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Communications in Mathematics and Statistics最新文献

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Even Character Degrees and Ito–Michler Theorem 偶数字符度和伊藤-米克勒定理
IF 0.9 4区 数学
Communications in Mathematics and Statistics Pub Date : 2024-01-18 DOI: 10.1007/s40304-023-00368-0
{"title":"Even Character Degrees and Ito–Michler Theorem","authors":"","doi":"10.1007/s40304-023-00368-0","DOIUrl":"https://doi.org/10.1007/s40304-023-00368-0","url":null,"abstract":"<h3>Abstract</h3> <p>Let <span> <span>(textrm{Irr}_2(G))</span> </span> be the set of linear and even-degree irreducible characters of a finite group <em>G</em>. In this paper, we prove that <em>G</em> has a normal Sylow 2-subgroup if <span> <span>(sum limits _{chi in textrm{Irr}_2(G)} chi (1)^m/sum limits _{chi in textrm{Irr}_2(G)} chi (1)^{m-1} &lt; (1+2^{m-1})/(1+2^{m-2}))</span> </span> for a positive integer <em>m</em>, which is the generalization of several recent results concerning the well-known Ito–Michler theorem.</p>","PeriodicalId":10575,"journal":{"name":"Communications in Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139499762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A Class of Polynomial Modules over Map Lie Algebras 映射李代数上的一类多项式模块
IF 0.9 4区 数学
Communications in Mathematics and Statistics Pub Date : 2024-01-17 DOI: 10.1007/s40304-023-00356-4
Hongjia Chen, Han Dai, Xingpeng Liu
{"title":"A Class of Polynomial Modules over Map Lie Algebras","authors":"Hongjia Chen, Han Dai, Xingpeng Liu","doi":"10.1007/s40304-023-00356-4","DOIUrl":"https://doi.org/10.1007/s40304-023-00356-4","url":null,"abstract":"<p>For any finitely generated unital commutative associative algebra <span>(mathcal {R})</span> over <span>(mathbb {C})</span> and any complex finite-dimensional simple Lie algebra <span>(mathfrak {g})</span> with a fixed Cartan subalgebra <span>(mathfrak {h})</span>, we classify all <span>(mathfrak {g}otimes mathcal {R})</span>-modules on <span>(U(mathfrak {h}))</span> such that <span>(mathfrak {h})</span> as a subalgebra of <span>(mathfrak {g}otimes mathcal {R})</span>, acts on <span>(U(mathfrak {h}))</span> by the multiplication. We construct these modules explicitly and study their module structures.</p>","PeriodicalId":10575,"journal":{"name":"Communications in Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139501530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Directional Entropy and Pinsker $$sigma $$ -Algebra for $$mathbb {Z}^{2}$$ -Actions 定向熵与平斯克 $$sigma $$ -代数的 $$mathbb {Z}^{2}$ -作用
IF 0.9 4区 数学
Communications in Mathematics and Statistics Pub Date : 2024-01-17 DOI: 10.1007/s40304-023-00369-z
Runju Wei, Leiye Xu, Xiaomin Zhou
{"title":"Directional Entropy and Pinsker $$sigma $$ -Algebra for $$mathbb {Z}^{2}$$ -Actions","authors":"Runju Wei, Leiye Xu, Xiaomin Zhou","doi":"10.1007/s40304-023-00369-z","DOIUrl":"https://doi.org/10.1007/s40304-023-00369-z","url":null,"abstract":"<p>In this paper, we study the directional entropy along irrational directions in <span>(mathbb {R}^2)</span> and present the structure of directional Pinsker <span>(sigma )</span>-algebra of <span>(mathbb {Z}^2)</span>-MPSs.</p>","PeriodicalId":10575,"journal":{"name":"Communications in Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139499815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Multiply Robust Estimation of Quantile Treatment Effects with Missing Responses 对有缺失应答的量化治疗效果进行多重稳健估计
IF 0.9 4区 数学
Communications in Mathematics and Statistics Pub Date : 2023-12-29 DOI: 10.1007/s40304-023-00380-4
{"title":"Multiply Robust Estimation of Quantile Treatment Effects with Missing Responses","authors":"","doi":"10.1007/s40304-023-00380-4","DOIUrl":"https://doi.org/10.1007/s40304-023-00380-4","url":null,"abstract":"<h3>Abstract</h3> <p>Causal inference and missing data have attracted significant research interests in recent years, while the current literature usually focuses on only one of these two issues. In this paper, we develop two multiply robust methods to estimate the quantile treatment effect (QTE), in the context of missing data. Compared to the commonly used average treatment effect, QTE provides a more complete picture of the difference between the treatment and control groups. The first one is based on inverse probability weighting, the resulting QTE estimator is root-<em>n</em> consistent and asymptotic normal, as long as the class of candidate models of propensity scores contains the correct model and so does that for the probability of being observed. The second one is based on augmented inverse probability weighting, which further relaxes the restriction on the probability of being observed. Simulation studies are conducted to investigate the performance of the proposed method, and the motivated CHARLS data are analyzed, exhibiting different treatment effects at various quantile levels.</p>","PeriodicalId":10575,"journal":{"name":"Communications in Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139063014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Unadjusted Langevin Algorithm for Non-convex Weakly Smooth Potentials 非凸弱光滑势的未调整朗格文算法
IF 0.9 4区 数学
Communications in Mathematics and Statistics Pub Date : 2023-12-09 DOI: 10.1007/s40304-023-00350-w
Dao Nguyen, Xin Dang, Yixin Chen
{"title":"Unadjusted Langevin Algorithm for Non-convex Weakly Smooth Potentials","authors":"Dao Nguyen, Xin Dang, Yixin Chen","doi":"10.1007/s40304-023-00350-w","DOIUrl":"https://doi.org/10.1007/s40304-023-00350-w","url":null,"abstract":"<p>Discretization of continuous-time diffusion processes is a widely recognized method for sampling. However, the canonical Euler Maruyama discretization of the Langevin diffusion process, referred as unadjusted Langevin algorithm (ULA), studied mostly in the context of smooth (gradient Lipschitz) and strongly log-concave densities, is a considerable hindrance for its deployment in many sciences, including statistics and machine learning. In this paper, we establish several theoretical contributions to the literature on such sampling methods for non-convex distributions. Particularly, we introduce a new mixture weakly smooth condition, under which we prove that ULA will converge with additional log-Sobolev inequality. We also show that ULA for smoothing potential will converge in <span>(L_{2})</span>-Wasserstein distance. Moreover, using convexification of nonconvex domain (Ma et al. in Proc Natl Acad Sci 116(42):20881–20885, 2019) in combination with regularization, we establish the convergence in Kullback–Leibler divergence with the number of iterations to reach <span>(epsilon )</span>-neighborhood of a target distribution in only polynomial dependence on the dimension. We relax the conditions of Vempala and Wibisono (Advances in Neural Information Processing Systems, 2019) and prove convergence guarantees under isoperimetry, and non-strongly convex at infinity.</p>","PeriodicalId":10575,"journal":{"name":"Communications in Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Local Influence Detection of Conditional Mean Dependence 条件均值依赖的局部影响检测
IF 0.9 4区 数学
Communications in Mathematics and Statistics Pub Date : 2023-11-20 DOI: 10.1007/s40304-023-00365-3
Tingyu Lai, Zhongzhan Zhang
{"title":"Local Influence Detection of Conditional Mean Dependence","authors":"Tingyu Lai, Zhongzhan Zhang","doi":"10.1007/s40304-023-00365-3","DOIUrl":"https://doi.org/10.1007/s40304-023-00365-3","url":null,"abstract":"<p>This article is focused on the problem to measure and test the conditional mean dependence of a response variable on a predictor variable. A local influence detection approach is developed combining with the martingale difference divergence (MDD) metric, and an efficient wild bootstrap implementation is given. The obtained new metric of the conditional mean dependence holds the merits of MDD, while it is more sensitive than the original one, and leads to a powerful test to nonlinear relationships. It is shown by simulations that the proposed test can achieve higher power for general conditional mean dependence relationships even in high-dimensional settings. Theoretical asymptotic properties of the local influence test statistic are given, and a real data analysis is also presented for further illustration. The localization idea could be combined with other conditional mean dependence metrics.</p>","PeriodicalId":10575,"journal":{"name":"Communications in Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138516389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Fischer–Marsden Conjecture and Equation in the Complex Hyperbolic Quadric 复双曲二次曲面中的fisher - marsden猜想和方程
4区 数学
Communications in Mathematics and Statistics Pub Date : 2023-10-28 DOI: 10.1007/s40304-023-00345-7
Young Jin Suh
{"title":"Fischer–Marsden Conjecture and Equation in the Complex Hyperbolic Quadric","authors":"Young Jin Suh","doi":"10.1007/s40304-023-00345-7","DOIUrl":"https://doi.org/10.1007/s40304-023-00345-7","url":null,"abstract":"","PeriodicalId":10575,"journal":{"name":"Communications in Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136233720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Shape Analysis by Computing Geodesics on a Manifold via Cubic B-splines 用三次b样条计算流形测地线的形状分析
4区 数学
Communications in Mathematics and Statistics Pub Date : 2023-10-27 DOI: 10.1007/s40304-023-00373-3
Qian Ni, Xuhui Wang
{"title":"Shape Analysis by Computing Geodesics on a Manifold via Cubic B-splines","authors":"Qian Ni, Xuhui Wang","doi":"10.1007/s40304-023-00373-3","DOIUrl":"https://doi.org/10.1007/s40304-023-00373-3","url":null,"abstract":"","PeriodicalId":10575,"journal":{"name":"Communications in Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136263409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Turán Number of Nonbipartite Graphs and the Product Conjecture Turán非二部图的数目与乘积猜想
4区 数学
Communications in Mathematics and Statistics Pub Date : 2023-10-25 DOI: 10.1007/s40304-023-00375-1
Xing Peng, Ge Song, Long-Tu Yuan
{"title":"Turán Number of Nonbipartite Graphs and the Product Conjecture","authors":"Xing Peng, Ge Song, Long-Tu Yuan","doi":"10.1007/s40304-023-00375-1","DOIUrl":"https://doi.org/10.1007/s40304-023-00375-1","url":null,"abstract":"","PeriodicalId":10575,"journal":{"name":"Communications in Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135169405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Cooperative Mean Field Game for Production Control with Sticky Price 具有粘性价格的生产控制合作平均场博弈
4区 数学
Communications in Mathematics and Statistics Pub Date : 2023-10-25 DOI: 10.1007/s40304-023-00370-6
Lijun Bo, Tongqing Li
{"title":"The Cooperative Mean Field Game for Production Control with Sticky Price","authors":"Lijun Bo, Tongqing Li","doi":"10.1007/s40304-023-00370-6","DOIUrl":"https://doi.org/10.1007/s40304-023-00370-6","url":null,"abstract":"","PeriodicalId":10575,"journal":{"name":"Communications in Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135111928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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