Download PDF The Shortest Way Home: A Novel
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In this paper, we develop a novel method to count the number of shortest paths between two nodes in probabilistic networks. Unlike earlier approaches, which uses the shortest path counting methods that are specifically designed for deterministic networks, our method builds a new mathematical model to express and compute the number of shortest paths. We prove the correctness of this model.
We compare our novel method to three existing shortest path counting methods on synthetic and real gene regulatory networks. Our experiments demonstrate that our method is scalable, and it outperforms the existing methods in accuracy. Application of our shortest path counting method to detect communities in probabilistic networks shows that our method successfully finds communities in probabilistic networks. Moreover, our experiments on cell cycle pathway among different cancer types exhibit that our method helps in uncovering key functional characteristics of biological networks.
Our Contributions. In this paper, we develop a novel method to count the shortest paths between a pair of nodes in probabilistic networks. The key challenge arises from the fact that since the topology of a network is uncertain, existence of paths are also uncertain. Furthermore, this uncertainty is governed through complex dependencies among paths through their shared edges. To capture such dependency between multiple paths, we build a novel polynomial model. Our model first builds a bipartite graph to describe the dependency among multiple paths. It then generates a special class of polynomials, called the x-polynomial to express this dependency. We prove that our model accurately counts the distribution of the number of shortest paths. Our experimental results on synthetic and real cancer datasets demonstrate that our algorithm successfully counts the number of shortest paths, while existing methods yield errors ranging from 12% to orders of magnitude depending on the network characteristics. We show that our method can be used to detect essential genes in a network. As a significant application of our novel shortest path counting method, we use it to identify communities in a given probabilistic network. We analyze the community structure in cell cycle pathway among different cancer types. Our results suggest that our method can help in uncovering key functional characteristics of the genes participating in those networks.
In summary, our experiments on synthetic and real datasets demonstrate that existing methods either under or over estimate the number of shortest paths with a large margin. The binary method performs the worst among the existing three methods under varying network sizes, average node degrees and probability distributions. In comparison to the existing methods, our novel method solves the shortest path counting problem accurately in a feasible time. The low accuracy level of existing methods suggests that our novel method is truly needed in the field since the existing methods might potentially lead to wrong biological implications. Our analysis on real datasets support our findings on synthetic data, and suggest that our approach could be used to discover key genes in biological systems.
In this paper, we presented a novel method to count the number of shortest paths in probabilistic biological networks. The dependency among multiple paths in probabilistic network makes shortest path counting a challenging problem. We developed a polynomial model to capture such dependency. Our experiments on both synthetic and real networks demonstrate that in comparison to existing methods, our method accurately counts the shortest paths in probabilistic networks. As an important application of our novel shortest path counting method, we use it to identify communities in biological networks. Our experiments show that we could detect communities of high quality in biological networks and identify their key functional characteristics. In future work, it would be interesting to use both the number and the length of shortest paths to characterize the structure of probabilistic biological networks.
Real-life decision-making problem has been demonstrated to cover the indeterminacy through single valued neutrosophic set. It is the extension of interval valued neutrosophic set. Most of the problems of real life involve some sort of uncertainty in it among which, one of the famous problem is finding a shortest path of the network. In this paper, a new score function is proposed for interval valued neutrosophic numbers and SPP is solved using interval valued neutrosophic numbers. Additionally, novel algorithms are proposed to find the neutrosophic shortest path by considering interval valued neutrosophic number, trapezoidal and triangular interval valued neutrosophic numbers for the length of the path in a network with illustrative example. Further, comparative analysis has been done for the proposed algorithm with the existing method with the shortcoming and advantage of the proposed method and it shows the effectiveness of the proposed algorithm.
In this part, introduction to the objective of the paper is given by presenting basic concepts and procedure of the shortest path problem (SPP) and the literature of review have been collected to know the recent work related to the presented concept which shows the novelty of the presented work
The rest of the paper is arranged as follows. In Sect. 1.2, literature of review has been collected. In Sect. 2, over view of interval valued neutrosophic set is given. In Sect. 3, novel algorithms are proposed to find the neutrosophic shortest path under interval valued neutrosophic environment and interval valued triangular and trapezoidal neutrosophic environments with the help of proposed score function. In Sect. 4, shortcoming of the existing methods, advantages of the proposed method and comparative analysis are presented for the proposed method with the existing method. In Sect. 5, conclusion of the presented work is given.
We introduce a novel Cytoscape plugin cytoHubba for ranking nodes in a network by their network features. CytoHubba provides 11 topological analysis methods including Degree, Edge Percolated Component, Maximum Neighborhood Component, Density of Maximum Neighborhood Component, Maximal Clique Centrality and six centralities (Bottleneck, EcCentricity, Closeness, Radiality, Betweenness, and Stress) based on shortest paths. Among the eleven methods, the new proposed method, MCC, has a better performance on the precision of predicting essential proteins from the yeast PPI network.
CytoHubba provide a user-friendly interface to explore important nodes in biological networks. It computes all eleven methods in one stop shopping way. Besides, researchers are able to combine cytoHubba with and other plugins into a novel analysis scheme. The network and sub-networks caught by this topological analysis strategy will lead to new insights on essential regulatory networks and protein drug targets for experimental biologists. According to cytoscape plugin download statistics, the accumulated number of cytoHubba is around 6,700 times since 2010. 153554b96e
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