In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise c...In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.展开更多
Learning to Rank(L2R)技术是对搜索结果进行排序,是近几年的研究热点。现关于L2R中的PairWise方法进行研究分析,PairWise方法将排序问题转化为二元分类问题,其缺点是只考虑两篇文档的相对顺序,而不考虑文档出现在搜索结果列表中的位置...Learning to Rank(L2R)技术是对搜索结果进行排序,是近几年的研究热点。现关于L2R中的PairWise方法进行研究分析,PairWise方法将排序问题转化为二元分类问题,其缺点是只考虑两篇文档的相对顺序,而不考虑文档出现在搜索结果列表中的位置。另外,不同的查询拥有的文档对数目不同,结果会向拥有文档对较多的查询偏移。对常用的PairWise算法的损失函数及其求解方法、基本思想、算法框架、效用评价以及算法应用进行概括分析。展开更多
Test of consistency is critical for the analytic hierarchy process(AHP) methodology. When a pairwise comparison matrix(PCM) fails the consistency test, the decision maker(DM) needs to make revisions. The state of the ...Test of consistency is critical for the analytic hierarchy process(AHP) methodology. When a pairwise comparison matrix(PCM) fails the consistency test, the decision maker(DM) needs to make revisions. The state of the art focuses on changing a single entry or creating a new matrix based on the original inconsistent matrix so that the modified matrix can satisfy the consistency requirement. However, we have noticed that the reason that causes inconsistency is not only numerical inconsistency, but also logical inconsistency, which may play a more important role in the whole inconsistency. Therefore, to realize satisfactory consistency, first of all, we should change some entries that form a directed circuit to make the matrix logically consistent, and then adjust other entries within acceptable deviations to make the matrix numerically consistent while preserving most of the original comparison information. In this paper, we firstly present some definitions and theories, based on which two effective methods are provided to identify directed circuits. Four optimization models are proposed to adjust the original inconsistent matrix. Finally, illustrative examples and comparison studies show the effectiveness and feasibility of our method.展开更多
Understanding the mechanism of gastrulation-the early phase in embryonic development where the blastula loses its symmetry and forms organized germ layers（i.e.endoderm,mesoderm,and ectoderm）-has long been a major ch...Understanding the mechanism of gastrulation-the early phase in embryonic development where the blastula loses its symmetry and forms organized germ layers（i.e.endoderm,mesoderm,and ectoderm）-has long been a major challenge to the field of developmental biology.A long standing objective in developmental biology is not only to direct the differentiation of ESCs into specific developmental lineages,but also to organize these differentiated lineages into spatially distinct arrangements resembling the physiological gastrulation.In vivo,research on embryo morphogenesis in lower animals has demonstrated the importance of mechanical forces<sup>[1-3]</sup>.In vitro,experiments of self-sorting utilize pairwise sorting assays where two types of differentiated germ cells are homogeneously mixed<sup>[4]</sup>.It has not been possible to study the or-展开更多
文摘In this paper,we introduce the real pairwise completely positive(RPCP)matrices with one of them is necessarily positive semidefinite while the other one is necessarily entrywise nonnegative,which has a real pairwise completely positive(RPCP)decomposition.We study the properties of RPCP matrices and give some necessary and sufficient conditions for a matrix pair to be RPCP.First,we give an equivalent decomposition for the RPCP matrices,which is different from the RPCP-decomposition and show that the matrix pair(X,X)is RPCP if and only if X is completely positive.Besides,we also prove that the RPCP matrices checking problem is equivalent to the separable completion problem.A semidefinite algorithm is also proposed for detecting whether or not a matrix pair is RPCP.The asymptotic and finite convergence of the algorithm are also discussed.If it is RPCP,we can further give a RPCP-decomposition for it;if it is not,we can obtain a certificate for this.
文摘Learning to Rank(L2R)技术是对搜索结果进行排序,是近几年的研究热点。现关于L2R中的PairWise方法进行研究分析,PairWise方法将排序问题转化为二元分类问题,其缺点是只考虑两篇文档的相对顺序,而不考虑文档出现在搜索结果列表中的位置。另外,不同的查询拥有的文档对数目不同,结果会向拥有文档对较多的查询偏移。对常用的PairWise算法的损失函数及其求解方法、基本思想、算法框架、效用评价以及算法应用进行概括分析。
基金supported by the National Natural Science Foundation of China(61601501 61502521)
文摘Test of consistency is critical for the analytic hierarchy process(AHP) methodology. When a pairwise comparison matrix(PCM) fails the consistency test, the decision maker(DM) needs to make revisions. The state of the art focuses on changing a single entry or creating a new matrix based on the original inconsistent matrix so that the modified matrix can satisfy the consistency requirement. However, we have noticed that the reason that causes inconsistency is not only numerical inconsistency, but also logical inconsistency, which may play a more important role in the whole inconsistency. Therefore, to realize satisfactory consistency, first of all, we should change some entries that form a directed circuit to make the matrix logically consistent, and then adjust other entries within acceptable deviations to make the matrix numerically consistent while preserving most of the original comparison information. In this paper, we firstly present some definitions and theories, based on which two effective methods are provided to identify directed circuits. Four optimization models are proposed to adjust the original inconsistent matrix. Finally, illustrative examples and comparison studies show the effectiveness and feasibility of our method.
基金supported by the funds from Huazhong University of Science and TechnologyUS NIH grant GM072744
文摘Understanding the mechanism of gastrulation-the early phase in embryonic development where the blastula loses its symmetry and forms organized germ layers（i.e.endoderm,mesoderm,and ectoderm）-has long been a major challenge to the field of developmental biology.A long standing objective in developmental biology is not only to direct the differentiation of ESCs into specific developmental lineages,but also to organize these differentiated lineages into spatially distinct arrangements resembling the physiological gastrulation.In vivo,research on embryo morphogenesis in lower animals has demonstrated the importance of mechanical forces<sup>[1-3]</sup>.In vitro,experiments of self-sorting utilize pairwise sorting assays where two types of differentiated germ cells are homogeneously mixed<sup>[4]</sup>.It has not been possible to study the or-
