Scenario tree reduction for multistage stochastic programs

A framework for the reduction of scenario trees as inputs of (linear) multistage stochastic programs is provided such that optimal values and approximate solution sets remain close to each other. The argument is based on upper bounds of the L _r -distance and the filtration distance, and on quantitative stability results for multistage stochastic programs. The important difference from scenario reduction in two-stage models consists in incorporating the filtration distance. An algorithm is presented for selecting and removing nodes of a scenario tree such that a prescribed error tolerance is met. Some numerical experience is reported.     

On multistage Stochastic Integer Programming for incorporating logical constraints in asset and liability management under uncertainty

We present a model for optimizing a mean-risk function of the terminal wealth for a fixed income asset portfolio restructuring with uncertainty in the interest rate path and the liabilities along a given time horizon. Some logical constraints are considered to be satisfied by the assets portfolio. Uncertainty is represented by a scenario tree and is dealt with by a multistage stochastic mixed 0-1 model with complete recourse. The problem is modelled as a splitting variable representation of the Deterministic Equivalent Model for the stochastic model, where the 0-1 variables and the continuous variables appear at any stage. A Branch-and-Fix Coordination approach for the multistage 0–1 program solving is proposed. Some computational experience is reported.      

基于数据挖掘的蔬菜图片病害自动分类

为了对蔬菜病害进行自动检测和分级,克服传统的评估方法检测成本高、划分等级随意性比较大的缺陷,探讨了基于蔬菜图像的病害等级自动分类,设计了预处理技术提取图片特征.具体方法是对叶片图像进行分割并转变为分布概率的灰度矢量.在此基础上利用数据挖掘技术建立决策树模型,利用该模型对未分级叶片的级别进行预测.还引入了元挖掘算法Bagging,与决策树模型综合使用,进一步提高了预测效果.实验表明这一蔬菜病害等级自动分类方法准确度较高,具有较好的实用价值.     

Vertex partitions of chordal graphs

A k‐tree is a chordal graph with no (k + 2)‐clique. An ?‐tree‐partition of a graph G is a vertex partition of G into ‘bags,’ such that contracting each bag to a single vertex gives an ?‐tree (after deleting loops and replacing parallel edges by a single edge). We prove that for all k ≥ ? ≥ 0, every k‐tree has an ?‐tree‐partition in which each bag induces a connected ‐tree. An analogous result is proved for oriented k‐trees. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 167–172, 2006     

A conditional limit theorem for tree-indexed random walk

We consider Galton–Watson trees associated with a critical offspring distribution and conditioned to have exactly n$n$ vertices. These trees are embedded in the real line by assigning spatial positions to the vertices, in such a way that the increments of the spatial positions along edges of the tree are independent variables distributed according to a symmetric probability distribution on the real line. We then condition on the event that all spatial positions are nonnegative. Under suitable assumptions on the offspring distribution and the spatial displacements, we prove that these conditioned spatial trees converge as n→∞$n\to \infty$, modulo an appropriate rescaling, towards the conditioned Brownian tree that was studied in previous work. Applications are given to asymptotics for random quadrangulations.     

On the unconditional subsequence property

We show that a construction of Johnson, Maurey and Schechtman leads to the existence of a weakly null sequence (fi) in ?₂(∑Lpi), where pi↓1, so that for all ε>0 and 1<q?2, every subsequence of (fi) admits a block basis (1+ε)-equivalent to the Haar basis for Lq. We give an example of a reflexive Banach space having the unconditional subsequence property but not uniformly so.     

Counting labelled trees with given indegree sequence

For a labelled tree on the vertex set [n]:={1,2,…,n}, define the direction of each edge ij to be i→j if i<j. The indegree sequence of T can be considered as a partition λ?n−1. The enumeration of trees with a given indegree sequence arises in counting secant planes of curves in projective spaces. Recently Ethan Cotterill conjectured a formula for the number of trees on [n] with indegree sequence corresponding to a partition λ. In this paper we give two proofs of Cotterill's conjecture: one is “semi-combinatorial” based on induction, the other is a bijective proof.     

New results on optimizing rooted triplets consistency

A set of phylogenetic trees with overlapping leaf sets is consistent if it can be merged without conflicts into a supertree. In this paper, we study the polynomial-time approximability of two related optimization problems called the maximum rooted triplets consistency problem (MaxRTC) and the minimum rooted triplets inconsistency problem (MinRTI) in which the input is a set R of rooted triplets, and where the objectives are to find a largest cardinality subset of R which is consistent and a smallest cardinality subset of R whose removal from R results in a consistent set, respectively. We first show that a simple modification to Wu’s Best-Pair-Merge-First heuristic Wu (2004) [38] results in a bottom-up-based 3-approximation algorithm for MaxRTC. We then demonstrate how any approximation algorithm for MinRTI could be used to approximate MaxRTC, and thus obtain the first polynomial-time approximation algorithm for MaxRTC with approximation ratio less than 3. Next, we prove that for a set of rooted triplets generated under a uniform random model, the maximum fraction of triplets which can be consistent with any phylogenetic tree is approximately one third. We then provide a deterministic construction of a triplet set having a similar property which is subsequently used to prove that both MaxRTC and MinRTI are -hard even if restricted to minimally dense instances. Finally, we prove that unless , MinRTI cannot be approximated within a ratio of c⋅lnn for some constant c>0 in polynomial time, where n denotes the cardinality of the leaf label set of R.     

基于故障树和混沌粒子群算法的锻压机床故障诊断方法

锻压机床由于生产效率高和材料利用率高的特点,被广泛应用于各领域.然而,锻压机床发生故障时,其故障种类繁多、故障数据量大,所以对锻压机床故障源的快速、准确诊断较困难.针对该问题,文章提出一种将故障树分析法和混沌粒子群算法相融合的方法,对锻压机床的故障源进行故障诊断.该方法是先通过故障树分析法对锻压机床的故障进行分析从而得到故障模式及其故障概率,然后由得到的故障模式和已知的故障维修经验分析归纳出故障模式的学习样本,再根据得到的故障概率运用混沌粒子群算法的遍历性快速、准确地诊断出锻压机床发生故障的精确位置.文章提出的方法以锻压机床的伺服系统为例进行了故障诊断实验,将该实验结果与遗传算法、粒子群算法进行对比.实验结果表明,文章的算法在锻压机床伺服系统的故障诊断中准确度更高、速度更快.     

关于树指标非齐次马氏链的广义熵遍历定理

主要研究了树指标非齐次马氏链的广义熵遍历定理.首先证明了树指标非齐次马氏链上的二元函数延迟平均的强极限定理.然后得到了树指标非齐次马氏链上状态出现延迟频率的强大数定律,以及树指标非齐次马氏链的广义熵遍历定理.作为推论,推广了一些已有结果.同时,证明了局部有限无穷树树指标有限状态随机过程广义熵密度的一致可积性.