Different Types Of Vertices Research Articles

GIS-Analysis Of The Ural Power Grid Vulnerability To The Impact Of Sleet And Wind

In this paper, we describe an experiment of complex power grid structure and wind and sleet mapping of territory using two different network indices: standard edge betweenness centrality and new author’s index – electrical grid centrality. Such analysis of the network allows to identify power lines with high load which could be vulnerable elements of the power grid. It is very important for strategic planning of power grids to reduce the risk of accidents by distributing loads across several lines so that they will be able to reserve each other. As a case territory for this research, we took the Ural united power system in Russia which is greatly exposed to different sleet and wind according to the statistics of the power grid operator. The degree of natural hazard consequences could be compensated by the network structure through alternative paths of energy supply or vice versa – increased if they are absent. At the same time, in this paper we consider that power grids have their own features from the graph theory point of view, for example multiple (parallel) edges, branches, different types of vertices. The existing index of edge betweenness centrality does not perfectly cope with them. We compare two indices characterizing power line importance within the system – betweenness centrality and electrical grid centrality and analyze the network structure features together with the spatial distribution of sleet and wind. As a result, we could identify bottlenecks in the study network. According to this study the most vulnerable power lines were detected, for example 500 kV Iriklinskaya CHP – Gazovaya and 500 kV Yuzhnouralskaya CHP-2 – Shagol power lines, that supply big cities such as Chelyabinsk and Orenburg and a bunch of industries around them.

Motifs, coherent configurations and second order network generation

In this paper we illuminate some algebraic-combinatorial structure underlying the second order networks (SONETS) random graph model of Zhao, Beverlin, Netoff and Nykamp and collaborators (Fuller, 2016; Zhao, 2012; Zhao et al. 2011). In particular we show that this algorithm is deeply connected with a certain homogeneous coherent configuration, a non-commuting generalization of the classical Johnson scheme. This algebraic structure underlies certain surprising, previously unobserved, identities satisfied by the covariance matrices in the SONETS model. We show that an understanding of this algebraic structure leads to simplified numerical methods for carrying out the linear algebra required to implement the SONETS algorithm. We also show that the SONETS method can be substantially generalized to allow different types of vertices and/or edges, and that these generalizations enjoy similar algebraic structure.

Cyclic connectivity index of fuzzy incidence graphs with applications in the highway system of different cities to minimize road accidents and in a network of different computers.

A parameter is a numerical factor whose values help us to identify a system. Connectivity parameters are essential in the analysis of connectivity of various kinds of networks. In graphs, the strength of a cycle is always one. But, in a fuzzy incidence graph (FIG), the strengths of cycles may vary even for a given pair of vertices. Cyclic reachability is an attribute that decides the overall connectedness of any network. In graph the cycle connectivity (CC) from vertex a to vertex b and from vertex b to vertex a is always one. In fuzzy graph (FG) the CC from vertex a to vertex b and from vertex b to vertex a is always same. But if someone is interested in finding CC from vertex a to an edge ab, then graphs and FGs cannot answer this question. Therefore, in this research article, we proposed the idea of CC for FIG. Because in FIG, we can find CC from vertex a to vertex b and also from vertex a to an edge ab. Also, we proposed the idea of CC of fuzzy incidence cycles (FICs) and complete fuzzy incidence graphs (CFIGs). The fuzzy incidence cyclic cut-vertex, fuzzy incidence cyclic bridge, and fuzzy incidence cyclic cut pair are established. A condition for CFIG to have fuzzy incidence cyclic cut-vertex is examined. Cyclic connectivity index and average cyclic connectivity index of FIG are also investigated. Three different types of vertices, such as cyclic connectivity increasing vertex, cyclically neutral vertex and, cyclic connectivity decreasing vertex, are also defined. The real-life applications of CC of FIG in a highway system of different cities to minimize road accidents and a computer network to find the best computers among all other computers are also provided.

Effective and efficient community search over large heterogeneous information networks

Recently, the topic of community search (CS) has gained plenty of attention. Given a query vertex, CS looks for a dense subgraph that contains it. Existing studies mainly focus on homogeneous graphs in which vertices are of the same type, and cannot be directly applied to heterogeneous information networks (HINs) that consist of multi-typed, interconnected objects, such as the bibliographic networks and knowledge graphs. In this paper, we study the problem of community search over large HINs; that is, given a query vertex q , find a community from an HIN containing q , in which all the vertices are with the same type of q and have close relationships. To model the relationship between two vertices of the same type, we adopt the well-known concept of meta-path , which is a sequence of relations defined between different types of vertices. We then measure the cohesiveness of the community by extending the classic minimum degree metric with a meta-path. We further propose efficient query algorithms for finding communities using these cohesiveness metrics. We have performed extensive experiments on five real large HINs, and the results show that the proposed solutions are effective for searching communities. Moreover, they are much faster than the baseline solutions.

Real-Time scheduling and analysis of parallel tasks on heterogeneous multi-cores

Heterogeneous multi-cores and parallel architectures have recently gained much attention owing to utilizing the strength of different architectures for offering higher performance. In this paper, we study the real-time scheduling of the directed acyclic graph (DAG) tasks upon the heterogeneous multi-core platform, i.e., a task contains different types of vertices, and the workload of each vertex must execute on its particular type of cores. Traditional researches use the work-conserving scheduling strategy to schedule such a typed DAG task and lead to pessimistic schedulability tests. To this end, we propose a novel scheduling algorithm for typed DAG tasks, which assigns each vertex a varying criticality that depends on the remaining workload of the vertex, and moreover, the vertex with higher criticality is more urgent to be executed. Under this scheduling strategy, we propose a new worst-case response time (WCRT) bound to verify the schedulability of DAG task supporting heterogeneous computing. Experiments with randomly generated workload show that the accuracy of our new WCRT is about 20% higher on average than the existing bounds.

Who is the infector? General multi-type epidemics and real-time susceptibility processes

AbstractWe couple a multi-type stochastic epidemic process with a directed random graph, where edges have random weights (traversal times). This random graph representation is used to characterise the fractions of individuals infected by the different types of vertices among all infected individuals in the large population limit. For this characterisation, we rely on the theory of multi-type real-time branching processes. We identify a special case of the two-type model in which the fraction of individuals of a certain type infected by individuals of the same type is maximised among all two-type epidemics approximated by branching processes with the same mean offspring matrix.

Label Propagation on K-partite Graphs with Heterophily

In this paper, for the first time, we study label propagation in heterogeneous graphs under heterophily assumption. Homophily label propagation (i.e., two connected nodes share similar labels) in homogeneous graph (with same types of vertices and relations) has been extensively studied before. Unfortunately, real-life networks (e.g., social networks) are heterogeneous, they contain different types of vertices (e.g., users, images, and texts) and relations (e.g., friendships and co-tagging) and allow for each node to propagate both the same and opposite copy of labels to its neighbors. We propose a $\mathcal {K}$ K -partite label propagation model to handle the mystifying combination of heterogeneous nodes/relations and heterophily propagation. With this model, we develop a novel label inference algorithm framework with update rules in near-linear time complexity. Since real networks change over time, we devise an incremental approach, which supports fast updates for both new data and evidence (e.g., ground truth labels) with guaranteed efficiency. We further provide a utility function to automatically determine whether an incremental or a re-modeling approach is favored. Extensive experiments on real datasets have verified the effectiveness and efficiency of our approach, and its superiority over the state-of-the-art label propagation methods.

A spectral method to find communities in bipartite networks

Community detection in complex networks that aims to find partitions of networks with dense intra-edges and sparse inter-edges, has recently attracted lots of interest in many fields. Specially, bipartite networks composed of two different types of vertices are the common representations for many real-world networks, such as actor–film, consumer–product networks, etc. In this paper, we show that optimizing Barber’s bipartite modularity, which is widely used to evaluate partitions of bipartite networks, can be reformulated as a spectral problem with appropriate relaxations. We further propose a new method combining singular value decomposition(SVD) and BRIM algorithm to obtain an optimal community partition. Compared with many other algorithms, the new method can give us a more detailed and comprehensive view of the original bipartite network for different cluster numbers k. We test our method on both synthetic networks and two benchmark data sets. Experimental results show that, our method is not only capable to extract a community partition with a larger bipartite modularity, but also converge to the exact underlying community partition when k is appropriately set, which helps to alleviate the resolution limit issue to some extent.

Generative Adversarial Network Based Heterogeneous Bibliographic Network Representation for Personalized Citation Recommendation

Network representation has been recently exploited for many applications, such as citation recommendation, multi-label classification and link prediction. It learns low-dimensional vector representation for each vertex in networks. Existing network representation methods only focus on incomplete aspects of vertex information (i.e., vertex content, network structure or partial integration), moreover they are commonly designed for homogeneous information networks where all the vertices of a network are of the same type. In this paper, we propose a deep network representation model that integrates network structure and the vertex content information into a unified framework by exploiting generative adversarial network, and represents different types of vertices in the heterogeneous network in a continuous and common vector space. Based on the proposed model, we can obtain heterogeneous bibliographic network representation for efficient citation recommendation. The proposed model also makes personalized citation recommendation possible, which is a new issue that a few papers addressed in the past. When evaluated on the AAN and DBLP datasets, the performance of the proposed heterogeneous bibliographic network based citation recommendation approach is comparable with that of the other network representation based citation recommendation approaches. The results also demonstrate that the personalized citation recommendation approach is more effective than the non-personalized citation recommendation approach.

A fast community detection method in bipartite networks by distance dynamics

Many real bipartite networks are found to be divided into two-mode communities. In this paper, we formulate a new two-mode community detection algorithm BiAttractor. It is based on distance dynamics model Attractor proposed by Shao et al. with extension from unipartite to bipartite networks. Since Jaccard coefficient of distance dynamics model is incapable to measure distances of different types of vertices in bipartite networks, our main contribution is to extend distance dynamics model from unipartite to bipartite networks using a novel measure Local Jaccard Distance (LJD). Furthermore, distances between different types of vertices are not affected by common neighbors in the original method. This new idea makes clear assumptions and yields interpretable results in linear time complexity O(|E|) in sparse networks, where |E| is the number of edges. Experiments on synthetic networks demonstrate it is capable to overcome resolution limit compared with existing other methods. Further research on real networks shows that this model can accurately detect interpretable community structures in a short time.

Terms of parity and distortion of coordination polyhedra in inorganic crystal chemistry

The coordination number parity law is formulated: the coordination polyhedra (CP) with the odd number of vertices, except for 3 (CP is a triangle), occur far less often than the polyhedra with the even number of vertices. CP with the odd number of vertices, except for the triangle, cannot be regular and have at least two different types of vertices and two sets of interatomic lengths. The main and first c.n. always keeps parity. A CP distortion due to crystal chemical causes tends to be minimum, obeying the pseudo-symmetry laws. A CP distortion, other things being equal, leads to an increase in the average bond length as compared to the regular polyhedron (distortion theorem). The value of the increase in the average interatomic distance depends on the degree of distortion by the linear or (for a very strong distortion) the square dependence. The histograms of the distribution frequencies of the interatomic lengths have a positive deviation from the Gauss normal distribution law. A free molecule or a complex ion having a distortion due to the directed configuration of chemical bonds or to the electronic effects of the Jahn-Teller type for transition metals, maintain it in the crystal structure as well. During the polymerization of radicals there arise specific distortion effects due to a various coordination environment of the bridging and apical ligands. One of the most general rules of the CP distortion is associated with a less symmetric and less homogenous environment of anions in comparison with that of cations and a higher polarizability of anions. An important exception from this rule is the group of compounds with the so called anion-centered tetrahedra in which more symmetrical positions are occupied, as a rule, by anions in the center of the tetrahedra.

The Degree Analysis of an Inhomogeneous Growing Network with Two Types of Vertices

We consider an inhomogeneous growing network with two types of vertices. The degree sequences of two different types of vertices are investigated, respectively. We not only prove that the asymptotical degree distribution of typesfor this process is power law with exponent2+1+δqs+β1-qs/αqs, but also give the strong law of large numbers for degree sequences of two different types of vertices by using a different method instead of Azuma’s inequality. Then we determine asymptotically the joint probability distribution of degree for pairs of adjacent vertices with the same type and with different types, respectively.

Randomised Reproducing Graphs

We introduce a model for a growing random graph based on simultaneous reproduction of the vertices. The model can be thought of as a generalisation of the reproducing graphs of Southwell and Cannings and Bonato et al to allow for a random element, and there are three parameters, $\alpha$, $\beta$ and $\gamma$, which are the probabilities of edges appearing between different types of vertices. We show that as the probabilities associated with the model vary there are a number of phase transitions, in particular concerning the degree sequence. If $(1+\alpha)(1+\gamma)<1$ then the degree distribution converges to a stationary distribution, which in most cases has an approximately power law tail with an index which depends on $\alpha$ and $\gamma$. If $(1+\alpha)(1+\gamma)>1$ then the degree of a typical vertex grows to infinity, and the proportion of vertices having any fixed degree $d$ tends to zero. We also give some results on the number of edges and on the spectral gap.

'Size-effect'-like distortions in quasicrystalline structures

Abstract We show in this paper that by applying size-effect distortions to a perfect Penrose tiling, on the basis that rhomb-edges which connect different types of vertices assume different lengths, we can obtain a diffraction pattern which shows remarkable similarity to the zero-level (h5 =0) section observed in decagonal Al71Co13Ni16. In particular a central clearly delineated decagon is observed, on the inside of which there is reduced intensity, and on the outside of which there is enhanced intensity. Such a transfer of intensity is characteristic of size-effect distortions in crystals but for these systems it is necessary to have disorder involving (at least) two types of atoms. In the present case the effect is observed with all vertices occupied by a single scatterer and the system remains topologically equivalent to the Penrose pattern with long range quasicrystallinity.

Feature Extraction of 3-D Object by Circular Range Sensing - Circular Range Acquisition and It’s Application to Polyhedra -

A method of feature extraction for 3-D objective surface by circular range acquisition is proposed and investigated. In the experimental system, circular range acquisition is realized by moving an optical range sensor mechanically along a circular path. A prototype of an optical range sensor, which adopting a 2.OmW He-Ne gas laser as a light source, 342(length) × 130(width) × 174mm(height) body size and 5kg weight was manufactured. This range sensor is mounted on the wrist of a SCARA robot (A3020, Hitachi). The range sensor is positioned sequentially at a point along the circular path with a given radius around the axis passing through the target point and detects the range to the corresponded point on the surface of an object. The surface feature around the target point is identified by investigating the variation of the acquired range data along the circular path. Applying the above operation to the surface of an object to be tested, surface features of an object can be extracted. Surface features, such as planes, vertices and edges, are represented as a polar coordinates representation of the range variation along the circular path. Thus, the circular range acquisition and the features extraction of the surface are applied to the different types of vertices on a polyhedra. Moreover, the circular range acquisitions tracing on the edge line are carried out over the surface of an object and experimental results are reported.

Modelling and optimization of supply chains on complex networks

In this paper, we extend the model for supply chains developed in [8]. The model consists of partial differential equations governing the dynamics on each processor. Furthermore, a modelling of different types of vertices is motivated and discussed. Then, optimization problems are introduced and numerically investigated. A comparison of computing times shows the efficiency of partial differential equations for solving supply chain problems.