Saturation Number of $tK_{l,l,l}$ in the Complete Tripartite Graph

For fixed graphs $F$ and $H$, a graph $G\subseteq F$ is $H$-saturated if there is no copy of $H$ in $G$, but for any edge $e\in E(F)\setminus E(G)$, there is a copy of $H$ in $G+e$. The saturation number of $H$ in $F$, denoted $sat(F,H)$, is the minimum number of edges in an $H$-saturated subgraph of $F$. In this paper, we study saturation numbers of $tK_{l,l,l}$ in complete tripartite graph $K_{n_1,n_2,n_3}$. For $t\ge 1$, $l\ge 1$ and $n_1,n_2$ and $n_3$ sufficiently large, we determine $sat(K_{n_1,n_2,n_3},tK_{l,l,l})$ exactly.

Effective Routing in Vehicular Adhoc Network (VANET) using an Bio-inspired Algorithm: Enhanced Deep Reinforcement Learning (EDRL) for Secure Wireless Communication

For improving the performance of city wide-ranging lane networks through the optimized control signal, we proposed a framework in Vehicular Adhoc Network (VANET). Node which reduces the traffic efficiency drastically is identified as critical node, with the help of defined framework. Tripartite graph is used for identifying critical node through vehicle trajectory in the over-all viewpoint. Enhanced Deep Reinforcement Learning (EDRL) method is introduced to control the traffic signal and gives appropriate decision for routing the data from Road Side Unit (RSU) to intermediate or destination node. Various experiments were done with proposed model and the result shows considerable efficiency in delay and travelling time of the node in VANET.

Inferring miRNA-disease associations using collaborative filtering and resource allocation on a tripartite graph

Background Developing efficient and successful computational methods to infer potential miRNA-disease associations is urgently needed and is attracting many computer scientists in recent years. The reason is that miRNAs are involved in many important biological processes and it is tremendously expensive and time-consuming to do biological experiments to verify miRNA-disease associations. Methods In this paper, we proposed a new method to infer miRNA-disease associations using collaborative filtering and resource allocation algorithms on a miRNA-disease-lncRNA tripartite graph. It combined the collaborative filtering algorithm in CFNBC model to solve the problem of imbalanced data and the method for association prediction established multiple types of known associations among multiple objects presented in TPGLDA model. Results The experimental results showed that our proposed method achieved a reliable performance with Area Under Roc Curve (AUC) and Area Under Precision-Recall Curve (AUPR) values of 0.9788 and 0.9373, respectively, under fivefold-cross-validation experiments. It outperformed than some other previous methods such as DCSMDA and TPGLDA. Furthermore, it demonstrated the ability to derive new associations between miRNAs and diseases among 8, 19 and 14 new associations out of top 40 predicted associations in case studies of Prostatic Neoplasms, Heart Failure, and Glioma diseases, respectively. All of these new predicted associations have been confirmed by recent literatures. Besides, it could discover new associations for new diseases (or miRNAs) without any known associations as demonstrated in the case study of Open-angle glaucoma disease. Conclusion With the reliable performance to infer new associations between miRNAs and diseases as well as to discover new associations for new diseases (or miRNAs) without any known associations, our proposed method can be considered as a powerful tool to infer miRNA-disease associations.

The Crossing Numbers of Join Products of Paths and Cycles with Four Graphs of Order Five

The main aim of the paper is to establish the crossing numbers of the join products of the paths and the cycles on n vertices with a connected graph on five vertices isomorphic to the graph K1,1,3\e obtained by removing one edge e incident with some vertex of order two from the complete tripartite graph K1,1,3. The proofs are done with the help of well-known exact values for the crossing numbers of the join products of subgraphs of the considered graph with paths and cycles. Finally, by adding some edges to the graph under consideration, we obtain the crossing numbers of the join products of other graphs with the paths and the cycles on n vertices.

PPIDomainMiner : Inferring domain-domain interactions from multiple sources of protein-protein interactions

Many biological processes are mediated by protein-protein interactions (PPIs). Because protein domains are the building blocks of proteins, PPIs likely rely on domain-domain interactions (DDIs). Several attempts exist to infer DDIs from PPI networks but the produced datasets are heterogeneous and sometimes not accessible, while the PPI interactome data keeps growing.We describe a new computational approach called “PPIDM” (Protein-Protein Interactions Domain Miner) for inferring DDIs using multiple sources of PPIs. The approach is an extension of our previously described “CODAC” (Computational Discovery of Direct Associations using Common neighbors) method for inferring new edges in a tripartite graph. The PPIDM method has been applied to seven widely used PPI resources, using as “Gold-Standard” a set of DDIs extracted from 3D structural databases. Overall, PPIDM has produced a dataset of 84, 552 non-redundant DDIs. Statistical significance (p-value) is calculated for each source of PPI and used to classify the PPIDM DDIs in Gold (9, 175 DDIs), Silver (24, 934 DDIs) and Bronze (50, 443 DDIs) categories. Dataset comparison reveals that PPIDM has inferred from the 2017 releases of PPI sources about 46% of the DDIs present in the 2020 release of the 3did database, not counting the DDIs present in the Gold-Standard. The PPIDM dataset contains more than 3, 250 DDIs that are consistent with nearly 10, 600 PPIs extracted from the IMEx database, and more than 23, 000 DDIs (27.5%) that are consistent with more than 62, 000 human PPIs extracted from the STRING database. Examples of newly inferred DDIs covering more than ten PPIs in the IMEx database are provided.Further exploitation of the PPIDM DDI reservoir includes the inventory of possible partners of a protein of interest and characterization of protein interactions at the domain level in combination with other methods. The result is publicly available at http://ppidm.loria.fr/.Author summaryWe revisit at a large scale the question of inferring DDIs from PPIs. Compared to previous studies, we take a unified approach accross multiple sources of PPIs. This approach is a method for inferring new edges in a tripartite graph setting and can be compared to link prediction approaches in knowledge graphs. Aggregation of several sources is performed using an optimized weighted average of the individual scores calculated in each source. A huge dataset of over 84K DDIs is produced which far exceeds the previous datasets. We show that a significant portion of the PPIDM dataset covers a large number of PPIs from curated (IMEx) or non curated (STRING) databases. Such a reservoir of DDIs deserves further exploration and can be combined with high-throughput methods such as cross-linking mass spectrometry to identify plausible protein partners of proteins of interest.