Drawing Weighted Directed Graph from It's Adjacency Matrix

This paper proposes an algorithm for building weighted directed graph, defmes the weighted directed relationship matrix of the graph, and describes algorithm implementation using this matrix. Based on this algorithm, an effective way for building and drawing weighted directed graphs is presented, forming a foundation for visual implementation of the algorithm in the graph theory.

A Note on the Spectral Radius of Weighted Signless Laplacian Matrix

A weighted graph is a graph that has a numeric label associated with each edge, called the weight of edge. In many applications, the edge weights are usually represented by nonnegative integers or square matrices. The weighted signless Laplacian matrix of a weighted graph is defined as the sum of adjacency matrix and degree matrix of same weighted graph. In this paper, a brief overview of the notation and concepts of weighted graphs that will be used throughout this study is given. In Section 2, the weighted signless Laplacian matrix of simple connected weighted graphs is considered, some upper bounds for the spectral radius of the weighted signless Laplacian matrix are obtained and some results on weighted and unweighted graphs are found.

基于Weighted-slope One的用户聚类推荐算法研究

针对传统协同过滤推荐算法存在的数据稀疏性以及实时性差的问题,提出一种基于Weighted-slope One的用户聚类推荐算法。该算法首先利用Weighted-slope One算法的思想对初始的用户-评分矩阵进行有效填充,降低数据的稀疏性;然后,结合初始聚类中心优化改进的K-means方法对用户进行聚类,生成相似用户集合,以缩小目标用户搜索最近邻的范围;最后,结合目标用户所属的聚类,利用基于用户的协同过滤算法搜索最近邻居,为目标用户推荐对应的产品。仿真实验结果表明,改进算法可以显著降低数据的稀疏度,同时提升推荐的准确性和实时性。

Patch-based vehicle logo detection with patch intensity and weight matrix

A patch-based method for detecting vehicle logos using prior knowledge is proposed.By representing the coarse region of the logo with the weight matrix of patch intensity and position,the proposed method is robust to bad and complex environmental conditions.The bounding-box of the logo is extracted by a thershloding approach.Experimental results show that 93.58% location accuracy is achieved with 1100 images under various environmental conditions,indicating that the proposed method is effective and suitable for the location of vehicle logo in practical applications.

Weighted Gauss-Seidel Precoder for Downlink Massive MIMO Systems

In this paper,a novel precoding scheme based on the Gauss-Seidel(GS)method is proposed for downlink massive multiple-input multiple-output(MIMO)systems.The GS method iteratively approximates the matrix inversion and reduces the overall complexity of the precoding process.In addition,the GS method shows a fast convergence rate to the Zero-forcing(ZF)method that requires an exact invertible matrix.However,to satisfy demanded error performance and converge to the error performance of the ZF method in the practical condition such as spatially correlated channels,more iterations are necessary for the GS method and increase the overall complexity.For efficient approximation with fewer iterations,this paper proposes a weighted GS(WGS)method to improve the approximation accuracy of the GS method.The optimal weights that accelerate the convergence rate by improved accuracy are computed by the least square(LS)method.After the computation of weights,the different weights are applied for each iteration of the GS method.In addition,an efficient method of weight computation is proposed to reduce the complexity of the LS method.The simulation results show that bit error rate(BER)performance for the proposed scheme with fewer iterations is better than the GS method in spatially correlated channels.

ON THE m^(th) ORDER DIFFERENCE SEQUENCE SPACE OF GENERALIZED WEIGHTED MEAN AND COMPACT OPERATORS

In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space l（u, v, p; △（m））, which consist of the sequences whose generalized weighted △（m）-difference means are in the linear space l（p） defined by I.J.Maddox. Also, we determine the basis of this space and compute its α-, β- and γ-duals. Further, we give the characterization of the classes of matrix mappings from l（u, v, p, △（m）） to l∞, c, and co. Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space lp（U, v, △（m）） （1 ≤ p 〈 ∞）.

A random forest algorithm based on similarity measure and dynamic weighted voting

The random forest model is universal and easy to understand, which is often used for classification and prediction. However, it uses non-selective integration and the majority rule to judge the final result, thus the difference between the decision trees in the model is ignored and the prediction accuracy of the model is reduced. Taking into consideration these defects, an improved random forest model based on confusion matrix (CM-RF)is proposed. The decision tree cluster is selectively constructed by the similarity measure in the process of constructing the model, and the result is output by using the dynamic weighted voting fusion method in the final voting session. Experiments show that the proposed CM-RF can reduce the impact of low-performance decision trees on the output result, thus improving the accuracy and generalization ability of random forest model.

Spatial weight matrix in dimensionality reduction reconstruction for microelectromechanical system-based photoacoustic microscopy

A micro-electromechanical system(MEMS)scanning mirror accelerates the raster scanning of optical-resolution photoacoustic microscopy(OR-PAM).However,the nonlinear tilt angular-voltage characteristic of a MEMS mirror introduces distortion into the maximum back-projection image.Moreover,the size of the airy disk,ultrasonic sensor properties,and thermal effects decrease the resolution.Thus,in this study,we proposed a spatial weight matrix(SWM)with a dimensionality reduction for image reconstruction.The three-layer SWM contains the invariable information of the system,which includes a spatial dependent distortion correction and 3D deconvolution.We employed an ordinal-valued Markov random field and the Harris Stephen algorithm,as well as a modified delay-and-sum method during a time reversal.The results from the experiments and a quantitative analysis demonstrate that images can be effectively reconstructed using an SWM;this is also true for severely distorted images.The index of the mutual information between the reference images and registered images was 70.33 times higher than the initial index,on average.Moreover,the peak signal-to-noise ratio was increased by 17.08%after 3D deconvolution.This accomplishment offers a practical approach to image reconstruction and a promising method to achieve a real-time distortion correction for MEMS-based OR-PAM.

Automatic generation of min-weighted persistent formations

This paper researched into some methods for generating min-weighted rigid graphs and min-weighted persistent graphs. Rigidity and persistence are currently used in various studies on coordination and control of autonomous multi-agent formations. To minimize the communication complexity of formations and reduce energy consumption, this paper introduces the rigidity matrix and presents three algorithms for generating rain-weighted rigid and min- weighted persistent graphs. First, the existence of a min-weighted rigid graph is proved by using the rigidity matrix, and algorithm 1 is presented to generate the min-weighted rigid graphs. Second, the algorithm 2 based on the rigidity matrix is presented to direct the edges of min-weighted rigid graphs to generate min-weighted persistent graphs. Third, the formations with range constraints are considered, and algorithm 3 is presented to find whether a framework can form a min-weighted persistent formation. Finally, some simulations are given to show the efficiency of our research.

RESEARCHES ON INVERSE ORDER RULE FOR WEIGHTED GENERALIZED INVERSE

The weighted generalized inverses have several important applications in researching the singular matrices,regularization methods for ill-posed problems, optimization problems and statis- tics problems.In this paper we further research inverse order rules of weighted generalizde inverse. From the view point of munerical algebra, the different methods we used in inverse order rules pro- vide beneficial means for theory and computing of generalized inverse matrices.

Research on consistency measurement and weight estimation approach of hybrid uncertain comparison matrix

The consistency measurement and weight estimation approach of the hybrid uncertain comparison matrix in the analytic hierarchy process （AHP） are studied. First, the decision-making satisfaction membership function is defined based on the decision making＇s allowable error. Then, the weight model based on the maximal satisfactory consistency idea is suggested, and the consistency index is put forward. Moreover, the weight distributing value model is developed to solve the decision making misleading problem since the multioptimization solutions in the former model. Finally, the weights are ranked based on the possibility degree approach to obtain the ultimate order.

Optimal strategy of searching FPD weights scanning matrix using GA-PSO

This paper discusses a kind of optimal method used for searching flat panel display （FPD） scanning matrix. The method adopts bionic algorithm： genetic algorithm （GA） and particle swarm optimization （PSO） algorithm. The method using single GA is more time-consuming, and the search efficiency is low in later evolution; the PSO algorithm is easily falling into the local optimal solution and appears the premature convergent phenomenon. Hence, a hybrid approach of GAPSO is found to optimize the search for high grayscale weights scanning matrix. Finally in the acceptable time, it finds a weight scanning matrix （WSM） of 256 gray scales with Matlab, whose scanning efficiency reaches 94.73% and the linearity is very good.

Correction to: Spatial weight matrix in dimensionality reduction reconstruction for micro-electromechanical system-based photoacoustic microscopy

Following publication of the original article[1],the keywords are missing in the article.Keywords:Photoacoustic microscopy,Spatial weight matrix,Dimensionality reduction,Distortion correction,Mutual information The original article has been updated.

Wide-Area Delay-Dependent Adaptive Supervisory Control of Multi-machine Power System Based on Improve Free Weighting Matrix Approach

The paper demonstrates the possibility to enhance the damping of inter-area oscillations using Wide Area Measurement (WAM) based adaptive supervisory controller (ASC) which considers the wide-area signal transmission delays. The paper uses an LMI-based iterative nonlinear optimization algorithm to establish a method of designing state-feedback controllers for power systems with a time-varying delay. This method is based on the delay-dependent stabilization conditions obtained by the improved free weighting matrix (IFWM) approach. In the stabilization conditions, the upper bound of feedback signal’s transmission delays is taken into consideration. Combining theoriesof state feedback control and state observer, the ASC is designed and time-delay output feedback robust controller is realized for power system. The ASC uses the input information from Phase Measurement Units (PMUs) in the system and dispatches supplementary control signals to the available local controllers. The design of the ASC is explained in detail and its performance validated by time domain simulations on a New England test power system (NETPS).

Gaussian Weighted Trajectory Method Ⅳ： No Rainbow Effect in Practice

The Gaussian weighted trajectory method （GWTM） is a practical implementation of classical S matrix theory （CSMT） in the random phase approximation, CSMT being the first and simplest semi-classical approach of molecular collisions, developped in the early seventies. Though very close in spirit to the purely classical description, GWTM accounts to some extent for the quantization of the different degrees-of-freedom involved in the processes. While CSMT may give diverging final state distributions, in relation to the rainbow effect of elastic scattering theory, GWTM has never led to such a mathematical catastrophe. The goal of the present note is to explain this finding.

Introducing Weighted Nodes to Evaluate the Cloud Computing Topology

Typical data centers house several powerful ICT (Information and Communication Technology) equipment such as servers, storage devices and network equipment that are high-energy consuming. The nature of these high-energy consuming equipment is mostly accountable for the very large quantities of emissions which are harmful and unfriendly to the environment. The costs associated with energy consumption in data centers increases as the need for more computational resources increases, so also the appalling effect of CO2 (Carbon IV Oxide) emissions on the environment from the constituent ICT facilities-Servers, Cooling systems, Telecommunication systems, Printers, Local Area Network etc. Energy related costs would traditionally account for about 42% (forty-two per cent) of the total costs of running a typical data center. There is a need to have a good balance between optimization of energy budgets in any data center and fulfillment of the Service Level Agreements (SLAs), as this ensures continuity/profitability of business and customer’s satisfaction. A greener computing from what used to be would not only save/sustain the environment but would also optimize energy and by implication saves costs. This paper addresses the challenges of sustainable (or green computing) in the cloud and proffer appropriate, plausible and possible solutions. The idle and uptime of a node and the traffic on its links (edges) has been a concern for the cloud operators because as the strength and weights of the links to the nodes (data centres) increases more energy are also being consumed by and large. It is hereby proposed that the knowledge of centrality can achieve the aim of energy sustainability and efficiency therefore enabling efficient allocation of energy resources to the right path. Mixed-Mean centrality as a new measure of the importance of a node in a graph is introduced, based on the generalized degree centrality. The mixed-mean centrality reflects not only the strengths (weights) and numbers of edges for degree centrality but it combines these features by also applying the closeness centrality measures while it goes further to include the weights of the nodes in the consideration for centrality measures. We illustrate the benefits of this new measure by applying it to cloud computing, which is typically a complex system. Network structure analysis is important in characterizing such complex systems.

Phosphorylation and biosynthesis of high molecular weight proteins of tumor nuclear matrix

Our previous studies showed a predominance of high molecular weight protein group in tumor nuclear matrices. Contrary to normal cells, proteins of this group are preferentially phosphorylated. Phosphoproteins of hepatoma nuclear matrix are selectively subjected to rapid proteolysis. By alkali treatment and a monoclonal antibody against phosphotyrosyl residue the presence of two high molecular weight bands of phosphotyrosyl-containing proteins was detected in nuclear matrices of tumor but not of normal liver cells. High molecular weight protein group of tumor nuclear matrices revealed also a rapid turnover and preferential incorporation of labeled amino acids selectively inhibited by chloramphenicol.

基于Matrix Profile的时间序列分割技术改进

时间序列分割是数据挖掘领域中的一个重要研究方向.目前基于矩阵轮廓(matrix profile,MP)的时间序列分割技术得到了越来越多研究人员的关注,并且取得了不错的研究成果.不过该技术及其衍生算法仍然存在不足:首先,基于矩阵轮廓的快速低代价语义分割算法中对给定活动状态的时间序列分割时,最近邻之间通过弧进行连接,会出现弧跨越非目标活动状态匹配相似子序列问题;其次,现有提取分割点算法在提取分割点时采用给定长度窗口,容易得到与真实值偏差较大的分割点,降低准确性.针对以上问题,提出一种限制弧跨越的时间序列分割算法(limit arc curve cross-FLOSS,LAC-FLOSS),该算法给弧添加权重,形成一种带权弧,并通过设置匹配距离阈值解决弧的跨状态子序列误匹配问题.此外,提出一种改进的提取分割点算法(improved extract regimes,IER),它通过纠正弧跨越(corrected arc crossings,CAC)序列的形状特性,从波谷中提取极值,避免直接使用窗口在非拐点处取到分割点的问题.在公开数据集datasets_seg和MobiAct上面进行对比实验,验证以上两种解决方案的可行性和有效性.

关于赋权非正则图的A_(α)特征值和特征向量

设G_(ω)=(G,ω)是一个赋权图,其邻接矩阵和赋权度对角矩阵分别A(G_(ω))和D(G_(ω))。对于α∈[0,1],G_(ω)的A_(α)-矩阵为A_(α)(G_(ω))=αD(G_(ω))+(1-α)A(G_(ω))。对于连通赋权非正则图G_(ω),给出了其关于A_(α)-特征值的一些界,并得到了A_(α)-谱半径对应的特征向量中最大分量与最小分量比值的下界。

基于现场可编程门阵列的矩阵求逆算法设计

由于自适应抗干扰算法在更新最优权值时存在时间延时,导致很难满足动态环境下的权值更新率要求。针对该情况已有学者对如何实现快速采样矩阵求逆算法进行研究,但仍存在只适用于低维矩阵,且权值更新率慢的问题。为解决上述问题,提出了一种基于Cholesky分解的采样矩阵求逆算法实现架构。该实现架构主要包括协方差矩阵计算模块、Cholesky分解模块、计算下三角矩阵L的逆矩阵模块、三角矩阵相乘和权值计算模块。设计采用流水线加状态机实现结构有效地解决了因高阶采样矩阵求逆运算量大产生的权值更新率慢的问题。仿真结果表明,在现场可编程门阵列(field programmable gate array,FPGA)的硬件平台上,对于56阶采样矩阵,在100 MHz工作频率下,一次权值的更新时间仅需要1.2 ms。本文所提的实现架构为自适应抗干扰快速求解权值提供了一种切实可行的解决方案,对存在类似需求的权值求解系统具有一定的参考价值。