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Network-based hierarchical heterogeneity analysis and applications to cancer omics data. 基于网络的层次异质性分析及其在癌症组学数据中的应用。
IF 1.6 2区 数学
Science China-Mathematics Pub Date : 2026-08-01 Epub Date: 2025-12-02 DOI: 10.1007/s11425-024-2435-2
Ruiyue Wang, Sanguo Zhang, Shuangge Ma
{"title":"Network-based hierarchical heterogeneity analysis and applications to cancer omics data.","authors":"Ruiyue Wang, Sanguo Zhang, Shuangge Ma","doi":"10.1007/s11425-024-2435-2","DOIUrl":"10.1007/s11425-024-2435-2","url":null,"abstract":"<p><p>In the study of complex diseases, heterogeneity analysis has been routinely conducted. A series of recent studies have suggested that network (graph)-based heterogeneity analysis can take a system perspective and be more informative than that based on simpler statistics such as mean and variance. In this article, we conduct Gaussian graphical model (GGM)-based heterogeneity analysis. Significantly advancing from the existing literature, we consider the scenario, where measurements can be decomposed into two parts, with the first and second parts for a rough grouping and a refined subgrouping, respectively. Additionally, the groups and subgroups have a nested structure, which enhances interpretability. A penalization approach is developed for simultaneous sparse estimation, grouping and subgrouping, and achieving the hierarchical structure. Its theoretical properties are rigorously established, and an effective computational algorithm is developed. Simulation demonstrates its competitive empirical performance. The analysis of data from the Pan-Cancer Analysis of Whole Genomes (PCAWG) further demonstrates its practical utility and leads to sensible findings.</p>","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"69 8","pages":"2181-2194"},"PeriodicalIF":1.6,"publicationDate":"2026-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13655714/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149167098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
One-cycles on Gushel-Mukai fourfolds and the Beauville-Voisin filtration Gushel-Mukai四层单循环过滤和Beauville-Voisin过滤
2区 数学
Science China-Mathematics Pub Date : 2023-11-09 DOI: 10.1007/s11425-022-2119-8
Ruxuan Zhang
{"title":"One-cycles on Gushel-Mukai fourfolds and the Beauville-Voisin filtration","authors":"Ruxuan Zhang","doi":"10.1007/s11425-022-2119-8","DOIUrl":"https://doi.org/10.1007/s11425-022-2119-8","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":" 16","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135293346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Rigidity of non-renormalizable Newton maps 不可重整的牛顿映射的刚性
2区 数学
Science China-Mathematics Pub Date : 2023-11-02 DOI: 10.1007/s11425-022-2136-1
Pascale Roesch, Yongcheng Yin, Jinsong Zeng
{"title":"Rigidity of non-renormalizable Newton maps","authors":"Pascale Roesch, Yongcheng Yin, Jinsong Zeng","doi":"10.1007/s11425-022-2136-1","DOIUrl":"https://doi.org/10.1007/s11425-022-2136-1","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"100 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135975912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the saturation number for singular cubic surfaces 关于奇异三次曲面的饱和数
2区 数学
Science China-Mathematics Pub Date : 2023-10-30 DOI: 10.1007/s11425-023-2227-9
Wang, Yuchao, Yao, Weili
{"title":"On the saturation number for singular cubic surfaces","authors":"Wang, Yuchao, Yao, Weili","doi":"10.1007/s11425-023-2227-9","DOIUrl":"https://doi.org/10.1007/s11425-023-2227-9","url":null,"abstract":"We investigate the distribution of rational points on singular cubic surfaces, whose coordinates have few prime factors. The key tools used are universal torsors, the circle method and results on linear equations in primes.","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136019670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A GMM approach in coupling internal data and external summary information with heterogeneous data populations 一种将内部数据和外部汇总信息与异构数据群耦合在一起的GMM方法
2区 数学
Science China-Mathematics Pub Date : 2023-10-30 DOI: 10.1007/s11425-022-2111-0
Jun Shao, Jinyi Wang, Lei Wang
{"title":"A GMM approach in coupling internal data and external summary information with heterogeneous data populations","authors":"Jun Shao, Jinyi Wang, Lei Wang","doi":"10.1007/s11425-022-2111-0","DOIUrl":"https://doi.org/10.1007/s11425-022-2111-0","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"6 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136133020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Triples of almost primes 几乎质数的三元组
2区 数学
Science China-Mathematics Pub Date : 2023-10-30 DOI: 10.1007/s11425-023-2226-5
Jiamin Li, Jianya Liu
{"title":"Triples of almost primes","authors":"Jiamin Li, Jianya Liu","doi":"10.1007/s11425-023-2226-5","DOIUrl":"https://doi.org/10.1007/s11425-023-2226-5","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136132330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
On the core entropy of Newton maps 关于牛顿映射的核心熵
2区 数学
Science China-Mathematics Pub Date : 2023-10-27 DOI: 10.1007/s11425-021-2010-1
Yan Gao
{"title":"On the core entropy of Newton maps","authors":"Yan Gao","doi":"10.1007/s11425-021-2010-1","DOIUrl":"https://doi.org/10.1007/s11425-021-2010-1","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"23 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136233682","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Permutation orbifolds of vertex operator superalgebras and associative algebras 顶点算子超代数和结合代数的置换轨道
2区 数学
Science China-Mathematics Pub Date : 2023-10-18 DOI: 10.1007/s11425-023-2214-3
Chongying Dong, Feng Xu, Nina Yu
{"title":"Permutation orbifolds of vertex operator superalgebras and associative algebras","authors":"Chongying Dong, Feng Xu, Nina Yu","doi":"10.1007/s11425-023-2214-3","DOIUrl":"https://doi.org/10.1007/s11425-023-2214-3","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135943416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The functional equations of Langlands Eisenstein series for SL(n, ℤ) SL(n, n)下Langlands Eisenstein级数的泛函方程
2区 数学
Science China-Mathematics Pub Date : 2023-10-16 DOI: 10.1007/s11425-023-2213-y
Goldfeld, Dorian, Stade, Eric, Woodbury, Michael
{"title":"The functional equations of Langlands Eisenstein series for SL(n, ℤ)","authors":"Goldfeld, Dorian, Stade, Eric, Woodbury, Michael","doi":"10.1007/s11425-023-2213-y","DOIUrl":"https://doi.org/10.1007/s11425-023-2213-y","url":null,"abstract":"This paper presents a very simple explicit description of Langlands Eisenstein series for ${rm SL}(n,mathbb Z)$. The functional equations of these Eisenstein series are heuristically derived from the functional equations of certain divisor sums and certain Whittaker functions that appear in the Fourier coefficients of the Eisenstein series. We conjecture that the functional equations are unique up to a real affine transformation of the $s$ variables defining the Eisenstein series and prove the uniqueness conjecture in certain cases.","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136077418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A remark on density theorems for Riemann’s zeta-function 黎曼函数密度定理的注解
2区 数学
Science China-Mathematics Pub Date : 2023-10-16 DOI: 10.1007/s11425-023-2215-7
János Pintz
{"title":"A remark on density theorems for Riemann’s zeta-function","authors":"János Pintz","doi":"10.1007/s11425-023-2215-7","DOIUrl":"https://doi.org/10.1007/s11425-023-2215-7","url":null,"abstract":"","PeriodicalId":54444,"journal":{"name":"Science China-Mathematics","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136182988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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