This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are glob...This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are globally convergent for general convex functions.展开更多
To subtract the slit function from the measured spectrum, a wavelet-based deconvolution method is proposed to obtain a regularized solution of the problem. The method includes reconstructing the signal from the wavele...To subtract the slit function from the measured spectrum, a wavelet-based deconvolution method is proposed to obtain a regularized solution of the problem. The method includes reconstructing the signal from the wavelet modulus maxima. For the purpose of maxima selection, the spatially selective noise filtration technique was used to distinguish modulus maxima produced by signal from the one created by noise. To test the method, sodium spectrum measured at a wide slit was deconvolved. He-Ne spectrum measured at the corresponding slit width was used as slit function. Sodium measured at a narrow slit was used as the reference spectrum. The deconvolutton result shows that this method can enhance the resolution of the degraded spectrum greatly.展开更多
Post-transcriptional modifications,including histone modifications and DNA methylation,alter the chromatin landscape to regulate gene expression,thus control various cellular processes in plants.EARLY FLOWERING IN SHO...Post-transcriptional modifications,including histone modifications and DNA methylation,alter the chromatin landscape to regulate gene expression,thus control various cellular processes in plants.EARLY FLOWERING IN SHORT DAYS(EFS)is the major contributor for H3K36 methylation in Arabidopsis and is important for plant development.Here,we find that EFS is expressed in different stages of embryo morphogenesis,and the efs mutant produces larger embryo that results in enlarged seeds.Further analysis reveals that an imprinted gene MOP9.5 is hypomethylated at the promoter region and its expression is derepressed in efs mutant.MOP9.5 promoter is marked by various epigenetic modifications,and we find that following the increase of H3K36me3,H3K27me3 and H3K9me2 levels are reduced in efs mutant.This data indicates an antagonistic regulation between H3K36me3 and DNA methylation,and/or H3K27me3 at MOP9.5.Our results further show that both maternal and paternal EFS alleles are responsible for the seed size regulation,which unraveled a novel function of EFS in plant development.展开更多
The paper intends to provide a framework for bringing about and understanding the most important and key dimensions of the Chinese Dream in a historical, sociocultural, sociopolitical and global nexus. It represents a...The paper intends to provide a framework for bringing about and understanding the most important and key dimensions of the Chinese Dream in a historical, sociocultural, sociopolitical and global nexus. It represents a part of global efforts to describe and interpret the holistic nature of the Chinese Dream concept both as an internal and external policy statement and as a new vocabulary in international relations lexicon. The paper seeks to deconstruct and demystify the implicit and explicit essence of the Chinese Dream concept in enlightening and critical ways at the time when China＇s developments and transformations are still undergoing and moving forward.展开更多
In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two ca...In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton's principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether's theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d'Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether's theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether's theorems for discrete systems. Several examples are given to illustrate the application of our results.展开更多
Let m, n 〉 1 be two coprime integers. In this paper, we prove that a finite solvable group is nilpotent if the set of the conjugacy class sizes of its primary and biprimary elements is {1, rn, n, mn}.
This paper aims to develop a new robust U-type test for high dimensional regression coefficients using the estimated U-statistic of order two and refitted cross-validation error variance estimation. It is proved that ...This paper aims to develop a new robust U-type test for high dimensional regression coefficients using the estimated U-statistic of order two and refitted cross-validation error variance estimation. It is proved that the limiting null distribution of the proposed new test is normal under two kinds of ordinary models.We further study the local power of the proposed test and compare with other competitive tests for high dimensional data. The idea of refitted cross-validation approach is utilized to reduce the bias of sample variance in the estimation of the test statistic. Our theoretical results indicate that the proposed test can have even more substantial power gain than the test by Zhong and Chen(2011) when testing a hypothesis with outlying observations and heavy tailed distributions. We assess the finite-sample performance of the proposed test by examining its size and power via Monte Carlo studies. We also illustrate the application of the proposed test by an empirical analysis of a real data example.展开更多
Despite fluctuations in embryo size within a species,the spatial gene expression pattern and hence the embryonic structure can nonetheless maintain the correct proportion to the embryo size.This is known as the scalin...Despite fluctuations in embryo size within a species,the spatial gene expression pattern and hence the embryonic structure can nonetheless maintain the correct proportion to the embryo size.This is known as the scaling phenomenon.For morphogen-induced patterning of gene expression,the positional information encoded in the local morphogen concentrations is decoded by the downstream genetic network(the decoder).In this paper,we show that the requirement of scaling sets severe constraints on the geometric structure of such a local decoder,which in turn enables deduction of mutants’behavior and extraction of regulation information without going into any molecular details.We demonstrate that the Drosophila gap gene system achieves scaling in the way consistent with our theory—the decoder geometry required by scaling correctly accounts for the observed gap gene expression pattern in nearly all maternal morphogen mutants.Furthermore,the regulation logic and the coding/decoding strategy of the gap gene system can also be revealed from the decoder geometry.Our work provides a general theoretical framework for a large class of problems where scaling output is achieved by non-scaling inputs and a local decoder,as well as a unified understanding of scaling,mutants’behavior,and gene regulation for the Drosophila gap gene system.展开更多
文摘This paper explores the convergence of a class of optimally conditioned self scaling variable metric (OCSSVM) methods for unconstrained optimization. We show that this class of methods with Wolfe line search are globally convergent for general convex functions.
文摘To subtract the slit function from the measured spectrum, a wavelet-based deconvolution method is proposed to obtain a regularized solution of the problem. The method includes reconstructing the signal from the wavelet modulus maxima. For the purpose of maxima selection, the spatially selective noise filtration technique was used to distinguish modulus maxima produced by signal from the one created by noise. To test the method, sodium spectrum measured at a wide slit was deconvolved. He-Ne spectrum measured at the corresponding slit width was used as slit function. Sodium measured at a narrow slit was used as the reference spectrum. The deconvolutton result shows that this method can enhance the resolution of the degraded spectrum greatly.
基金supported by National Key R&D Program (2016YFA0500800)the National Natural Science Foundation of China (31571322)+2 种基金Tsinghua-Peking Joint Center for Life Sciences1000 Young Talent Program of ChinaS.Shafiq and Wei Xu are supported by the postdoctoral fellowships from Tsinghua-Peking Joint Center for Life Sciences
文摘Post-transcriptional modifications,including histone modifications and DNA methylation,alter the chromatin landscape to regulate gene expression,thus control various cellular processes in plants.EARLY FLOWERING IN SHORT DAYS(EFS)is the major contributor for H3K36 methylation in Arabidopsis and is important for plant development.Here,we find that EFS is expressed in different stages of embryo morphogenesis,and the efs mutant produces larger embryo that results in enlarged seeds.Further analysis reveals that an imprinted gene MOP9.5 is hypomethylated at the promoter region and its expression is derepressed in efs mutant.MOP9.5 promoter is marked by various epigenetic modifications,and we find that following the increase of H3K36me3,H3K27me3 and H3K9me2 levels are reduced in efs mutant.This data indicates an antagonistic regulation between H3K36me3 and DNA methylation,and/or H3K27me3 at MOP9.5.Our results further show that both maternal and paternal EFS alleles are responsible for the seed size regulation,which unraveled a novel function of EFS in plant development.
文摘The paper intends to provide a framework for bringing about and understanding the most important and key dimensions of the Chinese Dream in a historical, sociocultural, sociopolitical and global nexus. It represents a part of global efforts to describe and interpret the holistic nature of the Chinese Dream concept both as an internal and external policy statement and as a new vocabulary in international relations lexicon. The paper seeks to deconstruct and demystify the implicit and explicit essence of the Chinese Dream concept in enlightening and critical ways at the time when China＇s developments and transformations are still undergoing and moving forward.
基金supported by the National Natural Science Foundations of China (Grant Nos.11072218 and 11272287)the Natural Science Foundations of Zhejiang Province of China (Grant No.Y6110314)
文摘In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton's principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether's theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d'Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether's theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether's theorems for discrete systems. Several examples are given to illustrate the application of our results.
基金supported by National Natural Science Foundation of China(Grant Nos.11201401 and 11101258)National Science Foundation for Postdoctoral Scientists of China(Grant No.20100480582)University of Jinan Research Funds for Doctors(Grant Nos.XBS1335 and XBS1336)
文摘Let m, n 〉 1 be two coprime integers. In this paper, we prove that a finite solvable group is nilpotent if the set of the conjugacy class sizes of its primary and biprimary elements is {1, rn, n, mn}.
基金supported by National Natural Science Foundation of China (Grant Nos. 11071022, 11231010 and 11471223)Beijing Center for Mathematics and Information Interdisciplinary ScienceKey Project of Beijing Municipal Educational Commission (Grant No. KZ201410028030)
文摘This paper aims to develop a new robust U-type test for high dimensional regression coefficients using the estimated U-statistic of order two and refitted cross-validation error variance estimation. It is proved that the limiting null distribution of the proposed new test is normal under two kinds of ordinary models.We further study the local power of the proposed test and compare with other competitive tests for high dimensional data. The idea of refitted cross-validation approach is utilized to reduce the bias of sample variance in the estimation of the test statistic. Our theoretical results indicate that the proposed test can have even more substantial power gain than the test by Zhong and Chen(2011) when testing a hypothesis with outlying observations and heavy tailed distributions. We assess the finite-sample performance of the proposed test by examining its size and power via Monte Carlo studies. We also illustrate the application of the proposed test by an empirical analysis of a real data example.
基金supported by the National Natural Science Foundation of China(12090053 and 32088101)。
文摘Despite fluctuations in embryo size within a species,the spatial gene expression pattern and hence the embryonic structure can nonetheless maintain the correct proportion to the embryo size.This is known as the scaling phenomenon.For morphogen-induced patterning of gene expression,the positional information encoded in the local morphogen concentrations is decoded by the downstream genetic network(the decoder).In this paper,we show that the requirement of scaling sets severe constraints on the geometric structure of such a local decoder,which in turn enables deduction of mutants’behavior and extraction of regulation information without going into any molecular details.We demonstrate that the Drosophila gap gene system achieves scaling in the way consistent with our theory—the decoder geometry required by scaling correctly accounts for the observed gap gene expression pattern in nearly all maternal morphogen mutants.Furthermore,the regulation logic and the coding/decoding strategy of the gap gene system can also be revealed from the decoder geometry.Our work provides a general theoretical framework for a large class of problems where scaling output is achieved by non-scaling inputs and a local decoder,as well as a unified understanding of scaling,mutants’behavior,and gene regulation for the Drosophila gap gene system.
