期刊：
CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE,2023年:- ISSN：0319-5724
通讯作者：
Liu, YY
作者机构：
[Jin, Shaojia; Liu, Yanyan] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.;[Jin, Shaojia] Wuhan Text Univ, Sch Math & Phys Sci, Wuhan 430200, Peoples R China.;[Mao, Guangcai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Mao, Guangcai] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Sun, Jianguo] Univ Missouri, Dept Stat, Columbia, MO USA.
通讯机构：
[Liu, YY ] W;Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China.
摘要：
Abstract This article discusses nonparametric estimation of a survival function in the presence of measurement errors on the observation of the failure time of interest. One situation where such issues arise would be clinical studies of chronic diseases where the observation on the time to the failure event of interest such as the onset of the disease relies on patient recall or chart review of electronic medical records. It is easy to see that both situations can be subject to measurement errors. To resolve this problem, we propose a simulation extrapolation approach to correct the bias induced by the measurement error. To overcome potential computational difficulties, we use spline regression to approximate the unspecified extrapolated coefficient function of time, and establish the asymptotic properties of our proposed estimator. The proposed method is applied to nonparametric estimation based on interval‐censored data. Extensive numerical experiments involving both simulated and actual study datasets demonstrate the feasibility of this proposed estimation procedure. Résumé Cet article traite de l'estimation non paramétrique d'une fonction de survie en présence d'erreurs de mesure lors de l'observation du temps de défaillance d'intérêt. Une situation où de telles problématiques se posent fréquemment est celle des études cliniques sur les maladies chroniques, où l'observation du temps écoulé jusqu'à l'événement de défaillance d'intérêt, tel que l'apparition de la maladie, repose sur la mémoire du patient ou sur l'examen des dossiers médicaux électroniques. Il est évident que ces deux contextes sont sujets à des erreurs de mesure. Pour résoudre ce défi, les auteurs de cet article proposent une approche d'extrapolation par simulation visant à corriger le biais induit par l'erreur de mesure. Afin de surmonter d'éventuelles complexités computationnelles, ils utilisent la régression spline pour approximer la fonction de coefficient extrapolée non spécifiée en fonction du temps, tout en établissant les propriétés asymptotiques de l'estimateur proposé. Cette méthode est ensuite appliquée à l'estimation non paramétrique basée sur des données censurées par intervalles. Des expérimentations numériques approfondies, incluant à la fois des jeux de données simulés et des données d'études réelles, mettent en évidence la faisabilité de cette procédure d'estimation proposée.
作者机构：
[Meknani, Bassem; Zhang, Jun] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Meknani, Bassem] Univ Freres Mentouri Constantine, Dept Math, Constantine, Algeria.;[Abdelhamid, Talaat] Menoufiya Univ, Fac Elect Engn, Phys & Math Engn Dept, Menoufia, Egypt.;[Abdelhamid, Talaat] Chinese Acad Sci, Shenzhen Inst Adv Technol, Shenzhen, Peoples R China.
通讯机构：
[Bassem Meknani] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, People's Republic of China<&wdkj&>Département de Mathematiques, Université frères Mentouri Constantine, Constantine, Algeria
关键词：
Almost periodic solutions;pseudo-almost periodic solutions;integral solutions;evolution equations;nonlocal initial conditions;34C27;34K14;35B15;37L05;47J35
作者机构：
[Deng, Yinbin; Xu, Liangshun; Guo, Yujin] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Yinbin Deng] S;School of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, China
关键词：
Bose-Einstein condensates;Gross-Pitaevskii functional;nonlinear elliptic system
摘要：
This paper is concerned with ground states of two-component trapped Bose-Einstein condensates passing an obstacle in Double-struck capital R-2, where the intraspecies interactions are attractive and the interspecies interactions are repulsive. We address the classification on the existence and non-existence of ground states. The limiting profiles of ground states are also studied by the energy analysis and the elliptic partial differential equation theory.
作者机构：
[Fu, Kang; Hu, Jianwei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Fu, K; Fu, Kang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei Province, Peoples R China.
通讯机构：
[Fu, K ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei Province, Peoples R China.
关键词：
community detection;multilayer network;profile-pseudo likelihood;stochastic block model;strong consistency
摘要：
The multilayer stochastic block model is one of the fundamental models in multilayer networks and is often used to represent multiple types of relations between different individuals. In this paper, we extend the profile-pseudo likelihood method for the single-layer stochastic block model to the case of the multilayer stochastic block model. Specifically, by assuming all network layers have identical community membership labels, we investigate the multilayer stochastic block model with a common community structure. In this paper, we develop a profile-pseudo likelihood algorithm to fit a multilayer stochastic block model and estimate the community label. Meantime, we prove that the algorithm has convergence guarantee and that the estimated community label is strongly consistent. Further, for estimating the number of communities K $$ K $$ , we extend the corrected Bayesian information criterion to multilayer stochastic block models. We also extend this algorithm to fit the multilayer degree-corrected stochastic block model. Both simulation studies and real-world data examples indicate that the proposed method works well.
摘要：
We obtain optimal lower bounds for the eigenvalues of the Dirac–Witten operator on locally reducible spacelike submanifolds in terms of intrinsic and extrinsic quantities. The limiting cases are also studied.
期刊：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2023年44(1):182-204 ISSN：1078-0947
通讯作者：
Guo, YJ
作者机构：
[Li, Yan; Guo, Yujin; Liang, Wenning] Cent China Normal Univ, Sch Math & Stat, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
通讯机构：
[Guo, YJ ] C;Cent China Normal Univ, Sch Math & Stat, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
关键词：
The planar Schrodinger-Poisson system;constraint minimizers;loga-rithmic potentials;asymptotic expansions;refined spike profiles
摘要：
This paper is concerned with constraint minimizers of the planar Schrodinger-Poisson system with a logarithmic convolution potential and a logarithmic external potential V (x) = ln(1+|x|(2)). It is known that minimizers exist if and only if the particle mass p > 0 satisfies p < p* for some threshold p* is an element of(0, infinity). As a continuation of [22], this paper is devoted to analyzing the refined spike profiles of constraint minimizers as p NE arrow p*.
作者机构：
[Liu, Ning; Jiang, Anguo] South China Univ Technol, Sch Math, Guangzhou 510640, Guangdong, Peoples R China.;[Jing, Naihuan] North Carolina State Univ, Dept Math, Raleigh, NC 27695 USA.;[Jing, Naihuan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Naihuan Jing] D;Department of Mathematics, North Carolina State University, Raleigh, USA<&wdkj&>School of Mathematics and Statistics, Central China Normal University, Wuhan, China
摘要：
We study the Q-Kostka polynomials
$$L_{\lambda \mu }(t)$$
by the vertex operator realization of the Q-Hall–Littlewood functions
$$G_{\lambda }(x;t)$$
and derive new formulae for
$$L_{\lambda \mu }(t)$$
. In particular, we have established stability property for the Q-Kostka polynomials. We also introduce spin Green polynomials
$$Y^{\lambda }_{\mu }(t)$$
as both an analogue of the Green polynomials and deformation of the spin irreducible characters of
$$\mathfrak S_n$$
. Iterative formulas of the spin Green polynomials are given and some favorable properties parallel to the Green polynomials are obtained. Tables of
$$Y^{\lambda }_{\mu }(t)$$
are included for
$$n\le 7.$$
作者：
Liu, C. H. U. A. N. G. Y. E.;Nguyen, N. G. H. I. E. M., V
期刊：
COMMUNICATIONS IN MATHEMATICAL SCIENCES,2023年21(3):641-669 ISSN：1539-6746
通讯作者：
Liu, C.
作者机构：
[Liu, C. H. U. A. N. G. Y. E.] Cent China Normal Univ, Sch Math & Stat, POB 71010, Wuhan 430079, Peoples R China.;[Liu, C. H. U. A. N. G. Y. E.] Cent China Normal Univ, Hubei Key Lab Math Sci, POB 71010, Wuhan 430079, Peoples R China.;[Nguyen, N. G. H. I. E. M., V] Utah State Univ, Dept Math & Stat, Logan, UT 84322 USA.
通讯机构：
[Liu, C.] S;School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, P.O. Box 71010, China
关键词：
abcd-system;BBMequation;Euler equations;KdV-equation;linear Schrödinger equation;NLS-equation;NLS-KdV system
摘要：
In this paper, we consider the following logarithmic Schrödinger equation $ \begin{equation*} -\varepsilon^2\Delta u + V(x)u = u\log u^2\ \ \text{in}\ {\mathbb R}^N, \end{equation*} $ where $ \varepsilon>0 $, $ N\ge 1 $, $ V(x)\in C({\mathbb R}^N, {\mathbb R}) $ is a continuous potential which can be unbounded below. By variational methods and penalized idea, we show that the problem has a family of solutions $ u_{\varepsilon} $ concentrating at any finite given local minima of $ V $. Our results generalize the single peak case in [36] to the multi-peak case but the penalization in this paper is different.
期刊：
Results in Mathematics,2023年78(3):1-19 ISSN：1422-6383
通讯作者：
Shuchao Li<&wdkj&>Wanting Sun
作者机构：
[Li, Shuchao; Sun, Wanting] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Shuchao Li; Wanting Sun] F;Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, People’s Republic of China<&wdkj&>Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, People’s Republic of China
关键词：
Adjacency matrix;second largest eigenvalue;outerplanar graph;\(\{K_{2, 3}, K_4\}\)-minor free graph
摘要：
Let
$$\lambda _2$$
be the second largest eigenvalue of the adjacency matrix of a connected graph. In 2021, Liu, Chen and Stanić determined all the connected
$$\{K_{1,3}, K_5 -e\}$$
-free graphs whose second largest eigenvalue
$$\lambda _2\leqslant 1$$
. In this paper, we completely identify all the connected
$$\{K_{2,3},K_4\}$$
-minor free graphs whose second largest eigenvalue does not exceed 1. That is, we characterize all the connected outerplanar graphs satisfying
$$\lambda _2\leqslant 1$$
. Furthermore, all the maximal outerplanar graphs having the same property can be deduced by our result obtained in this paper. Our main tools include analyzing the local structure of the outerplanar graph with respect to its girth.
作者机构：
[Li, Hui-Sheng; Tu, Jia-Juan; Yan, Hong] Ctr Intelligent Multidimens Data Anal, Hong Kong Sci Pk, Hong Kong 999077, Peoples R China.;[Li, Hui-Sheng; Zhang, Xiao-Fei] Cent China Normal Univ, Sch Math & Stat, Dept Stat, Wuhan 430079, Peoples R China.;[Li, Hui-Sheng; Zhang, Xiao-Fei] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Yan, Hong] City Univ Hong Kong, Dept Elect Engn, Hong Kong 999077, Peoples R China.
通讯机构：
[Zhang, XF ] C;Cent China Normal Univ, Sch Math & Stat, Dept Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
摘要：
Motivation: Spatially resolved gene expression profiles are the key to exploring the cell type spatial distributions and understanding the architecture of tissues. Many spatially resolved transcriptomics (SRT) techniques do not provide single-cell resolutions, but they measure gene expression profiles on captured locations (spots) instead, which are mixtures of potentially heterogeneous cell types. Currently, several cell-type deconvolution methods have been proposed to deconvolute SRT data. Due to the different model strategies of these methods, their deconvolution results also vary. Results: Leveraging the strengths of multiple deconvolution methods, we introduce a new weighted ensemble learning deconvolution method, EnDecon, to predict cell-type compositions on SRT data in this work. EnDecon integrates multiple base deconvolution results using a weighted optimization model to generate a more accurate result. Simulation studies demonstrate that EnDecon outperforms the competing methods and the learned weights assigned to base deconvolution methods have high positive correlations with the performances of these base methods. Applied to real datasets from different spatial techniques, EnDecon identifies multiple cell types on spots, localizes these cell types to specific spatial regions and distinguishes distinct spatial colocalization and enrichment patterns, providing valuable insights into spatial heterogeneity and regionalization of tissues. Availability and implementation : The source code is available at https://github.com/Zhangxf-ccnu/EnDecon. Contact: zhangxf@ccnu.edu.cn Supplementary information: Supplementary data are available at Bioinformatics online.
作者：
Chen, Haixia;Wang, Chunhua;Xie, Huafei;Zhou, Yang
期刊：
ANNALI DI MATEMATICA PURA ED APPLICATA,2023年 ISSN：0373-3114
通讯作者：
Wang, CH
作者机构：
[Chen, Haixia] Hanyang Univ, Coll Nat Sci, Dept Math, 222 Wangsimni Ro, Seoul 04763, South Korea.;[Wang, Chunhua; Wang, CH] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Xie, Huafei] Nanyang Normal Univ, Sch Math & Stat, Nanyang 473061, Peoples R China.;[Zhou, Yang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Wang, CH ] C;Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Critical Sobolev exponents;Non-degeneracy;Local Pohozaev identities;Green's function
摘要：
We revisit the well-known Brezis-Nirenberg problem {- Delta u = u (N+2/N-2) + epsilon u, in Omega, u > 0, in Omega, u = 0, on partial derivative Omega, where epsilon > 0 and Omega subset of RN are a smooth bounded domain with N >= 3. The existence of multi-bump solutions to above problem for small parameter epsilon > 0 was obtained by Musso and Pistoia (Indiana Univ Math J 51:541-579, 2002). However, to our knowledge, whether themulti-bump solutions are non-degenerate that is open. Here, we give some straightforward answer on this question under some suitable assumptions for the Green's function of - Delta in Omega, which enriches the qualitative analysis on the solutions of Brezis-Nirenberg problem and can be viewed as a generalization of Grossi (Nonlinear Differ Equ Appl 12:227-241, 2005) where the non-degeneracy of a single-bump solution has been proved. And the main idea is the blow-up analysis based on the local Pohozaev identities.
期刊：
Journal of Differential Equations,2023年343:263-284 ISSN：0022-0396
通讯作者：
Shuai, W
作者机构：
[Shuai, W; Shuai, Wei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Shuai, W; Shuai, Wei] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Shuai, W ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Logarithmic nonlinearity;Multiplicity of solutions;Variational methods
摘要：
We are interested in the following elliptic equation {-Delta u = a(x)u log vertical bar u vertical bar, x is an element of Omega, (0.1) u = 0, on partial derivative Omega, where Omega is a bounded domain of R-N (N >= 2) with smooth boundary partial derivative Omega, and a(x) is an element of C(Omega). The existence and multiplicity of solutions are obtained by using variational methods. Quite surprisingly, the existence of solutions is deeply influenced by the sign of a(x). More precisely, (i) if a(x) > 0, equation (0.1) possesses a sequence of solutions whose energy and H-0(1)(Omega)-norms diverge to positive infinity; (ii) if a(x) < 0, equation (0.1) possesses a sequence of solutions whose energy and H-0(1)(Omega)-norms converge to zero; (iii) if a(x) is sign-changing, equation (0.1) possesses two sequences of solutions: one sequence of solutions is with energy and H-0(1)(Omega)-norms diverging to positive infinity, while the other one is with energy and H-0(1)(Omega)-norms converging to zero. (c) 2022 Elsevier Inc. All rights reserved.
