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.

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.

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.

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.

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。

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。

昆都仑泄洪冲沙洞结构静动力三维有限元配筋计算

昆都仑水库是一座以防洪、供水为主的综合利用的中型水库。为改善水库泄洪条件,新建泄洪冲沙洞并布置于库区右岸山体内。首先,构建了泄洪冲沙洞三维有限元模型,模拟了各结构的精细构造部位;然后,采用三维线性有限单元法对泄洪冲沙洞开展静动力工况下变形、应力分析计算,基于有限元内力法进行内力计算并提出相应配筋方案;最后,进行结构限裂复核验算。选取的配筋计算方案实用可靠,为工程设计提供指导、验证复核作用并成功付诸实施。

基于实时视频流的3D人体姿势和形状估计

为满足元宇宙、游戏及虚拟现实等应用场景中对实时视频流3D人体姿势和形状估计准确性和真实性的要求,提出了一种基于时间注意力机制的3D人体姿势和形状估计方法。首先,提取图像特征,并将其输入运动连续注意力模块以更好地校准需要注意的时间序列范围;随后,使用实时特征注意力集成模块以有效地组合当前帧与过去帧的特征表示;最后,通过人体参数回归网络得到最终结果,并使用基于图卷积的生成对抗网络判断模型是否来自真实的人体运动数据。相较于之前基于实时视频流的方法,在主流数据集上加速度误差平均减少了30%的同时,网络参数与计算量减少了65%,在实际测试中实现了每秒55~60帧的3D人体姿态和形状估计速度,为元宇宙、游戏及虚拟现实等应用场景提供更好的用户体验和更高的应用价值。

基于局部线性重叠聚类算法的网络攻击溯源分析方法

科技的进步使得不法组织可以利用各种先进的攻击手段,对特定目标进行隐匿的、长期持续性的网络攻击。当前大部分研究基于大数据、机器学习和图谱的方法进行攻击溯源检测,从而还原攻击全貌,但其存在检测识别正确率低、算力开销大等问题。为此,提出了一种基于溯源图谱的网络攻击分析方法,利用安全产品日志中的攻击特征划分攻击社团,并结合资产和攻击信息的局部线性关系进行重叠聚类,从而还原攻击路径。该算法已应用于某企业安全运行监管系统,实践证明,其能够有效地溯源系统被入侵的过程与痕迹,改善网络安全威胁感知和预警能力。

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.

Translating Linear Temporal Logic Formula s into Automata

To combat the well-known state-space explosion problem in Propositional Linear Temporal Logic (PLTL) model checking, a novel algorithm capable of translating PLTL formulas into Nondeterministic Automata (NA) in an efficient way is proposed. The algorithm firstly transforms PLTL formulas into their non-free forms, then it further translates the non-free formulas into their Normal Forms (NFs), next constructs Normal Form Graphs (NFGs) for NF formulas, and it finally transforms NFGs into the NA which accepts both finite words and infinite words. The experimental data show that the new algorithm reduces the average number of nodes of target NA for a benchmark formula set and selected formulas in the literature, respectively. These results indicate that the PLTL model checking technique employing the new algorithm generates a smaller state space in verification of concurrent systems.

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 andΔ( a positive integer k, T)it is proved that≤ sakk( T) ≤Δ( T)- 1+ 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.