Minimal Realization of Linear Graph Models for Multi-physics Systems

An engineering system may consist of several different types of components,belonging to such physical"domains"as mechanical,electrical,fluid,and thermal.It is termed a multi-domain(or multi-physics)system.The present paper concerns the use of linear graphs(LGs)to generate a minimal model for a multi-physics system.A state-space model has to be a minimal realization.Specifically,the number of state variables in the model should be the minimum number that can completely represent the dynamic state of the system.This choice is not straightforward.Initially,state variables are assigned to all the energy-storage elements of the system.However,some of the energy storage elements may not be independent,and then some of the chosen state variables will be redundant.An approach is presented in the paper,with illustrative examples in the mixed fluid-mechanical domains,to illustrate a way to recognize dependent energy storage elements and thereby obtain a minimal state-space model.System analysis in the frequency domain is known to be more convenient than in the time domain,mainly because the relevant operations are algebraic rather than differential.For achieving this objective,the state space model has to be converted into a transfer function.The direct way is to first convert the state-space model into the input-output differential equation,and then substitute the time derivative by the Laplace variable.This approach is shown in the paper.The same result can be obtained through the transfer function linear graph(TF LG)of the system.In a multi-physics system,first the physical domains have to be converted into an equivalent single domain(preferably,the output domain of the system),when using the method of TFLG.This procedure is illustrated as well,in the present paper.

2-Walk Linear Graphs with Small Number of Cycles

A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph.In this paper,we show some necessary conditions that a 2-walk（a,b）-linear graph must obey.Using these conditions and some basic theorems in graph theory,we characterize all 2-walk linear graphs with small cyclic graphs without pendants.The results are given in sort on unicyclic,bicyclic,tricyclic graphs.

Some Structural Properties of 2-Walk (a, b)-Linear Graphs

A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph. In this paper, we show some structural properties that a 2-walk （a, b）-linear graph holds. According to these properties, we can estimate and characterize more 2-walk linear graphs that have exactly two main eigenvalues.

Optimization Algorithms of PERT/CPM Network Diagrams in Linear Diophantine Fuzzy Environment

The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representation procedures approach are initially static,but in the Project Evaluation and Review Technique(PERT)approach,they are probabilistic.This study proposes a novel way of project review and assessment methodology for a project network in a linear Diophantine fuzzy(LDF)environment.The LDF expected task time,LDF variance,LDF critical path,and LDF total expected time for determining the project network are all computed using LDF numbers as the time of each activity in the project network.The primary premise of the LDF-PERT approach is to address ambiguities in project network activity timesmore simply than other approaches such as conventional PERT,Fuzzy PERT,and so on.The LDF-PERT is an efficient approach to analyzing symmetries in fuzzy control systems to seek an optimal decision.We also present a new approach for locating LDF-CPM in a project network with uncertain and erroneous activity timings.When the available resources and activity times are imprecise and unpredictable,this strategy can help decision-makers make better judgments in a project.A comparison analysis of the proposed technique with the existing techniques has also been discussed.The suggested techniques are demonstrated with two suitable numerical examples.

DEGENERATE OPTIMAL BASIS GRAPHS IN LINEAR PROGRAMMING

The basis graph \%G\% for a linear programming consists of all bases under pivot transformations. A degenerate optimal basis graph G * is a subgraph of \%G\% induced by all optimal bases at a degenerate optimal vertex x 0. In this paper, several conditions for the characterization of G * are presented.

Fault Diagnosis Based on Graph Theory and Linear Discriminant Principle in Electric Power Network

In this paper, we adopt a novel topological approach to fault diagnosis. In our researches, global information will be introduced into electric power network, we are using mainly BFS of graph theory algorithms and linear discriminant principle to resolve fast and exact analysis of faulty components and faulty sections, and finally accomplish fault diagnosis. The results of BFS and linear discriminant are identical. The main technical contributions and innovations in this paper include, introducing global information into electric power network, developing a novel topological analysis to fault diagnosis. Graph theory algorithms can be used to model many different physical and abstract systems such as transportation and communication networks, models for business administration, political science, and psychology and so on. And the linear discriminant is a procedure used to classify an object into one of several a priori groupings dependent on the individual characteristics of the object. In the study of fault diagnosis in electric power network, graph theory algorithms and linear discriminant technology must also have a good prospect of application.

Feasible schemes for preparing all five-photon graph states

We propose feasible experimental schemes for preparing all five-photon graph states. Our schemes require only linear optical elements, photon detectors and post-selection, which are available in current experiment so that these schemes are within the reach of the current technology.

Realization of the Linear Tree that Corresponds to a Fundamental Loop Matrix

Graph realization from a matrix is an important topic in network topology. This paper presents an algorithm for the realization of a linear tree based on the study of the properties of the number of the single-link loops that are incident to each tree branch in the fundamental loop matrix Bf. The proposed method judges the pendent properties of the tree branches, determines their order one by one and then achieves the realization of the linear tree. The graph that corresponds to Bf is eventually constructed by adding links to the obtained linear tree. The proposed method can be extended for the realization of a general tree.

On k-Star Arboricity of Graphs

A star forest is a forest whose components are stars. The star arboricity of a graph G,denoted by sa（ G）,is the minimum number of star forests needed to decompose G. Let k be a positive integer. A k-star forest is a forest whose components are stars of order at most k ＋ 1. The k-star arboricity of a graph G,denoted by sak（ G）,is the minimum number of k-star forests needed to decompose G. In this paper,it is proved that if any two vertices of degree 3 are nonadjacent in a subcubic graph G then sa2（ G） ≤2.For general subcubic graphs G, a polynomial-time algorithm is described to decompose G into three 2-star forests. For a tree T and[Δ k, T）/k]t≤ sak（ T） ≤[Δ（ T）- 1/K]＋1,where Δ（ T） is the maximum degree of T.kMoreover,a linear-time algorithm is designed to determine whether sak（ T） ≤m for any tree T and any positive integers m and k.

Generalized Krein Parameters of a Strongly Regular Graph

We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.

Unsupervised Linear Discriminant Analysis

An algorithm for unsupervised linear discriminant analysis was presented. Optimal unsupervised discriminant vectors are obtained through maximizing covariance of all samples and minimizing covariance of local k-nearest neighbor samples. The experimental results show our algorithm is effective.

The First Eccentric Zagreb Index of Linear Polycene Parallelogram of Benzenoid

Let G = (V,E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges, e = uv∈E(G), d(u) is degree of vertex u. Then the first Zagreb polynomial and the first Zagreb index Zg1(G,x) and Zg1(G) of the graph G are defined as Σuv∈E(G)x(du+dv) and Σe=uv∈E(G)(du+dv) respectively. Recently Ghorbani and Hosseinzadeh introduced the first Eccentric Zagreb index as Zg1*=Σuv∈E(G)(ecc(v)+ecc(u)), that ecc(u) is the largest distance between u and any other vertex v of G. In this paper, we compute this new index (the first Eccentric Zagreb index or third Zagreb index) of an infinite family of linear Polycene parallelogram of benzenoid.

融合双图卷积与门控线性单元的方面级情感分析模型

方面级情感分析旨在确定句子中给定方面的情感极性。现有的基于图神经网络的方面级情感分析存在以下2个方面的不足:忽略了不同类型的句法依存关系和语料库中的词共现信息,以及不能准确地控制情感信息流向给定方面。针对以上问题,提出融合双图卷积与门控线性单元(GLU)的方面级情感分析模型。该模型首先采用全局词汇图来编码语料库中的词共现信息,在词汇图和句法图上利用分类概括结构来区分各种词共现频率和不同类型的句法依存关系。然后分别在2个图上进行双层卷积,继而使用Bi Affine变换模块作为桥梁,在2个图卷积网络模块之间有效地交换相关特征,从而有效地融合句法信息和词汇信息。最后利用GLU控制情感信息流向给定方面,使模型可以更专注地分析与该方面相关的情感信息,避免不相关的情感信息影响对给定方面的情感分析结果,从而提高分析的准确性。实验结果表明,在Twitter、Laptop14、Restaurant15和Restaurant16数据集上,该模型的准确率分别达到74.82%、77.61%、82.29%和89.81%,F1值分别达到72.97%、73.52%、67.72%和73.37%,方面级情感分类效果明显优于其他基线模型。

基于特征调制图神经网络的智能合约源码漏洞检测

随着区块链技术的广泛应用,智能合约的安全问题引起广泛关注。针对智能合约源码向字节码转化会丢失部分语义信息,而现有深度学习漏洞检测方法不能很好地检测重入漏洞和时间戳漏洞等问题,本文提出一种基于特征调制图神经网络的智能合约源码漏洞检测方法(GNN-film)。首先,分析重入漏洞和时间戳漏洞的特点,使用智能合约源码构建图结构并将其精简化;其次,搭建基于特征级线性调制的图神经网络模型,利用该网络模型强大的特征调制能力对合约漏洞特征进行精确表示;最后,将精简化后的图结构数据输入搭建的模型中获得检测结果。实验结果显示,本文方法对重入漏洞和时间戳漏洞检测的准确率达到91.00%和91.64%,相较基于图神经网络的方法分别提升了4.20百分点和9.70百分点,证明本文方法对相关漏洞检测的能力要优于其他检测工具。

基于Zhang-Hager线搜索的改进近似最优梯度法

提出一种改进的近似最优梯度法,求解图划分问题中的无约束目标函数.先用修正的BFGS更新公式及选取BB类步长的线性组合作为标量矩阵得到近似最优步长,再引入参数对经典的Zhang-Hager线搜索形式进行改进,构建算法框架并给出R线性收敛性证明.实验结果表明,改进算法提高了原算法的性能.

基于动态图注意力与标签传播的实体对齐

实体对齐是多源数据库融合的有效方法,旨在找出多源知识图谱中的共指实体。近年来,图卷积网络(GCN)已成为实体对齐表示学习的新范式,然而,不同组织构建知识图谱的目标及规则存在巨大差异,要求实体对齐模型能够准确发掘知识图谱之间的长尾实体特征,并且现有的GCN实体对齐模型过于注重关系三元组的结构表示学习,忽略了属性三元组丰富的语义信息。为此,提出一种实体对齐模型,引入动态图注意力网络聚合属性结构三元组表示,降低无关属性结构对实体表示的影响。同时,为缓解知识图谱的关系异构问题,引入多维标签传播对实体邻接矩阵的不同维度进行压缩,将实体特征根据压缩后的知识图谱邻接关系进行传播以获得关系结构表示,最后通过线性规划算法对实体表示相似度矩阵进行迭代以得到最终的对齐结果。在公开数据集ENFR-15K、EN-ZH-15K以及中文医学数据集MED-BBK-9K上进行实验,结果表明,该模型的Hits@1分别为0.942、0.926、0.427,Hits@10分别为0.963、0.952、0.604,MRR分别为0.949、0.939、0.551,消融实验结果也验证了模型中各模块的有效性。

效应改变法和有向无环图在线性回归变量筛选中的应用及实现

目的 通过实例展示如何应用在线工具DAGitty和R实现有向无环图(DAG)联合效应改变法(CIE)筛选线性回归中需要调整的混杂。方法 基于DATADRYAD的Jung, Su-Young J eettaall.(2019)数据包,假设暴露因素为BMI_ICU,结局为Death_28D,混杂包括Sex等9个变量为混杂因素。本文以逻辑回归模型为例,首先应用在线工具DAGitty将变量间的因果关系可视化,并自动识别需要调整的混杂;然后使用R批量筛选出使暴露因素的效应量变化超过10%的混杂。结果 经DAG未发现中介变量,在单因素模型中逐一加入混杂,或在全变量模型中逐一剔除混杂后BMI_ICU的效应量变化均未超过10%,综上,暂没有需要调整的混杂。结论 通过DAGitty和R可以简便、有效、快速的实现DAG联合CIE筛选线性回归中的混杂,其他线性回归类型可在此基础上稍作修改。

基于线特征的多视点云配准算法

针对多视点云配准精度低、稳定性差等问题,提出了基于线特征的多视点云配准模型(line-based multiview point cloud registration,LMR)。基于二分法的点云特征线提取方法获取多视点云特征线,利用李代数求解点云变换矩阵雅可比矩阵,构建基于非线性最小二乘优化方法的多视点云配准模型。通过配准地面激光扫描数据集验证了该方法的有效性。定量分析与结果表明,LMR提取多视点云特征线,通过全局优化多视点云位姿参数,有效提高了点云配准精度。

Inverse kinematic deriving and actuator control of Delta robot using symbolic computation technology

In order to effectively derive the inverse kinematic solution of the Delta robot and realize actuator control a description of the linear graph principle for automatically generating kinematic equations in a mechanical system as well as the symbolic computation implementation of this procedure is reviewed and projected into the Delta robot. Based on the established linear graph representation the explicit symbolic expression of constraint equations and inverse kinematic solutions are obtained successfully using a symbolic computation engine Maple so that actuator control and trajectory tracking can be directly realized.Two practical motions the circular path and Adept motion are simulated for the validation of symbolic solutions respectively.Results indicate that the simulation satisfies the requirement of the quick motion within an acceptable threshold. Thus the precision of kinematic response can be confirmed and the correctness of inverse solution is verified.

基于键合图的环切机构动力学建模及其非线性振动研究

管道切口端面的质量是保障管路系统安全运行的重要因素之一,但在管道切削过程中存在非线性因素,可能会导致切管机发生混沌、拟周期等有害振动,从而影响切削精度和加工质量。因此,揭示切管机动力学失稳的机制以避免有害振动是改善运转性能、提高切削精度的关键。以一种刀旋式切管机的环切机构为对象,基于键合图理论建立了机构的动力学模型,通过计算灵敏度确定了关键动力学参数,并综合应用分岔图、Lyapunov指数图、相图、时间响应图等,揭示了关键参数的分岔机制。结果表明,随着激励幅值、激励频率和基座弹性系数等参数的变化,系统会存在倍周期分岔、Hopf分岔、混沌和吸引子共存等复杂动力学行为,从而产生严重降低切削质量的振动和运动突变。研究结果可为该机构后续动态性能优化和有害振动抑制提供参考。