Hierarchical Model-Based Clustering for Large Datasets

In recent years, hierarchical model-based clustering has provided promising results in a variety of applications. However, its use with large datasets has been hindered by a time and memory complexity that are at least quadratic in the number of observations. To overcome this difficulty, this article proposes to start the hierarchical agglomeration from an efficient classification of the data in many classes rather than from the usual set of singleton clusters. This initial partition is derived from a subgraph of the minimum spanning tree associated with the data. To this end, we develop graphical tools that assess the presence of clusters in the data and uncover observations difficult to classify. We use this approach to analyze two large, real datasets: a multiband MRI image of the human brain and data on global precipitation climatology. We use the real datasets to discuss ways of integrating the spatial information in the clustering analysis. We focus on two-stage methods, in which a second stage of processing using established methods is applied to the output from the algorithm presented in this article, viewed as a first stage.     

二元函数连续性条件之探析

对二元函数连续性判定条件给出了详细分析,强调有关问题的关键点,纠正了常见的模糊认识,得到一系列连续性充分条件及其推广形式．     

On the cut‐off phenomenon for the transitivity of randomly generated subgroups

Consider K ≥ 2 independent copies of the random walk on the symmetric group S_N starting from the identity and generated by the products of either independent uniform transpositions or independent uniform neighbor transpositions. At any time $nin mathbb{N}$, let G_n be the subgroup of S_N generated by the K positions of the chains. In the uniform transposition model, we prove that there is a cut‐off phenomenon at time N ln(N)/(2K) for the non‐existence of fixed point of G_n and for the transitivity of G_n, thus showing that these properties occur before the chains have reached equilibrium. In the uniform neighbor transposition model, a transition for the non‐existence of a fixed point of G_n appears at time of order $N^{1+frac{2}{K}}$ (at least for K ≥ 3), but there is no cut‐off phenomenon. In the latter model, we recover a cut‐off phenomenon for the non‐existence of a fixed point at a time proportional to N by allowing the number K to be proportional to ln(N). The main tools of the proofs are spectral analysis and coupling techniques. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2012     

Fully Invariant Subgroups of Abelian p-Groups with Finite Ulm–Kaplansky Invariants

We study primary groups containing proper fully invariant subgroups isomorphie to the group. The admissable sequence of Ulm–Kaplansky invariants for primary groups is introduced. Using these sequences, If-groups are described in the classes of seperable and periodically complete groups.     

Infeasible-interior-point algorithm for a class of nonmonotone complementarity problems and its computational complexity

This paper presents an infeasible-interior-point algorithm for a class of nonmonotone complementarity problems, and analyses its convergence and computational complexity. The results indicate that the proposed algorithm is a polynomial-time one.     

A note on 3‐factorizations of K10*

In this note, we enumerate all nonisomorphic 3‐factorizations of K₁₀. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 379–383, 2001     

STABILITY OF DELAY DIFFERENTIAL SYSTEMS BY SEVERAL LIAPUNOV FUNCTIONS

1 IntroductionConsider the functional differential equations (FDE's) with finite delay ofthe form:where x,(0) = x(t 0) for --r 5 0 5 0 with some r 2 0 and f: [T, co] x C RI with C = C([--r, 0], R') the space of continuous functions mapping [--r, 0]into l-dimensional real space RI. For any yi E C we define the norm of yi as:where l' I is any norm in RI.Inspired by the ideas in [l--3], we develop a new technique in this work tostudy the stability of FDE's, where the components xl) xZt…     

Ball numbers of platonic bodies

The ball number function is extended here to platonic bodies and corresponding generalized uniform distributions on platonic spheres are considered. A platonic disintegration formula of the Lebesgue measure is proved as well as a thin layers property.     

Chip-Firing and the Critical Group of a Graph

A variant of the chip-firing game on a graph is defined. It is shown that the set of configurations that are stable and recurrent for this game can be given the structure of an abelian group, and that the order of the group is equal to the tree number of the graph. In certain cases the game can be used to illuminate the structure of the group.     

weyl群的定义关系及其应用

首 先深化 Ｒ． Ｓｔｅｉｎｂｅｒｇ 关于 Ｗ ｅｙｌ 群定义 关系的一个定 理,作为应 用,对 Ｂｌ , Ｃｌ 型 Ｗ ｅｙｌ群分别构造了一 个指数为２的正 规子群