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13
Structural Vulnerability Assessment of Electric Power Grids
"... Abstract—Cascading failures are the typical reasons of blackouts in power grids. The grid topology plays an important role in determining the dynamics of cascading failures in power grids. Measures for vulnerability analysis are crucial to assure a higher level of robustness of power grids. Metrics ..."
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Abstract—Cascading failures are the typical reasons of blackouts in power grids. The grid topology plays an important role in determining the dynamics of cascading failures in power grids. Measures for vulnerability analysis are crucial to assure a higher level of robustness of power grids. Metrics from Complex Networks are widely used to investigate the grid vulnerability. Yet, these purely topological metrics fail to capture the real behaviour of power grids. This paper proposes a metric, the effective graph resistance, as a vulnerability measure to determine the critical components in a power grid. Differently than the existing purely topological measures, the effective graph resistance accounts for the electrical properties of power grids such as power flow allocation according to Kirchoff laws. To demonstrate the applicability of the effective graph resistance, a quantitative vulnerability assessment of the IEEE 118 buses power system is performed. The simulation results verify the effectiveness of the effective graph resistance to identify the critical transmission lines in a power grid. I.
A network approach for power grid robustness against cascading failures
 Phys. Soc
"... AbstractCascading failures are one of the main reasons for blackouts in electrical power grids. Stable power supply requires a robust design of the power grid topology. Currently, the impact of the grid structure on the grid robustness is mainly assessed by purely topological metrics, that fail to ..."
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AbstractCascading failures are one of the main reasons for blackouts in electrical power grids. Stable power supply requires a robust design of the power grid topology. Currently, the impact of the grid structure on the grid robustness is mainly assessed by purely topological metrics, that fail to capture the fundamental properties of the electrical power grids such as power flow allocation according to Kirchhoff's laws. This paper deploys the effective graph resistance as a metric to relate the topology of a grid to its robustness against cascading failures. Specifically, the effective graph resistance is deployed as a metric for network expansions (by means of transmission line additions) of an existing power grid. Four strategies based on network properties are investigated to optimize the effective graph resistance, accordingly to improve the robustness, of a given power grid at a low computational complexity. Experimental results suggest the existence of Braess's paradox in power grids: bringing an additional line into the system occasionally results in decrease of the grid robustness. This paper further investigates the impact of the topology on the Braess's paradox, and identifies specific substructures whose existence results in Braess's paradox in power grids. Careful assessment of the design and expansion choices of grid topologies incorporating the insights provided by this paper optimizes the robustness of a power grid, while avoiding the Braess's paradox in the system.
Approximation algorithms for reducing the spectral radius to control epidemic spread.” SDM
, 2015
"... The largest eigenvalue of the adjacency matrix of a network (referred to as the spectral radius) is an important metric in its own right. Further, for several models of epidemic spread on networks (e.g., the ‘flulike ’ SIS model), it has been shown that an epidemic dies out quickly if the spectral ..."
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The largest eigenvalue of the adjacency matrix of a network (referred to as the spectral radius) is an important metric in its own right. Further, for several models of epidemic spread on networks (e.g., the ‘flulike ’ SIS model), it has been shown that an epidemic dies out quickly if the spectral radius of the graph is below a certain threshold that depends on the model parameters. This motivates a strategy to control epidemic spread by reducing the spectral radius of the underlying network. In this paper, we develop a suite of provable approximation algorithms for reducing the spectral radius by removing the minimum cost set of edges (modeling quarantining) or nodes (modeling vaccinations), with different time and quality tradeoffs. Our main algorithm, GreedyWalk, is based on the idea of hitting closed walks of a given length, and gives an O(log2 n)approximation, where n denotes the number of nodes; it also performs much better in practice compared to all prior heuristics proposed for this problem. We further present a novel sparsification method to improve its running time. In addition, we give a new primaldual based algorithm with an even better approximation guarantee (O(log n)), albeit with slower running time. We also give lower bounds on the worstcase performance of some of the popular heuristics. Finally we demonstrate the applicability of our algorithms and the properties of our solutions via extensive experiments on multiple synthetic and real networks. 1
The impact of the topology on cascading failures in electric power grids
"... Cascading failures are one of the main reasons for blackouts in power transmission grids. The topology of a power grid, together with its operative state determine, for the most part, the robustness of the power grid against cascading failures. Secure electrical power supply requires, together wit ..."
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Cascading failures are one of the main reasons for blackouts in power transmission grids. The topology of a power grid, together with its operative state determine, for the most part, the robustness of the power grid against cascading failures. Secure electrical power supply requires, together with careful operation, a robust design of the electrical power grid topology. This paper investigates the impact of a power grid topology on its robustness against cascading failures. Currently, the impact of the topology on a grid robustness is mainly assessed by using purely topological approaches that fail to capture the essence of electric power flow. This paper proposes a metric, the effective graph resistance, that relates the topology of a power grid to its robustness against cascading failures by deliberate attacks, while also taking the fundamental characteristics of the electric power grid into account such as power flow allocation according to Kirchoff Laws. Experimental verification shows that the proposed metric anticipates the grid robustness accurately. The proposed metric is used to optimize a grid topology for a higher level of robustness. To demonstrate its applicability, the metric is applied on the IEEE 118 bus power system to improve its robustness against cascading failures. 1
Bayesian discovery of threat networks
 CoRR
"... Abstract—A novel unified Bayesian framework for network detection is developed, under which a detection algorithm is derived based on random walks on graphs. The algorithm detects threat networks using partial observations of their activity, and is proved to be optimum in the NeymanPearson sense. T ..."
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Abstract—A novel unified Bayesian framework for network detection is developed, under which a detection algorithm is derived based on random walks on graphs. The algorithm detects threat networks using partial observations of their activity, and is proved to be optimum in the NeymanPearson sense. The algorithm is defined by a graph, at least one observation, and a diffusion model for threat. A link to wellknown spectral detection methods is provided, and the equivalence of the random walk and harmonic solutions to the Bayesian formulation is proven. A general diffusion model is introduced that utilizes spatiotemporal relationships between vertices, and is used for a specific spacetime formulation that leads to significant performance improvements on coordinated covert networks. This performance is demonstrated using a new hybrid mixedmembership blockmodel introduced to simulate random covert networks with realistic properties. Index Terms—Network detection, optimal detection, maximum likelihood detection, community detection, network theory (graphs), graph theory, diffusion on graphs, random walks on graphs, dynamic network models, Bayesian methods, harmonic analysis, eigenvector centrality, Laplace equations. I.
Decentralized Protection Strategies against SIS Epidemics in Networks
, 2014
"... Defining an optimal protection strategy against viruses, spam propagation or any other kind of contamination process is an important feature for designing new networks and architectures. In this work, we consider decentralized optimal protection strategies when a virus is propagating over a network ..."
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Defining an optimal protection strategy against viruses, spam propagation or any other kind of contamination process is an important feature for designing new networks and architectures. In this work, we consider decentralized optimal protection strategies when a virus is propagating over a network through a SIS epidemic process. We assume that each node in the network can fully protect itself from infection at a constant cost, or the node can use recovery software, once it is infected. We model our system using a game theoretic framework and find pure, mixed equilibria, and the Price of Anarchy (PoA) in several network topologies. Further, we propose both a decentralized algorithm and an iterative procedure to compute a pure equilibrium in the general case of multiple communities network. Finally, we evaluate the algorithms and give numerical illustrations of all our results.
Controlling Propagation at Group Scale on Networks
"... Abstract—Given a network with groups, such as a contactnetwork grouped by ages, which are the best groups to immunize to control the epidemic? Equivalently, how to best choose communities in social networks like Facebook to stop rumors from spreading? Immunization is an important problem in multip ..."
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Abstract—Given a network with groups, such as a contactnetwork grouped by ages, which are the best groups to immunize to control the epidemic? Equivalently, how to best choose communities in social networks like Facebook to stop rumors from spreading? Immunization is an important problem in multiple different domains like epidemiology, public health, cyber security and social media. Additionally, clearly immunization at group scale (like schools and communities) is more realistic due to constraints in implementations and compliance (e.g., it is hard to ensure specific individuals take the adequate vaccine). Hence efficient algorithms for such a “groupbased ” problem can help publichealth experts take more practical decisions. However most prior work has looked into individualscale immunization. In this paper, we study the problem of controlling propagation at group scale. We formulate novel socalled Group Immunization problems for multiple natural settings (for both threshold and cascadebased contagion models under both nodelevel and edgelevel interventions) and develop multiple efficient algorithms, including provably approximate solutions. Finally, we show the effectiveness of our methods via extensive experiments on real and synthetic datasets. I.