The canonical decomposition of a bipartite graph is a new decompositionmethod that involves three operators, parallel, series and K+S. The class of weak bisblit graphs is totally decomposable with respect of these operators, and the class of bicographs is totally decomposable with respect of parallel and series operators. We prove in this paper that the class of bipartite (P_6,C_6)-free graphs is exactly the class of bipartite graphs that are totally decomposable with respect of parallel and K+S operators. We simplify the recognition algorithm of weak-bisplit graphs to adepte with bipartite (P_6,C_6)-free graphs. As a result of this adapted algorithm, we prsent efficient solutions in this class of graphs for two optimization graph problems, the first is the maximm balanced bi-clique problem and the the second is the maximum independent set problem.

We will try to use the approach of labeled cycle cover sum to count the number of hamiltonian cycles in a special type of bipartite graphs, with 4k + 2 vertices which can also be considered as an alternative method to check hamiltonicity in such bipartite graphs. This graph is such that, there exists at least 1 vertex which is not a part of any cycle of size 4m + 2 where m < k, in O∗(1.414n) time. The algorithm is inspired by Bjorklund’s approach where instead of working on the field of GF(2k), we will be working on C.

Wireless sensor networks (WSNs) are a critical research area with numerous practical applications. WSNs are utilized in real-life scenarios, including environmental monitoring, healthcare, industrial automation, smart homes, and agriculture. As WSNs advance and become more sophisticated, they offer limitless opportunities for innovative solutions in various fields. However, due to their unattended nature, it is essential to develop strategies to improve their performance without draining the battery power of the sensor nodes, which is their most valuable resource. This paper proposes a novel sink mobility model based on constructing a bipartite graph from a deployed wireless sensor network. Using the bipartite graph’s properties, the mobile sink node can visit stationary sensor nodes in an optimal way to collect data and transmit it to the base station. We evaluated the proposed approach through simulations using the NS-2 simulator to investigate the performance of wireless sensor networks when adopting this mobility model. Our results show that using the proposed approach can significantly enhance the performance of wireless sensor networks while conserving the energy of the sensor nodes.

In IP networks, packet forwarding is destination-based and hop-by-hop, and routes are built as needed. Kwong et al. introduced a protection routing in which packet delivery to the destination node can proceed uninterrupted in the event of any single node or link failure. He then shows that “whether there is a protection routing to the destination” is NP-complete. Tapolcai find that two completely independent spanning trees, abbreviated as CISTs, can be used to configure the protection routing. In this paper, we propose dual protection routing trees, denoted as dual-PRTs to replace CISTs, which are less restrictive than CISTs. Next, we propose a transformation algorithm that uses dual-PRTs to configure the protection routing. Taking complete graphs Kn, complete bipartite graphs Km,n, hypercubes Qn, locally twisted cubes LTQn as examples, we provide a recursive method to construct dual-PRTs on them. This article will show that there are no two CISTs on K3,3, Q3, and LTQ3, but there exist dual-PRTs that can be used to configure the protection routing. As shown in the performance evaluation of simulation results, for both Qn and LTQn, we get the average path length of protection routing configured by dual-PRTs is shorter than that by two CISTs.

Solving maximum matching problems in bipartite graphs is critical in fields such as computational biology and social network analysis. This study introduces HybridGNN, a novel graph neural network model designed to efficiently address complex matching problems at scale. HybridGNN combines the capabilities of Graph Attention Networks (GAT), GATv2, and Graph SAGE (SAGEConv) layers, integrating techniques like mixed precision training, gradient accumulation, and Jumping Knowledge networks to enhance computational efficiency and performance. Additionally, the incorporation of Graph Isomorphism Networks (GIN) enhances the model's ability to discriminate between structurally different graphs. A time complexity analysis shows that HybridGNN achieves efficient computation across different layers. When evaluated on an email communication dataset, HybridGNN outperformed traditional algorithms such as Hopcroft-Karp, particularly on large and complex graphs. These results demonstrate that HybridGNN offers a powerful and efficient approach for solving maximum matching problems in bipartite graphs, with potential applications in various fields requiring analysis of large-scale and complex graph data.

We present a new method of estimating fitness of countries and complexity of products by exploiting a non-linear non-homogeneous map applied to the publicly available information on the goods exported by a country. The non homogeneous terms guarantee both convergence and stability. After a suitable rescaling of the relevant quantities, the non homogeneous terms are eventually set to zero so that this new method is parameter free. This new map reproduces the findings of the method proposed by Tacchella et al. [1], and allows for an approximate analytic solution in case of actual binarized matrices based on the Revealed Comparative Advantage (RCA) indicator. This solution is connected with a new quantity describing the neighborhood of nodes in bipartite graphs, representing in this work the relations between countries and exported products. Moreover, we define the new indicator of country net-efficiency quantifying how a country efficiently invests in capabilities able to generate innovative complex high quality products. Eventually, we demonstrate analytically the local convergence of the algorithm.

In this work we identify combinations of technological activities that signal the presence local capabilities in a country to successfully export a product. We use country-level patent and trade data to generate a multi-layer network, and we apply maximization of entropy to generate synthetic data to effectively divide signal from noise. We show that in several sectors the signal far exceed the noise. Our exercise provides robust evidence of the presence of synergies between technologies to explain trade performances in specific markets. This can be highly useful for policy makers, to inform industrial and innovation policies.

In this paper, a class of coupled competitive neural networks, which subject to disturbance and discontinuous activation functions, is concerned. To realize the fixed-time quasi-bipartite synchronization, an aperiodic intermittent controller is initially designed. Subsequently, by combining the fixed-time stability theory and nonsmooth analysis, several criteria are established to ensure the bipartite synchronization in fixed time. Moreover, synchronization error bounds and settling time estimates are provided. Finally, numerical simulations are presented to verify the main results.

Multipartite bacteria have one chromosome and one or more chromid. Chromids are believed to have properties that enhance genomic flexibility, making them a favored integration site for new genes. However, the mechanism by which chromosomes and chromids jointly contribute to this flexibility is not clear. To shed light on this, we analyzed the openness of chromosomes and chromids of the two bacteria, Vibrio and Pseudoalteromonas, both in the Enterobacterales order of gamma-proteobacteria, and compared it with monopartite genomes in the same order. We applied pangenome analysis, codon usage analysis and the HGTector software to detect horizontally transferred genes. Our findings suggest that the chromids of Vibrio and Pseudoalteromonas likely originated from two separate plasmid acquisition events. Bipartite genomes were found to be more open compared to monopartite. We found that the shell and cloud pangene categories drive the openness of bipartite genomes in Vibrio and Pseudoalteromonas. Based on this and our two recent studies, we propose a hypothesis that explains how chromids and the chromosome terminus region contribute to the genomic plasticity of bipartite genomes.

Geminiviruses possess single-stranded, circular DNA genomes, and control the transcription of their late genes, including BV1 of many bipartite begomoviruses, through transcriptional activation by the early expressing AC2 protein. DNA binding by AC2 is not sequence-specific, hence the specificity of AC2 activation is thought to be conferred by plant transcription factors (TFs) recruited by AC2 in infected cells. However, the exact TFs AC2 recruits are not known for most viruses. Here we report a systematic examination of the BV1 promoter (PBV1) of mungbean yellow mosaic virus (MYMV) for conserved promoter motifs. We found that MYMV PBV1 contains three abscisic acid (ABA)-responsive elements (ABREs) within its first 70 nucleotides. Deleting these ABREs, or mutating them all via site-directed mutagenesis, abolished the capacity of PBV1 to respond to AC2-mediated transcriptional activation. Furthermore, ABRE and other related ABA-responsive elements were prevalent in more than a dozen Old World begomoviruses we inspected. Together these findings suggest that ABA-responsive TFs may be recruited by AC2 to BV1 promoters of these viruses to confer specificity to AC2 activation. These observations are expected to guide the search for the actual TF(s), furthering our understanding of the mechanism of AC2 action.