A RIGOROUS PROOF ON CIRCULAR WIRELENGTH FOR HYPERCUBES

We study embeddings of the n-dimensional hypercube into the circuit with 2nvertices.We prove that the circular wirelength attains a minimum by gray coding;that was called the CT conjecture by Chavez and Trapp(Discrete Applied Mathematics,1998).This problem had claimed to be settled by Ching-Jung Guu in her doctoral dissertation“The circular wirelength problem for hypercubes”(University of California,Riverside,1997).Many argue there are gaps in her proof.We eliminate the gaps in her dissertation.

On Restricted Connectivity and Extra Connectivity of Hypercubes and Folded Hypercubes

Given a graph G and a non-negative integer h, the h-restricted connectivity κh（G） of G is the minimum cardinality of a set of vertices of G, in which at least h neighbors of any vertex is not included, if any, whose deletion disconnects G and every remaining component has the minimum degree of vertex at least h; and the h-extra connectivity κh（G） of G is the minimum cardinality of a set of vertices of G, if any, whose deletion disconnects G and every remaining component has order more than h. This paper shows that for the hypercube Qn and the folded hypercube FQn, κ1（Qn）=κ（1）（Qn）=2n-2 for n≥3, κ2（Qn）=3n-5 for n≥4, κ1（FQn）=κ（1）（FQn）=2n for n≥4 and κ（2）（FQn）=4n-4 for n≥8.

On the extra edge-connectivity of hypercubes

The classical hypercube structure is a popular topological architecture in parallel computing environments and a large number of variations based on the hypercube were posed in the past three decades. Reliability evaluation of systems is important to the design and maintenance of multiprocessor systems. The h-extra edge-connectivity of graph G（V, E） is a kind of measure for the reliability of interconnection systems, which is defined as the minimum cardinality of a subset of edge set, if any, whose deletion disconnects G and such that every re- maining component has at least h vertices. This paper shows that the h-extra edge-connectivity 2n-1 2n-1 of the hypercube Qn is a constant 2n-1 for 2n-1/3≤ h2n-1, and n ≥ 4, which extends the result of [Bounding the size of the subgraph induced by m vertices and extra edge-connectivity of hypercubes, Discrete Applied Mathematics, 2013, 161（16）： 2753-2757].

Restricted-Faults Identification in Folded Hypercubes under the PMC Diagnostic Model

System-level fault identification is a key subject for maintaining the reliability of multiprocessor interconnected systems. This task requires fast and accurate inferences based on big volume of data, and the problem of fault identification in an unstructured graph has been proved to be NP-hard （non-deterministic polynomial-time hard）. In this paper, we adopt the PMC diagnostic model （first proposed by Preparata, Metze, and Chien） as the foundation of point-to-point probing technology, and a system contains only restricted-faults if every of its fault-free units has at least one fault-free neighbor. Under this condition we propose an efficient method of identifying restricted-faults in the folded hypercube, which is a promising alternative to the popular hypercube topology.

On Embedding of m-Sequential k-ary Trees into Hypercubes

In this paper, we present an algorithm for embedding an m-sequential k-ary tree into its optimal hypercube with dilation at most 2 and prove its correctness.

A Proof for g-Good-Neighbor Diagnosability of Exchanged Hypercubes

The diagnosability of a multiprocessor system or an interconnection network is an important research topic. The system and an interconnection network have an underlying topology, which is usually presented by a graph. In this paper, we show proof for the g-good-neighbor diagnosability of the exchanged hypercube EH (s,t) under the PMC model and MM* model.

The Non-inclusion Diagnosability of Hypercubes Under the PMC Model

Diagnosability of a multiprocessor system is an important measure of the reliability of interconnection networks.System-level diagnosis is a primary strategy to identify the faulty processors in a multiprocessor system.Based on a sound assumption proposed by Zhu et al.recently,we proposed a new diagnosability named non-inclusion diagnosability and showed that the non-inclusion diagnosability t_(N)(Q_(n))of the hypercube under the PMC model is 2n-2.That is,assume that if two vertex sets F_(1) and F_(2) are both consistent with a syndrome and F_(1)C F_(2),then F_(2) is not the faulty set which we are looking for;the faulty set F is 1-step diagnosable if|F|≤2n-2 in Q_(n) under the PMC model.

On r-Hued Coloring of Hypercubes

For positive integers k and r,a(k,r)-coloring of graph G is a proper vertex k-coloring of G such that the neighbors of any vertex v∈V(G)receive at least min{d_(G)(v),r}different colors.The r-hued chromatic number of G,denoted χ_(r)(G),is the smallest integer k such that G admits a(k,r)-coloring.Let Q_(n) be the n-dimensional hypercube.For any integers n and r with n≥2 and 2≤r≤5,we investigated the behavior of χ_(r)(Q_(n)),and determined the exact value of χ_(2)(Q_(n))and χ_(3)(Q_(n))for all positive integers n.

LINEAR REGRESSION OF INTERVAL-VALUED DATA BASED ON COMPLETE INFORMATION IN HYPERCUBES

Recent years have witnessed an increasing interest in interval-valued data analysis. As one of the core topics, linear regression attracts particular attention. It attempts to model the relationship between one or more explanatory variables and a response variable by fitting a linear equation to the interval-valued observations. Despite of the well-known methods such as CM, CRM and CCRM proposed in the literature, further study is still needed to build a regression model that can capture the complete information in interval-valued observations. To this end, in this paper, we propose the novel Complete Information Method （CIM） for linear regression modeling. By dividing hypercubes into informative grid data, CIM defines the inner product of interval-valued variables, and transforms the regression modeling into the computation of some inner products. Experiments on both the synthetic and real-world data sets demonstrate the merits of CIM in modeling interval-valued data, and avoiding the mathematical incoherence introduced by CM and CRM.

Performance of Multicast Communication on Hypercubes

Based upon hypercube multiprocessor systems,this paper analyses in detail the communication performance under the background of the greedy multicast algorithm GMA.The mean delay time of a mes- sage both at a node and in the system under multicasting is derived.For the sake of contrast,the delay of multicast message is compared with that of multiple one-to-one messages.

Fault-Tolerant Cycles Embedding in Folded Hypercubes

The generalized conditional fault-tolerant embedding is investigated, in which the n-dimensional folded hypercube networks （denoted by FQn） acts as the host graph, and the longest fault-free cycle represents the guest graph. Under the conditions looser than that of previous works, it is shown that FQn has a cycle with length at least 2n -21F, I when the number of faulty vertices and non-critical edges is at most 2n-4; where ｜Fv｜ is the number of faulty vertices. It provides further theoretical evidence for the fact that FQn has excellent node-fault-tolerance and edge-fault-tolerance when used as a topology of large scale computer networks.

A Fault-Tolerant and Heuristic Routing Algorithm for Faulty Hypercubes

A fault-tolerant and heuristic routing algorithm for faulty hypercube sys-tems is described. To improve the efficiency, the algorithm adopts a heuristic backtracking strategy and each node has an array to record its all neighbors'faulty link information to avoid unnecessary searching for the known faulty links. Furthermore, the faulty link information is dynamically accumulated and the technique of heuristically searching for optimal link is used. The algo rithm routes messages through the minimum feasible path between the sender and receiver if at Ieast one such path ekists, and ta.kes the optimal path with higher probability when faulty links exist in the faulty hypercube.

The Edge-pancyclicity of Generalized Hypercubes

Generalized hypercubes （denoted by Q（d1,d2,... ,dn）） is an important network topology for parallel processing computer systems. Some methods of forming big cycle from small cycles and links have been developed. Basing on which, we has proved that in generalized hypercubes, every edge can be contained on a cycle of every length from 3 to IV（G）I inclusive and all kinds of length cycles have been constructed. The edgepanciclieity and node-pancilicity of generalized hypercubes can be applied in the topology design of computer networks to improve the network performance.

CYCLES EMBEDDING ON FOLDED HYPERCUBES WITH FAULTY NODES

Let FFv be the set of faulty nodes in an n-dimensional folded hypercube FQn with ｜FFv｜ ≤ n - 1 and all faulty vertices are not adjacent to the same vertex. In this paper, we show that if n ≥ 4, then every edge of FQn - FFv lies on a fault-free cycle of every even length from 6 to 2n - 2｜FFv｜.

Simulation of internal nitrogen release from bottom sediments in an urban lake using a nitrogen flux model

Nutrient release from sediment is considered a significant source for overlying water. Given that nutrient release mechanisms in sediment are complex and difficult to simulate, traditional approaches commonly use assigned parameter values to simulate these processes. In this study, a nitrogen flux model was developed and coupled with the water quality model of an urban lake. After parameter sensitivity analyses and model calibration and validation, this model was used to simulate nitrogen exchange at the sediment–water interface in eight scenarios. The results showed that sediment acted as a buffer in the sediment–water system. It could store or release nitrogen at any time, regulate the distribution of nitrogen between sediment and the water column, and provide algae with nitrogen. The most effective way to reduce nitrogen levels in urban lakes within a short time is to reduce external nitrogen loadings. However, sediment release might continue to contribute to the water column until a new balance is achieved. Therefore, effective measures for reducing sediment nitrogen should be developed as supplementary measures. Furthermore, model parameter sensitivity should be individually examined for different research subjects.

Sensitivity analysis of factors affecting gravity dam anti-sliding stability along a foundation surface using Sobol method

The anti-sliding stability of a gravity dam along its foundation surface is a key problem in the design of gravity dams.In this study,a sensitivity analysis framework was proposed for investigating the factors affecting gravity dam anti-sliding stability along the foundation surface.According to the design specifications,the loads and factors affecting the stability of a gravity dam were comprehensively selected.Afterwards,the sensitivity of the factors was preliminarily analyzed using the Sobol method with Latin hypercube sampling.Then,the results of the sensitivity analysis were verified with those obtained using the Garson method.Finally,the effects of different sampling methods,probability distribution types of factor samples,and ranges of factor values on the analysis results were evaluated.A case study of a typical gravity dam in Yunnan Province of China showed that the dominant factors affecting the gravity dam anti-sliding stability were the anti-shear cohesion,upstream and downstream water levels,anti-shear friction coefficient,uplift pressure reduction coefficient,concrete density,and silt height.Choice of sampling methods showed no significant effect,but the probability distribution type and the range of factor values greatly affected the analysis results.Therefore,these two elements should be sufficiently considered to improve the reliability of the dam anti-sliding stability analysis.

光RP(k)网络上Hypercube通信模式的波长指派算法

波长指派是光网络设计的基本问题,设计波长指派算法是洞察光网络通信能力的基本方法.基于光RP(k)网络,讨论了其波长指派问题. 含有N=2n个节点的Hypercube通信模式,构造了节点间的一种排列次序Xn,并设计了RP(k)网络上的波长指派算法.在构造该算法的过程中,得到了在环网络上实现n维Hypercube通信模式的波长指派算法.这两个算法具有较高的嵌入效率.在RP(k)网络上,实现Hypercube通信模式需要max{2,52n-5/3}个波长.而在环网络上,实现该通信模式需要复用N/3+N/12个波长,比已有算法需要复用N/3+N/4个波长有较大的改进.这两个算法对于光网络的设计具有较大的指导价值.

低偏差OALHD的构造

本文给出了利用均匀设计和正交表构造低偏差 ＯＡＬＨ设计的方法，该方法构造的设计既有优良的均匀性又具有正交设计的均衡性，一个更重要的优点是可以构造较大样本容量的设计点集。本文同时给出了某些参数的均匀设计表，这些设计优于现有的均匀设计，具有实用价值．

大跨度斜拉桥可靠度评估方法研究

针对大型复杂桥梁结构极限状态方程一般难以显式表达的特点,提出了基于神经网络的大跨度斜拉桥可靠度评估方法.通过Latin hypercube抽样技术对随机参数进行抽样,应用大跨度斜拉桥非线性有限元进行分析.通过对随机抽样的样本数据进行训练,应用神经网络的非线性映射和泛化技术,对大跨度斜拉桥的极限状态方程进行数值模拟.通过极限状态方程对随机变量的偏导数,求解结构可靠指标的优化问题,计算大跨度斜拉桥的可靠指标.结果表明:对于隐式极限状态方程的大跨度斜拉桥可靠度评估问题,本文方法具有较高的计算精度和较好的计算效率;荷载布置方式、作用位置等对斜拉桥可靠指标有很大影响;计入3种几何非线性效应后斜拉桥偏于不安全,其中斜拉索垂度非线性效应的影响最为显著.

基于机群并行通信处理器HCP的选播通信操作算法

在我们自行研制的并行通信处理器ＨＰＣ基础上，给出了一种基于Ｈｙｐｅｒｃｕｂｅ互连网络环境下的通信处理器ＨＣＰ的选播通信算法，该算法可实现网络上的一个ＨＣＰ向其他任意多个ＨＣＰ发送相同的Ｆｒａｍｅ的操作。