Global Stocktake is an important component of the global climate governance mechanism.The first Global Stocktake under the Paris Agreement in 2023 has clarified collective progress and identified the paths to bridge g...Global Stocktake is an important component of the global climate governance mechanism.The first Global Stocktake under the Paris Agreement in 2023 has clarified collective progress and identified the paths to bridge gaps,but its understanding in the academic and policy communities is not yet systematic and comprehensive.Therefore,this study adopts textual analysis,timeline analysis,and game theory methods to comprehensively analyze the process and outcomes of the first Global Stocktake.The study finds that:①The first Global Stocktake underwent three stages,including scientific enhancement,technical dialogue,and political consensus,and took more than five years to reach the final outcome of the United Arab Emirates(UAE)Consensus in which the 1.5℃temperature control target anchored in the scientific enhancement stage set the general tone for the stocktake.②The first Global Stocktake focused on three specific areas—mitigation,adaptation,means of implementation and support—to fully realize the signaling effect.③The most prominent outcome of the stocktake is the new consensus on“transitioning away from all fossil fuels in energy systems”,which specifies the direction for countries to update their nationally determined contributions in 2025 and for the international community to conduct the second Global Stocktake in 2028.④The four groups of countries,namely,developed countries,emerging economies,hydrocarbon-exporting-oriented economies,and climate-vulnerable countries,have different interests and hold distinct core positions,which constrain each other but advance the global stocktake process as a whole.⑤The outcomes of the stocktake are comprehensive and systematic,with as many as 196 consensus items;however,the detailed targets for the three major focus areas are unclear and rigid,and need to be strengthened in the second global stocktake.The study suggests that,on the one hand,China needs to strengthen its policy research in the light of the outcomes of the first Global Stocktake and prepare for the submission of updated nationally determined contribution in 2025 for 2035,which should be consistent with the 1.5℃temperature control target.On the other hand,China should continue to take advantage of the zero-carbon industry to lead global climate change action and expand national development right and international communication capacity.展开更多
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 meth...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.展开更多
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 Diric...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 point.In particular,{0}is not a polar set with respect to X.The 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^2.The 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.展开更多
The traditional approaches to false discovery rate(FDR)control in multiple hypothesis testing are usually based on the null distribution of a test statistic.However,all types of null distributions,including the theore...The traditional approaches to false discovery rate(FDR)control in multiple hypothesis testing are usually based on the null distribution of a test statistic.However,all types of null distributions,including the theoretical,permutation-based and empirical ones,have some inherent drawbacks.For example,the theoretical null might fail because of improper assumptions on the sample distribution.Here,we propose a null distributionfree approach to FDR control for multiple hypothesis testing in the case-control study.This 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 known.Competitive decoy tests are constructed from permutations of original samples and are used to estimate the false target discoveries.We prove that this approach controls the FDR when the score function is symmetric and the scores are independent between different tests.Simulation demonstrates that it is more stable and powerful than two popular traditional approaches,even in the existence of dependency.Evaluation is also made on two real datasets,including an arabidopsis genomics dataset and a COVID-19 proteomics dataset.展开更多
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 n...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 measure.Using 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 saddles.Interesting open questions on exact supports of limit measures are proposed.展开更多
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 ...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 〉lOOs of human cell types and tissues. Decoding these epJgenomes 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.展开更多
Single-cell RNA sequencing(scRNA-seq)provides a powerful tool to determine expression patterns of thousands of individual cells.However,the analysis of scRNA-seq data remains a computational challenge due to the high ...Single-cell RNA sequencing(scRNA-seq)provides a powerful tool to determine expression patterns of thousands of individual cells.However,the analysis of scRNA-seq data remains a computational challenge due to the high technical noise such as the presence of dropout events that lead to a large proportion of zeros for expressed genes.Taking into account the cell heterogeneity and the relationship between dropout rate and expected expression level,we present a cell sub-population based bounded low-rank(PBLR)method to impute the dropouts of scRNA-seq data.Through application to both simulated and real scRNA-seq datasets,PBLR is shown to be effective in recovering dropout events,and it can dramaimprove the low・dimensional representation and the recovery of gene-gene relationships masked by dropout events compared to several state-of-the-art methods・Moreover,PBLR also detects accurate and robust cell sub-populations automatically,shedding light on its flexibility and generality for scRNA-seq data analysis.展开更多
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...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：//www.zhanglabtools.net/BMTK.展开更多
Nonnegative Matrix Factorization(NMF)is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning.However,deep learning networks,with their carefully...Nonnegative Matrix Factorization(NMF)is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning.However,deep learning networks,with their carefully designed hierarchical structure,can combine hidden features to form more representative features for pattern recognition.In this paper,we proposed sparse deep NMF models to analyze complex data for more accurate classification and better feature interpretation.Such models are designed to learn localized features or generate more discriminative representations for samples in distinct classes by imposing L1-norm penalty on the columns of certain factors.By extending a one-layer model into a multilayer model with sparsity,we provided a hierarchical way to analyze big data and intuitively extract hidden features due to nonnegativity.We adopted the Nesterov’s accelerated gradient algorithm to accelerate the computing process.We also analyzed the computing complexity of our frameworks to demonstrate their efficiency.To improve the performance of dealing with linearly inseparable data,we also considered to incorporate popular nonlinear functions into these frameworks and explored their performance.We applied our models using two benchmarking image datasets,and the results showed that our models can achieve competitive or better classification performance and produce intuitive interpretations compared with the typical NMF and competing multilayer models.展开更多
Cell type-specific genomic regulation is driven by the binding of transcription factors(TFs)in accessible genomic regions.Thus,chromatin accessibility can be used to identify cis-regulatory elements and directly depic...Cell type-specific genomic regulation is driven by the binding of transcription factors(TFs)in accessible genomic regions.Thus,chromatin accessibility can be used to identify cis-regulatory elements and directly depict cellular identity.Single-cell Assay for Transposase-Accessible Chromatin using sequencing(Single-cell ATAC-seq or scATAC-seq)has enabled genome-wide profiling of chromatin accessibility at single-cell resolution and can thus reveal epigenetic heterogeneity at cellular level[1].展开更多
We consider the point vortex model associated to the modified Surface Quasi-Geostrophic(mSQG) equations on the two dimensional torus. It is known that this model is well posed for almost every initial conditions. We s...We consider the point vortex model associated to the modified Surface Quasi-Geostrophic(mSQG) equations on the two dimensional torus. It is known that this model is well posed for almost every initial conditions. We show that, when the system is perturbed by a certain space-dependent noise, it admits a unique global solution for any initial configuration. We also present an explicit example for the deterministic system on the plane where three different point vortices collapse.展开更多
3D Burgers equation is an important model for turbulence.It is natural to expect the long-time behaviour for this hydrodynamics equation.However,there is no result about the long-time behaviour for this deterministic ...3D Burgers equation is an important model for turbulence.It is natural to expect the long-time behaviour for this hydrodynamics equation.However,there is no result about the long-time behaviour for this deterministic model.Surprisingly,if the system is perturbed by stochastic noise,we establish the existence and uniqueness of invariant measure for 3D stochastic Burgers equation.展开更多
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 poin...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 averages.Next,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 and.Under the same conditions,we obtain a generalization of(0.1)in the product space with replaced by.Here is a Borel measurable function on,.Finally,we characterize the triviality of the tail-algebra of the i.i.d.random variables under a sublinear expectation.展开更多
Consider the two-dimensional, incompressible Navier-Stokes equations on torus T^2= [-π, π]^2 driven by a degenerate multiplicative noise in the vorticity formulation（abbreviated as SNS）： dwt = ν？w_tdt ＋B（Kw_t...Consider the two-dimensional, incompressible Navier-Stokes equations on torus T^2= [-π, π]^2 driven by a degenerate multiplicative noise in the vorticity formulation（abbreviated as SNS）： dwt = ν？w_tdt ＋B（Kw_t, w_t）dt ＋ Q（w_t）dW t. We prove that the solution to SNS is continuous differentiable in initial value. We use the Malliavin calculus to prove that the semigroup{P_t}_t≥0 generated by the SNS is asymptotically strong Feller. Moreover, we use the coupling method to prove that the solution to SNS has a weak form of irreducibility.Under almost the same Hypotheses as that given by Odasso, Prob. Theory Related Fields, 140： 41–82（2005）with a different method, we get an exponential ergodicity under a stronger norm.展开更多
Single-cell Hi-C technology provides an unprecedented opportunity to reveal chromatin structure in individual cells.However,high sequencing cost impedes the generation of biological Hi-C data with high sequencing dept...Single-cell Hi-C technology provides an unprecedented opportunity to reveal chromatin structure in individual cells.However,high sequencing cost impedes the generation of biological Hi-C data with high sequencing depths and multiple replicates for downstream analysis.Here,we developed a single-cell Hi-C simulator(scHi-CSim)that generates high-fidelity data for benchmarking.scHi-CSim merges neighboring cells to overcome the sparseness of data,samples interactions in distance-stratified chromosomes to maintain the heterogeneity of single cells,and estimates the empirical distribution of restriction fragments to generate simulated data.We demonstrated that scHi-CSim can generate high-fidelity data by comparing the performance of single-cell clustering and detection of chromosomal high-order structures with raw data.Furthermore,scHi-CSim is flexible to change sequencing depth and the number of simulated replicates.We showed that increasing sequencing depth could improve the accuracy of detecting topologically associating domains.We also used scHi-CSim to generate a series of simulated datasets with different sequencing depths to benchmark scHi-C clustering methods.展开更多
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 condition...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 conditions.Consequently,the expected ergodicity for this turbulence model is established.展开更多
基金supported by the National Natural Science Foundation of China“Study on the Construction of China’s Economic Transformation Model Toward Carbon Neutrality”[Grant No.72140001].
文摘Global Stocktake is an important component of the global climate governance mechanism.The first Global Stocktake under the Paris Agreement in 2023 has clarified collective progress and identified the paths to bridge gaps,but its understanding in the academic and policy communities is not yet systematic and comprehensive.Therefore,this study adopts textual analysis,timeline analysis,and game theory methods to comprehensively analyze the process and outcomes of the first Global Stocktake.The study finds that:①The first Global Stocktake underwent three stages,including scientific enhancement,technical dialogue,and political consensus,and took more than five years to reach the final outcome of the United Arab Emirates(UAE)Consensus in which the 1.5℃temperature control target anchored in the scientific enhancement stage set the general tone for the stocktake.②The first Global Stocktake focused on three specific areas—mitigation,adaptation,means of implementation and support—to fully realize the signaling effect.③The most prominent outcome of the stocktake is the new consensus on“transitioning away from all fossil fuels in energy systems”,which specifies the direction for countries to update their nationally determined contributions in 2025 and for the international community to conduct the second Global Stocktake in 2028.④The four groups of countries,namely,developed countries,emerging economies,hydrocarbon-exporting-oriented economies,and climate-vulnerable countries,have different interests and hold distinct core positions,which constrain each other but advance the global stocktake process as a whole.⑤The outcomes of the stocktake are comprehensive and systematic,with as many as 196 consensus items;however,the detailed targets for the three major focus areas are unclear and rigid,and need to be strengthened in the second global stocktake.The study suggests that,on the one hand,China needs to strengthen its policy research in the light of the outcomes of the first Global Stocktake and prepare for the submission of updated nationally determined contribution in 2025 for 2035,which should be consistent with the 1.5℃temperature control target.On the other hand,China should continue to take advantage of the zero-carbon industry to lead global climate change action and expand national development right and international communication capacity.
基金supported by NCMIS, National Natural Science Foundation of China (Grant Nos.11871458 and 11688101)Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No.QYZDB-SSW-SYS017)。
文摘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.
基金supported by National Natural Science Foundation of China (Grant Nos. 11688101 and 11801546)Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences (Grant No. 2008DP173182)
文摘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 point.In particular,{0}is not a polar set with respect to X.The 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^2.The 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.
基金supported by the National Key R&D Program of China(No.2018YFB0704304)the National Natural Science Foundation of China(Nos.32070668,62002231,61832003,61433014)the K.C.Wong Education Foundation。
文摘The traditional approaches to false discovery rate(FDR)control in multiple hypothesis testing are usually based on the null distribution of a test statistic.However,all types of null distributions,including the theoretical,permutation-based and empirical ones,have some inherent drawbacks.For example,the theoretical null might fail because of improper assumptions on the sample distribution.Here,we propose a null distributionfree approach to FDR control for multiple hypothesis testing in the case-control study.This 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 known.Competitive decoy tests are constructed from permutations of original samples and are used to estimate the false target discoveries.We prove that this approach controls the FDR when the score function is symmetric and the scores are independent between different tests.Simulation demonstrates that it is more stable and powerful than two popular traditional approaches,even in the existence of dependency.Evaluation is also made on two real datasets,including an arabidopsis genomics dataset and a COVID-19 proteomics dataset.
基金supported by National Natural Science Foundation of China(Grant Nos.11771295,11431014,11931004 and 11371252)Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182)。
文摘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 measure.Using 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 saddles.Interesting open questions on exact supports of limit measures are proposed.
文摘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 〉lOOs of human cell types and tissues. Decoding these epJgenomes 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.
基金This work was supported by the National Key R&D Program of China(2019YFA0709501)the National Natural Science Foundation of China(11661141019 and 61621003)+1 种基金the Nati onal Ten Thousa nd Tale nt Program for Young Top-notch Talents,the CAS Frontier Science Research Key Project for Top Young Scientist(QYZDB-SSW-SYS008)and Shanghai Municipal Science and Technology Major Project(2017SHZDZX01).
文摘Single-cell RNA sequencing(scRNA-seq)provides a powerful tool to determine expression patterns of thousands of individual cells.However,the analysis of scRNA-seq data remains a computational challenge due to the high technical noise such as the presence of dropout events that lead to a large proportion of zeros for expressed genes.Taking into account the cell heterogeneity and the relationship between dropout rate and expected expression level,we present a cell sub-population based bounded low-rank(PBLR)method to impute the dropouts of scRNA-seq data.Through application to both simulated and real scRNA-seq datasets,PBLR is shown to be effective in recovering dropout events,and it can dramaimprove the low・dimensional representation and the recovery of gene-gene relationships masked by dropout events compared to several state-of-the-art methods・Moreover,PBLR also detects accurate and robust cell sub-populations automatically,shedding light on its flexibility and generality for scRNA-seq data analysis.
基金This work has been supported by the National Natural Science Foundation of China （Nos. 61621003, 61422309, 61379092 and 11661141019）, the Strategic Priority Research Program of the Chinese Academy of Sciences （CAS） （XDB13040600） and CAS Frontier Science Research Key Project for Top Young Scientist （QYZDB-SSW-SYS008）.
文摘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：//www.zhanglabtools.net/BMTK.
基金supported by the National Natural Science Foundation of China(Nos.11661141019 and 61621003)the National Ten Thousand Talent Program for Young Topnotch Talents+1 种基金Chinese Academy Science(CAS)Frontier Science Research Key Project for Top Young Scientist(No.QYZDB-SSW-SYS008)the Key Laboratory of Random Complex Structures and Data Science,CAS(No.2008DP173182).
文摘Nonnegative Matrix Factorization(NMF)is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning.However,deep learning networks,with their carefully designed hierarchical structure,can combine hidden features to form more representative features for pattern recognition.In this paper,we proposed sparse deep NMF models to analyze complex data for more accurate classification and better feature interpretation.Such models are designed to learn localized features or generate more discriminative representations for samples in distinct classes by imposing L1-norm penalty on the columns of certain factors.By extending a one-layer model into a multilayer model with sparsity,we provided a hierarchical way to analyze big data and intuitively extract hidden features due to nonnegativity.We adopted the Nesterov’s accelerated gradient algorithm to accelerate the computing process.We also analyzed the computing complexity of our frameworks to demonstrate their efficiency.To improve the performance of dealing with linearly inseparable data,we also considered to incorporate popular nonlinear functions into these frameworks and explored their performance.We applied our models using two benchmarking image datasets,and the results showed that our models can achieve competitive or better classification performance and produce intuitive interpretations compared with the typical NMF and competing multilayer models.
基金supported by the National Key R&D Program of China(2019YFA0709501)the National Natural Science Foundation of China(61621003)+1 种基金the National Ten Thousand Talent Program for Young Top-notch Talents,the CAS Frontier Science Research Key Project for Top Young Scientist(QYZDB-SSW-SYS008)the Shanghai Municipal Science and Technology Major Project(2017SHZDZX01).
文摘Cell type-specific genomic regulation is driven by the binding of transcription factors(TFs)in accessible genomic regions.Thus,chromatin accessibility can be used to identify cis-regulatory elements and directly depict cellular identity.Single-cell Assay for Transposase-Accessible Chromatin using sequencing(Single-cell ATAC-seq or scATAC-seq)has enabled genome-wide profiling of chromatin accessibility at single-cell resolution and can thus reveal epigenetic heterogeneity at cellular level[1].
基金The first author is supported by the National Natural Science Foundation of China(Grant Nos.11571347,11688101)the Youth Innovation Promotion Association,CAS(Grant No.2017003)。
文摘We consider the point vortex model associated to the modified Surface Quasi-Geostrophic(mSQG) equations on the two dimensional torus. It is known that this model is well posed for almost every initial conditions. We show that, when the system is perturbed by a certain space-dependent noise, it admits a unique global solution for any initial configuration. We also present an explicit example for the deterministic system on the plane where three different point vortices collapse.
基金This research is supported by the National Key R&D Program of China(Grant Nos.2020YFA0712700,2018YFA0703901)National Natural Science Foundation of China(Grant Nos.11871458,11688101)Key Research Program of Frontier Sciences,CAS(Grant No.QYZDB-SSW-SYS017).
文摘Peng,S.[6]proved the law of large numbers under a sublinear expectation.In this paper,we give its error estimates by Stein’s method.
基金supported by National Key R&D Program of China(Grant Nos.2020YFA0712700)NNSF of China(Grant Nos.12090014,11931004,11971077)+3 种基金Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182)Chongqing Key Laboratory of Analytic Mathematics and Applications,Chongqing UniversityNatural Science Foundation Project of CQ(Grant No.cstc2020jcyj-msxmX0441)Fundamental Research Funds for the Central Universities(Grant No.2020CDJ-LHZZ-027)。
文摘3D Burgers equation is an important model for turbulence.It is natural to expect the long-time behaviour for this hydrodynamics equation.However,there is no result about the long-time behaviour for this deterministic model.Surprisingly,if the system is perturbed by stochastic noise,we establish the existence and uniqueness of invariant measure for 3D stochastic Burgers equation.
基金supported by National Key R&D Program of China(Grant Nos.2020YFA0712700,2018YFA0703901)NSFCs(Grant No.11871458)Key Research Program of Frontier Sciences,CAS(Grant No.QYZDBSSW-SYS017).
文摘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 averages.Next,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 and.Under the same conditions,we obtain a generalization of(0.1)in the product space with replaced by.Here is a Borel measurable function on,.Finally,we characterize the triviality of the tail-algebra of the i.i.d.random variables under a sublinear expectation.
基金supported by the National Natural Science Foundation of China(No.11371041,11431014)the Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(No.2008DP173182)+3 种基金supported by NSFC(No.11501195)a Scientific Research Fund of Hunan Provincial Education Department(No.17C0953)the Youth Scientific Research Fund of Hunan Normal University(No.Math140650)the Construct Program of the Key Discipline in Hunan Province
文摘Consider the two-dimensional, incompressible Navier-Stokes equations on torus T^2= [-π, π]^2 driven by a degenerate multiplicative noise in the vorticity formulation（abbreviated as SNS）： dwt = ν？w_tdt ＋B（Kw_t, w_t）dt ＋ Q（w_t）dW t. We prove that the solution to SNS is continuous differentiable in initial value. We use the Malliavin calculus to prove that the semigroup{P_t}_t≥0 generated by the SNS is asymptotically strong Feller. Moreover, we use the coupling method to prove that the solution to SNS has a weak form of irreducibility.Under almost the same Hypotheses as that given by Odasso, Prob. Theory Related Fields, 140： 41–82（2005）with a different method, we get an exponential ergodicity under a stronger norm.
基金supported by the National Natural Science Foundation of China(61873198 and 62132015 to L.G.,62002275 to Y.Y.,and 61621003 to S.Z.)the National Key ResearchandDevelopment ProgramoCf hina(2019YFA0709501)+1 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences(XDA16021400 and XDPB17 to S.z.)the Key-Area Research and Development of Guangdong Province(2020B1111190001).
文摘Single-cell Hi-C technology provides an unprecedented opportunity to reveal chromatin structure in individual cells.However,high sequencing cost impedes the generation of biological Hi-C data with high sequencing depths and multiple replicates for downstream analysis.Here,we developed a single-cell Hi-C simulator(scHi-CSim)that generates high-fidelity data for benchmarking.scHi-CSim merges neighboring cells to overcome the sparseness of data,samples interactions in distance-stratified chromosomes to maintain the heterogeneity of single cells,and estimates the empirical distribution of restriction fragments to generate simulated data.We demonstrated that scHi-CSim can generate high-fidelity data by comparing the performance of single-cell clustering and detection of chromosomal high-order structures with raw data.Furthermore,scHi-CSim is flexible to change sequencing depth and the number of simulated replicates.We showed that increasing sequencing depth could improve the accuracy of detecting topologically associating domains.We also used scHi-CSim to generate a series of simulated datasets with different sequencing depths to benchmark scHi-C clustering methods.
基金Supported by National Key R and D Program of China(Grant No.2020YFA0712700)NSFC(Grant Nos.11931004,11971077,12090014)+3 种基金Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182)Chongqing Key Laboratory of Analytic Mathematics and Applications,Chongqing University,Natural Science Foundation Project of CQ(Grant No.cstc2020jcyjmsxmX0441)Fundamental Research Funds for the Central Universities(Grant No.2020CDJ-LHZZ-027)UIC Start-up Research Fund(Grant No.UICR0700072-24)。
文摘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 conditions.Consequently,the expected ergodicity for this turbulence model is established.
