基于二叉树的簇内分层密钥管理方案

通过对基于分簇的数据融合隐私保护算法CPDA的分析,提出了一种基于簇内分层随机密钥管理方案.它使用二叉树的逻辑结构,对簇内节点进行重新组织后,传输各自的切片数据,再通过建立密钥树的逻辑层次结构.对整个组密钥进行管理最终实现了在数据融合的同时,保护数据安全通过实验分析,相比于分簇隐私数据融合协议CPDA在具有更好的隐私保护性的同时,更低的数据通信量以及良好的可扩展性.     

一种动态获取簇核心的自动聚类tNN-MEANS算法

K-means算法是一种非常重要的聚类算法,然而算法的聚类效果受簇的个数、初始中心点位置的影响很大.提出基于优化初始中心集合和中心移动算法tNN-MEANS,算法有效解决了以下三个问题:1)准确确定大规模数据集中簇的个数;2)精确确定全局高密度的核心区域;3)克服了簇中存在多个高密度区域的问题.运用UCI数据集分别对X-means算法、DBSCAN算法和tNN-MEANS算法进行对比实验,实验结果验证了tNN-MEANS算法的聚类精度、确定簇的个数、蔟划分的正确率等性能均优于与之对比的其它算法.     

非平衡数据集的支持向量域分类预测模型研究

基于非平衡数据集的支持向量域分类模型,提出了一种银行客户个人信用预测方法.首先分析了信用预测的主要方法及其不足,然后研究了支持向量域分类模型及其参数的非负二次规划乘性更新算法,进而提出基于支持向量域分类模型的银行客户个人信用预测方法,最后使用人工数据和实际数据对提出方法与支持向量机预测方法进行对比实验.实验结果表明对于银行客户个人信用预测的非平衡数据分析问题,基于支持向量域模型的分类预测方法更有效.     

簇飞行航天器网络节点距离分布的高斯近似

簇飞行航天器因其节点间几何结构松散,节点间相对有界成为分布式空间系统研究热点之一.基于建立的簇飞行航天器节点移动模型,运用经验统计的分析方法,研究了簇飞行航天器节点间距离分布,采用高斯函数拟合,近似得到了节点距离分布的概率密度函数;为便于分析,还采用八阶多项式拟合节点距离分布的概率密度函数,并与高斯函数拟合残差和相对熵比较分析.结果表明,高斯函数效果更好,为研究簇飞行航天器网络性能提供重要理论基础.     

基于迁移学习的客户信用评估模型研究

客户信用评估是银行等金融企业日常经营活动中的重要组成部分。一般违约样本在客户总体中只占少数,而能按时还款客户样本占多数,这就是客户信用评估中常见的类别不平衡问题。目前,用于客户信用评估的方法尚不能有效解决少数类样本稀缺带来的类别不平衡。本研究引入迁移学习技术整合系统内外部信息,以解决少数类样本稀缺带来的类别不平衡问题。为了提高对来自系统外部少数类样本信息的使用效率,构建了一种新的迁移学习模型:以基于集成技术的迁移装袋模型为基础,使用两阶段抽样和数据分组处理技术分别对其基模型生成和集成策略进行改进。运用重庆某商业银行信用卡客户数据进行的实证研究结果表明:与目前客户信用评估的常用方法相比,新模型能更好地处理绝对稀缺条件下类别不平衡对客户信用评估的影响,特别对占少数的违约客户有更好的预测精度。     

基于罚函数方法的Leach协议

为延长无线传感器网络生存时长、减少网络能量消耗,首先将自适应粒子群优化算法应用于Leach协议,获得每一轮的最优簇头集;再基于罚函数方法,对集合中处于边缘位置的感知节点以及基站附近能量较低的感知节点进行惩罚,降低其当选为簇头的概率.通过大量仿真实验表明,协议对网络中簇头节点的选取更加合理,死亡节点分布由外而内,使节点能量负载更加均衡.     

CFRP修复缺陷钢板应力解析模型

在使用碳纤维复合材料(carbon fiber reinforced polymer, CFRP)修复钢结构腐蚀缺陷的修复方式中,CFRP应力及胶层应力是确定碳纤维修复结构承载能力的关键。基于平截面假设,得到弯矩作用下应力与应变分布;基于胶层剪切模型,得到胶层剪应力与CFRP和钢板位移间的关系;基于力的平衡,得到CFRP和钢板的应力关系。结合得到的各种材料之间关系,推导出轴力和弯矩联合作用状态下CFRP双面修复钢板的CFRP与胶层应力分布解析解。采用数值分析对CFRP双侧粘贴修复缺陷钢板进行分析,分析结果与解析结果具有一致性,同时获得了CFRP双侧粘贴修复缺陷钢板的应力分布特点,以及构件可能发生破坏的位置,为计算构件极限承载力提供了基础。     

节点密度的度量方法及其应用

应用随机分布的节点集进行函数逼近时,点的支撑域的大小对逼近的有效性及精度有很大影响.为研究移动最小二乘法中最优的支撑域半径,首先给出了一种全新的节点密度的概念,它不仅能刻画节点分布的疏密程度,而且其计算算法简单,也便于点的支撑域半径的选取;其次,基于节点密度的概念给出了搜索支撑域内节点的领域搜索算法,与通常使用的全域搜索算法相比,领域搜索算法提高了计算效率,节省了搜索节点需要的时间;最后给出算例,验证文中提出的计算点的支撑域半径算法的有效性.     

一类五次微分系统的定性分析

对一类五次平面多项式微分系统进行了定性分析.给出原点的中心与等时中心条件及极限环的存在性.研究了此系统无穷远点的性态,该无穷远点是高次奇点,并运用把大角域分为若干小角域的方法对此高次奇点在不定号情形下轨线的分布情况进行讨论.     

时长不等数据的vine-copula建模及多资产组合VaR分析

传统的copula模型在对二维以上相依结构建模时存在参数过少的缺陷,vine copula理论基本弥补了这一缺陷.介绍了vine copula理论以及其相对于传统多元模型的优势,尤其提出了vine copula对于时长不一致的数据进行建模具有数据利用率较高的特性,给出了这类数据vine copula的建模步骤以及基于极大似然估计的统计推断.最后对国内A股市场的五种金融股票的联合分布进行建模,并利用蒙特卡罗方法对资产组合的VaR进行了模拟.     

When linear and weak discrepancy are equal

The linear discrepancy of a poset P is the least k such that there is a linear extension L of P such that if x and y are incomparable, then |h_L(x)−h_L(y)|≤k, whereas the weak discrepancy is the least k such that there is a weak extension W of P such that if x and y are incomparable, then |h_W(x)−h_W(y)|≤k. This paper resolves a question of Tanenbaum, Trenk, and Fishburn on characterizing when the weak and linear discrepancy of a poset are equal. Although it is shown that determining whether a poset has equal weak and linear discrepancy is -complete, this paper provides a complete characterization of the minimal posets with equal weak and linear discrepancy. Further, these minimal posets can be completely described as a family of interval orders.     

The fractional weak discrepancy of a partially ordered set

In this paper we introduce the notion of the fractional weak discrepancy of a poset, building on previous work on weak discrepancy in [J.G. Gimbel and A.N. Trenk, On the weakness of an ordered set, SIAM J. Discrete Math. 11 (1998) 655-663; P.J. Tanenbaum, A.N. Trenk, P.C. Fishburn, Linear discrepancy and weak discrepancy of partially ordered sets, ORDER 18 (2001) 201-225; A.N. Trenk, On k-weak orders: recognition and a tolerance result, Discrete Math. 181 (1998) 223-237]. The fractional weak discrepancywd_F(P) of a poset P=(V,?) is the minimum nonnegative k for which there exists a function f:V→R satisfying (1) if a?b then f(a)+1?f(b) and (2) if a∥b then |f(a)-f(b)|?k. We formulate the fractional weak discrepancy problem as a linear program and show how its solution can also be used to calculate the (integral) weak discrepancy. We interpret the dual linear program as a circulation problem in a related directed graph and use this to give a structural characterization of the fractional weak discrepancy of a poset.     

Linear Discrepancy and Weak Discrepancy of Partially Ordered Sets

The linear discrepancy of a partially ordered set P=(X,) is the least integer k for which there exists an injection f: XZ satisfying (i) if xy then f(x)<f(y) and (ii) if xy then |f(x)–f(y)|k. This concept is closely related to the weak discrepancy of P studied previously. We prove a number of properties of linear and weak discrepancies and relate them to other poset parameters. Both parameters have applications in ranking the elements of a partially ordered set so that the difference in rank of incomparable elements is minimized.     

Range of the Fractional Weak Discrepancy Function

In this paper we describe the range of values that can be taken by the fractional weak discrepancy of a poset and characterize semiorders in terms of these values. In [6], we defined the fractional weak discrepancy of a poset to be the minimum nonnegative for which there exists a function satisfying (1) if then and (2) if then . This notion builds on previous work on weak discrepancy in [3, 7, 8]. We prove here that the range of values of the function is the set of rational numbers that are either at least one or equal to for some nonnegative integer . Moreover, is a semiorder if and only if , and the range taken over all semiorders is the set of such fractions .The third author's work was supported in part by a Wellesley College Brachman Hoffman Fellowship.     

The total linear discrepancy of an ordered set

In this paper we introduce the notion of the total linear discrepancy of a poset as a way of measuring the fairness of linear extensions. If L is a linear extension of a poset P, and x,y is an incomparable pair in P, the height difference between x and y in L is |L(x)−L(y)|. The total linear discrepancy of P in L is the sum over all incomparable pairs of these height differences. The total linear discrepancy of P is the minimum of this sum taken over all linear extensions L of P. While the problem of computing the (ordinary) linear discrepancy of a poset is NP-complete, the total linear discrepancy can be computed in polynomial time. Indeed, in this paper, we characterize those linear extensions that are optimal for total linear discrepancy. The characterization provides an easy way to count the number of optimal linear extensions.     

模糊信息差异及唯一性定理证明

定义了模糊相对熵,基于模糊熵和距离定义了模糊信息差异、拟模糊信息差异,并讨论了模糊信息差异唯一性定理以及模糊信息差异的性质.     

A Characterisation of Posets that Are nearly Antichains

We present a characterisation of posets of size n with linear discrepancy n − 2. These are the posets that are “furthest” from a linear order without being an antichain. This revised version was published online in September 2006 with corrections to the Cover Date.     

Fractional weak discrepancy and interval orders

The fractional weak discrepancywd_F(P) of a poset P=(V,?) was introduced in [A. Shuchat, R. Shull, A. Trenk, The fractional weak discrepancy of a partially ordered set, Discrete Applied Mathematics 155 (2007) 2227-2235] as the minimum nonnegative k for which there exists a function satisfying (i) if a?b then f(a)+1≤f(b) and (ii) if a∥b then |f(a)−f(b)|≤k. In this paper we generalize results in [A. Shuchat, R. Shull, A. Trenk, Range of the fractional weak discrepancy function, ORDER 23 (2006) 51-63; A. Shuchat, R. Shull, A. Trenk, Fractional weak discrepancy of posets and certain forbidden configurations, in: S.J. Brams, W.V. Gehrlein, F.S. Roberts (Eds.), The Mathematics of Preference, Choice, and Order: Essays in Honor of Peter C. Fishburn, Springer, New York, 2009, pp. 291-302] on the range of the wd_F function for semiorders (interval orders with no induced ) to interval orders with no , where n≥3. In particular, we prove that the range for such posets P is the set of rationals that can be written as r/s, where 0≤s−1≤r<(n−2)s. If wd_F(P)=r/s and P has an optimal forcing cycle C with and , then r≤(n−2)(s−1). Moreover when s≥2, for each r satisfying s−1≤r≤(n−2)(s−1) there is an interval order having such an optimal forcing cycle and containing no.     

Bracketing numbers for axis-parallel boxes and applications to geometric discrepancy

In the first part of this paper we derive lower bounds and constructive upper bounds for the bracketing numbers of anchored and unanchored axis-parallel boxes in the d$d$-dimensional unit cube.