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Null-free False Discovery Rate Control Using Decoy Permutations

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Acta Mathematicae Applicatae Sinica 2022年第2期38卷 235-253页

作者： Kun He Mengjie Li Yan Fu Fuzhou Gong Xiaoming Sun Institute of Computing Technology Chinese Academy of SciencesBeijing 100190China CEMS NCMISRCSDSAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China

The traditional approaches to false discovery rate(FDR)control in multiple hypothesis testing are usually based on the null distribution of a test ***,all types of null distributions,including the theoretical,permutation-based and empirical ones,have some inherent *** example,the theoretical null might fail because of improper assumptions on the sample ***,we propose a null distributionfree approach to FDR control for multiple hypothesis testing in the case-control *** approach,named target-decoy procedure,simply builds on the ordering of tests by some statistic or score,the null distribution of which is not required to be *** decoy tests are constructed from permutations of original samples and are used to estimate the false target *** prove that this approach controls the FDR when the score function is symmetric and the scores are independent between different *** demonstrates that it is more stable and powerful than two popular traditional approaches,even in the existence of *** is also made on two real datasets,including an arabidopsis genomics dataset and a COVID-19 proteomics dataset.

关键词： multiple testing false discovery rate null distribution-free p-value-free decoy permutations knockoff filter

A strong law of large numbers under sublinear expectations

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Probability, Uncertainty and Quantitative Risk 2023年第3期8卷 333-350页

作者： Yongsheng Song rcsds Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

We consider a sequence of independent and identically distributed(i.i.d.)random variables{ξ_(k)}under a sublinear expectation E=sup_(P∈Θ).We first give a new proof to the fact that,under each P∈Θ,any cluster point of the empirical ***,we consider sublinear expectations on a Polish space,and show that for each constantμ∈[μ,μ^(-)],there exists a probability P_(μ)∈Θsuch thatlim_(n→∞)ξ_(n)=μ,P_(μ-a.s.,(0.1))supposing thatΘis weakly compact *** the same conditions,we obtain a generalization of(0.1)in the product space with replaced *** is a Borel measurable function on,.Finally,we characterize the triviality of the tail-algebra of the *** variables under a sublinear expectation.

关键词： Law of large numbers Tailσ-algebra Sublinear expectation

Gradient estimates for nonlinear diffusion semigroups by coupling methods

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Science China Mathematics 2021年第5期64卷 1093-1108页

In this paper, we obtain gradient estimates for certain nonlinear partial differential equations by coupling methods. First, we derive uniform gradient estimates for certain semi-linear PDEs based on the coupling method introduced by Wang in 2011 and the theory of backward SDEs. Then we generalize Wang's coupling to the G-expectation space and obtain gradient estimates for nonlinear diffusion semigroups, which correspond to the solutions of certain fully nonlinear PDEs.

关键词： gradient estimates coupling methods G-expectation nonlinear PDEs

On the Dirichlet form of three-dimensional Brownian motion conditioned to hit the origin

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Science China Mathematics 2019年第8期62卷 1477-1492页

作者： Patrick J. Fitzsimmons Liping Li Department of Mathematics University of California at San Diego San Diego CA 92093-0112 USA rcsds HCMS Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

Our concern in this paper is the energy form induced by an eigenfunction of a self-adjoint extension of the restriction of the Laplace operator to C_c^∞(R^3\{0}).We will prove that this energy form is a regular Dirichlet form with core C_c^∞(R^3).The associated diffusion X behaves like a 3-dimensional Brownian motion with a mild radial drift when far from 0,subject to an ever-stronger push toward 0 near that *** particular,{0}is not a polar set with respect to *** diffusion X is rotation invariant,and admits a skew-product representation before hitting{0}:its radial part is a diffusion on(0,∞)and its angular part is a time-changed Brownian motion on the sphere S^*** radial part of X is a"reflected"extension of the radial part of X^0(the part process of X before hitting{0}).Moreover,X is the unique reflecting extension of X^0,but X is not a semi-martingale.

关键词： Dirichlet form reflected extension rotationally invariant process Fukushima’s decomposition

Large-scale determination and characterization of cell type-specific regulatory elements in the human genorne

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Journal of Molecular Cell Biology 2017年第6期9卷 463-476页

作者： Can Wang Shihua Zhang NCMIS CEMS RCSDS Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 China

Histone modifications have been widely elucidated to play vital roles in gene regulation and cell identity. The Roadmap Epigenomics Consortium generated a reference catalog of several key histone modifications across >100s of human cell types and tissues. Decoding these epigenomes into functional regulatory elements is a challenging task in computational biology. To this end, we adopted a differential chromatin modification analysis framework to comprehensively determine and characterize cell type-specific regulatory elements (CSREs) and their histone modification codes in the human epigenomes of five histone modifications across 127 tissues or cell types. The CSREs show significant relevance with cell type-specific biological functions and diseases and cell identity. Clustering of CSREs with their specificity signals reveals distinct histone codes, demonstrating the diversity of functional roles of CSREs within the same cell or tissue. Last but not least, dynamics of CSREs from close cell types or tissues can give a detailed view of developmental processes such as normal tissue development and cancer occurrence.

关键词：房间类型元素规章织物开发计算生物学生物功能路线图

Noise effect on the 2D stochastic Burgers equation

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Acta Mathematica Sinica,English Series 2023年

作者： Zhao DONG Jiang-Lun WU Guoli ZHOU Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science (IRADS) UIC 4. Corresponding author School of Statistics and Mathematics Chongqing University Beijing Normal University-Hong Kong Baptist University United International College rcsds Academy of Mathematics and Systems Science Chinese Academy of Sciences

By comprehensive utilizing of the geometry structure of 2D Burgers equation and the stochastic noise, we find the decay properties of the solution to the stochastic 2D Burgers equation with Dirichlet boundary conditio...

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BMTK： a toolkit for determining modules in biological bipartite networks

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Frontiers of Electrical and Electronic Engineering in China 2018年第2期6卷 186-192页

作者： Bei Wang Jinyu Chen Shihua Zhang NCMIS CEMS RCSDS Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 China

Background： Module detection is widely used to analyze and visualize biological networks. A number of methods and tools have been developed to achieve it. Meanwhile, bipartite module detection is also very useful for mining and analyzing bipartite biological networks and a few methods have been developed for it. However, there is few user- friendly toolkit for this task. Methods： To this end, we develop an online web toolkit BMTK, which implements seven existing methods. Results： BMTK provides a uniform operation platform and visualization function, standardizes input and output format, and improves algorithmic structure to enhance computing speed. We also apply this toolkit onto a drug-target bipartite network to demonstrate its effectiveness. Conclusions： BMTK will be a powerful tool for detecting bipartite modules in diverse bipartite biological networks. Availability： The web application is freely accessible at http：//***/BMTK.

关键词： network biology module detection biological bipartite networks

A criterion on a repeller being a null set of any limit measure for stochastic differential equations

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Science China Mathematics 2021年第2期64卷 221-238页

作者： Lifeng Chen Zhao Dong Jifa Jiang Mathematics and Science College Shanghai Normal UniversityShanghai 200234China rcsds Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

This paper studies limit behaviors of stationary measures for stochastic ordinary differential equations with nondegenerate noise and presents a criterion to guarantee that a repeller with zero Lebesgue measure is a null set of any limit *** this criterion,we first provide a series of nontrivial concrete examples to show that their repelling limit cycles or quasi-periodic orbits are null sets for all limit measures,which deduces that all their limit measures are concentrated on stable equilibria and stable limit cycles or quasi-periodic orbits,and *** open questions on exact supports of limit measures are proposed.

关键词： stationary measure limit measure support Lyapunov function repelling limit cycle repelling quasi-periodic orbit

A single-nucleus transcriptomic atlas of the dog hippocampus reveals the potential relationship between specific cell types and domestication

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National Science Review 2022年第11期9卷 108-120页

作者： Qi-Jun Zhou Xingyan Liu Longlong Zhang Rong Wang Tingting Yin Xiaolu Li Guimei Li Yuqi He Zhaoli Ding Pengcheng Ma Shi-Zhi Wang Bingyu Mao Shihua Zhang Guo-Dong Wang State Key Laboratory of Genetic Resources and Evolution Kunming Institute of ZoologyChinese Academy of Sciences NCMIS CEMS RCSDSAcademy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences Kunming College of Life Science University of Chinese Academy of Sciences College of Life Science University of Chinese Academy of Sciences Genomic Center of Biodiversity Kunming Institute of ZoologyChinese Academy of Sciences Center for Excellence in Animal Evolution and Genetics Chinese Academy of Sciences Key Laboratory of Systems Health Science of Zhejiang Province School of Life ScienceHangzhou Institute for Advanced StudyUniversity of Chinese Academy of Sciences

The process of domestication has led to dramatic differences in behavioral traits between domestic dogs and gray wolves. Whole-genome research found that a class of putative positively selected genes were related to various aspects of learning and memory, such as long-term potentiation and long-term depression. In this study, we constructed a single-nucleus transcriptomic atlas of the dog hippocampus to illustrate its cell types, cell lineage and molecular features. Using the transcriptomes of 105 057 nuclei from the hippocampus of a Beagle dog, we identified 26 cell clusters and a putative trajectory of oligodendrocyte *** analysis revealed a significant convergence between dog differentially expressed genes(DEGs) and putative positively selected genes(PSGs). Forty putative PSGs were DEGs in glutamatergic neurons, especially in Cluster 14, which is related to the regulation of nervous system development. In summary, this study provides a blueprint to understand the cellular mechanism of dog domestication.

关键词： dog single-nucleus RNA sequencing hippocampus domestication