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Single-cell omics: experimental workflow, data analyses and applications

Science China Life sciences 2025年第1期68卷 5-102页

作者： Fengying Sun Haoyan Li Dongqing Sun Shaliu Fu Lei Gu Xin Shao Qinqin Wang Xin Dong Bin Duan Feiyang Xing Jun Wu Minmin Xiao Fangqing Zhao Jing-Dong J.Han Qi Liu Xiaohui Fan Chen Li Chenfei Wang Tieliu Shi Department of Clinical Laboratory the Affiliated Wuhu Hospital of East China Normal University (The Second People's Hospital of Wuhu City) Pharmaceutical Informatics Institute College of Pharmaceutical SciencesZhejiang University Key Laboratory of Spine and Spinal Cord Injury Repair and Regeneration (Tongji University) Ministry of EducationOrthopaedic DepartmentTongji HospitalBioinformatics DepartmentSchool of Life Sciences and TechnologyTongji University Frontier Science Center for Stem Cells School of Life Sciences and TechnologyTongji University Translational Medical Center for Stem Cell Therapy and Institute for Regenerative Medicine Shanghai East HospitalBioinformatics DepartmentSchool of Life Sciences and TechnologyTongji University Research Institute of Intelligent Computing Zhejiang Lab Shanghai Research Institute for Intelligent Autonomous Systems Center for Single-cell Omics School of Public HealthShanghai Jiao Tong University School of Medicine National Key Laboratory of Chinese Medicine Modernization Innovation Center of Yangtze River DeltaZhejiang University Center for Bioinformatics and Computational Biology Shanghai Key Laboratory of Regulatory Biologythe Institute of Biomedical Sciences and School of Life SciencesEast China Normal University Beijing Institutes of Life Science Chinese Academy of Sciences Peking-Tsinghua Center for Life sciences Academy for Advanced Interdisciplinary StudiesCenter for Quantitative Biology (CQB)Peking University Zhejiang Key Laboratory of Precision Diagnosis and Therapy for Major Gynecological Diseases Women's HospitalZhejiang University School of Medicine Key Laboratory of Advanced Theory and Application in statistics and Data Science-MOE School of StatisticsEast China Normal University

Cells are the fundamental units of biological systems and exhibit unique development trajectories and molecular features. Our exploration of how the genomes orchestrate the formation and maintenance of each cell, and control the cellular phenotypes of various organismsis, is both captivating and intricate. Since the inception of the first single-cell RNA technology, technologies related to single-cell sequencing have experienced rapid advancements in recent years. These technologies have expanded horizontally to include single-cell genome, epigenome,proteome, and metabolome, while vertically, they have progressed to integrate multiple omics data and incorporate additional information such as spatial sc RNA-seq and CRISPR screening. Single-cell omics represent a groundbreaking advancement in the biomedical field,offering profound insights into the understanding of complex diseases, including cancers. Here, we comprehensively summarize recent advances in single-cell omics technologies, with a specific focus on the methodology section. This overview aims to guide researchers in selecting appropriate methods for single-cell sequencing and related data analysis.

关键词： single-cell sequencing genome epigenome proteomics metabolomics multimodal spatial transcriptomics CRISPR screening

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CONTACT PROCESS ON HEXAGONAL LATTICE

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Acta Mathematica Scientia 2010年第3期30卷 769-790页

作者：姚强李群昌 Department of statistics and actuarial Science School of Finance and Statistics East China Normal University school of Mathematical sciences Peking University

In this article, we discuss several properties of the basic contact process on hexagonal lattice H, showing that it behaves quite similar to the process on d-dimensional lattice Zd in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite space-time condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process.

关键词： Hexagonal lattice contact process critical value complete convergence theorem rate of growth

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Asymptotic false discovery control of the Benjamini-Hochberg procedure for pairwise comparisons

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Science China Mathematics 2025年第1期 223-252页

作者： Weidong Liu Dennis Leung Qi-Man Shao school of Mathematical sciences Shanghai Jiao Tong University school of Mathematics and statistics University of Melbourne Department of statistics and Data Science SICMSouthern University of Science and Technology

In a one-way analysis-of-variance(ANOVA) model,the number of pairwise comparisons can become large even with a moderate number of *** by this,we consider a regime with a growing number of groups and prove that,when testing pairwise comparisons,the Benjamini-Hochberg(BH) procedure can asymptotically control false discoveries,despite the fact that the involved t-statistics do not exhibit the wellknown positive dependence structure required for exact false discovery rate(FDR) *** Tukey's perspective that the difference between the means of any two groups cannot be exactly zero,our main result provides control over the directional false discovery rate and directional false discovery proportion.A key technical contribution of our work is demonstrating that the dependence among the t-statistics is sufficiently weak to establish the convergence result typically required for asymptotic FDR *** analysis does not rely on conventional assumptions such as normality,variance homogeneity,or a balanced design,thereby offering a theoretical foundation for applications in more general settings.

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Ruin Probabilities in Cox Risk Models with Two Dependent Classes of Business

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Acta Mathematica Sinica,English Series 2007年第7期23卷 1281-1288页

作者： Jun Yi GUO Kam C.YUEN Ming ZHOU school of Mathematical sciences and LPMC Nankai University Department of statistics and actuarial Science The University of Hong Kong

In this paper we consider risk processes with two classes of business in which the two claim-number processes are dependent Cox processes. We first assume that the two claim-number processes have a two-dimensional Markovian intensity. Under this assumption, we not only study the sum of the two individual risk processes but also investigate the two-dimensional risk process formed by considering the two individual processes separately. For each of the two risk processes we derive an expression for the ruin probability, and then construct an upper bound for the ruin probability. We next assume that the intensity of the two claim-number processes follows a Markov chain. In this case, we examine the ruin probability of the sum of the two individual risk processes. Specifically, a differential system for the ruin probability is derived and numerical results are obtained for exponential claim sizes.

关键词： Cox risk model ruin probability Markov process infinitesimal generator

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Alternative Approach to the Optimality of the Threshold Strategy for Spectrally Negative Lvy Processes

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Acta Mathematicae Applicatae Sinica 2013年第4期29卷 705-716页

作者： Ying SHEN Chuan-cun YIN Kam Chuen YUEN school of Mathematical sciences Qufu Normal UniversityChina Department of statistics and actuarial Science The University of Hong Kong

Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy process. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. In this paper, we show that a threshold strategy （also called refraction strategy） forms an optimal strategy under the condition that the Levy measure has a completely monotone density.

关键词： Spectrally negative Levy process optimal dividend problem scale function complete monotonic-ity threshold strategy

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VARIOUS NOTIONS OF ORTHOGONALITY IN NORMED SPACES

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Acta Mathematica Scientia 2013年第5期33卷 1387-1397页

作者： N.B.OKELO J.O.AGURE P.O.OLECHE school of Mathematics and actuarial Science Jaramogi Oginga Odinga University of Science and Technology school of Mathematics Statistics and Actuarial Science Maseno University

In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid- ered. Results on orthogonality of the range and the kern... 详细信息

关键词： orthogonality normed space elementary operator

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Asymptotics of the goodness-of-fit test for a partial linear model with randomly censored data

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Science China Mathematics 2003年第2期46卷 145-158页

作者：陈敏 Kam C.YUEN 朱力行 Academy of Mathematics and System sciences Chinese Academy of Sciences Department of statistics and actuarial Science the University of Hong Kong Department of statistics and actuarial Science the University of Hong Kong Hong Kong China

In this paper, we discuss the problem of testing the hypothesis that the underlying regression isa partial linear model. A test statistic, which is based on the quadratic form of a cusum process of residuals,is proposed. The asymptotic distributions of the test statistic under null hypothesis and the local alternativehypothesis are given. The number simulation shows that the test is available.

关键词： partial linear regression random censoring empirical process model checking

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Optimal Investment and Premium Control in a Nonlinear Diffusion Model

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Acta Mathematicae Applicatae Sinica 2017年第4期33卷 945-958页

作者： Ming ZHOU Kam Chuen YUEN Chuan-cun YIN China Institute for actuarial Science Central University of Finance and Economics Department of statistics and actuarial Science the University of Hong Kong school of statistics Qufu Normal University

This paper considers the optimal investment and premium control problem in a diffusion approxi- mation to a non-homogeneous compound Poisson process. In the nonlinear diffusion model, it is assumed that there is an unspecified monotone function describing the relationship between the safety loading of premium and the time-varying claim arrival rate. Hence, in addition to the investment control, the premium rate can be served as a control variable in the optimization problem. Specifically, the problem is investigated in two cases：（i） maximizing the expected utility of terminal wealth, and （ii） minimizing the probability of ruin respectively. In both cases, some properties of the value functions are derived, and closed-form expressions for the optimal policies and the value functions are obtained. The results show that the optimal investment policy and the optimal premium control policy are dependent on each other. Most interestingly, as an example, we show that the nonlinear diffusion model reduces to a diffusion model with a quadratic drift coefficient when the function associated with the premium rate and the claim arrival rate takes a special form. This example shows that the model of study represents a class of nonlinear stochastic control risk model.

关键词： CARA utility dependent control policies Hamilton-Jacobi-Bellman (HJB) equation investment premium control

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The Hilbert expansion of the Boltzmann equation in the incompressible Euler level in a channel

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Science China Mathematics 2025年第1期 39-88页

作者： Feimin Huang Weiqiang Wang Yong Wang Feng Xiao Academy of Mathematics and Systems Science Chinese Academy of Sciences school of Mathematical sciences University of Chinese Academy of Sciences Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) School of Mathematics and StatisticsHunan Normal University

The study of the hydrodynamic limit of the Boltzmann equation with physical boundary is a challenging problem due to the appearance of the viscous and Knudsen boundary *** this paper,the hydrodynamic limit from the Boltzmann equation with the specular reflection boundary condition to the incompressible Euler equations in a channel is *** on the multi-scaled Hilbert expansion,the equations with boundary conditions and compatibility conditions for interior solutions,and viscous and Knudsen boundary layers are derived under different scaling,***,some uniform estimates for the interior solutions,and viscous and Knudsen boundary layers are *** the help of the L2-L∞framework and the uniform estimates obtained above,the solutions to the Boltzmann equation are constructed by the truncated Hilbert expansion with multiscales,and hence the hydrodynamic limit in the incompressible Euler level is justified.

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Multiplicative forms on Poisson groupoids

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Science China Mathematics 2025年第1期 169-206页

作者： Zhuo Chen Honglei Lang Zhangju Liu Department of Mathematical sciences Tsinghua University College of Science China Agricultural University school of Mathematics and statistics Henan University

First,we prove a decomposition formula for any multiplicative differential form on a Lie groupoid ***,we prove that if G is a Poisson Lie groupoid,then the space ?mult·（G） of multiplicative forms on G has a differential graded Lie algebra（DGLA） ***,when combined with ?·（M）,which is the space of forms on the base manifold M of G,?mult·（G） forms a canonical DGLA crossed *** supplements a previously known fact that multiplicative multi-vector fields on G form a DGLA crossed module with the Schouten algebra Γ（∧·A） stemming from the Lie algebroid A of G.

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