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Rainbow Pancyclicity in a Collection of Graphs Under the Dirac-type Condition

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 269-274页

作者： Lu-yi LI Ping LI Xue-liang LI center for combinatorics and lpmc Nankai UniversityTianjin 300071China School of Mathematics and Statistics Shaanxi Normal UniversityXi’an 710062China

Let G={Gi:i∈[n]} be a collection of not necessarily distinct n-vertex graphs with the same vertex set V,where G can be seen as an edge-colored(multi)graph and each Gi is the set of edges with color i.A graph F on V is called rainbow if any two edges of F come from different Gis’.We say that G is rainbow pancyclic if there is a rainbow cycle Cℓof lengthℓin G for each integerℓ2[3,n].In 2020,Joos and Kim proved a rainbow version of Dirac’s theorem:Ifδ(Gi)≥2/n for each i∈[n],then there is a rainbow Hamiltonian cycle in *** this paper,under the same condition,we show that G is rainbow pancyclic except that n is even and G consists of n copies of Kn/2,n/*** result supports the famous meta-conjecture posed by Bondy.

关键词： rainbow Hamiltonian cycle rainbow pancyclic meta-conjecture

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A New Class of Strong Orthogonal Arrays of Strength Three

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Journal of Systems Science & Complexity 2024年第3期37卷 1233-1250页

作者： WANG Chunyan LIU Min-Qian YANG Jinyu center for Applied Statistics and School of Statistics Renmin University of ChinaBeijing 100872China School of Statistics and Data Science LPMC&KLMDASRNankai UniversityTianjin 300071China

Strong orthogonal arrays(SOAs) were recently introduced and studied as a class of spacefilling designs for computer experiments. To surely realize better space-filling properties, SOAs of strength three or higher are desirable. In addition, orthogonality is also an important property for designs of computer experiments, because it guarantees that the estimates of the main effects are uncorrelated. This paper first provides a systematic study on the construction of(nearly) orthogonal strength-three SOAs with better space-filling properties. The newly proposed strength-three SOAs enjoy almost the same space-filling properties of strength-four SOAs, and can accommodate much more columns than the latter. Moreover, they are(nearly) orthogonal and flexible in run sizes. The construction methods are straightforward to implement, and their theoretical supports are well established. In addition to the theoretical results, many designs are tabulated for practical needs.

关键词： Computer experiment orthogonality space-filling property strong orthogonal array

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Immanant positivity for Catalan-Stieltjes matrices

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Frontiers of Mathematics in China 2022年第5期17卷 887-903页

作者： Ethan Y.H.LI Grace M.X.LI Arthur L.B.YANG Candice X.T.ZHANG center for combinatorics LPMCNankai UniversityTianjin 300071China

We give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel *** obtain these sufficient conditions,we construct new planar networks with a recursive nature for Catalan-Stieltjes *** applications,we provide a unified way to produce inequalities for many combinatorial polynomials,such as the Eulerian polynomials,Schröder polynomials,and Narayana polynomials.

关键词： Immanant character Catalan-Stieltjes matrices Hankel matrices planar network

Hypergraph Turan Numbers of Vertex Disjoint Cycles

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Acta Mathematicae Applicatae Sinica 2022年第1期38卷 229-234页

作者： Ran GU Xue-liang LI Yong-tang SHI center for combinatorics and lpmc Nankai UniversityTianjin 300071China

The Turan number of a k-uniform hypergraph H,denoted by exk(n;H),is the maximum number of edges in any k-uniform hypergraph F on n vertices which does not contain H as a *** Cl(k)denote the family of all k-uniform minimal cycles of length l;S(l1,…,lr)denote the family of hypergraphs consisting of unions of r vertex disjoint minimal cycles of lengthl1,…lr,respectively,and Cl(k)denote a k-uniform linear cycle of length *** determine precisely exk(n;S(l1,…,lr)and exk(n;Cl1(k),…,Cl1(k)for sufficiently large *** results extend recent results of Füredi and Jiang who determined the Turan numbers for single k-uniform minimal cycles and linear cycles.

关键词： Turan number cycles extremal hypergraphs

scEpiTools: a database to comprehensively interrogate analytic tools for single-cell epigenomic data

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Journal of Genetics and Genomics 2024年第4期51卷 462-465页

作者： Zijing Gao Xiaoyang Chen Zhen Li Xuejian Cui Qun Jiang Keyi Li Shengquan Chen Rui Jiang Ministry of Education Key Laboratory of Bioinformatics Bioinformatics Division at the Beijing National Research Center for Information Science and TechnologyCenter for Synthetic and Systems BiologyDepartment of AutomationTsinghua UniversityBeijing 100084China School of Mathematical Sciences and lpmc Nankai UniversityTianjin 300071China

Recent advances in single-cell sequencing technologies provide significant implications for understanding cellular heterogeneity,developmental biology,and disease *** fully exploit the potential of these data,numerous tools have been proposed for upstream and downstream *** the the single-cell RNA sequencing(scRNA-seq)community,scRNA-tools(Zappia et al.,2018)was proposed to help researchers navigate the plethora of tools by *** its inception,scRNA-tools has been widely used and its updated version further reveals trends in the field with over 1000 collected tools(Zappia and Theis,2021),providing a valuable guidance in selecting tools for analyses.

关键词： analytic selecting Tools

Bounds for the Rainbow Disconnection Numbers of Graphs

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Acta Mathematica Sinica,English Series 2022年第2期38卷 384-396页

作者： Xu Qing BAI Zhong HUANG Xue Liang LI center for combinatorics and lpmc Nankai UniversityTianjin 300071P.R.China

An edge-cut of an edge-colored connected graph is called a rainbow cut if no two edges in the edge-cut are colored the *** edge-colored graph is rainbow disconnected if for any two distinct vertices u and v of the graph,there exists a rainbow cut separating u and *** a connected graph G,the rainbow disconnection number of G,denoted by rd(G),is defined as the smallest number of colors required to make G rainbow *** this paper,we first give some upper bounds for rd(G),and moreover,we completely characterize the graphs which meet the upper bounds of the NordhausGaddum type result obtained early by ***,we propose a conjecture that for any connected graph G,either rd(G)=λ^(+)(G)or rd(G)=λ^(+)(G)+1,whereλ^(+)(G)is the upper edge-connectivity,and prove that the conjecture holds for many classes of graphs,which supports this ***,we prove that for an odd integer k,if G is a k-edge-connected k-regular graph,thenχ’(G)=k if and only if rd(G)=*** implies that there are infinitely many k-edge-connected k-regular graphs G for which rd(G)=λ^(+)(G)for odd k,and also there are infinitely many k-edge-connected k-regular graphs G for which rd(G)=λ^(+)(G)+1 for odd *** k=3,the result gives rise to an interesting result,which is equivalent to the famous Four-Color ***,we give the relationship between rd(G)of a graph G and the rainbow vertex-disconnection number rvd(L(G))of the line graph L(G)of G.

关键词： Edge-coloring edge-connectivity rainbow disconnection coloring(number) line graph

SCREEN:predicting single-cell gene expression perturbation responses via optimal transport

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Frontiers of Computer Science 2024年第3期18卷 255-257页

作者： Haixin WANG Yunhan WANG Qun JIANG Yan ZHANG Shengquan CHEN Cadre Medical Department The 1st Clinical CenterChinese PLA General HospitalBeijing 100853China School of Statistics Renmin University of ChinaBeijing 100872China Ministry of Education Key Laboratory of Bioinformatics Bioinformatics Division of BNRISTDepartment of AutomationTsinghua UniversityBeijing 100084China School of Mathematical Sciences and lpmc Nankai UniversityTianjin 300071China

1 Introduction Recent advances in single-cell RNA sequencing(scRNA-seq)have enabled the study of how individual cells respond to various external perturbations such as drug stimulation at gene expression level[1].Precisely inferring perturbation responses allows us to explore how and why individual tumor cells evade cancer treatment,greatly advancing personalized medicine research and deepening our understanding of biological mechanisms[2].However,considering the high costs of sequencing and the complexity of obtaining perturbed samples,utilizing computational methods to predict cellular responses to perturbations holds great potential[2].

关键词： stimulation perturbation deepening

Variable Selection for High-dimensional Cox Model with Error Rate Control

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Journal of Systems Science & Complexity 2024年

作者： HE Baihua SHI Hongwei GUO Xu ZOU Changliang ZHU Lixing International Institute of Finance School of Management University of Science and Technology of China School of Statistics Beijing Normal University School of Statistics and Data Science LPMC KLMDASR and LEBPS Nankai University center for Statistics and Data Science Beijing Normal University at Zhuhai Department of Mathematics Hong Kong Baptist University

Simultaneously finding active predictors and controlling the false discovery rate(FDR) for high-dimensional survival data is an important but challenging statistical problem. In this paper, the authors propose a novel variable selection procedure with error rate control for the high-dimensional Cox model. By adopting a data-splitting strategy, the authors construct a series of symmetric statistics and then utilize the symmetry property to derive a data-driven threshold to achieve error rate *** authors establish finite-sample and asymptotic FDR control results under some mild *** results as well as a real data application show that the proposed approach successfully controls FDR and is often more powerful than the competing approaches.

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Upper bounds of Schubert polynomials

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Science China Mathematics 2022年第6期65卷 1319-1330页

作者： Neil Jiuyu Fan Peter Long Guo Department of Mathematics Sichuan UniversityChengdu 610064China center for combinatorics LPMCNankai UniversityTianjin 300071China

Let w be a permutation of{1,2,...,n},and let D(w)be the Rothe diagram of *** Schubert polynomial■w_(x)can be realized as the dual character of the flagged Weyl module associated with D(w).This implies the following coefficient-wise inequality:Min_(x)≤■_(w)(x)≤Max_(w)xwhere both Min_(w)(x)and Max_(w)(x)are polynomials determined by D(w).Fink et al.(2018)found that■w_(x)equals the lower bound Min_(w)(x)if and only if w avoids twelve permutation *** this paper,we show that■w_(x)reaches the upper bound Max_(w)(x)if and only if w avoids two permutation patterns 1432 and ***,for any given compositionα∈Z^(n)≥0,one can define a lower bound Min_(α)(x)and an upper bound Max_(α)(x)for the key polynomialκ_(α)(x).Hodges and Yong(2020)established thatκ_(α)(x)equals Min_(α)(x)if and only ifαavoids five composition *** show thatκ_(α)(x)equals Max_(α)(x)if and only ifαavoids a single composition pattern(0,2).As an application,we obtain that whenαavoids(0,2),the key polynomialκ_(α)(x)is Lorentzian,partially verifying a conjecture of Huh et al.(2019).

关键词： Schubert polynomial key polynomial flagged Weyl module upper bound Lorentzian polynomial