Workflow nets (WF-nets for short) are a mathematical model of real world workflows. A WF-net is often updated in accordance with the change of real world. This may cause places that are redundant from the viewpoint of the behavior. Such places are called implicit. We first proposed a necessary and sufficient condition to find implicit places. Then we proved that removing of implicit places is a reduction operation which forms branching bisimilarity. We also constructed an algorithm for the reduction. Next, we applied the proposed reduction operation to WF-net refactoring. Then we showed the usefulness of the proposed refactoring with two examples.

The controllability of complex networks has attracted increasing attention within various scientific fields. Many power grids are complex networks with some common topological characteristics such as small-world and scale-free features. This Letter investigate the controllability of some real power grids in comparison with classical complex network models with the same number of nodes. Several conclusions are drawn after detailed analyses using several real power grids together with Erdös-Rényi (ER) random networks, Wattz-Strogatz (WS) small-world networks, Barabási-Albert (BA) scale-free networks and configuration model (CM) networks. The main conclusion is that most driver nodes of power grids are hub-free nodes with low nodal degree values of 1 or 2. The controllability of power grids is determined by degree distribution and heterogeneity, and power grids are harder to control than WS networks and CM networks while easier than BA networks. Some power grids are relatively difficult to control because they require a far higher ratio of driver nodes than ER networks, while other power grids are easier to control for they require a driver node ratio less than or equal to ER random networks.

The power grid defines one of the most important technological networks of our times and has been widely studied as a kind of complex network. It has been developed for more than one century and becomes an extremely huge and seemingly robust system. But it becomes extremely fragile as well because some unexpected minimal failures may lead to sudden and massive blackouts. Many works have been carried out to investigate the structural vulnerability of power grids from the topological point of view based on the complex network theory. This Letter focuses on the structural vulnerability of the power grid under the effect of selective node removal. We propose a new kind of node centrality called overall information centrality (OIC) to guide the node removal attack. We test the effectiveness of our centrality in guiding the node removal based on several IEEE power grids. Simulation results show that, compared with other node centralities such as degree centrality (DC), betweenness centrality (BC) and closeness centrality (CC), our OIC is more effective to guide the node removal and can destroy the power grid in less steps.

Compared with traditional static anonymous communication networks, the P2P architecture can provide higher anonymity in communication. However, the P2P architecture also leads to more challenges, such as route, stability, trust and so on. In this paper, we present WindTalker, a P2P-based low-latency anonymous communication network. It is a pure decentralized mix network and can provide low-latency services which help users hide their real identity in communication. In order to ensure stability and reliability, WindTalker imports "seed nodes" to help a peer join in the P2P network and the peer nodes can use gossip-based protocol to exchange active information. Moreover, WindTalker uses layer encryption to ensure the information of relayed messages cannot be leaked. In addition, malicious nodes in the network are the major threat to anonymity of P2P anonymous communication, so WindTalker imports a trust mechanism which can help the P2P network exclude malicious nodes and optimize the strategy of peer discovery, tunnel construction, and relaying etc. in anonymous communications. We deploy peer nodes of WindTalker in our campus network to test reliability and analyze anonymity in theory. The network measurement and simulation analysis shows that WindTalker can provide low-latency and reliable anonymous communication services.

Robustness of complex networks is an essential subject for improving their performance when vertices or links are removed due to potential threats. In recent years, significant advancements have been achieved in this field by many researchers. In this paper we show an overview from a novel statistic perspective. We present a brief review about complex networks at first including 2 primary network models, 12 popular attack strategies and the most convincing network robustness metrics. Then, we focus on the correlations of 12 attack strategies with each other, and the difference of the correlations from one network model to the other. We are also curious about the robustness of networks when vertices are removed according to different attack strategies and the difference of robustness from one network model to the other. Our aim is to observe the correlation mechanism of centralities for distinct network models, and compare the network robustness when different centralities are applied as attacking directors to distinct network models. What inspires us is that maybe we can find a paradigm that combines several high-destructive attack strategies to find the optimal strategy based on the deep learning framework.

The application of complex network theory to power grid analysis has been a hot topic in recent years, which mainly manifests itself in four aspects. The first aspect is to model power system networks. The second aspect is to reveal the topology of the grid itself. The third aspect is to reveal the inherent vulnerability and weakness of the power network itself and put forward the pertinent improvement measures to provide guidance for the construction of power grid. The last aspect is to analyze the mechanism of cascading failure and establish the cascading fault model of large power failure. In the past ten years, by using the complex network theory, many researchers have investigated the structural vulnerability of power grids from the point of view of topology. This letter studies the structural vulnerability of power grids according to the effect of selective node removal. We apply several kinds of node centralities including recently-presented second-order centrality (SOC) to guide the node removal attack. We test the effectiveness of all these centralities in guiding the node removal based on several IEEE power grids. Simulation results show that, compared with other node centralities, the SOC is relatively effective in guiding the node removal and can destroy the power grid with negative degree-degree correlation in less steps.