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.
摘要：
A strong edge-coloring of a graph G is a proper edge-coloring such that every path of length 3 uses three different colors. The strong chromatic index of G, denoted by chi(s)'(G), is the least possible number of colors in a strong edge-coloring of G. Let G be a graph, mad(G) be the maximum average degree and delta be the maximum degree of G. In this paper, we prove that if delta >= 6 and mad(G) < 23/8 , then chi is(G) <= 3 delta - 1; if delta >= 7 and mad(G) < 26/9 , then chi is(G) <= 3 delta -1, which partially improves the result of Choi et al. (2018) who proved that if delta > 7 and mad(G) < 3, then chi is(G) <= 3 delta. (C) 2022 Elsevier B.V. All rights reserved.
摘要：
Let
$$\varvec{x}_1,\ldots ,\varvec{x}_n$$
be a random sample of size n from a p-dimensional population distribution, where
$$p=p(n)\rightarrow \infty$$
. Consider a symmetric matrix
$$W=X^\top X$$
with parameters n and p, where
$$X=(\varvec{x}_1,\ldots ,\varvec{x}_n)^\top$$
. In this paper, motivated by model selection theory in high-dimensional statistics, we mainly investigate the asymptotic behavior of the eigenvalues of the principal minors of the random matrix W. For the Gaussian case, under a simple condition that
$$m=o(n/\log p)$$
, we obtain the asymptotic results on maxima and minima of the eigenvalues of all
$$m\times m$$
principal minors of W. We also extend our results to general distributions with some moment conditions. Moreover, we gain the asymptotic results of the extreme eigenvalues of the principal minors in the case of the real Wigner matrix. Finally, similar results for the maxima and minima of the eigenvalues of all the principal minors with a size smaller than or equal to m are also given.
作者机构：
[Zhao, Yue; Zhao, Y] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhao, Yue; Zhao, Y] Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
通讯机构：
[Zhao, Y ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;Cent China Normal Univ, Key Lab Nonlinear Anal & Applicat, Minist Educ, Wuhan 430079, Peoples R China.
摘要：
This paper is concerned with the inverse scattering problem of determining the unknown coefficients for a nonlinear two-dimensional Schrodinger equation. We establish for the first time the increasing stability of the inverse scattering problem from the multi-frequency far-field pattern for nonlinear equations. To achieve this goal, we prove the existence of a holomorphic region and an upper bound for the solution with respect to the complex wavenumber, which also leads to the well-posedness of the direct scattering problem. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the unknown coefficients, where the latter decreases as the upper bound of the frequency increases.& COPY; 2023 Elsevier B.V. All rights reserved.
期刊：
Journal of Fixed Point Theory and Applications,2023年25(2):1-31 ISSN：1661-7738
通讯作者：
Wang, CH
作者机构：
[Wang, Chunhua; Wang, CH] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Wang, Chunhua; Wang, CH] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan, Peoples R China.;[Wang, Qingfang] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430023, Peoples R China.;[Yang, Jing] Jiangsu Univ Sci & Technol, Sch Sci, Zhenjiang 212003, Peoples R China.
通讯机构：
[Wang, CH ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan, Peoples R China.
摘要：
We study the following nonlinear critical elliptic equation
$$\begin{aligned} -\Delta u+\epsilon Q(y)u=u^{\frac{N+2}{N-2}},\;\;\; u>0\;\;\;\hbox { in } {\mathbb {R}}^N, \end{aligned}$$
where
$$\epsilon >0$$
is small and
$$N\ge 5.$$
Assuming that Q(y) is periodic in
$$y_1$$
with period 1 and has a local minimum at 0 satisfying
$$Q(0)>0,$$
we prove the existence and local uniqueness of infinitely many bubbling solutions of it. This local uniqueness result implies that some bubbling solutions preserve the symmetry of the potential function Q(y), i.e., the bubbling solution whose blow-up set is
$$\{(jL,0,\ldots ,0):j=0,\pm 1, \pm 2,\ldots , \pm m\}$$
must be periodic in
$$y_{1}$$
provided that
$$\epsilon $$
goes to zero and L is any positive integer, where m is the number of the bubbles which is large enough but independent of
$$\epsilon .$$
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
期刊：
Bulletin of the Malaysian Mathematical Sciences Society,2023年46(1):1-8 ISSN：0126-6705
通讯作者：
Xiaolan Hu
作者机构：
[Legass, Belayneh-Mengistu; Hu, Xiaolan] Cent China Normal Univ, Sch Math & Stat, POB 71010, Wuhan 430079, Peoples R China.;[Legass, Belayneh-Mengistu; Hu, Xiaolan] Cent China Normal Univ, Hubei Key Lab Math Sci, POB 71010, Wuhan 430079, Peoples R China.
通讯机构：
[Xiaolan Hu] S;School of Mathematics and Statistics, and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, People’s Republic of China
摘要：
An injective k-edge coloring of a graph
$$G=(V(G),E(G))$$
is a k-edge coloring
$$\varphi $$
of G such that
$$\varphi (e_1)\ne \varphi (e_3)$$
for any three consecutive edges
$$e_1,e_2$$
and
$$e_3$$
of a path or a 3-cycle. The injective edge chromatic index of G, denoted by
$$\chi _i'(G)$$
, is the minimum k such that G has an injective k-edge coloring. In this paper, we consider the injective edge coloring of the generalized Petersen graph P(n,k). We show that
$$\chi _i'(P(n,k))\le 4$$
if
$$n\equiv 0(mod~4)$$
and
$$k\equiv 1(mod~2)$$
; and
$$\chi _i'(P(n,k))\le 5$$
if
$$n\equiv 2(mod~4)$$
and
$$k\equiv 1(mod~2)$$
. Moreover,
$$\chi _i'(P(n,3))\le 5$$
,
$$\chi _i'(P(2k+1,k))\le 5$$
and
$$\chi _i'(P(2k+2,k))\le 5$$
.
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
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.
期刊：
Applied Mathematics and Computation,2023年438:127556 ISSN：0096-3003
通讯作者：
Sun, Wanting(wtsun2018@sina.com)
作者机构：
[Li, Shuchao; Liu, Xin; Sun, Wanting] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Yan, Lixia] Wuhan Business Univ, Sch Informat & Engn, Wuhan 430070, Peoples R China.
通讯机构：
[Wanting Sun] F;Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China
摘要：
The Steiner k-eccentricity of a vertex in a graph G is the maximum Steiner distance over all k-subsets containing the vertex. The average Steiner k-eccentricity of G is the mean value of all vertices' Steiner k-eccentricities in G. Let T-n be the set of all n-vertex trees, T-n,T-Delta be the set of n-vertex trees with maximum degree Delta, T-n,Delta(k) be the set of n-vertex trees with exactly k vertices of a given maximum degree Delta, and let MTnk be the set of n-vertex trees with exactly k vertices of maximum degree. In this paper, we first determine the sharp upper bound on the average Steiner 3-eccentricity of n-vertex trees with a given degree sequence. The corresponding extremal graphs are characterized. Consequently, together with majorization theory, all graphs among T-n,Delta(k) (resp. T-n,T-Delta, MTnk, T-n) having the maximum average Steiner 3-eccentricity are identified. Then we characterize the unique n-vertex tree with a given segment sequence having the minimum average Steiner 3-eccentricity. Finally, we determine all n-vertex trees with a given number of segments having the minimum average Steiner 3-eccentricity. (C) 2022 Elsevier Inc. All rights reserved.
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.
期刊：
DESIGNS CODES AND CRYPTOGRAPHY,2023年91(10):3263-3284 ISSN：0925-1022
通讯作者：
Luo, JQ
作者机构：
[Luo, Jinquan; Ma, Wen] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;[Luo, Jinquan; Ma, Wen] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan, Peoples R China.
通讯机构：
[Luo, JQ ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan, Peoples R China.
关键词：
Pomset;Label;Block;MDS codes;Perfect codes
摘要：
In this paper, we introduce codes equipped with pomset block metric. A Singleton type bound for pomset block codes is obtained. Code achieving the Singleton bound, called a maximum distance separable code (for short, MDS (
$${\mathbb {P}},\pi $$
)-code) is also investigated. We extend the concept of I-perfect codes and r-perfect codes to pomset block metric. The relation between I-perfect codes and MDS
$$({\mathbb {P}},\pi )$$
-codes is also considered. When all blocks have the same dimension, we prove the duality theorem for codes and study the weight distribution of MDS pomset block codes when the pomset is a chain.
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.
摘要：
Let E = K(n, m, D) be a Bedford-McMullen carpet with expanding factors n, m and digit set D. We call a = (aj)m-1 j=0 the distribution sequence of D where aj = #{i; (i, j) & ISIN; D}. Under a certain vertical separation condition, Li et al. (2013) [7] showed that if two totally disconnected Bedford-McMullent carpets share the same distribution sequence, then they are Lipschitz equivalent. In this paper, we define a metric & rho; on D & INFIN; and call (D & INFIN;, & rho;) a half-symbolic space. We show that if E is totally disconnected and satisfies the vertical separation condition, then E is Lipschitz equivalent to (D & INFIN;, & rho;). Thanks to this result, we extend the result of Li et al. by showing that two Bedford-McMullen carpets K(n, m, D) and K(n, m, D ⠃) are Lipschitz equivalent if a, the distribution sequence of D, is a permutation of a ⠃, the distribution sequence of D ⠃, and that a and a ⠃ satisfy a certain color matchable condition. & COPY; 2023 Elsevier Inc. All rights reserved.
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：
Let $M=(\begin {smallmatrix}\rho ^{-1} & 0 \\0 & \rho ^{-1} \\\end {smallmatrix})$ be an expanding real matrix with $0<\rho <1$, and let ${\mathcal D}_n=\{(\begin {smallmatrix} 0\\ 0 \end {smallmatrix}),(\begin {smallmatrix} \sigma _n\\ 0 \end {smallmatrix}),(\begin {smallmatrix} 0\\ \gamma _n \end {smallmatrix})\}$ be digit sets with $\sigma _n,\gamma _n\in \{-1,1\}$ for each $n\ge 1$. Then the infinite convolution\n$$ \begin{align*}\mu_{M,\{{\mathcal D}_n\}}=\delta_{M^{-1}{\mathcal D}_1}\ast\delta_{M^{-2}{\mathcal D}_2}\ast\cdots\end{align*} $$\nis called a Moran–Sierpinski measure. We give a necessary and sufficient condition for $L^2(\,\mu _{M,\{{\mathcal D}_n\}})$ to admit an infinite orthogonal set of exponential functions. Furthermore, we give the exact cardinality of orthogonal exponential functions in $L^2(\,\mu _{M,\{{\mathcal D}_n\}})$ when $L^2(\,\mu _{M,\{{\mathcal D}_n\}})$ does not admit any infinite orthogonal set of exponential functions based on whether $\rho $ is a trinomial number or not.
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.
摘要：
It has been established that the local mass of blow-up solutions to Toda systems associated with the simple Lie algebras |$\textbf{A}_{n}$|, |$\textbf{B}_{n}$|, |$\textbf{C}_{n}$|, and |$\textbf{G}_{2}$| can be represented by a finite Weyl group. In particular, at each blow-up point, after a sequence of bubbling steps (via scaling) is performed, the transformation of the local mass at each step corresponds to the action of an element in the Weyl group. In this article, we present the results in the same spirit for the affine |$\textbf{B}_{2}^{(1)}$| Toda system with singularities. Compared with the Toda system with simple Lie algebras, the computation of local masses is more challenging due to the infinite number of elements of the affine Weyl group of type |$\textbf{B}_{2}^{(1)}$|. In order to give an explicit expression for the local mass formula, we introduce two free integers and write down all the possibilities into |$8$| types. This shows a striking difference to previous results on Toda systems with simple Lie algebras. The main result of this article seems to provide the first major advance in understanding the relation between the blow-up analysis of affine Toda system and the affine Weyl group of the associated Lie algebras.
