In this study,a novel reconstruction method based on a backpropagation(BP)neural network algorithm that demonstrates high accuracy,broad applicability,and robust noise resistance is proposed.The average reconstruction error calculated using the BP network(8.0%)was much lower than that obtained using traditional numerical methods(26.5%).In addition,the BP method can accurately reconstruct BIX spectra of samples with an unknown range of tritium and exhibits wide applicability to spectra with various tritium distributions.Furthermore,the BP network demonstrates superior accuracy and stability compared to numerical methods when reconstructing the spectra,with a relative uncertainty ranging from 0 to 10%.This study highlights the advantages of BP networks in accurately reconstructing the tritium depth profile from BIXS and promotes their further application in tritium detection.展开更多
Background:The reconstruction of clonal haplotypes and their evolutionary history in evolving populations is a common problem in both microbial evolutionary biology and cancer biology.The clonal theory of evolution pr...Background:The reconstruction of clonal haplotypes and their evolutionary history in evolving populations is a common problem in both microbial evolutionary biology and cancer biology.The clonal theory of evolution provides a theoretical framework for modeling the evolution of clones.Results:In this paper,we review the theoretical framework and assumptions over which the clonal reconstruction problem is formulated.We formally define the problem and then discuss the complexity and solution space of the problem.Various methods have been proposed to find the phylogeny that best explains the observed data.We categorize these methods based on the type of input data that they use(space-resolved or time-resolved),and also based on their computational formulation as either combinatorial or probabilistic.It is crucial to understand the different types of input data because each provides essential but distinct information for drastically reducing the solution space of the clonal reconstruction problem.Complementary information provided by single cell sequencing or from whole genome sequencing of randomly isolated clones can also improve the accuracy of clonal reconstruction.We briefly review the existing algorithms and their relationships.Finally we summarize the tools that are developed for either directly solving the clonal reconstruction problem or a related computational problem.Conclusions:In this review,we discuss the various formulations of the problem of inferring the clonal evolutionary history from allele frequeny data,review existing algorithms and catergorize them according to their problem formulation and solution approaches.We note that most of the available clonal inference algorithms were developed for elucidating tumor evolution whereas clonal reconstruction for unicellular genomes are less addressed.We conclude the review by discussing more open problems such as the lack of benchmark datasets and comparison of performance between available tools.展开更多
文摘We build a computer program to reconstruct convex bodies using even L_(p)surface area measures for p≥1.Firstly,we transform the minimization problem Pi,which is equivalent to solving the even L_(p)Minkowski problem,into a convex optimization problem P4 with a finite number of constraints.This transformation makes it suitable for computational resolution.Then,we prove that the approximate solutions obtained by solving the problem P4 converge to the theoretical solution when N and k are sufficiently large.Finally,based on the convex optimization problem P_(4),we provide an algorithm for reconstructing convex bodies from even L_(p)surface area measures,and present several examples implemented using MATLAB.
基金supported by the National Nature Science Foundation of China(Nos.12027901 and 12041202)Synchrotron Radiation Joint Fund of University of Science and Technology of China(Nos.KY2090000059 and KY2090000054)。
文摘There is a contradiction between the evolution rate of materials and the time resolution of SR-CT characterization in the in situ synchrotron radiation computed tomography(SR-CT)characterization of ultrafast evolution process.The sampling strategy of the ultra-sparse angle is an effective method for improving time resolution.Accurate reconstruction under sparse sampling conditions has always been a bottleneck problem.In recent years,convolutional neural networks have shown outstanding advantages in sparse-angle CT reconstruction given the development of deep learning.However,existing ideas did not consider the expression of high-frequency details in neural networks,limiting their application in accurate SR-CT characterization.A novel high-frequency information-constrained deep learning network(HFIC-Net)is proposed in response to this problem.Additional high-frequency information constraints are added to improve the accuracy of the reconstruction results.Further,a series of numerical reconstruction experiments are conducted to verify this new method,and the results indicate that the reconstruction results of HFIC-Net method effectively improve reconstruction quality.This new method uses only eight-angle projections to achieve the reconstruction effect of the filtered backprojection method(FBP)method in 360 projections.The results of the HFIC-Net method demonstrate clear boundaries and accurate detailed structures,correcting the misinformation caused by using other methods.For quantitative evaluation,the SSIM used to evaluate image structure similarity is increased from 0.1951,0.9212,and 0.9308 for FBP,FBP-Conv,and DDC-Net,respectively,to 0.9620 for HFIC-Net.Finally,the results of actual SR-CT experimental data indicate that the new method can suppress artifacts and achieve accurate reconstruction,and it is suitable for the in situ SR-CT accurate characterization of ultxafast evolution process.
基金supported by the National Key Research and Development Program of China(No.2022YFE03170003)the National Natural Science Foundation of China(Nos.12305403 and 12275243).
文摘β-ray-induced X-ray spectroscopy(BIXS)is a promising method for tritium detection in solid materials because of its unique advantages,such as large detection depth,nondestructive testing capabilities,and low requirements for sample preparation.However,high-accuracy reconstruction of the tritium depth profile remains a significant challenge for this technique.In this study,a novel reconstruction method based on a backpropagation(BP)neural network algorithm that demonstrates high accuracy,broad applicability,and robust noise resistance is proposed.The average reconstruction error calculated using the BP network(8.0%)was much lower than that obtained using traditional numerical methods(26.5%).In addition,the BP method can accurately reconstruct BIX spectra of samples with an unknown range of tritium and exhibits wide applicability to spectra with various tritium distributions.Furthermore,the BP network demonstrates superior accuracy and stability compared to numerical methods when reconstructing the spectra,with a relative uncertainty ranging from 0 to 10%.This study highlights the advantages of BP networks in accurately reconstructing the tritium depth profile from BIXS and promotes their further application in tritium detection.
文摘Background:The reconstruction of clonal haplotypes and their evolutionary history in evolving populations is a common problem in both microbial evolutionary biology and cancer biology.The clonal theory of evolution provides a theoretical framework for modeling the evolution of clones.Results:In this paper,we review the theoretical framework and assumptions over which the clonal reconstruction problem is formulated.We formally define the problem and then discuss the complexity and solution space of the problem.Various methods have been proposed to find the phylogeny that best explains the observed data.We categorize these methods based on the type of input data that they use(space-resolved or time-resolved),and also based on their computational formulation as either combinatorial or probabilistic.It is crucial to understand the different types of input data because each provides essential but distinct information for drastically reducing the solution space of the clonal reconstruction problem.Complementary information provided by single cell sequencing or from whole genome sequencing of randomly isolated clones can also improve the accuracy of clonal reconstruction.We briefly review the existing algorithms and their relationships.Finally we summarize the tools that are developed for either directly solving the clonal reconstruction problem or a related computational problem.Conclusions:In this review,we discuss the various formulations of the problem of inferring the clonal evolutionary history from allele frequeny data,review existing algorithms and catergorize them according to their problem formulation and solution approaches.We note that most of the available clonal inference algorithms were developed for elucidating tumor evolution whereas clonal reconstruction for unicellular genomes are less addressed.We conclude the review by discussing more open problems such as the lack of benchmark datasets and comparison of performance between available tools.
