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.

A model based on a high-resolution flux matrix explains the spread of diseases in a spatial network and the effect of mitigation strategies

Propagation of an epidemic across a spatial network of communities is described by a variant of the SIR model accompanied by an intercommunity infectivity matrix. This matrix is estimated from fluxes between communities, obtained from cell-phone tracking data recorded in the USA between March 2020 and February 2021. We have applied this model to the 2020 dynamics of the SARS-CoV-2 pandemic. We find that the numbers of susceptible and infected individuals predicted by the model agree with the reported cases in each community by fitting just one global parameter representing the frequency of interaction between individuals. The effect of "shelter-in-place" policies introduced across the USA at the onset of the pandemic is clearly seen in our results. We then consider the effect that alternative policies would have had, namely restricting long-range travel. We find that this policy is successful in decreasing the epidemic size and slowing down the spread, at the expense of a substantial restriction on mobility as a function of distance. When long-distance mobility is suppressed, this policy results in a traveling wave of infections, which we characterize analytically. In particular, we show the dependence of the wave velocity and profile on the transmission parameters. Finally, we discuss a policy of selectively constraining travel based on an edge-betweenness criterion.

A New Edge Betweenness Measure Using a Game Theoretical Approach: An Application to Hierarchical Community Detection

In this paper we formally define the hierarchical clustering network problem (HCNP) as the problem to find a good hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the final picture of the clustering process. To address it, we introduce a new hierarchical clustering algorithm in networks, based on a new shortest path betweenness measure. To calculate it, the communication between each pair of nodes is weighed by the importance of the nodes that establish this communication. The weights or importance associated to each pair of nodes are calculated as the Shapley value of a game, named as the linear modularity game. This new measure, (the node-game shortest path betweenness measure), is used to obtain a hierarchical partition of the network by eliminating the link with the highest value. To evaluate the performance of our algorithm, we introduce several criteria that allow us to compare different dendrograms of a network from two point of view: modularity and homogeneity. Finally, we propose a faster algorithm based on a simplification of the node-game shortest path betweenness measure, whose order is quadratic on sparse networks. This fast version is competitive from a computational point of view with other hierarchical fast algorithms, and, in general, it provides better results.

Identifying Influential Edges by Node Influence Distribution and Dissimilarity Strategy

Identifying influential edges in a complex network is a fundamental topic with a variety of applications. Considering the topological structure of networks, we propose an edge ranking algorithm DID (Dissimilarity Influence Distribution), which is based on node influence distribution and dissimilarity strategy. The effectiveness of the proposed method is evaluated by the network robustness R and the dynamic size of the giant component and compared with well-known existing metrics such as Edge Betweenness index, Degree Product index, Diffusion Intensity and Topological Overlap index in nine real networks and twelve BA networks. Experimental results show the superiority of DID in identifying influential edges. In addition, it is verified through experimental results that the effectiveness of Degree Product and Diffusion Intensity algorithm combined with node dissimilarity strategy has been effectively improved.

A New Edge betweenness Measure Using a Game Theoretical Approach : An Application to Hierarchical Community Detection

In this paper we formally define the hierarchical clustering network problem (HCNP) as the problem to find a good hierarchical partition of a network. This new problem focuses on the dynamic process of the clustering rather than on the final picture of the clustering process. To address it, we introduce a new hierarchical clustering algorithm in networks, based on a new shortest path betweenness measure. To calculate it, the communication between each pair of nodes is weighed by the importance of the nodes that establish this communication. The weights or importance associated to each pair of nodes are calculated as the Shapley value of a game, named as the linear modularity game. This new measure, (the node-game shortest path betweenness measure), is used to obtain a hierarchical partition of the network by eliminating the link with the highest value. To evaluate the performance of our algorithm, we introduce several criteria that allow us to compare different dendrograms of a network from two point of view: modularity and homogeneity. Finally, we propose a faster algorithm based on a simplification of the node-game shortest path betweenness measure, whose order is quadratic on sparse networks. This fast version is competitive from a computational point of view with other hierarchical fast algorithms, and, in general, it provides better results.

Targeted pandemic containment through identifying local contact network bottlenecks

Decision-making about pandemic mitigation often relies upon simulation modelling. Models of disease transmission through networks of contacts–between individuals or between population centres–are increasingly used for these purposes. Real-world contact networks are rich in structural features that influence infection transmission, such as tightly-knit local communities that are weakly connected to one another. In this paper, we propose a new flow-based edge-betweenness centrality method for detecting bottleneck edges that connect nodes in contact networks. In particular, we utilize convex optimization formulations based on the idea of diffusion with p-norm network flow. Using simulation models of COVID-19 transmission through real network data at both individual and county levels, we demonstrate that targeting bottleneck edges identified by the proposed method reduces the number of infected cases by up to 10% more than state-of-the-art edge-betweenness methods. Furthermore, the proposed method is orders of magnitude faster than existing methods.

Dynamic Analysis Method for Fault Propagation Behaviour of Machining Centres

Fault propagation behaviour analysis is the basis of fault diagnosis and health maintenance. Traditional fault propagation studies are mostly based on a priori knowledge of a causality model combined with rule-based reasoning, disregarding the limitations of experience and the dynamic characteristics of the system that cause deviations in the identification of critical fault sources. Thus, this paper proposes a dynamic analysis method for fault propagation behaviour of machining centres that combines fault propagation mechanisms with model structure characteristics. This paper uses the design structure matrix (DSM) to establish the fault propagation hierarchy structure model. Considering the correlation of fault time, the fault probability function of a component is obtained and the fault influence degree of nodes are calculated. By introducing the Copula and Coupling degree functions, the fault influence degree of the edges between the same level and different levels are calculated, respectively. This paper constructs a fault propagation intensity model by integrating the edge betweenness and uses it as an index to analyze real-time fault propagation behaviour. Finally, a certain type of machining centre is taken as an example for specific application. This study can provide as a reference for the fault maintenance and reliability growth of a machining centre.

Network Path Convergence Shapes Low-Level Processing in the Visual Cortex

Hierarchical counterstream via feedforward and feedback interactions is a major organizing principle of the cerebral cortex. The counterstream, as a topological feature of the network of cortical areas, is captured by the convergence and divergence of paths through directed links. So defined, the convergence degree (CD) reveals the reciprocal nature of forward and backward connections, and also hierarchically relevant integrative properties of areas through their inward and outward connections. We asked if topology shapes large-scale cortical functioning by studying the role of CD in network resilience and Granger causal coupling in a model of hierarchical network dynamics. Our results indicate that topological synchronizability is highly vulnerable to attacking edges based on CD, while global network efficiency depends mostly on edge betweenness, a measure of the connectedness of a link. Furthermore, similar to anatomical hierarchy determined by the laminar distribution of connections, CD highly correlated with causal coupling in feedforward gamma, and feedback alpha-beta band synchronizations in a well-studied subnetwork, including low-level visual cortical areas. In contrast, causal coupling did not correlate with edge betweenness. Considering the entire network, the CD-based hierarchy correlated well with both the anatomical and functional hierarchy for low-level areas that are far apart in the hierarchy. Conversely, in a large part of the anatomical network where hierarchical distances are small between the areas, the correlations were not significant. These findings suggest that CD-based and functional hierarchies are interrelated in low-level processing in the visual cortex. Our results are consistent with the idea that the interplay of multiple hierarchical features forms the basis of flexible functional cortical interactions.

Coword and Cluster Analysis for the Romance of the Three Kingdoms

The Romance of the Three Kingdoms (RTK) is a classical Chinese historical novel by Luo Guanzhong. This paper establishes a research framework of analyzing the novel by utilizing coword and cluster analysis technology. At the beginning, we segment the full text of the novel, extracting the names of historical figures in the RTK novel. Based on the coword analysis, a social network of historical figures is constructed. We calculate several network features and enforce the cluster analysis. In addition, a modified clustering method using edge betweenness is proposed to improve the effect of clustering. Finally, both quantified and visualized results are displayed to confirm our approach.