作者机构：
[Cao, Li] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China.;[He, Xing-Gang] Cent China Normal Univ, Coll Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[He, Xing-Gang] C;Cent China Normal Univ, Coll Math & Stat, Wuhan 430079, Peoples R China.
期刊：
Linear Algebra and its Applications,2012年436(12):4400-4411 ISSN：0024-3795
通讯作者：
Li, Shuchao
作者机构：
[Zhang, Minjie; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Zhang, Minjie] Huangshi Inst Technol, Fac Math & Phys, Huangshi 435003, Peoples R China.
通讯机构：
[Li, Shuchao] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
会议名称：
Workshop on Theory and Applications of Matrices Described by Patterns
会议时间：
JAN 31-FEB 05, 2010
会议地点：
Banff, CANADA
会议主办单位：
[Li, Shuchao;Zhang, Minjie] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.^[Zhang, Minjie] Huangshi Inst Technol, Fac Math & Phys, Huangshi 435003, Peoples R China.
摘要：
Let T-n(c) be the set of the complements of trees on n vertices. In this paper we characterize the unique graph whose least eigenvalue of the signless Laplacian attains the minimum among all graphs in T-n(C)\{K-1,n-1(C)), where K-1,n-1(C) is the complement of the star graph on n vertices. (C) 2011 Elsevier Inc. All rights reserved.
期刊：
ELECTRONIC JOURNAL OF COMBINATORICS,2012年19(4):P48 ISSN：1077-8926
通讯作者：
Li, Shuchao
作者机构：
[Wang, Shujing; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Shuchao] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
关键词：
subtrees;Wiener index;leaves;bipartition;q-ary tree;domination number
摘要：
When considering the total number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to some other graphical indices in applications. Along this line, it is interesting to study that over some types of trees with a given order, which trees minimize or maximize this number. Here are our main results: (1) The extremal tree which minimizes the total number of subtrees among n-vertex trees with k pendants is characterized. (2) The extremal tree which maximizes (resp. minimizes) the total number of subtrees among n-vertex trees with a given bipartition is characterized. (3) The extremal tree which minimizes the total number of subtrees among the set of all q-ary trees with n non-leaf vertices is identified. (4) The extremal n-vertex tree with given domination number maximizing the total number of subtrees is characterized.
摘要：
Embryonic stem cells are conventionally differentiated by modulating specific growth factors in the cell culture media. Recently the effect of cellular mechanical microenvironment in inducing phenotype specific differentiation has attracted considerable attention. We have shown the possibility of inducing endoderm differentiation by culturing the stem cells on fibrin substrates of specific stiffness [1]. Here, we analyze the regulatory network involved in such mechanically induced endoderm differentiation under two different experimental configurations of 2-dimensional and 3-dimensional culture, respectively. Mouse embryonic stem cells are differentiated on an array of substrates of varying mechanical properties and analyzed for relevant endoderm markers. The experimental data set is further analyzed for identification of co-regulated transcription factors across different substrate conditions using the technique of bi-clustering. Overlapped bi-clusters are identified following an optimization formulation, which is solved using an evolutionary algorithm. While typically such analysis is performed at the mean value of expression data across experimental repeats, the variability of stem cell systems reduces the confidence on such analysis of mean data. Bootstrapping technique is thus integrated with the bi-clustering algorithm to determine sets of robust bi-clusters, which is found to differ significantly from corresponding bi-clusters at the mean data value. Analysis of robust bi-clusters reveals an overall similar network interaction as has been reported for chemically induced endoderm or endodermal organs but with differences in patterning between 2-dimensional and 3-dimensional culture. Such analysis sheds light on the pathway of stem cell differentiation indicating the prospect of the two culture configurations for further maturation.
作者：
CHEN Sheng’an 1,2 1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, Hubei, China;2. School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, Hubei, China
作者机构：
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, Hubei, China;School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning 437100, Hubei, China;[Sheng’an Chen] School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei, China<&wdkj&>School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning, Hubei, China
通讯机构：
[Sheng’an Chen] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei, China<&wdkj&>School of Mathematics and Statistics, Hubei University of Science and Technology, Xianning, Hubei, China
关键词：
CHARACTER;DEGREES;CONJUGACY;class;SIZES;group;structures;character degrees;conjugacy class sizes;group structures
摘要：
Let G be a finite group and π be a set of primes including at least two elements. We write cd（G） and cs（G） to denote the set of complex irreducible character degrees and conjugacy class sizes of G , respectively, and write π（m）to denote the set of all prime divisors of a positive integer m . For any 1≠m∈cd（G） and 1≠m∈cs（G）, in this note, we shall present the corresponding group structures of finite group G in the case π（m）=π , respectively, which generalizes the result of finite groups with character degrees of two distinct primes. Furthermore, we shall see that the influence of the two sets on the group structure is analogous.
