A highly clustered scale-free network evolved by random walking

In present paper, we propose a highly clustered weighted network model that incorporates the addition of a new node with some links, new links between existing nodes and the edge's weight dynamical evolution based on weight-dependent walks at each time step. The analytical approach and numerical simulation show that the system grows into a weighted network with the power-law distributions of strength, weight and degree. The weight-dependent walk length l will not influence the strength distribution, but the clustering coefficient of the network is sensitive to l. Particularly, the clustering coefficient is especially high and almost independent of the network size when l=2.     

对不平衡类分类的一种组合方法

具有不平衡类分布的数据集在许多实际应用中是很常见的,但由于类分布不平衡,给那些已有的分类算法带来了很多问题。一种为处理不平衡类问题而开发的基于决策树和人工神经网络的有效组合方法被讨论。它基于数据抽样的方法构建组合分类器,并利用ROC曲线(Receiver Operating Characteristic curve)作为评价挖掘性能的分析工具,最后在PAKDD2007竞赛活动提供的实际数据上进行了有效性验证。     

有效微观状态数与系综变换

首先提出有效微观状态数的概念，以及为出发点阐明尽管主其本质看他们都与孤立系的微观状态数的地位相当，证明了对于不同独立参量的系统，相应的有效微观状态数都扮演了特性函数的角色，于是由独立参量的各种组合会有各种有效微观状态数，从而有各种相应的系综。     

Amalgamation of partitions from multiple segmentation bases: A comparison of non-model-based and model-based methods

The segmentation of customers on multiple bases is a pervasive problem in marketing research. For example, segmentation service providers partition customers using a variety of demographic and psychographic characteristics, as well as an array of consumption attributes such as brand loyalty, switching behavior, and product/service satisfaction. Unfortunately, the partitions obtained from multiple bases are often not in good agreement with one another, making effective segmentation a difficult managerial task. Therefore, the construction of segments using multiple independent bases often results in a need to establish a partition that represents an amalgamation or consensus of the individual partitions. In this paper, we compare three methods for finding a consensus partition. The first two methods are deterministic, do not use a statistical model in the development of the consensus partition, and are representative of methods used in commercial settings, whereas the third method is based on finite mixture modeling. In a large-scale simulation experiment the finite mixture model yielded better average recovery of holdout (validation) partitions than its non-model-based competitors. This result calls for important changes in the current practice of segmentation service providers that group customers for a variety of managerial goals related to the design and marketing of products and services.     

Computing finest mincut partitions of a graph and application to routing problems

Let G=(V,E,w) be an n-vertex graph with edge weights w>0. We propose an algorithm computing all partitions of V into mincuts of G such that the mincuts in the partitions cannot be partitioned further into mincuts. There are O(n) such finest mincut partitions. A mincut is a non-empty proper subset of V such that the total weight of edges with exactly one end in the subset is minimal. The proposed algorithm exploits the cactus representation of mincuts and has the same time complexity as cactus construction. An application to the exact solution of the general routing problem is described.     

Schur Q-polynomials, multiple hypergeometric series and enumeration of marked shifted tableaux

We study Schur Q-polynomials evaluated on a geometric progression, or equivalently q-enumeration of marked shifted tableaux, seeking explicit formulas that remain regular at q=1. We obtain several such expressions as multiple basic hypergeometric series, and as determinants and pfaffians of continuous q-ultraspherical or continuous q-Jacobi polynomials. As special cases, we obtain simple closed formulas for staircase-type partitions.     

Solving clusterization problems using groups of algorithms

Clusterization is one of the most widespread problems in data analysis. There are many approaches and methods for its solution. However, the result of clusterization strongly depends on the choice of the feature space, on the object proximity measures, and on the method used to formalize the concepts of the object and cluster equivalence. As a result, different solutions can be far apart from each other; they can be degenerate or be quite different from the actually existing groupings. In this paper, clusterization obtained by groups of algorithms is considered; these methods make it possible to construct consistent solutions that best match the actually existing groupings.     

电介质的结构级别和性质

用组合系综说明了慢效应中的剩余极化．从时域介电谱的慢分量可计算出驻极体中冷冻极化的理论曲线，其结果和实验一致．慢极化属于非马尔可夫过程，其历史记忆效应使电动力学中除麦克斯韦场方程之外还要补充源方程．证明了线性介电响应中存在复介电常数的充分和必要条件为极化过程是马尔可夫过程．在聚合物的β转变中，二级和三级结构运动的恢复力系数出现抛物线型软化．     

不精确数据的相似度及其在聚类分析中的应用

基本包含度理论，提出不精确数据的一种相似度，并讨论基于此相似度的不精确数据的聚类方法。