期刊：
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS,2023年53(5):1571-1585 ISSN：0035-7596
通讯作者：
Li, SC
作者机构：
[Sun, Wanting] Shandong Univ, Data Sci Inst, Jinan, Peoples R China.;[Li, Shuchao; Li, SC] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan, Peoples R China.;[Li, Shuchao; Li, SC] Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.;[Li, Xuechao] Univ Georgia, Div Acad Enhancement, Athens, GA USA.
通讯机构：
[Li, SC ] C;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan, Peoples R China.;Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.
摘要：
A graph is split if its vertex set can be partitioned into a clique and an independent set. A split graph is (x,y)-bidegreed if each of its vertex degrees is equal to either x or y. Each connected split graph is of diameter at most 3. In 2017, Nikiforov proposed the A(alpha)-matrix, which is the convex combination of the adjacency matrix and the diagonal matrix of vertex degrees of the graph G. It is well-known that a connected graph of diameter l contains at least l+1 distinct A(alpha)-eigenvalues. A graph is said to be l alpha-extremal with respect to its A(alpha)-matrix if the graph is of diameter l having exactly l+1 distinct A(alpha)-eigenvalues. In this paper, using the association of split graphs with combinatorial designs, the connected 2(alpha)-extremal (resp. 3(alpha)-extremal) bidegreed split graphs are classified. Furthermore, all connected bidegreed split graphs of diameter 2 having just 4 distinct A(alpha)-eigenvalues are identified.
作者机构：
[Li, Gongbao] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, GB ] C;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
关键词：
Kirchhoff type equations;potential functions having non-degenerate critical points;the Lyapunov-Schmidt reduction method;multi-peak solutions;existence and local uniqueness
摘要：
In this paper, we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations
$$ - \left({{\varepsilon ^2}a + \varepsilon b\int_{{\mathbb{R}^3}} {|\nabla u{|^2}}} \right)\,\,\Delta u + V(x)u = {u^p},\,\,\,\,\,\,u > 0\,\,\,\,\,{\rm{in}}\,\,\,{\mathbb{R}^3},$$
which concentrate at non-degenerate critical points of the potential function V(x), where a, b > 0, 1 < p < 5 are constants, and ε > 0 is a parameter. Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity, we establish the existence and local uniqueness results of multi-peak solutions, which concentrate at {ai}1≤i≤k, where {ai}1≤i≤k are non-degenerate critical points of V(x) as ε → 0.
作者机构：
[Xie, Minghong] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Tan, Zhong] Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.;[Tan, Zhong] Xiamen Univ, Shenzhen Res Inst, Shenzhen 518057, Peoples R China.
通讯机构：
[Tan, Z ] X;Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China.;Xiamen Univ, Shenzhen Res Inst, Shenzhen 518057, Peoples R China.
关键词：
spatiotemporal EIT problem;fractional Dirichlet-to-Neumann operator;critical exponent;bubbling phenomena
摘要：
We study a spatiotemporal EIT problem with a dynamical boundary condition for the fractional Dirichlet-to-Neumann operator with a critical exponent. There are three major ingredients in this paper. The first is the finite time blowup and the decay estimate of the global solution with a lower-energy initial value. The second ingredient is the Lq(2 ≤ q < ∞) estimate of the global solution applying the Moser iteration, which allows us to show that any global solution is a classical solution. The third, which is the main ingredient of this paper, explores the long time asymptotic behavior of global solutions close to the stationary solution and the bubbling phenomenons by means of a concentration compactness principle.
作者机构：
[Qu, Lianqiang] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Sun, LQ; Sun, Liuquan] Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China.;[Sun, Yanqing] Univ North Carolina Charlotte, Dept Math & Stat, 9201 Univ City Blvd, Charlotte, NC 28223 USA.
通讯机构：
[Sun, LQ ] C;Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China.
摘要：
Quantile regression has become a widely used tool for analysing competing risk data. However, quantile regression for competing risk data with a continuous mark is still scarce. The mark variable is an extension of cause of failure in a classical competing risk model where cause of failure is replaced by a continuous mark only observed at uncensored failure times. An example of the continuous mark variable is the genetic distance that measures dissimilarity between the infecting virus and the virus contained in the vaccine construct. In this article, we propose a novel mark-specific quantile regression model. The proposed estimation method borrows strength from data in a neighbourhood of a mark and is based on an induced smoothed estimation equation, which is very different from the existing methods for competing risk data with discrete causes. The asymptotic properties of the resulting estimators are established across mark and quantile continuums. In addition, a mark-specific quantile-type vaccine efficacy is proposed and its statistical inference procedures are developed. Simulation studies are conducted to evaluate the finite sample performances of the proposed estimation and hypothesis testing procedures. An application to the first HIV vaccine efficacy trial is provided.
期刊：
IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS,2023年27(6):3061-3071 ISSN：2168-2194
通讯作者：
Zhao, Weizhong;Shen, XJ
作者机构：
[Shen, Xianjun; Wang, Haodong; Wang, Yue; Zhao, Weizhong; Zhao, WZ; Shen, XJ; Jiang, Xingpeng; Li, Dandan] Cent China Normal Univ, Sch Comp, Hubei Prov Key Lab Artificial Intelligence & Smart, Wuhan 430079, Peoples R China.;[Sun, Han] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Shen, Xianjun; Wang, Haodong; Wang, Yue; Zhao, Weizhong; Zhao, WZ; Shen, XJ; Jiang, Xingpeng; Li, Dandan] Cent China Normal Univ, Natl Language Resources Monitoring & Res Ctr Netwo, Wuhan 430079, Peoples R China.
通讯机构：
[Zhao, WZ; Shen, XJ ] C;Cent China Normal Univ, Sch Comp, Hubei Prov Key Lab Artificial Intelligence & Smart, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Natl Language Resources Monitoring & Res Ctr Netwo, Wuhan 430079, Peoples R China.
关键词：
graph representation learning;heterogeneous information network;multi-head attention mechanism;Phage-host interactions prediction
摘要：
In the treatment of bacterial infectious diseases, overuse of antibiotics may lead to not only bacterial resistance to antibiotics but also dysbiosis of beneficial bacteria which are essential for maintaining normal human life activities. Instead, phage therapy, which invades and lyses specific pathogenic bacteria without affecting beneficial bacteria, becomes more and more popular to treat bacterial infectious diseases. For the effective phage therapy, it requires to accurately predict potential phage-host interactions from heterogeneous information network consisting of bacteria and phages. Although many models have been proposed for predicting phage-host interactions, most methods fail to consider fully the sparsity and unconnectedness of phage-host heterogeneous information network, deriving the undesirable performance on phage-host interactions prediction. To address the challenge, we propose an effective model called GERMAN-PHI for predicting Phage-Host Interactions via Graph Embedding Representation learning with Multi-head Attention mechaNism. In GERMAN-PHI, the multi-head attention mechanism is utilized to learn representations of phages and hosts from multiple perspectives of phage-host associations, addressing the sparsity and unconnectedness in phage-host heterogeneous information network. More specifically, a module of GAT with talking-heads is employed to learn representations of phages and bacteria, on which neural induction matrix completion is conducted to reconstruct the phage-host association matrix. Results of comprehensive experiments demonstrate that GERMAN-PHI performs better than the state-of-the-art methods on phage-host interactions prediction. In addition, results of case study for two high-risk human pathogens show that GERMAN-PHI can predict validated phages with high accuracy, and some potential or new associated phages are provided as well.
作者机构：
[Deng, Yinbin] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[He, Qihan] Guangxi Univ, Coll Math & Informat Sci, Guangxi Ctr Math Res, Nanning 530003, Peoples R China.;[Pan, Yiqing] Beibu Gulf Univ, Coll Sci, Qinzhou 535011, Peoples R China.;[Zhong, Xuexiu] South China Normal Univ, South China Res Ctr Appl Math & Interdisciplinary, Guangzhou 510631, Peoples R China.
通讯机构：
[He, Q.] C;College of Mathematics and Information Science, China
摘要：
We consider the existence and nonexistence of the positive solution for the following Br & eacute;zis- Nirenberg problem with logarithmic perturbation: ?-delta u= |u|( 2*-2)u+ lambda u+ mu u u log(2) xE omega, u=0 xE 8 omega, where omega c RN is a bounded open domain, lambda,mu ER,N >_3 and 2 & lowast; := 2 - N is the critical Sobolev exponent for N 2 the embedding H0 omega L omega 1( ) y & lowast;( ). The uncertainty of the sign of s logs2 in (0, +oo) has some interest in itself. 2 We will show the existence of positive ground state solution, which is of mountain pass type provided lambda E R, mu > 0 and N >_ 4. While the case of mu < 0 is thornier. However, for N = 3, 4, lambda E (-oo, lambda 1(omega)), we can also establish the existence of positive solution under some further suitable assumptions. A nonexistence result is also obtained for mu < 0 and - (N-2)mu/2 (N-2)mu /2(-(N-2)mu/2) log lambda lambda(1 )omega 0 ( ) >_ if N >_ 3. Comparing with the results in the study by Br & eacute;zis and Nirenberg (Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), 437-477), some new interesting phenomenon occurs when the parameter mu on logarithmic perturbation is not zero.
期刊：
IEEE Transactions on Information Theory,2023年69(2):941-950 ISSN：0018-9448
通讯作者：
Liu, H.
作者机构：
[Chen, Bocong] South China Univ Technol, Sch Math, Guangzhou 510641, Peoples R China.;[Liu, Hongwei] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Liu, H.] C;Central China Normal University, China
关键词：
Codes;Measurement;Upper bound;Symbols;Shape;Hamming distances;Decoding;Symbol-pair read channel;symbol-pair code;coding theory;codes for storage media
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：
Journal of Mathematical Biology,2023年86(2):1-3 ISSN：0303-6812
通讯作者：
Jicai Huang<&wdkj&>Hao Wang
作者机构：
[Huang, Jicai; Pan, Qin] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Wang, Hao] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada.
通讯机构：
[Jicai Huang] S;[Hao Wang] D;School of Mathematics and Statistics, Central China Normal University, Wuhan, People’s Republic of China<&wdkj&>Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada
作者机构：
[Zhang, Xiao-Fei; Xiong, Yi-Xuan; Wang, Meng-Guo] School of Mathematics and Statistics, Central China Normal University, Wuhan, China;[Zhang, Xiao-Fei; Xiong, Yi-Xuan; Wang, Meng-Guo] Key Laboratory of Nonlinear Analysis & Applications (Ministry of Education), Central China Normal University, Wuhan, China;[Chen, Luonan] State Key Laboratory of Cell Biology, Shanghai Institute of Biochemistry and Cell Biology, Center for Excellence in Molecular Cell Science, Chinese Academy of Sciences, Shanghai, China;[Chen, Luonan] School of Life Science and Technology, ShanghaiTech University, Shanghai, China;[Chen, Luonan] Key Laboratory of Systems Health Science of Zhejiang Province, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Chinese Academy of Sciences, Hangzhou, China
摘要：
The recent advances in single-cell RNA sequencing (scRNA-seq) techniques have stimulated efforts to identify and characterize the cellular composition of complex tissues. With the advent of various sequencing techniques, automated cell-type annotation using a well-annotated scRNA-seq reference becomes popular. But it relies on the diversity of cell types in the reference, which may not capture all the cell types present in the query data of interest. There are generally unseen cell types in the query data of interest because most data atlases are obtained for different purposes and techniques. Identifying previously unseen cell types is essential for improving annotation accuracy and uncovering novel biological discoveries. To address this challenge, we propose mtANN (multiple-reference-based scRNA-seq data annotation), a new method to automatically annotate query data while accurately identifying unseen cell types with the aid of multiple references. Key innovations of mtANN include the integration of deep learning and ensemble learning to improve prediction accuracy, and the introduction of a new metric that considers three complementary aspects to distinguish between unseen cell types and shared cell types. Additionally, we provide a data-driven method to adaptively select a threshold for identifying previously unseen cell types. We demonstrate the advantages of mtANN over state-of-the-art methods for unseen cell-type identification and cell-type annotation on two benchmark dataset collections, as well as its predictive power on a collection of COVID-19 datasets. The source code and tutorial are available at https://github.com/Zhangxf-ccnu/mtANN.
作者机构：
[Yu, Yuantian; Zhou, Zihan] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Geng, Xianya] Anhui Univ Sci & Technol, Sch Math & Big Data, Huainan, Peoples R China.
通讯机构：
[Xianya Geng] S;School of Mathematics and Big Data, Anhui University of Science & Technology, Huainan, China
摘要：
This article gives some fundamental introduction to spectra of mixed graphs via its kgeneralized Hermitian adjacency matrix. This matrix is indexed by the vertices of the mixed graph, and the entry corresponding to an arc from uto vis equal to the kth root of unity e(-2pi/k) (and its symmetric entry is e(-2pi/k)); the entry corresponding to an undirected edge is equal to 1, and 0 otherwise. For all positive integers k, the non-zero entries of the above matrix are chosen from the gain set {1, e(2pi/k), e(-2pi/k)}, which is not closed under multiplication when k >= 4. In this paper, for all positive integers k, we extract all the mixed graphs whose k-generalized Hermitian adjacency rank (H-k-rank for short) is 3, which partially answers a question proposed by Wissing and van Dam [34]. Furthermore, we study the spectral determination of mixed graphs with H-k-rank 2 and 3, respectively. (C) 2022 Elsevier B.V. All rights reserved.
摘要：
The Keller–Segel model is a paradigm to describe the chemotactic mechanism, which plays a vital role on the physiological and pathological activities of uni-cellular and multi-cellular organisms. One of the most interesting variants is the coupled system with the intrinsic growth, which admits many complex nontrivial patterns. This paper is devoted to the construction of multi-spiky solutions to the Keller–Segel models with the logistic source in 2D. Assuming that the chemo-attractive rate is large, we apply the inner-outer gluing scheme to nonlocal cross-diffusion system and prove the existence of multiple boundary and interior spikes. The numerical simulations are presented to highlight our theoretical results.
