Minimal functional routes in directed graphs with dependent edges

Graphs are mathematical structures used to model a set of objects and the relations between them. One of the basic concepts of graph theory, the path, has wide real‐world applications. In classic graph models, edges ending at a node are assumed to be independent. However, many real graphs/networks can only be correctly described by considering a dependency among nodes or edges. Paths in such graphs may not be functional if the conditional dependency is ignored. In this study, we investigate the routing problem in directed graphs with dependent edges represented by general graph models as alternatives to hypergraphs. We define a minimal functional route (MFR) as a minimal set of nodes and edges that can independently perform information transfer between two given nodes, and formulate the determination of MFRs as a graph search problem. A depth‐first‐search (DFS) top‐down algorithm, an iterative integer linear programming (ILP) bottom‐up algorithm, and a subgraph‐growing bottom‐up algorithm are devised subsequently to solve this problem. Numerical experiments verify the effectiveness of the algorithms. The defined MFR problem and the proposed algorithms are expected to find many practical applications.     

Distributed consensus filter on directed switching graphs

We consider distributed estimation on a directed graph with switching topologies. Motivated by a recent PI consensus filter, we modify the protocol and remove the requirement of bidirectional exchange of neighboring gains for fixed topologies. We then extend the protocol to switching topologies and propose a new hybrid consensus filter design. Convergence results under both balanced directed, and general directed graphs are given for switching graphs. Consensus error bounds are analytically derived in the case of time‐varying inputs. Satisfactory simulation results are shown. Copyright © 2014 John Wiley & Sons, Ltd.     

Dynamic consensus estimation of weighted average on directed graphs

Recent applications call for distributed weighted average estimation over sensor networks, where sensor measurement accuracy or environmental conditions need to be taken into consideration in the final consensused group decision. In this paper, we propose new dynamic consensus filter design to distributed estimate weighted average of sensors’ inputs on directed graphs. Based on recent advances in the filed, we modify the existing proportional-integral consensus filter protocol to remove the requirement of bi-directional gain exchange between neighbouring sensors, so that the algorithm works for directed graphs where bi-directional communications are not possible. To compensate for the asymmetric structure of the system introduced by such a removal, sufficient gain conditions are obtained for the filter protocols to guarantee the convergence. It is rigorously proved that the proposed filter protocol converges to the weighted average of constant inputs asymptotically, and to the weighted average of time-varying inputs with a bounded error. Simulations verify the effectiveness of the proposed protocols.     

Transformations of fuzzy graphs specified by <Emphasis Type="Italic">FD</Emphasis>-grammars

The categorical approach is proposed to formalize transformations of FD-graphs that consist of networks of distributed components whose nodes are specified by fuzzy graphs. Necessary and sufficient conditions are formally defined for FD-graph transformations that do not violate structure integrity and can be constructed componentwise. FD-grammars that generalize fuzzy graph grammars are proposed to describe the admissible transformations of FD-graphs. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 129–147, March–April 2007.     

Multi-level association rules and directed graphs for spatial data analysis

We propose a methodology that upgrades the methods of the Lagrangian analysis of surface sea-water parcels. This methodology includes data mining with efficient visualization techniques, namely, spatial–temporal association rules and multi-level directed graphs with different levels of space and time granularity. In the resulting multi-level directed graphs we can intertwine knowledge from various disciplines related to oceanography (in our application) and perform the mining of such graphs. We evaluate the proposed methodology on Lagrangian tracking of virtual particles in the velocity field of the numerical model called the Mediterranean Ocean Forecasting Model (MFS). We describe an efficient algorithm based on label propagation clustering, which finds cycles and paths in multi-level directed graphs and reveals how the number and size of the cycles depend on the seasons. In addition, we offer three interesting results of the visualization and mining of such graphs, that is, the 12 months periodicity of the exchange of water masses among sea areas, the separation of Mediterranean Sea circulation in summer and winter situations, obtained with the hierarchical clustering of multi-level directed graphs, and finally, with visualization with multi-level directed graphs we confirm the reversal of sea circulation in the Ionian Sea over the last decades. The aforementioned results received a very favorable evaluation from oceanographic experts.     

运用有向图进行中文分词研究

首先说明了分词在中文信息处理中的作用,然后介绍了分词系统中的关键技术。提出了一种基于有向图的中文分词算法,该算法首先构造中文分词有向图,然后计算中文分词有向图中所有可能的切分路径,最后利用了最少分词原则、汉字之间的互信息和词语的频率等信息给中文分词有向图中的每条切分路径打分,分数最高的路径就对应正确的切分结果。开放测试结果表明分词精确率可达90%以上。     

Toward a mathematical theory of graph-generative systems and its applications

This paper presents some formal generative specifications for describing the graph languages consisting of the sets of directed graphs with labeled arcs. Some mathematical results are introduced. In addition, we consider applications to specification technique for data structures and complexity measure of computer software. Finally, directions for future research are indicated.     

基于有向图的二进制文件结构化比较机制研究

通过对二进制文件结构化比较方法的研究,提出了基于有向图的二进制文件结构化比较方法及实现算法.和基于指令比较的二进制文件比较方法相比,二进制文件结构化比较方法更注重二进制文件在逻辑结构上的变化,而且更加简单.     

一种基于有向图的工作流测试方法

已有工作流测试方法在测试完备性和充分性方面存在不足。针对此问题文章对有向图工作流模型进行扩展,提出了一种新的工作流测试方法,设计并实现了其算法。该方法能够自动生成完备且充分的测试路径和测试用例。实例验证该方法有效。     

一种基于有向无环图的本体内聚度度量方法

目前,随着本体的广泛使用和快速发展,本体在结构与语义上变得越来越复杂。如何对本体的质量进行评估成为本体构建和重用的主要问题。在本体构建过程中,对本体进行评估有利于对本体进行重构和优化,以构建高质量的本体。在本体重用过程中,可以帮助用户在候选本体集中选择最优结构的本体。提出一种基于有向无环图(DAG)的本体内聚度度量方法,首先依据有向无环图的结构提出一组本体内聚度度量指标;然后根据已有的度量验证框架对其进行验证,说明度量指标在理论上有效;最后使用经典本体数据集进行实验,说明所提出的本体内聚度度量方法的合理性和有效性,有利于本体的构建和重用。     

Verification of conceptual schemata based on hybrid object-oriented and logic paradigm

Contemporary conceptual modelling languages are concerned with the representational adequacy of knowledge about a universe of discourse and with the efficient organization of this knowledge in structures that help overcome the problems of size and complexity in the modelled reality. In the paper it is argued that a conceptual modelling language should also facilitate the verification of captured requirements by exercising the conceptual schemata derived from the use of such a language. A conceptual modelling language is presented that is based on a hybrid representation scheme that makes use of object-oriented and logic approaches, and it is shown how this language can be used to verify requirements during the development of information systems.     

基于大数据时代的数据可视化应用分析

如今随着数据采集、存储和数据分析技术飞速发展,大幅度降低了数据储存和处理的成本,我们即将步入一个大数据时代。大数据时代的改革将海量数据处理变为可能,而且大幅降低了处理成本,促使越来越多跨专业学科的人才投入到大数据的开发应用中来。如何才能让大型数据集变得简单和易于理解,可视化无疑是最有效的途径。对大数据背景下的数据可视化应用展开研究,将有助于我们发展和创新数据可视化技术。     

基于有向图的数据流图的E-R模型构建方法

建立概念模型是数据库设计的重要步骤之一,E-R模型是数据库设计中广泛采用的概念模型。本文提出利用业务分析过程中形成的数据流图,把数据流图抽象为有向图,从而构建E-R模型的方法。在大型系统数据库设计过程中,使用这一方法可以快速构建局部应用的E-R模型,大大缩短数据库设计过程中构建E-R模型所耗费的时间。实例验证了本方法在实际工程项目中的实用性和有效性。     

基于十字链表的多刚体系统的数据存储

针对多刚体系统数据存储的不足,对多刚体系统的结构图与图论的有向图之间的关系进行了研究,提出了一种新的基于十字链表的链式存储模型.该存储模型不但较好地解决了复杂多刚体系统的存储问题,而且充分满足了在存储物理多刚体系统时的结构正确性和数据完备性要求,避免了非树形多刚体向树形多刚体的回路切除转换,使多刚体系统在数学建模与数据存储方面达到高度一致.     

基于图像数据挖掘的有向图模型检索方法

为充分挖掘图像数据信息,提出了一种有向图模型检索方法,结合距离测度初次检索和有向图距离二次检索提高图像检索性能。首先,采用传统的纹理、边缘和颜色特征以及特征之间的欧氏距离测度来进行初次检索,得到一个查询排序列表;在此基础上,结合距离测度与余弦测度设计图像之间的相关测度,在不同的相关测度阈值下构建图像数据集的有向图模型集合;最后,计算有向图距离,据此进行二次检索,降低误检现象。在COREL和ImageCLEF两个数据集上的图像检索实验结果表明,该方法的平均精确度和平均召回率指标高。     

Defining the abstract syntax of visual languages with advanced graph grammars—A case study based on behavior trees

Diagrammatic visual languages can increase the ability of engineers to model and understand complex systems. However, to effectively use visual models, the syntax and semantics of these languages should be defined precisely. Since most diagrammatic visual models that are currently used to specify systems can be described as (directed) typed graphs, graph grammars have been identified as a suitable formalism to describe the abstract syntax of visual modeling languages. In this article, we investigate how advanced graph-transformation techniques, such as conditional, structure-generic and type-generic graph-transformation rules, can help to improve and simplify the specification of the abstract syntax of a visual modeling language. To demonstrate the practicability of an approach that unifies these advanced graph-transformation techniques, we define the abstract syntax of behavior trees (BTs), a graphical specification language for functional requirements. Additionally, we provide a translational semantics of BTs by formalizing a translation scheme to the input language of the SAL model checking tool for each of the graph-transformation rules.     

基于Pi-演算的扩展有向图工作流模型及验证

为了加强工作流模型对业务流程的描述能力,提出了一种扩展有向图工作流模型及其验证方法.针对基于有向图工作流模型的不足,提出了扩展有向图工作流模型,并给出了该模型的定义和图形符号描述.在用Pi-演算准确描述扩展有向图工作流模型的基础上,给出了用Pi-演算分析和验证扩展有向图工作流模型正确性的方法.最后,结合实验对扩展有向图工作流模型及验证方法进行了仔细分析,实验结果表明了该工作流模型及验证方法的有效性和正确性.     

A study on multi-dimensional products of graphs and hybrid logics

In this work, we address some issues related to products of graphs and products of modal logics. Our main contribution is the presentation of a necessary and sufficient condition for a countable and connected graph to be a product, using a property called intransitivity. We then proceed to describe this property in a logical language. First, we show that intransitivity is not modally definable and also that no necessary and sufficient condition for a graph to be a product can be modally definable. Then, we exhibit a formula in a hybrid language that describes intransitivity. With this, we get a logical characterization of products of graphs of arbitrary dimensions. We then use this characterization to obtain two other interesting results. First, we determine that it is possible to test in polynomial time, using a model-checking algorithm, whether a finite connected graph is a product. This test has cubic complexity in the size of the graph and quadratic complexity in its number of dimensions. Finally, we use this characterization of countable connected products to provide sound and complete axiomatic systems for a large class of products of modal logics. This class contains the logics defined by product frames obtained from Kripke frames that satisfy connectivity, transitivity and symmetry plus any additional property that can be defined by a pure hybrid formula. Most sound and complete axiomatic systems presented in the literature are for products of a pair of modal logics, while we are able, using hybrid logics, to provide sound and complete axiomatizations for many products of arbitrary dimensions.     

基于有向图建模的航天器自动化测试研究与实现

为了提高航天器测试效率及测试质量,研究了在无法给出航天器数学模型的情况下利用知识定义方法实现自动化测试的原理.通过对航天器静态测试和动态测试任务的分析,建立了航天器测试任务中测试业务的数学表示模型.基于有向图理论,建立了航天器测试过程的基本模型,提出了一种形式简单、易于理解、便于应用的表格方式航天器自动化测试语言(SATL),给出了SATL应用示例,开发了航天器自动化测试软件(SATS).SATL和SATS成功应用于"神舟"飞船及多颗卫星各阶段测试,实际应用表明了该方案具有较强的工程实用性.