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Essential proteins are important participants in various life activities and play a vital role in the survival and reproduction of life. The network-based centrality methods are a common way to identify essential proteins for protein interaction networks. Due to the differences between the existing centrality methods, it is a feasible approach to improve the identification accuracy of essential proteins by combining centrality methods. In this paper, we propose a centrality combination method based on feature selection. First, the measure values of the 14 classical centrality methods are viewed as feature data. Then, a subset of the relevant features is selected according to the importance of features. Finally, the centrality methods corresponding to the selected features are combined by using the geometric mean method for the identification of essential proteins. To verify the effectiveness of the combination method, we apply the combination method on the original static protein interaction network (SPIN), the dynamic protein interaction network (DPIN) and the refined dynamic protein interaction network (RDPIN), and compare the result with those by each single centrality method (LAC, DC, DMNC, NC, TP, CLC, BC, LC, CC, KC, CR, EC, PR, LR). The experimental results on the identification of essential proteins shows that the combination method achieves better results in prediction performance than the 14 centrality mehtods in terms of the prediction precision, sensitivity, specificity, positive predictive value, negative predictive value, F-measure and accuracy rate. It has been illustrated that the proposed method can help to identify essential proteins more accurately.

Constructing dynamic protein interaction networks (DPIN) is a common way to improve identification accuracy of essential proteins. The existing methods usually aggregate DPIN into a single-layer network where all nodes are sorted by their importance. This treatment makes the dynamic information about proteins in multiple layers lost in the single layer, and thus affects the identification accuracy of essential proteins. This paper proposes a node ranking method based on multiple layers for DPIN to address the problem. First, we calculate the centrality values of all nodes for each time-specific layer, then work out the centrality score of each node by dividing the total of its centrality values across all layers by its layer activity, and finally sort the importance of all nodes by their centrality scores. Different from the methods based on single layer, our method makes full use of centrality values of each protein in time-specific layers, and thus can more effectively utilize the dynamic information of proteins. To evaluate the effectiveness of the node ranking method based on multiple layers, we apply ten network-based centrality methods on multiple layers and compare the results with those on a single layer. Then the predictive performance of the ten centrality methods are validated in terms of sensitivity, specificity, positive predictive value, negative predictive value, F-measure and accuracy. The experimental results for the identification of essential proteins show that the node ranking method based on multiple layers is superior to those based on a single layer and can help to identify essential proteins more accurate.

Several semantics models are adopted by time Petri nets for different applications. Yet they have some limitations on schedulability analysis of flexible manufacturing systems. The scheduling scope of a strong semantics model is greatly limited because of the impact of strong timing requirements, perhaps keeping some optimal schedules out of the consideration. A weak semantics model cannot guarantee the scheduling timeliness as there lacks strong timing enforcement. A mixed semantics model cannot ensure that independent transitions with overlapping firing interval fire in an interleaving way, thus affecting the search for the optimal schedules. In this paper, we present a relaxed mixed semantics model for time Petri nets to address these problems by redefining the firability rules of transitions. In our model, the firability of a transition is determined by maximal concurrent sets containing the transition. This treatment not only extends the scheduling scope of TPN model greatly while avoiding the generation of invalid schedules, but also solves the problem of concurrent scheduling of independent transitions. A state class method is then proposed to support the verification and analysis of temporal properties. Finally, we apply the proposed model to schedulability analysis of a job shop scheduling problem, and compare the features of four semantics models.